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### Running command:
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* using log directory ‘/Users/biocbuild/bbs-3.21-bioc/meat/goSorensen.Rcheck’
* using R Under development (unstable) (2024-11-20 r87352)
* using platform: x86_64-apple-darwin20
* R was compiled by
    Apple clang version 14.0.0 (clang-1400.0.29.202)
    GNU Fortran (GCC) 12.2.0
* running under: macOS Monterey 12.7.6
* using session charset: UTF-8
* using option ‘--no-vignettes’
* checking for file ‘goSorensen/DESCRIPTION’ ... OK
* checking extension type ... Package
* this is package ‘goSorensen’ version ‘1.9.0’
* package encoding: UTF-8
* checking package namespace information ... OK
* checking package dependencies ...Warning: unable to access index for repository https://CRAN.R-project.org/src/contrib:
  cannot open URL 'https://CRAN.R-project.org/src/contrib/PACKAGES'
 OK
* checking if this is a source package ... OK
* checking if there is a namespace ... OK
* checking for hidden files and directories ... OK
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* checking for sufficient/correct file permissions ... OK
* checking whether package ‘goSorensen’ can be installed ... OK
* checking installed package size ... OK
* checking package directory ... OK
* checking ‘build’ directory ... OK
* checking DESCRIPTION meta-information ... OK
* checking top-level files ... OK
* checking for left-over files ... OK
* checking index information ... OK
* checking package subdirectories ... OK
* checking code files for non-ASCII characters ... OK
* checking R files for syntax errors ... OK
* checking whether the package can be loaded ... OK
* checking whether the package can be loaded with stated dependencies ... OK
* checking whether the package can be unloaded cleanly ... OK
* checking whether the namespace can be loaded with stated dependencies ... OK
* checking whether the namespace can be unloaded cleanly ... OK
* checking dependencies in R code ... OK
* checking S3 generic/method consistency ... OK
* checking replacement functions ... OK
* checking foreign function calls ... OK
* checking R code for possible problems ... OK
* checking Rd files ... OK
* checking Rd metadata ... OK
* checking Rd cross-references ... OK
* checking for missing documentation entries ... OK
* checking for code/documentation mismatches ... OK
* checking Rd \usage sections ... OK
* checking Rd contents ... OK
* checking for unstated dependencies in examples ... OK
* checking contents of ‘data’ directory ... OK
* checking data for non-ASCII characters ... OK
* checking data for ASCII and uncompressed saves ... OK
* checking installed files from ‘inst/doc’ ... OK
* checking files in ‘vignettes’ ... OK
* checking examples ... OK
Examples with CPU (user + system) or elapsed time > 5s
                    user system elapsed
hclustThreshold  163.232 28.998 192.722
buildEnrichTable  50.188  5.276  55.931
enrichedIn        40.833  5.186  46.300
* checking for unstated dependencies in ‘tests’ ... OK
* checking tests ...
  Running ‘test_gosorensen_funcs.R’
 OK
* checking for unstated dependencies in vignettes ... NOTE
'library' or 'require' calls not declared from:
  ‘GO.db’ ‘ggplot2’ ‘ggrepel’
* checking package vignettes ... OK
* checking running R code from vignettes ... SKIPPED
* checking re-building of vignette outputs ... SKIPPED
* checking PDF version of manual ... OK
* DONE

Status: 1 NOTE
See
  ‘/Users/biocbuild/bbs-3.21-bioc/meat/goSorensen.Rcheck/00check.log’
for details.

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### Running command:
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###   /Library/Frameworks/R.framework/Resources/bin/R CMD INSTALL goSorensen
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* installing to library ‘/Library/Frameworks/R.framework/Versions/4.5-x86_64/Resources/library’
* installing *source* package ‘goSorensen’ ...
** using staged installation
Warning in person1(given = given[[i]], family = family[[i]], middle = middle[[i]],  :
  Invalid ORCID iD: ‘0000-0002-4736-699’.
** R
** data
** inst
** byte-compile and prepare package for lazy loading
** help
*** installing help indices
** building package indices
** installing vignettes
** testing if installed package can be loaded from temporary location
** testing if installed package can be loaded from final location
** testing if installed package keeps a record of temporary installation path
* DONE (goSorensen)

R Under development (unstable) (2024-11-20 r87352) -- "Unsuffered Consequences"
Copyright (C) 2024 The R Foundation for Statistical Computing
Platform: x86_64-apple-darwin20

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Type 'license()' or 'licence()' for distribution details.

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Type 'contributors()' for more information and
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Type 'q()' to quit R.

> library(goSorensen)


Attaching package: 'goSorensen'

The following object is masked from 'package:utils':

    upgrade

> 
> # A contingency table of GO terms mutual enrichment
> # between gene lists "atlas" and "sanger":
> data(tab_atlas.sanger_BP3)
> tab_atlas.sanger_BP3
                 Enriched in sanger
Enriched in atlas TRUE FALSE
            TRUE    38    31
            FALSE    2   452
> ?tab_atlas.sanger_BP3
tab_atlas.sanger_BP3        package:goSorensen         R Documentation

_C_r_o_s_s-_t_a_b_u_l_a_t_i_o_n _o_f _e_n_r_i_c_h_e_d _G_O _t_e_r_m_s _a_t _l_e_v_e_l _3 _o_f _o_n_t_o_l_o_g_y _B_P _i_n _t_w_o
_g_e_n_e _l_i_s_t_s

_D_e_s_c_r_i_p_t_i_o_n:

     From the "Cancer gene list" of Bushman Lab, a collection of gene
     lists related with cancer, for gene lists "Atlas" and "Sanger",
     this dataset is the cross-tabulation of all GO terms of ontology
     BP at level 3 which are: Enriched in both lists, enriched in
     sanger but not in atlas, non-enriched in sanger but enriched in
     atlas and non-enriched in both lists. Take it just as an
     illustrative example, non up-to-date for changes in the gene lists
     or changes in the GO. The present version was obtained under
     Bioconductor 3.17.

_U_s_a_g_e:

     data(tab_atlas.sanger_BP3)
     
_F_o_r_m_a_t:

     An object of class "table" representing a 2x2 contingency table.

_S_o_u_r_c_e:

     <http://www.bushmanlab.org/links/genelists>


> class(tab_atlas.sanger_BP3)
[1] "table"
> 
> # Sorensen-Dice dissimilarity on this contingency table:
> ?dSorensen
dSorensen              package:goSorensen              R Documentation

_C_o_m_p_u_t_a_t_i_o_n _o_f _t_h_e _S_o_r_e_n_s_e_n-_D_i_c_e _d_i_s_s_i_m_i_l_a_r_i_t_y

_D_e_s_c_r_i_p_t_i_o_n:

     Computation of the Sorensen-Dice dissimilarity

_U_s_a_g_e:

     dSorensen(x, ...)
     
     ## S3 method for class 'table'
     dSorensen(x, check.table = TRUE, ...)
     
     ## S3 method for class 'matrix'
     dSorensen(x, check.table = TRUE, ...)
     
     ## S3 method for class 'numeric'
     dSorensen(x, check.table = TRUE, ...)
     
     ## S3 method for class 'character'
     dSorensen(x, y, check.table = TRUE, ...)
     
     ## S3 method for class 'list'
     dSorensen(x, check.table = TRUE, ...)
     
     ## S3 method for class 'tableList'
     dSorensen(x, check.table = TRUE, ...)
     
_A_r_g_u_m_e_n_t_s:

       x: either an object of class "table", "matrix" or "numeric"
          representing a 2x2 contingency table, or a "character" vector
          (a set of gene identifiers) or "list" or "tableList" object.
          See the details section for more information.

     ...: extra parameters for function 'buildEnrichTable'.

check.table: Boolean. If TRUE (default), argument 'x' is checked to
          adequately represent a 2x2 contingency table, by means of
          function 'nice2x2Table'.

       y: an object of class "character" representing a vector of valid
          gene identifiers (e.g., ENTREZ).

_D_e_t_a_i_l_s:

     Given a 2x2 arrangement of frequencies (either implemented as a
     "table", a "matrix" or a "numeric" object):

       n_{11}   n_{10} 
       n_{01}  n_{00}, 
      
     this function computes the Sorensen-Dice dissimilarity

                   { n_10 + n_01}/{2 n_11 + n_10 + n_01}.               
     
     The subindex '11' corresponds to those GO terms enriched in both
     lists, '01' to terms enriched in the second list but not in the
     first one, '10' to terms enriched in the first list but not
     enriched in the second one and '00' corresponds to those GO terms
     non enriched in both gene lists, i.e., to the double negatives, a
     value which is ignored in the computations.

     In the "numeric" interface, if 'length(x) >= 3', the values are
     interpreted as (n_11, n_01, n_10, n_00), always in this order and
     discarding extra values if necessary. The result is correct,
     regardless the frequencies being absolute or relative.

     If 'x' is an object of class "character", then 'x' (and 'y') must
     represent two "character" vectors of valid gene identifiers (e.g.,
     ENTREZ). Then the dissimilarity between lists 'x' and 'y' is
     computed, after internally summarizing them as a 2x2 contingency
     table of joint enrichment. This last operation is performed by
     function 'buildEnrichTable' and "valid gene identifiers (e.g.,
     ENTREZ)" stands for the coherency of these gene identifiers with
     the arguments 'geneUniverse' and 'orgPackg' of 'buildEnrichTable',
     passed by the ellipsis argument '...' in 'dSorensen'.

     If 'x' is an object of class "list", the argument must be a list
     of "character" vectors, each one representing a gene list
     (character identifiers). Then, all pairwise dissimilarities
     between these gene lists are computed.

     If 'x' is an object of class "tableList", the Sorensen-Dice
     dissimilarity is computed over each one of these tables. Given k
     gene lists (i.e. "character" vectors of gene identifiers) l1, l2,
     ..., lk, an object of class "tableList" (typically constructed by
     a call to function 'buildEnrichTable') is a list of lists of
     contingency tables t(i,j) generated from each pair of gene lists i
     and j, with the following structure:

     $l2

     $l2$l1$t(2,1)

     $l3

     $l3$l1$t(3,1), $l3$l2$t(3,2)

     ...

     $lk

     $lk$l1$t(k,1), $lk$l2$t(k,2), ..., $lk$l(k-1)t(k,k-1)

_V_a_l_u_e:

     In the "table", "matrix", "numeric" and "character" interfaces,
     the value of the Sorensen-Dice dissimilarity. In the "list" and
     "tableList" interfaces, the symmetric matrix of all pairwise
     Sorensen-Dice dissimilarities.

_M_e_t_h_o_d_s (_b_y _c_l_a_s_s):

        • 'dSorensen(table)': S3 method for class "table"

        • 'dSorensen(matrix)': S3 method for class "matrix"

        • 'dSorensen(numeric)': S3 method for class "numeric"

        • 'dSorensen(character)': S3 method for class "character"

        • 'dSorensen(list)': S3 method for class "list"

        • 'dSorensen(tableList)': S3 method for class "tableList"

_S_e_e _A_l_s_o:

     'buildEnrichTable' for constructing contingency tables of mutual
     enrichment, 'nice2x2Table' for checking contingency tables
     validity, 'seSorensen' for computing the standard error of the
     dissimilarity, 'duppSorensen' for the upper limit of a one-sided
     confidence interval of the dissimilarity, 'equivTestSorensen' for
     an equivalence test.

_E_x_a_m_p_l_e_s:

     # Gene lists 'atlas' and 'sanger' in 'allOncoGeneLists' dataset. Table of joint enrichment
     # of GO terms in ontology BP at level 3.
     data(tab_atlas.sanger_BP3)
     tab_atlas.sanger_BP3
     ?tab_atlas.sanger_BP3
     dSorensen(tab_atlas.sanger_BP3)
     
     # Table represented as a vector:
     conti4 <- c(56, 1, 30, 471)
     dSorensen(conti4)
     # or as a plain matrix:
     dSorensen(matrix(conti4, nrow = 2))
     
     # This function is also appropriate for proportions:
     dSorensen(conti4 / sum(conti4))
     
     conti3 <- c(56, 1, 30)
     dSorensen(conti3)
     
     # Sorensen-Dice dissimilarity from scratch, directly from two gene lists:
     # (These examples may be considerably time consuming due to many enrichment
     # tests to build the contingency tables of joint enrichment)
     # data(allOncoGeneLists)
     # ?allOncoGeneLists
     
     # Obtaining ENTREZ identifiers for the gene universe of humans:
     # library(org.Hs.eg.db)
     # humanEntrezIDs <- keys(org.Hs.eg.db, keytype = "ENTREZID")
     
     # (Time consuming, building the table requires many enrichment tests:)
     # dSorensen(allOncoGeneLists$atlas, allOncoGeneLists$sanger,
     #           onto = "BP", GOLevel = 3,
     #           geneUniverse = humanEntrezIDs, orgPackg = "org.Hs.eg.db")
     
     # Essentially, the above code makes the same as:
     # tab_atlas.sanger_BP3 <- buildEnrichTable(allOncoGeneLists$atlas, allOncoGeneLists$sanger,
     #                                     onto = "BP", GOLevel = 3,
     #                                     geneUniverse = humanEntrezIDs, orgPackg = "org.Hs.eg.db")
     # dSorensen(tab_atlas.sanger_BP3)
     # (Quite time consuming, all pairwise dissimilarities:)
     # dSorensen(allOncoGeneLists,
     #           onto = "BP", GOLevel = 3,
     #           geneUniverse = humanEntrezIDs, orgPackg = "org.Hs.eg.db")
     

> dSorensen(tab_atlas.sanger_BP3)
[1] 0.3027523
> 
> # Standard error of this Sorensen-Dice dissimilarity estimate:
> ?seSorensen
seSorensen             package:goSorensen              R Documentation

_S_t_a_n_d_a_r_d _e_r_r_o_r _o_f _t_h_e _s_a_m_p_l_e _S_o_r_e_n_s_e_n-_D_i_c_e _d_i_s_s_i_m_i_l_a_r_i_t_y, _a_s_y_m_p_t_o_t_i_c
_a_p_p_r_o_a_c_h

_D_e_s_c_r_i_p_t_i_o_n:

     Standard error of the sample Sorensen-Dice dissimilarity,
     asymptotic approach

_U_s_a_g_e:

     seSorensen(x, ...)
     
     ## S3 method for class 'table'
     seSorensen(x, check.table = TRUE, ...)
     
     ## S3 method for class 'matrix'
     seSorensen(x, check.table = TRUE, ...)
     
     ## S3 method for class 'numeric'
     seSorensen(x, check.table = TRUE, ...)
     
     ## S3 method for class 'character'
     seSorensen(x, y, check.table = TRUE, ...)
     
     ## S3 method for class 'list'
     seSorensen(x, check.table = TRUE, ...)
     
     ## S3 method for class 'tableList'
     seSorensen(x, check.table = TRUE, ...)
     
_A_r_g_u_m_e_n_t_s:

       x: either an object of class "table", "matrix" or "numeric"
          representing a 2x2 contingency table, or a "character" (a set
          of gene identifiers) or "list" or "tableList" object. See the
          details section for more information.

     ...: extra parameters for function 'buildEnrichTable'.

check.table: Boolean. If TRUE (default), argument 'x' is checked to
          adequately represent a 2x2 contingency table. This checking
          is performed by means of function 'nice2x2Table'.

       y: an object of class "character" representing a vector of gene
          identifiers (e.g., ENTREZ).

_D_e_t_a_i_l_s:

     This function computes the standard error estimate of the sample
     Sorensen-Dice dissimilarity, given a 2x2 arrangement of
     frequencies (either implemented as a "table", a "matrix" or a
     "numeric" object):

       n_{11}   n_{10} 
       n_{01}  n_{00}, 
      
     The subindex '11' corresponds to those GO terms enriched in both
     lists, '01' to terms enriched in the second list but not in the
     first one, '10' to terms enriched in the first list but not
     enriched in the second one and '00' corresponds to those GO terms
     non enriched in both gene lists, i.e., to the double negatives, a
     value which is ignored in the computations.

     In the "numeric" interface, if 'length(x) >= 3', the values are
     interpreted as (n_11, n_01, n_10), always in this order.

     If 'x' is an object of class "character", then 'x' (and 'y') must
     represent two "character" vectors of valid gene identifiers (e.g.,
     ENTREZ). Then the standard error for the dissimilarity between
     lists 'x' and 'y' is computed, after internally summarizing them
     as a 2x2 contingency table of joint enrichment. This last
     operation is performed by function 'buildEnrichTable' and "valid
     gene identifiers (e.g., ENTREZ)" stands for the coherency of these
     gene identifiers with the arguments 'geneUniverse' and 'orgPackg'
     of 'buildEnrichTable', passed by the ellipsis argument '...' in
     'seSorensen'.

     In the "list" interface, the argument must be a list of
     "character" vectors, each one representing a gene list (character
     identifiers). Then, all pairwise standard errors of the
     dissimilarity between these gene lists are computed.

     If 'x' is an object of class "tableList", the standard error of
     the Sorensen-Dice dissimilarity estimate is computed over each one
     of these tables. Given k gene lists (i.e. "character" vectors of
     gene identifiers) l1, l2, ..., lk, an object of class "tableList"
     (typically constructed by a call to function 'buildEnrichTable')
     is a list of lists of contingency tables t(i,j) generated from
     each pair of gene lists i and j, with the following structure:

     $l2

     $l2$l1$t(2,1)

     $l3

     $l3$l1$t(3,1), $l3$l2$t(3,2)

     ...

     $lk

     $lk$l1$t(k,1), $lk$l2$t(k,2), ..., $lk$l(k-1)t(k,k-1)

_V_a_l_u_e:

     In the "table", "matrix", "numeric" and "character" interfaces,
     the value of the standard error of the Sorensen-Dice dissimilarity
     estimate. In the "list" and "tableList" interfaces, the symmetric
     matrix of all standard error dissimilarity estimates.

_M_e_t_h_o_d_s (_b_y _c_l_a_s_s):

        • 'seSorensen(table)': S3 method for class "table"

        • 'seSorensen(matrix)': S3 method for class "matrix"

        • 'seSorensen(numeric)': S3 method for class "numeric"

        • 'seSorensen(character)': S3 method for class "character"

        • 'seSorensen(list)': S3 method for class "list"

        • 'seSorensen(tableList)': S3 method for class "tableList"

_S_e_e _A_l_s_o:

     'buildEnrichTable' for constructing contingency tables of mutual
     enrichment, 'nice2x2Table' for checking the validity of enrichment
     contingency tables, 'dSorensen' for computing the Sorensen-Dice
     dissimilarity, 'duppSorensen' for the upper limit of a one-sided
     confidence interval of the dissimilarity, 'equivTestSorensen' for
     an equivalence test.

_E_x_a_m_p_l_e_s:

     # Gene lists 'atlas' and 'sanger' in 'Cangenes' dataset. Table of joint enrichment
     # of GO terms in ontology BP at level 3.
     data(tab_atlas.sanger_BP3)
     tab_atlas.sanger_BP3
     dSorensen(tab_atlas.sanger_BP3)
     seSorensen(tab_atlas.sanger_BP3)
     
     # Contingency table as a numeric vector:
     seSorensen(c(56, 1, 30, 47))
     seSorensen(c(56, 1, 30))
     
     # (These examples may be considerably time consuming due to many enrichment
     # tests to build the contingency tables of mutual enrichment)
     # data(allOncoGeneLists)
     # ?allOncoGeneLists
     
     # Standard error of the sample Sorensen-Dice dissimilarity, directly from
     # two gene lists, from scratch:
     # seSorensen(allOncoGeneLists$atlas, allOncoGeneLists$sanger,
     #            onto = "BP", GOLevel = 3,
     #            geneUniverse = humanEntrezIDs, orgPackg = "org.Hs.eg.db")
     # Essentially, the above code makes the same as:
     # ctab_atlas.sanger_BP3 <- buildEnrichTable(allOncoGeneLists$atlas, allOncoGeneLists$sanger,
     #                                     onto = "BP", GOLevel = 3,
     #                                     geneUniverse = humanEntrezIDs, orgPackg = "org.Hs.eg.db")
     # ctab_atlas.sanger_BP3
     # seSorensen(ctab_atlas.sanger_BP3)
     # tab_atlas.sanger_BP3 and ctab_atlas.sanger_BP3 have exactly the same result.
     
     # All pairwise standard errors (quite time consuming):
     # seSorensen(allOncoGeneLists,
     #            onto = "BP", GOLevel = 3,
     #            geneUniverse = humanEntrezIDs, orgPackg = "org.Hs.eg.db")
     

> seSorensen(tab_atlas.sanger_BP3)
[1] 0.05058655
> 
> # Upper 95% confidence limit for the Sorensen-Dice dissimilarity:
> ?duppSorensen
duppSorensen            package:goSorensen             R Documentation

_U_p_p_e_r _l_i_m_i_t _o_f _a _o_n_e-_s_i_d_e_d _c_o_n_f_i_d_e_n_c_e _i_n_t_e_r_v_a_l (_0, _d_U_p_p] _f_o_r _t_h_e
_S_o_r_e_n_s_e_n-_D_i_c_e _d_i_s_s_i_m_i_l_a_r_i_t_y

_D_e_s_c_r_i_p_t_i_o_n:

     Upper limit of a one-sided confidence interval (0, dUpp] for the
     Sorensen-Dice dissimilarity

_U_s_a_g_e:

     duppSorensen(x, ...)
     
     ## S3 method for class 'table'
     duppSorensen(
       x,
       dis = dSorensen.table(x, check.table = FALSE),
       se = seSorensen.table(x, check.table = FALSE),
       conf.level = 0.95,
       z.conf.level = qnorm(1 - conf.level),
       boot = FALSE,
       nboot = 10000,
       check.table = TRUE,
       ...
     )
     
     ## S3 method for class 'matrix'
     duppSorensen(
       x,
       dis = dSorensen.matrix(x, check.table = FALSE),
       se = seSorensen.matrix(x, check.table = FALSE),
       conf.level = 0.95,
       z.conf.level = qnorm(1 - conf.level),
       boot = FALSE,
       nboot = 10000,
       check.table = TRUE,
       ...
     )
     
     ## S3 method for class 'numeric'
     duppSorensen(
       x,
       dis = dSorensen.numeric(x, check.table = FALSE),
       se = seSorensen.numeric(x, check.table = FALSE),
       conf.level = 0.95,
       z.conf.level = qnorm(1 - conf.level),
       boot = FALSE,
       nboot = 10000,
       check.table = TRUE,
       ...
     )
     
     ## S3 method for class 'character'
     duppSorensen(
       x,
       y,
       conf.level = 0.95,
       boot = FALSE,
       nboot = 10000,
       check.table = TRUE,
       ...
     )
     
     ## S3 method for class 'list'
     duppSorensen(
       x,
       conf.level = 0.95,
       boot = FALSE,
       nboot = 10000,
       check.table = TRUE,
       ...
     )
     
     ## S3 method for class 'tableList'
     duppSorensen(
       x,
       conf.level = 0.95,
       boot = FALSE,
       nboot = 10000,
       check.table = TRUE,
       ...
     )
     
_A_r_g_u_m_e_n_t_s:

       x: either an object of class "table", "matrix" or "numeric"
          representing a 2x2 contingency table, or a "character" (a set
          of gene identifiers) or "list" or "tableList" object. See the
          details section for more information.

     ...: additional arguments for function 'buildEnrichTable'.

     dis: Sorensen-Dice dissimilarity value. Only required to speed
          computations if this value is known in advance.

      se: standard error estimate of the sample dissimilarity. Only
          required to speed computations if this value is known in
          advance.

conf.level: confidence level of the one-sided confidence interval, a
          numeric value between 0 and 1.

z.conf.level: standard normal (or bootstrap, see arguments below)
          distribution quantile at the '1 - conf.level' value. Only
          required to speed computations if this value is known in
          advance. Then, the argument 'conf.level' is ignored.

    boot: boolean. If TRUE, 'z.conf.level' is computed by means of a
          bootstrap approach instead of the asymptotic normal approach.
          Defaults to FALSE.

   nboot: numeric, number of initially planned bootstrap replicates.
          Ignored if 'boot == FALSE'. Defaults to 10000.

check.table: Boolean. If TRUE (default), argument 'x' is checked to
          adequately represent a 2x2 contingency table. This checking
          is performed by means of function 'nice2x2Table'.

       y: an object of class "character" representing a vector of gene
          identifiers (e.g., ENTREZ).

_D_e_t_a_i_l_s:

     This function computes the upper limit of a one-sided confidence
     interval for the Sorensen-Dice dissimilarity, given a 2x2
     arrangement of frequencies (either implemented as a "table", a
     "matrix" or a "numeric" object):

       n_{11}   n_{10} 
       n_{01}  n_{00}, 
      
     The subindex '11' corresponds to those GO terms enriched in both
     lists, '01' to terms enriched in the second list but not in the
     first one, '10' to terms enriched in the first list but not
     enriched in the second one and '00' corresponds to those GO terms
     non enriched in both gene lists, i.e., to the double negatives, a
     value which is ignored in the computations, except if 'boot ==
     TRUE'.

     In the "numeric" interface, if 'length(x) >= 4', the values are
     interpreted as (n_11, n_01, n_10, n_00), always in this order and
     discarding extra values if necessary.

     Arguments 'dis', 'se' and 'z.conf.level' are not required. If
     known in advance (e.g., as a consequence of previous computations
     with the same data), providing its value may speed the
     computations.

     By default, 'z.conf.level' corresponds to the 1 - conf.level
     quantile of a standard normal N(0,1) distribution, as the
     studentized statistic (^d - d) / ^se) is asymptotically N(0,1). In
     the studentized statistic, d stands for the "true" Sorensen-Dice
     dissimilarity, ^d to its sample estimate and ^se for the estimate
     of its standard error. In fact, the normal is its limiting
     distribution but, for finite samples, the true sampling
     distribution may present departures from normality (mainly with
     some inflation in the left tail). The bootstrap method provides a
     better approximation to the true sampling distribution. In the
     bootstrap approach, 'nboot' new bootstrap contingency tables are
     generated from a multinomial distribution with parameters 'size ='
     n11 + n01 + n10 + n00 and probabilities %. Sometimes, some of
     these generated tables may present so low frequencies of
     enrichment that make them unable for Sorensen-Dice computations.
     As a consequence, the number of effective bootstrap samples may be
     lower than the number of initially planned bootstrap samples
     'nboot'. Computing in advance the value of argument 'z.conf.level'
     may be a way to cope with these departures from normality, by
     means of a more adequate quantile function. Alternatively, if
     'boot == TRUE', a bootstrap quantile is internally computed.

     If 'x' is an object of class "character", then 'x' (and 'y') must
     represent two "character" vectors of valid gene identifiers (e.g.,
     ENTREZ). Then the confidence interval for the dissimilarity
     between lists 'x' and 'y' is computed, after internally
     summarizing them as a 2x2 contingency table of joint enrichment.
     This last operation is performed by function 'buildEnrichTable'
     and "valid gene identifiers (e.g., ENTREZ)" stands for the
     coherency of these gene identifiers with the arguments
     'geneUniverse' and 'orgPackg' of 'buildEnrichTable', passed by the
     ellipsis argument '...' in 'dUppSorensen'.

     In the "list" interface, the argument must be a list of
     "character" vectors, each one representing a gene list (character
     identifiers). Then, all pairwise upper limits of the dissimilarity
     between these gene lists are computed.

     In the "tableList" interface, the upper limits are computed over
     each one of these tables. Given gene lists (i.e. "character"
     vectors of gene identifiers) l1, l2, ..., lk, an object of class
     "tableList" (typically constructed by a call to function
     'buildEnrichTable') is a list of lists of contingency tables
     t(i,j) generated from each pair of gene lists i and j, with the
     following structure:

     $l2

     $l2$l1$t(2,1)

     $l3

     $l3$l1$t(3,1), $l3$l2$t(3,2)

     ...

     $lk

     $lk$l1$t(k,1), $lk$l2$t(k,2), ..., $lk$l(k-1)t(k,k-1)

_V_a_l_u_e:

     In the "table", "matrix", "numeric" and "character" interfaces,
     the value of the Upper limit of the confidence interval for the
     Sorensen-Dice dissimilarity. When 'boot == TRUE', this result also
     haves a an extra attribute: "eff.nboot" which corresponds to the
     number of effective bootstrap replicats, see the details section.
     In the "list" and "tableList" interfaces, the result is the
     symmetric matrix of all pairwise upper limits.

_M_e_t_h_o_d_s (_b_y _c_l_a_s_s):

        • 'duppSorensen(table)': S3 method for class "table"

        • 'duppSorensen(matrix)': S3 method for class "matrix"

        • 'duppSorensen(numeric)': S3 method for class "numeric"

        • 'duppSorensen(character)': S3 method for class "character"

        • 'duppSorensen(list)': S3 method for class "list"

        • 'duppSorensen(tableList)': S3 method for class "tableList"

_S_e_e _A_l_s_o:

     'buildEnrichTable' for constructing contingency tables of mutual
     enrichment, 'nice2x2Table' for checking contingency tables
     validity, 'dSorensen' for computing the Sorensen-Dice
     dissimilarity, 'seSorensen' for computing the standard error of
     the dissimilarity, 'equivTestSorensen' for an equivalence test.

_E_x_a_m_p_l_e_s:

     # Gene lists 'atlas' and 'sanger' in 'Cangenes' dataset. Table of joint enrichment
     # of GO terms in ontology BP at level 3.
     data(tab_atlas.sanger_BP3)
     ?tab_atlas.sanger_BP3
     duppSorensen(tab_atlas.sanger_BP3)
     dSorensen(tab_atlas.sanger_BP3) + qnorm(0.95) * seSorensen(tab_atlas.sanger_BP3)
     # Using the bootstrap approximation instead of the normal approximation to
     # the sampling distribution of (^d - d) / se(^d):
     duppSorensen(tab_atlas.sanger_BP3, boot = TRUE)
     
     # Contingency table as a numeric vector:
     duppSorensen(c(56, 1, 30, 47))
     duppSorensen(c(56, 1, 30))
     
     # Upper confidence limit for the Sorensen-Dice dissimilarity, from scratch,
     # directly from two gene lists:
     # (These examples may be considerably time consuming due to many enrichment
     # tests to build the contingency tables of mutual enrichment)
     # data(allOncoGeneLists)
     # ?allOncoGeneLists
     
     # Obtaining ENTREZ identifiers for the gene universe of humans:
     # library(org.Hs.eg.db)
     # humanEntrezIDs <- keys(org.Hs.eg.db, keytype = "ENTREZID")
     
     # Computing the Upper confidence limit:
     # duppSorensen(allOncoGeneLists$atlas, allOncoGeneLists$sanger,
     #              onto = "CC", GOLevel = 5,
     #              geneUniverse = humanEntrezIDs, orgPackg = "org.Hs.eg.db")
     # Even more time consuming (all pairwise values):
     # duppSorensen(allOncoGeneLists,
     #              onto = "CC", GOLevel = 5,
     #              geneUniverse = humanEntrezIDs, orgPackg = "org.Hs.eg.db")
     

> duppSorensen(tab_atlas.sanger_BP3)
[1] 0.3859598
> # This confidence limit is based on an assimptotic normal N(0,1)
> # approximation to the distribution of (dSampl - d) / se, where
> # dSampl stands for the sample dissimilarity, d for the true dissimilarity
> # and se for the sample dissimilarity standard error estimate.
> 
> # Upper confidence limit but using a Student's t instead of a N(0,1)
> # (just as an example, not recommended -no theoretical justification)
> df <- sum(tab_atlas.sanger_BP3[1:3]) - 2
> duppSorensen(tab_atlas.sanger_BP3, z.conf.level = qt(1 - 0.95, df))
[1] 0.3870921
> 
> # Upper confidence limit but using a bootstrap approximation
> # to the sampling distribution, instead of a N(0,1)
> set.seed(123)
> duppSorensen(tab_atlas.sanger_BP3, boot = TRUE)
[1] 0.3941622
attr(,"eff.nboot")
[1] 10000
> 
> # Some computations on diverse data structures:
> badConti <- as.table(matrix(c(501, 27, 36, 12, 43, 15, 0, 0, 0),
+                             nrow = 3, ncol = 3,
+                             dimnames = list(c("a1","a2","a3"),
+                                             c("b1", "b2","b3"))))
> tryCatch(nice2x2Table(badConti), error = function(e) {return(e)})
<simpleError in nice2x2Table.table(badConti): Not a 2x2 table>
> 
> incompleteConti <- badConti[1,1:min(2,ncol(badConti)), drop = FALSE]
> incompleteConti
    b1  b2
a1 501  12
> tryCatch(nice2x2Table(incompleteConti), error = function(e) {return(e)})
<simpleError in nice2x2Table.table(incompleteConti): Not a 2x2 table>
> 
> contiAsVector <- c(32, 21, 81, 1439)
> nice2x2Table(contiAsVector)
[1] TRUE
> contiAsVector.mat <- matrix(contiAsVector, nrow = 2)
> contiAsVector.mat
     [,1] [,2]
[1,]   32   81
[2,]   21 1439
> contiAsVectorLen3 <- c(32, 21, 81)
> nice2x2Table(contiAsVectorLen3)
[1] TRUE
> 
> tryCatch(dSorensen(badConti), error = function(e) {return(e)})
<simpleError in nice2x2Table.table(x): Not a 2x2 table>
> 
> # Apparently, the next order works fine, but returns a wrong value!
> dSorensen(badConti, check.table = FALSE)
[1] 0.05915493
> 
> tryCatch(dSorensen(incompleteConti), error = function(e) {return(e)})
<simpleError in nice2x2Table.table(x): Not a 2x2 table>
> dSorensen(contiAsVector)
[1] 0.6144578
> dSorensen(contiAsVector.mat)
[1] 0.6144578
> dSorensen(contiAsVectorLen3)
[1] 0.6144578
> dSorensen(contiAsVectorLen3, check.table = FALSE)
[1] 0.6144578
> dSorensen(c(0,0,0,45))
[1] NaN
> 
> tryCatch(seSorensen(badConti), error = function(e) {return(e)})
<simpleError in nice2x2Table.table(x): Not a 2x2 table>
> tryCatch(seSorensen(incompleteConti), error = function(e) {return(e)})
<simpleError in nice2x2Table.table(x): Not a 2x2 table>
> seSorensen(contiAsVector)
[1] 0.04818012
> seSorensen(contiAsVector.mat)
[1] 0.04818012
> seSorensen(contiAsVectorLen3)
[1] 0.04818012
> seSorensen(contiAsVectorLen3, check.table = FALSE)
[1] 0.04818012
> tryCatch(seSorensen(contiAsVectorLen3, check.table = "not"), error = function(e) {return(e)})
<simpleError in seSorensen.numeric(contiAsVectorLen3, check.table = "not"): Argument 'check.table' must be logical>
> seSorensen(c(0,0,0,45))
[1] NaN
> 
> tryCatch(duppSorensen(badConti), error = function(e) {return(e)})
<simpleError in nice2x2Table.table(x): Not a 2x2 table>
> tryCatch(duppSorensen(incompleteConti), error = function(e) {return(e)})
<simpleError in nice2x2Table.table(x): Not a 2x2 table>
> duppSorensen(contiAsVector)
[1] 0.6937071
> duppSorensen(contiAsVector.mat)
[1] 0.6937071
> set.seed(123)
> duppSorensen(contiAsVector, boot = TRUE)
[1] 0.6922658
attr(,"eff.nboot")
[1] 10000
> set.seed(123)
> duppSorensen(contiAsVector.mat, boot = TRUE)
[1] 0.6922658
attr(,"eff.nboot")
[1] 10000
> duppSorensen(contiAsVectorLen3)
[1] 0.6937071
> # Bootstrapping requires full contingency tables (4 values)
> set.seed(123)
> tryCatch(duppSorensen(contiAsVectorLen3, boot = TRUE), error = function(e) {return(e)})
<simpleError in duppSorensen.numeric(contiAsVectorLen3, boot = TRUE): Bootstraping requires a numeric vector of 4 frequencies>
> duppSorensen(c(0,0,0,45))
[1] NaN
> 
> # Equivalence test, H0: d >= d0 vs  H1: d < d0 (d0 = 0.4444)
> ?equivTestSorensen
equivTestSorensen          package:goSorensen          R Documentation

_E_q_u_i_v_a_l_e_n_c_e _t_e_s_t _b_a_s_e_d _o_n _t_h_e _S_o_r_e_n_s_e_n-_D_i_c_e _d_i_s_s_i_m_i_l_a_r_i_t_y

_D_e_s_c_r_i_p_t_i_o_n:

     Equivalence test based on the Sorensen-Dice dissimilarity,
     computed either by an asymptotic normal approach or by a bootstrap
     approach.

_U_s_a_g_e:

     equivTestSorensen(x, ...)
     
     ## S3 method for class 'table'
     equivTestSorensen(
       x,
       d0 = 1/(1 + 1.25),
       conf.level = 0.95,
       boot = FALSE,
       nboot = 10000,
       check.table = TRUE,
       ...
     )
     
     ## S3 method for class 'matrix'
     equivTestSorensen(
       x,
       d0 = 1/(1 + 1.25),
       conf.level = 0.95,
       boot = FALSE,
       nboot = 10000,
       check.table = TRUE,
       ...
     )
     
     ## S3 method for class 'numeric'
     equivTestSorensen(
       x,
       d0 = 1/(1 + 1.25),
       conf.level = 0.95,
       boot = FALSE,
       nboot = 10000,
       check.table = TRUE,
       ...
     )
     
     ## S3 method for class 'character'
     equivTestSorensen(
       x,
       y,
       d0 = 1/(1 + 1.25),
       conf.level = 0.95,
       boot = FALSE,
       nboot = 10000,
       check.table = TRUE,
       ...
     )
     
     ## S3 method for class 'list'
     equivTestSorensen(
       x,
       d0 = 1/(1 + 1.25),
       conf.level = 0.95,
       boot = FALSE,
       nboot = 10000,
       check.table = TRUE,
       ...
     )
     
     ## S3 method for class 'tableList'
     equivTestSorensen(
       x,
       d0 = 1/(1 + 1.25),
       conf.level = 0.95,
       boot = FALSE,
       nboot = 10000,
       check.table = TRUE,
       ...
     )
     
_A_r_g_u_m_e_n_t_s:

       x: either an object of class "table", "matrix", "numeric",
          "character", "list" or "tableList". See the details section
          for more information.

     ...: extra parameters for function 'buildEnrichTable'.

      d0: equivalence threshold for the Sorensen-Dice dissimilarity, d.
          The null hypothesis states that d >= d0, i.e., inequivalence
          between the compared gene lists and the alternative that d <
          d0, i.e., equivalence or dissimilarity irrelevance (up to a
          level d0).

conf.level: confidence level of the one-sided confidence interval, a
          value between 0 and 1.

    boot: boolean. If TRUE, the confidence interval and the test
          p-value are computed by means of a bootstrap approach instead
          of the asymptotic normal approach. Defaults to FALSE.

   nboot: numeric, number of initially planned bootstrap replicates.
          Ignored if 'boot == FALSE'. Defaults to 10000.

check.table: Boolean. If TRUE (default), argument 'x' is checked to
          adequately represent a 2x2 contingency table (or an aggregate
          of them) or gene lists producing a correct table. This
          checking is performed by means of function 'nice2x2Table'.

       y: an object of class "character" representing a list of gene
          identifiers (e.g., ENTREZ).

_D_e_t_a_i_l_s:

     This function computes either the normal asymptotic or the
     bootstrap equivalence test based on the Sorensen-Dice
     dissimilarity, given a 2x2 arrangement of frequencies (either
     implemented as a "table", a "matrix" or a "numeric" object):

       n_{11}   n_{10} 
       n_{01}  n_{00}, 
      
     The subindex '11' corresponds to those GO terms enriched in both
     lists, '01' to terms enriched in the second list but not in the
     first one, '10' to terms enriched in the first list but not
     enriched in the second one and '00' corresponds to those GO terms
     non enriched in both gene lists, i.e., to the double negatives, a
     value which is ignored in the computations.

     In the "numeric" interface, if 'length(x) >= 4', the values are
     interpreted as (n_11, n_01, n_10, n_00), always in this order and
     discarding extra values if necessary.

     If 'x' is an object of class "character", then 'x' (and 'y') must
     represent two "character" vectors of valid gene identifiers (e.g.,
     ENTREZ). Then the equivalence test is performed between 'x' and
     'y', after internally summarizing them as a 2x2 contingency table
     of joint enrichment. This last operation is performed by function
     'buildEnrichTable' and "valid gene identifiers (e.g., ENTREZ)"
     stands for the coherency of these gene identifiers with the
     arguments 'geneUniverse' and 'orgPackg' of 'buildEnrichTable',
     passed by the ellipsis argument '...' in 'equivTestSorensen'.

     If 'x' is an object of class "list", each of its elements must be
     a "character" vector of gene identifiers (e.g., ENTREZ). Then all
     pairwise equivalence tests are performed between these gene lists.

     Class "tableList" corresponds to objects representing all mutual
     enrichment contingency tables generated in a pairwise fashion:
     Given gene lists l1, l2, ..., lk, an object of class "tableList"
     (typically constructed by a call to function 'buildEnrichTable')
     is a list of lists of contingency tables tij generated from each
     pair of gene lists i and j, with the following structure:

     $l2

     $l2$l1$t21

     $l3

     $l3$l1$t31, $l3$l2$t32

     ...

     $lk$l1$tk1, $lk$l2$tk2, ..., $lk$l(k-1)tk(k-1)

     If 'x' is an object of class "tableList", the test is performed
     over each one of these tables.

     The test is based on the fact that the studentized statistic (^d -
     d) / ^se is approximately distributed as a standard normal. ^d
     stands for the sample Sorensen-Dice dissimilarity, d for its true
     (unknown) value and ^se for the estimate of its standard error.
     This result is asymptotically correct, but the true distribution
     of the studentized statistic is not exactly normal for finite
     samples, with a heavier left tail than expected under the Gaussian
     model, which may produce some type I error inflation. The
     bootstrap method provides a better approximation to this
     distribution. In the bootstrap approach, 'nboot' new bootstrap
     contingency tables are generated from a multinomial distribution
     with parameters 'size =' (n11 + n01 + n10 + n00) and probabilities
     %. Sometimes, some of these generated tables may present so low
     frequencies of enrichment that make them unable for Sorensen-Dice
     computations. As a consequence, the number of effective bootstrap
     samples may be lower than the number of initially planned ones,
     'nboot', but our simulation studies concluded that this makes the
     test more conservative, less prone to reject a truly false null
     hypothesis of inequivalence, but in any case protects from
     inflating the type I error.

     In a bootstrap test result, use 'getNboot' to access the number of
     initially planned bootstrap replicates and 'getEffNboot' to access
     the number of finally effective bootstrap replicates.

_V_a_l_u_e:

     For all interfaces (except for the "list" and "tableList"
     interfaces) the result is a list of class "equivSDhtest" which
     inherits from "htest", with the following components:

     statistic the value of the studentized statistic (dSorensen(x) -
          d0) / seSorensen(x)

     p.value the p-value of the test

     conf.int the one-sided confidence interval (0, dUpp]

     estimate the Sorensen dissimilarity estimate, dSorensen(x)

     null.value the value of d0

     stderr the standard error of the Sorensen dissimilarity estimate,
          seSorensen(x), used as denominator in the studentized
          statistic

     alternative a character string describing the alternative
          hypothesis

     method a character string describing the test

     data.name a character string giving the names of the data

     enrichTab the 2x2 contingency table of joint enrichment whereby
          the test was based

     For the "list" and "tableList" interfaces, the result is an
     "equivSDhtestList", a list of objects with all pairwise
     comparisons, each one being an object of "equivSDhtest" class.

_M_e_t_h_o_d_s (_b_y _c_l_a_s_s):

        • 'equivTestSorensen(table)': S3 method for class "table"

        • 'equivTestSorensen(matrix)': S3 method for class "matrix"

        • 'equivTestSorensen(numeric)': S3 method for class "numeric"

        • 'equivTestSorensen(character)': S3 method for class
          "character"

        • 'equivTestSorensen(list)': S3 method for class "list"

        • 'equivTestSorensen(tableList)': S3 method for class
          "tableList"

_S_e_e _A_l_s_o:

     'nice2x2Table' for checking and reformatting data, 'dSorensen' for
     computing the Sorensen-Dice dissimilarity, 'seSorensen' for
     computing the standard error of the dissimilarity, 'duppSorensen'
     for the upper limit of a one-sided confidence interval of the
     dissimilarity. 'getTable', 'getPvalue', 'getUpper', 'getSE',
     'getNboot' and 'getEffNboot' for accessing specific fields in the
     result of these testing functions. 'update' for updating the
     result of these testing functions with alternative equivalence
     limits, confidence levels or to convert a normal result in a
     bootstrap result or the reverse.

_E_x_a_m_p_l_e_s:

     # Gene lists 'atlas' and 'sanger' in 'allOncoGeneLists' dataset. Table of joint enrichment
     # of GO terms in ontology BP at level 3.
     data(tab_atlas.sanger_BP3)
     tab_atlas.sanger_BP3
     equivTestSorensen(tab_atlas.sanger_BP3)
     # Bootstrap test:
     equivTestSorensen(tab_atlas.sanger_BP3, boot = TRUE)
     
     # Equivalence tests from scratch, directly from gene lists:
     # (These examples may be considerably time consuming due to many enrichment
     # tests to build the contingency tables of mutual enrichment)
     # data(allOncoGeneLists)
     # ?allOncoGeneLists
     
     # Obtaining ENTREZ identifiers for the gene universe of humans:
     library(org.Hs.eg.db)
     humanEntrezIDs <- keys(org.Hs.eg.db, keytype = "ENTREZID")
     
     # Computing the equivalence test:
     # equivTestSorensen(allOncoGeneLists$atlas, allOncoGeneLists$sanger,
     #                   geneUniverse = humanEntrezIDs, orgPackg = "org.Hs.eg.db",
     #                   onto = "BP", GOLevel = 3)
     # Bootstrap instead of normal approximation test:
     # equivTestSorensen(allOncoGeneLists$atlas, allOncoGeneLists$sanger,
     #                   geneUniverse = humanEntrezIDs, orgPackg = "org.Hs.eg.db",
     #                   onto = "BP", GOLevel = 3,
     #                   boot = TRUE)
     
     # Essentially, the above code makes:
     # ctab_atlas.sanger_BP3 <- buildEnrichTable(allOncoGeneLists$atlas, allOncoGeneLists$sanger,
     #                                   geneUniverse = humanEntrezIDs, orgPackg = "org.Hs.eg.db",
     #                                   onto = "BP", GOLevel = 3)
     # ctab_atlas.sanger_BP3
     # equivTestSorensen(ctab_atlas.sanger_BP3)
     # equivTestSorensen(ctab_atlas.sanger_BP3, boot = TRUE)
     # (Note that building first the contingency table may be advantageous to save time!)
     # The object tab_atlas.sanger_BP3 and ctab_atlas.sanger_BP3 are exactly the same
     
     # All pairwise equivalence tests:
     # equivTestSorensen(allOncoGeneLists,
     #                   geneUniverse = humanEntrezIDs, orgPackg = "org.Hs.eg.db",
     #                   onto = "BP", GOLevel = 3)
     
     
     # Equivalence test on a contingency table represented as a numeric vector:
     equivTestSorensen(c(56, 1, 30, 47))
     equivTestSorensen(c(56, 1, 30, 47), boot = TRUE)
     equivTestSorensen(c(56, 1, 30))
     # Error: all frequencies are needed for bootstrap:
     try(equivTestSorensen(c(56, 1, 30), boot = TRUE), TRUE)
     

> equiv.atlas.sanger <- equivTestSorensen(tab_atlas.sanger_BP3)
> equiv.atlas.sanger

	Normal asymptotic test for 2x2 contingency tables based on the
	Sorensen-Dice dissimilarity

data:  tab_atlas.sanger_BP3
(d - d0) / se = -2.801, p-value = 0.002547
alternative hypothesis: true equivalence limit d0 is less than 0.4444444
95 percent confidence interval:
 0.0000000 0.3859598
sample estimates:
Sorensen dissimilarity 
             0.3027523 
attr(,"se")
standard error 
    0.05058655 

> getTable(equiv.atlas.sanger)
                 Enriched in sanger
Enriched in atlas TRUE FALSE
            TRUE    38    31
            FALSE    2   452
> getPvalue(equiv.atlas.sanger)
    p-value 
0.002547349 
> 
> tryCatch(equivTestSorensen(badConti), error = function(e) {return(e)})
<simpleError in nice2x2Table.table(x): Not a 2x2 table>
> tryCatch(equivTestSorensen(incompleteConti), error = function(e) {return(e)})
<simpleError in nice2x2Table.table(x): Not a 2x2 table>
> equivTestSorensen(contiAsVector)

	Normal asymptotic test for 2x2 contingency tables based on the
	Sorensen-Dice dissimilarity

data:  contiAsVector
(d - d0) / se = 3.5287, p-value = 0.9998
alternative hypothesis: true equivalence limit d0 is less than 0.4444444
95 percent confidence interval:
 0.0000000 0.6937071
sample estimates:
Sorensen dissimilarity 
             0.6144578 
attr(,"se")
standard error 
    0.04818012 

> equivTestSorensen(contiAsVector.mat)

	Normal asymptotic test for 2x2 contingency tables based on the
	Sorensen-Dice dissimilarity

data:  contiAsVector.mat
(d - d0) / se = 3.5287, p-value = 0.9998
alternative hypothesis: true equivalence limit d0 is less than 0.4444444
95 percent confidence interval:
 0.0000000 0.6937071
sample estimates:
Sorensen dissimilarity 
             0.6144578 
attr(,"se")
standard error 
    0.04818012 

> set.seed(123)
> equivTestSorensen(contiAsVector.mat, boot = TRUE)

	Bootstrap test for 2x2 contingency tables based on the Sorensen-Dice
	dissimilarity (10000 bootstrap replicates)

data:  contiAsVector.mat
(d - d0) / se = 3.5287, p-value = 0.9996
alternative hypothesis: true equivalence limit d0 is less than 0.4444444
95 percent confidence interval:
 0.0000000 0.6922658
sample estimates:
Sorensen dissimilarity 
             0.6144578 
attr(,"se")
standard error 
    0.04818012 

> equivTestSorensen(contiAsVectorLen3)

	Normal asymptotic test for 2x2 contingency tables based on the
	Sorensen-Dice dissimilarity

data:  contiAsVectorLen3
(d - d0) / se = 3.5287, p-value = 0.9998
alternative hypothesis: true equivalence limit d0 is less than 0.4444444
95 percent confidence interval:
 0.0000000 0.6937071
sample estimates:
Sorensen dissimilarity 
             0.6144578 
attr(,"se")
standard error 
    0.04818012 

> 
> tryCatch(equivTestSorensen(contiAsVectorLen3, boot = TRUE), error = function(e) {return(e)})
<simpleError in equivTestSorensen.numeric(contiAsVectorLen3, boot = TRUE): Bootstraping requires a numeric vector of 4 frequencies>
> 
> equivTestSorensen(c(0,0,0,45))

	No test performed due non finite (d - d0) / se statistic

data:  c(0, 0, 0, 45)
(d - d0) / se = NaN, p-value = NA
alternative hypothesis: true equivalence limit d0 is less than 0.4444444
95 percent confidence interval:
   0 NaN
sample estimates:
Sorensen dissimilarity 
                   NaN 
attr(,"se")
standard error 
           NaN 

> 
> # Sorensen-Dice computations from scratch, directly from gene lists
> data(allOncoGeneLists)
> ?allOncoGeneLists
allOncoGeneLists          package:goSorensen           R Documentation

_7 _g_e_n_e _l_i_s_t_s _p_o_s_s_i_b_l_y _r_e_l_a_t_e_d _w_i_t_h _c_a_n_c_e_r

_D_e_s_c_r_i_p_t_i_o_n:

     An object of class "list" of length 7. Each one of its elements is
     a "character" vector of gene identifiers (e.g., ENTREZ). Only gene
     lists of length almost 100 were taken from their source web. Take
     these lists just as an illustrative example, they are not
     automatically updated.

_U_s_a_g_e:

     data(allOncoGeneLists)
     
_F_o_r_m_a_t:

     An object of class "list" of length 7. Each one of its elements is
     a "character" vector of ENTREZ gene identifiers .

_S_o_u_r_c_e:

     <http://www.bushmanlab.org/links/genelists>


> 
> library(org.Hs.eg.db)
Loading required package: AnnotationDbi
Loading required package: stats4
Loading required package: BiocGenerics
Loading required package: generics

Attaching package: 'generics'

The following objects are masked from 'package:base':

    as.difftime, as.factor, as.ordered, intersect, is.element, setdiff,
    setequal, union


Attaching package: 'BiocGenerics'

The following objects are masked from 'package:stats':

    IQR, mad, sd, var, xtabs

The following objects are masked from 'package:base':

    Filter, Find, Map, Position, Reduce, anyDuplicated, aperm, append,
    as.data.frame, basename, cbind, colnames, dirname, do.call,
    duplicated, eval, evalq, get, grep, grepl, is.unsorted, lapply,
    mapply, match, mget, order, paste, pmax, pmax.int, pmin, pmin.int,
    rank, rbind, rownames, sapply, saveRDS, table, tapply, unique,
    unsplit, which.max, which.min

Loading required package: Biobase
Welcome to Bioconductor

    Vignettes contain introductory material; view with
    'browseVignettes()'. To cite Bioconductor, see
    'citation("Biobase")', and for packages 'citation("pkgname")'.

Loading required package: IRanges
Loading required package: S4Vectors

Attaching package: 'S4Vectors'

The following object is masked from 'package:utils':

    findMatches

The following objects are masked from 'package:base':

    I, expand.grid, unname

> humanEntrezIDs <- keys(org.Hs.eg.db, keytype = "ENTREZID")
> # First, the mutual GO node enrichment tables are built, then computations
> # proceed from these contingency tables.
> # Building the contingency tables is a slow process (many enrichment tests)
> normTest <- equivTestSorensen(allOncoGeneLists[["atlas"]], allOncoGeneLists[["sanger"]],
+                               listNames = c("atlas", "sanger"),
+                               onto = "BP", GOLevel = 5,
+                               geneUniverse = humanEntrezIDs, orgPackg = "org.Hs.eg.db")

> normTest

	Normal asymptotic test for 2x2 contingency tables based on the
	Sorensen-Dice dissimilarity

data:  tab
(d - d0) / se = -7.6163, p-value = 1.306e-14
alternative hypothesis: true equivalence limit d0 is less than 0.4444444
95 percent confidence interval:
 0.0000000 0.3604408
sample estimates:
Sorensen dissimilarity 
             0.3373016 
attr(,"se")
standard error 
    0.01406763 

> 
> # To perform a bootstrap test from scratch would be even slower:
> # set.seed(123)
> # bootTest <- equivTestSorensen(allOncoGeneLists[["atlas"]], allOncoGeneLists[["sanger"]],
> #                               listNames = c("atlas", "sanger"),
> #                               boot = TRUE,
> #                               onto = "BP", GOLevel = 5,
> #                               geneUniverse = humanEntrezIDs, orgPackg = "org.Hs.eg.db")
> # bootTest
> 
> # It is much faster to upgrade 'normTest' to be a bootstrap test:
> set.seed(123)
> bootTest <- upgrade(normTest, boot = TRUE)
> bootTest

	Bootstrap test for 2x2 contingency tables based on the Sorensen-Dice
	dissimilarity (10000 bootstrap replicates)

data:  tab
(d - d0) / se = -7.6163, p-value = 9.999e-05
alternative hypothesis: true equivalence limit d0 is less than 0.4444444
95 percent confidence interval:
 0.0000000 0.3604667
sample estimates:
Sorensen dissimilarity 
             0.3373016 
attr(,"se")
standard error 
    0.01406763 

> # To know the number of planned bootstrap replicates:
> getNboot(bootTest)
[1] 10000
> # To know the number of valid bootstrap replicates:
> getEffNboot(bootTest)
[1] 10000
> 
> # There are similar methods for dSorensen, seSorensen, duppSorensen, etc. to
> # compute directly from a pair of gene lists.
> # They are quite slow for the same reason as before (many enrichment tests).
> # dSorensen(allOncoGeneLists[["atlas"]], allOncoGeneLists[["sanger"]],
> #           listNames = c("atlas", "sanger"),
> #           onto = "BP", GOLevel = 5,
> #           geneUniverse = humanEntrezIDs, orgPackg = "org.Hs.eg.db")
> # seSorensen(allOncoGeneLists[["atlas"]], allOncoGeneLists[["sanger"]],
> #            listNames = c("atlas", "sanger"),
> #            onto = "BP", GOLevel = 5,
> #            geneUniverse = humanEntrezIDs, orgPackg = "org.Hs.eg.db")
> #
> # duppSorensen(allOncoGeneLists[["atlas"]], allOncoGeneLists[["sanger"]],
> #              listNames = c("atlas", "sanger"),
> #              onto = "BP", GOLevel = 5,
> #              geneUniverse = humanEntrezIDs, orgPackg = "org.Hs.eg.db")
> #
> # set.seed(123)
> # duppSorensen(allOncoGeneLists[["atlas"]], allOncoGeneLists[["sanger"]],
> #              boot = TRUE,
> #              listNames = c("atlas", "sanger"),
> #              onto = "BP", GOLevel = 5,
> #              geneUniverse = humanEntrezIDs, orgPackg = "org.Hs.eg.db")
> # etc.
> 
> # To build the contingency table first and then compute from it, may be a more flexible
> # and saving time strategy, in general:
> ?buildEnrichTable
buildEnrichTable          package:goSorensen           R Documentation

_C_r_e_a_t_e_s _a _2_x_2 _e_n_r_i_c_h_m_e_n_t _c_o_n_t_i_n_g_e_n_c_y _t_a_b_l_e _f_r_o_m _t_w_o _g_e_n_e _l_i_s_t_s, _o_r _a_l_l
_p_a_i_r_w_i_s_e _c_o_n_t_i_n_g_e_n_c_y _t_a_b_l_e_s _f_o_r _a "_l_i_s_t" _o_f _g_e_n_e _l_i_s_t_s.

_D_e_s_c_r_i_p_t_i_o_n:

     Creates a 2x2 enrichment contingency table from two gene lists, or
     all pairwise contingency tables for a "list" of gene lists.

_U_s_a_g_e:

     buildEnrichTable(x, ...)
     
     ## Default S3 method:
     buildEnrichTable(
       x,
       y,
       listNames = c("gene.list1", "gene.list2"),
       check.table = TRUE,
       geneUniverse,
       orgPackg,
       onto,
       GOLevel,
       showEnrichedIn = TRUE,
       pAdjustMeth = "BH",
       pvalCutoff = 0.01,
       qvalCutoff = 0.05,
       parallel = FALSE,
       nOfCores = 1,
       ...
     )
     
     ## S3 method for class 'character'
     buildEnrichTable(
       x,
       y,
       listNames = c("gene.list1", "gene.list2"),
       geneUniverse,
       orgPackg,
       onto,
       GOLevel,
       showEnrichedIn = TRUE,
       check.table = TRUE,
       pAdjustMeth = "BH",
       pvalCutoff = 0.01,
       qvalCutoff = 0.05,
       parallel = FALSE,
       nOfCores = 1,
       ...
     )
     
     ## S3 method for class 'list'
     buildEnrichTable(
       x,
       check.table = TRUE,
       geneUniverse,
       orgPackg,
       onto,
       GOLevel,
       showEnrichedIn = TRUE,
       pAdjustMeth = "BH",
       pvalCutoff = 0.01,
       qvalCutoff = 0.05,
       parallel = FALSE,
       nOfCores = min(detectCores() - 1, length(x) - 1),
       ...
     )
     
_A_r_g_u_m_e_n_t_s:

       x: either an object of class "character" (or coerzable to
          "character") representing a vector of gene identifiers (e.g.,
          ENTREZ) or an object of class "list". In this second case,
          each element of the list must be a "character" vector of gene
          identifiers (e.g., ENTREZ). Then, all pairwise contingency
          tables between these gene lists are built.

     ...: Additional parameters for internal use (not used for the
          moment)

       y: an object of class "character" (or coerzable to "character")
          representing a vector of gene identifiers (e.g., ENTREZ).

listNames: a character(2) with the gene lists names originating the
          cross-tabulated enrichment frequencies. Only in the
          "character" or default interface.

check.table: Logical The resulting table must be checked. Defaults to
          TRUE.

geneUniverse: character vector containing the universe of genes from
          where gene lists have been extracted. This vector must be
          obtained from the annotation package declared in 'orgPackg'.
          For more details see README File.

orgPackg: A string with the name of the genomic annotation package
          corresponding to a specific species to be analyzed, which
          must be previously installed and activated. For more details
          see README File.

    onto: string describing the ontology. Either "BP", "MF" or "CC".

 GOLevel: An integer, the GO ontology level.

showEnrichedIn: Boolean. If TRUE (default), the cross-table of enriched
          and non-enriched GO terms vs Gene Lists names (obtained from
          the 'enrichedIn' function) is automatically saved in the
          Global Environment.

pAdjustMeth: string describing the adjust method, either "BH", "BY" or
          "Bonf", defaults to 'BH'.

pvalCutoff: adjusted pvalue cutoff on enrichment tests to report

qvalCutoff: qvalue cutoff on enrichment tests to report as significant.
          Tests must pass i) pvalueCutoff on unadjusted pvalues, ii)
          pvalueCutoff on adjusted pvalues and iii) qvalueCutoff on
          qvalues to be reported

parallel: Logical. Defaults to FALSE but put it at TRUE for parallel
          computation.

nOfCores: Number of cores for parallel computations. Only in "list"
          interface.

_D_e_t_a_i_l_s:

     The arguments 'parallel' and 'nOfCores' are ignored in the
     'default' and "character" interfaces, but included for possible
     future developments; they only apply to the "list" interface. In
     the "list" interface, 'parallel' defaults to FALSE but there is
     the possibility of some time saving when the number of gene lists
     (the length of 'x' in the "list" interface) is high. The trade off
     between the time spent initializing parallel computing and the
     possible time gain due to parallelization must be considered in
     each application and computer.

_V_a_l_u_e:

     in the "character" interface, an object of class "table". It
     represents a 2x2 contingency table, the cross-tabulation of the
     enriched GO terms in two gene lists: "Number of enriched GO terms
     in list 1 (TRUE, FALSE)" x "Number of enriched Go terms in list 2
     (TRUE, FALSE)". In the "list" interface, the result is an object
     of class "tableList" with all pairwise tables. Class "tableList"
     corresponds to objects representing all mutual enrichment
     contingency tables generated in a pairwise fashion: Given gene
     lists (i.e. "character" vectors of gene identifiers) l1, l2, ...,
     lk, an object of class "tableList" is a list of lists of
     contingency tables t(i,j) generated from each pair of gene lists i
     and j, with the following structure:

     $l2

     $l2$l1$t(2,1)

     $l3

     $l3$l1$t(3,1), $l3$l2$t(3,2)

     ...

     $lk

     $lk$l1$t(k,1), $lk$l2$t(k,2), ..., $lk$l(k-1)t(K,k-1)

_M_e_t_h_o_d_s (_b_y _c_l_a_s_s):

        • 'buildEnrichTable(default)': S3 default method

        • 'buildEnrichTable(character)': S3 method for class
          "character"

        • 'buildEnrichTable(list)': S3 method for class "list"

_E_x_a_m_p_l_e_s:

     # Obtaining ENTREZ identifiers for the gene universe of humans:
     library(org.Hs.eg.db)
     humanEntrezIDs <- keys(org.Hs.eg.db, keytype = "ENTREZID")
     
     # Gene lists to be explored for enrichment:
     data(allOncoGeneLists)
     ?allOncoGeneLists
     
     # Table of joint GO term enrichment between gene lists Vogelstein and sanger,
     # for ontology MF at GO level 6.
     vog.VS.sang <- buildEnrichTable(allOncoGeneLists[["Vogelstein"]],
                                     allOncoGeneLists[["sanger"]],
                                     geneUniverse = humanEntrezIDs, orgPackg = "org.Hs.eg.db",
                                     onto = "MF", GOLevel = 6, listNames = c("Vogelstein", "sanger"))
     vog.VS.sang
     # All tables of mutual enrichment:
     all.tabs <- buildEnrichTable(allOncoGeneLists,
                                  geneUniverse = humanEntrezIDs, orgPackg = "org.Hs.eg.db",
                                  onto = "MF", GOLevel = 6)
     all.tabs$waldman
     

> tab <- buildEnrichTable(allOncoGeneLists[["atlas"]], allOncoGeneLists[["sanger"]],
+                         listNames = c("atlas", "sanger"),
+                         onto = "BP", GOLevel = 5,
+                         geneUniverse = humanEntrezIDs, orgPackg = "org.Hs.eg.db")
> 
> tab
                 Enriched in sanger
Enriched in atlas TRUE FALSE
            TRUE   501   458
            FALSE   52  9463
> 
> # (Here, an obvious faster possibility would be to recover the enrichment contingency
> # table from the previous normal test result:)
> tab <- getTable(normTest)
> tab
                 Enriched in sanger
Enriched in atlas TRUE FALSE
            TRUE   501   458
            FALSE   52  9463
> 
> tst <- equivTestSorensen(tab)
> tst

	Normal asymptotic test for 2x2 contingency tables based on the
	Sorensen-Dice dissimilarity

data:  tab
(d - d0) / se = -7.6163, p-value = 1.306e-14
alternative hypothesis: true equivalence limit d0 is less than 0.4444444
95 percent confidence interval:
 0.0000000 0.3604408
sample estimates:
Sorensen dissimilarity 
             0.3373016 
attr(,"se")
standard error 
    0.01406763 

> set.seed(123)
> bootTst <- equivTestSorensen(tab, boot = TRUE)
> bootTst

	Bootstrap test for 2x2 contingency tables based on the Sorensen-Dice
	dissimilarity (10000 bootstrap replicates)

data:  tab
(d - d0) / se = -7.6163, p-value = 9.999e-05
alternative hypothesis: true equivalence limit d0 is less than 0.4444444
95 percent confidence interval:
 0.0000000 0.3604667
sample estimates:
Sorensen dissimilarity 
             0.3373016 
attr(,"se")
standard error 
    0.01406763 

> 
> dSorensen(tab)
[1] 0.3373016
> seSorensen(tab)
[1] 0.01406763
> # or:
> getDissimilarity(tst)
Sorensen dissimilarity 
             0.3373016 
attr(,"se")
standard error 
    0.01406763 
> 
> duppSorensen(tab)
[1] 0.3604408
> getUpper(tst)
   dUpper 
0.3604408 
> 
> set.seed(123)
> duppSorensen(tab, boot = TRUE)
[1] 0.3604667
attr(,"eff.nboot")
[1] 10000
> getUpper(bootTst)
   dUpper 
0.3604667 
> 
> # To perform from scratch all pairwise tests (or other Sorensen-Dice computations)
> # is even much slower. For example, all pairwise...
> # Dissimilarities:
> # # allPairDiss <- dSorensen(allOncoGeneLists,
> # #                          onto = "BP", GOLevel = 5,
> # #                          geneUniverse = humanEntrezIDs, orgPackg = "org.Hs.eg.db")
> # # allPairDiss
> #
> # # Still time consuming but faster: build all tables computing in parallel:
> # allPairDiss <- dSorensen(allOncoGeneLists,
> #                          onto = "BP", GOLevel = 5,
> #                          geneUniverse = humanEntrezIDs, orgPackg = "org.Hs.eg.db",
> #                          parallel = TRUE)
> # allPairDiss
> 
> # Standard errors:
> # seSorensen(allOncoGeneLists,
> #            onto = "BP", GOLevel = 5,
> #            geneUniverse = humanEntrezIDs, orgPackg = "org.Hs.eg.db")
> #
> # Upper confidence interval limits:
> # duppSorensen(allOncoGeneLists,
> #              onto = "BP", GOLevel = 5,
> #              geneUniverse = humanEntrezIDs, orgPackg = "org.Hs.eg.db")
> # All pairwise asymptotic normal tests:
> # allTests <- equivTestSorensen(allOncoGeneLists,
> #                               onto = "BP", GOLevel = 5,
> #                               geneUniverse = humanEntrezIDs, orgPackg = "org.Hs.eg.db")
> # getPvalue(allTests, simplify = FALSE)
> # getPvalue(allTests)
> # p.adjust(getPvalue(allTests), method = "holm")
> # To perform all pairwise bootstrap tests from scratch is (slightly)
> # even more time consuming:
> # set.seed(123)
> # allBootTests <- equivTestSorensen(allOncoGeneLists,
> #                                   boot = TRUE,
> #                                   onto = "BP", GOLevel = 5,
> #                                   geneUniverse = humanEntrezIDs, orgPackg = "org.Hs.eg.db")
> # Not all bootstrap replicates may conduct to finite statistics:
> # getNboot(allBootTests)
> 
> # Given the normal tests (object 'allTests'), it is much faster to upgrade
> # it to have the bootstrap tests:
> # set.seed(123)
> # allBootTests <- upgrade(allTests, boot = TRUE)
> # getPvalue(allBootTests, simplify = FALSE)
> 
> # Again, the faster and more flexible possibility may be:
> # 1) First, build all pairwise enrichment contingency tables (slow first step):
> # allTabsBP.4 <- buildEnrichTable(allOncoGeneLists,
> #                                 onto = "BP", GOLevel = 5,
> #                                 geneUniverse = humanEntrezIDs, orgPackg = "org.Hs.eg.db")
> # allTabsBP.4
> 
> # Better, directly use the dataset available at this package, goSorensen:
> data(allTabsBP.4)
> allTabsBP.4
$cangenes
$cangenes$atlas
                    Enriched in atlas
Enriched in cangenes TRUE FALSE
               TRUE     0     0
               FALSE  420  3383
attr(,"onto")
[1] "BP"
attr(,"GOLevel")
[1] 4


$cis
$cis$atlas
               Enriched in atlas
Enriched in cis TRUE FALSE
          TRUE    80     3
          FALSE  340  3380

$cis$cangenes
               Enriched in cangenes
Enriched in cis TRUE FALSE
          TRUE     0    83
          FALSE    0  3720
attr(,"onto")
[1] "BP"
attr(,"GOLevel")
[1] 4


$miscellaneous
$miscellaneous$atlas
                         Enriched in atlas
Enriched in miscellaneous TRUE FALSE
                    TRUE   198    21
                    FALSE  222  3362

$miscellaneous$cangenes
                         Enriched in cangenes
Enriched in miscellaneous TRUE FALSE
                    TRUE     0   219
                    FALSE    0  3584
attr(,"onto")
[1] "BP"
attr(,"GOLevel")
[1] 4

$miscellaneous$cis
                         Enriched in cis
Enriched in miscellaneous TRUE FALSE
                    TRUE    70   149
                    FALSE   13  3571


$sanger
$sanger$atlas
                  Enriched in atlas
Enriched in sanger TRUE FALSE
             TRUE   209    24
             FALSE  211  3359

$sanger$cangenes
                  Enriched in cangenes
Enriched in sanger TRUE FALSE
             TRUE     0   233
             FALSE    0  3570
attr(,"onto")
[1] "BP"
attr(,"GOLevel")
[1] 4

$sanger$cis
                  Enriched in cis
Enriched in sanger TRUE FALSE
             TRUE    68   165
             FALSE   15  3555

$sanger$miscellaneous
                  Enriched in miscellaneous
Enriched in sanger TRUE FALSE
             TRUE   151    82
             FALSE   68  3502


$Vogelstein
$Vogelstein$atlas
                      Enriched in atlas
Enriched in Vogelstein TRUE FALSE
                 TRUE   220    32
                 FALSE  200  3351

$Vogelstein$cangenes
                      Enriched in cangenes
Enriched in Vogelstein TRUE FALSE
                 TRUE     0   252
                 FALSE    0  3551
attr(,"onto")
[1] "BP"
attr(,"GOLevel")
[1] 4

$Vogelstein$cis
                      Enriched in cis
Enriched in Vogelstein TRUE FALSE
                 TRUE    68   184
                 FALSE   15  3536

$Vogelstein$miscellaneous
                      Enriched in miscellaneous
Enriched in Vogelstein TRUE FALSE
                 TRUE   156    96
                 FALSE   63  3488

$Vogelstein$sanger
                      Enriched in sanger
Enriched in Vogelstein TRUE FALSE
                 TRUE   217    35
                 FALSE   16  3535


$waldman
$waldman$atlas
                   Enriched in atlas
Enriched in waldman TRUE FALSE
              TRUE   264    39
              FALSE  156  3344

$waldman$cangenes
                   Enriched in cangenes
Enriched in waldman TRUE FALSE
              TRUE     0   303
              FALSE    0  3500
attr(,"onto")
[1] "BP"
attr(,"GOLevel")
[1] 4

$waldman$cis
                   Enriched in cis
Enriched in waldman TRUE FALSE
              TRUE    77   226
              FALSE    6  3494

$waldman$miscellaneous
                   Enriched in miscellaneous
Enriched in waldman TRUE FALSE
              TRUE   203   100
              FALSE   16  3484

$waldman$sanger
                   Enriched in sanger
Enriched in waldman TRUE FALSE
              TRUE   181   122
              FALSE   52  3448

$waldman$Vogelstein
                   Enriched in Vogelstein
Enriched in waldman TRUE FALSE
              TRUE   192   111
              FALSE   60  3440


attr(,"onto")
[1] "BP"
attr(,"GOLevel")
[1] 4
attr(,"class")
[1] "tableList" "list"     
> class(allTabsBP.4)
[1] "tableList" "list"     
> # 2) Then perform all required computatios from these enrichment contingency tables...
> # All pairwise tests:
> allTests <- equivTestSorensen(allTabsBP.4)
> allTests
$cangenes
$cangenes$atlas

	No test performed due not finite (d - d0) / se statistic

data:  tab
(d - d0) / se = Inf, p-value = NA
alternative hypothesis: true equivalence limit d0 is less than 0.4444444
95 percent confidence interval:
   0 NaN
sample estimates:
Sorensen dissimilarity 
                     1 
attr(,"se")
standard error 
             0 



$cis
$cis$atlas

	Normal asymptotic test for 2x2 contingency tables based on the
	Sorensen-Dice dissimilarity

data:  tab
(d - d0) / se = 8.807, p-value = 1
alternative hypothesis: true equivalence limit d0 is less than 0.4444444
95 percent confidence interval:
 0.0000000 0.7262589
sample estimates:
Sorensen dissimilarity 
             0.6819085 
attr(,"se")
standard error 
    0.02696312 


$cis$cangenes

	No test performed due not finite (d - d0) / se statistic

data:  tab
(d - d0) / se = Inf, p-value = NA
alternative hypothesis: true equivalence limit d0 is less than 0.4444444
95 percent confidence interval:
   0 NaN
sample estimates:
Sorensen dissimilarity 
                     1 
attr(,"se")
standard error 
             0 



$miscellaneous
$miscellaneous$atlas

	Normal asymptotic test for 2x2 contingency tables based on the
	Sorensen-Dice dissimilarity

data:  tab
(d - d0) / se = -2.8406, p-value = 0.002252
alternative hypothesis: true equivalence limit d0 is less than 0.4444444
95 percent confidence interval:
 0.0000000 0.4174355
sample estimates:
Sorensen dissimilarity 
             0.3802817 
attr(,"se")
standard error 
    0.02258792 


$miscellaneous$cangenes

	No test performed due not finite (d - d0) / se statistic

data:  tab
(d - d0) / se = Inf, p-value = NA
alternative hypothesis: true equivalence limit d0 is less than 0.4444444
95 percent confidence interval:
   0 NaN
sample estimates:
Sorensen dissimilarity 
                     1 
attr(,"se")
standard error 
             0 


$miscellaneous$cis

	Normal asymptotic test for 2x2 contingency tables based on the
	Sorensen-Dice dissimilarity

data:  tab
(d - d0) / se = 2.5804, p-value = 0.9951
alternative hypothesis: true equivalence limit d0 is less than 0.4444444
95 percent confidence interval:
 0.0000000 0.5950555
sample estimates:
Sorensen dissimilarity 
             0.5364238 
attr(,"se")
standard error 
    0.03564549 



$sanger
$sanger$atlas

	Normal asymptotic test for 2x2 contingency tables based on the
	Sorensen-Dice dissimilarity

data:  tab
(d - d0) / se = -3.8566, p-value = 5.748e-05
alternative hypothesis: true equivalence limit d0 is less than 0.4444444
95 percent confidence interval:
 0.0000000 0.3959452
sample estimates:
Sorensen dissimilarity 
             0.3598775 
attr(,"se")
standard error 
    0.02192764 


$sanger$cangenes

	No test performed due not finite (d - d0) / se statistic

data:  tab
(d - d0) / se = Inf, p-value = NA
alternative hypothesis: true equivalence limit d0 is less than 0.4444444
95 percent confidence interval:
   0 NaN
sample estimates:
Sorensen dissimilarity 
                     1 
attr(,"se")
standard error 
             0 


$sanger$cis

	Normal asymptotic test for 2x2 contingency tables based on the
	Sorensen-Dice dissimilarity

data:  tab
(d - d0) / se = 3.5799, p-value = 0.9998
alternative hypothesis: true equivalence limit d0 is less than 0.4444444
95 percent confidence interval:
 0.0000000 0.6271347
sample estimates:
Sorensen dissimilarity 
             0.5696203 
attr(,"se")
standard error 
    0.03496631 


$sanger$miscellaneous

	Normal asymptotic test for 2x2 contingency tables based on the
	Sorensen-Dice dissimilarity

data:  tab
(d - d0) / se = -4.3974, p-value = 5.479e-06
alternative hypothesis: true equivalence limit d0 is less than 0.4444444
95 percent confidence interval:
 0.0000000 0.3739718
sample estimates:
Sorensen dissimilarity 
             0.3318584 
attr(,"se")
standard error 
    0.02560313 



$Vogelstein
$Vogelstein$atlas

	Normal asymptotic test for 2x2 contingency tables based on the
	Sorensen-Dice dissimilarity

data:  tab
(d - d0) / se = -4.6585, p-value = 1.593e-06
alternative hypothesis: true equivalence limit d0 is less than 0.4444444
95 percent confidence interval:
 0.0000000 0.3802668
sample estimates:
Sorensen dissimilarity 
             0.3452381 
attr(,"se")
standard error 
    0.02129595 


$Vogelstein$cangenes

	No test performed due not finite (d - d0) / se statistic

data:  tab
(d - d0) / se = Inf, p-value = NA
alternative hypothesis: true equivalence limit d0 is less than 0.4444444
95 percent confidence interval:
   0 NaN
sample estimates:
Sorensen dissimilarity 
                     1 
attr(,"se")
standard error 
             0 


$Vogelstein$cis

	Normal asymptotic test for 2x2 contingency tables based on the
	Sorensen-Dice dissimilarity

data:  tab
(d - d0) / se = 4.4076, p-value = 1
alternative hypothesis: true equivalence limit d0 is less than 0.4444444
95 percent confidence interval:
 0.0000000 0.6498536
sample estimates:
Sorensen dissimilarity 
             0.5940299 
attr(,"se")
standard error 
    0.03393844 


$Vogelstein$miscellaneous

	Normal asymptotic test for 2x2 contingency tables based on the
	Sorensen-Dice dissimilarity

data:  tab
(d - d0) / se = -4.2339, p-value = 1.148e-05
alternative hypothesis: true equivalence limit d0 is less than 0.4444444
95 percent confidence interval:
 0.0000000 0.3790962
sample estimates:
Sorensen dissimilarity 
             0.3375796 
attr(,"se")
standard error 
    0.02524032 


$Vogelstein$sanger

	Normal asymptotic test for 2x2 contingency tables based on the
	Sorensen-Dice dissimilarity

data:  tab
(d - d0) / se = -23.128, p-value < 2.2e-16
alternative hypothesis: true equivalence limit d0 is less than 0.4444444
95 percent confidence interval:
 0.0000000 0.1292852
sample estimates:
Sorensen dissimilarity 
             0.1051546 
attr(,"se")
standard error 
    0.01467036 



$waldman
$waldman$atlas

	Normal asymptotic test for 2x2 contingency tables based on the
	Sorensen-Dice dissimilarity

data:  tab
(d - d0) / se = -9.3848, p-value < 2.2e-16
alternative hypothesis: true equivalence limit d0 is less than 0.4444444
95 percent confidence interval:
 0.0000000 0.3003348
sample estimates:
Sorensen dissimilarity 
             0.2697095 
attr(,"se")
standard error 
    0.01861884 


$waldman$cangenes

	No test performed due not finite (d - d0) / se statistic

data:  tab
(d - d0) / se = Inf, p-value = NA
alternative hypothesis: true equivalence limit d0 is less than 0.4444444
95 percent confidence interval:
   0 NaN
sample estimates:
Sorensen dissimilarity 
                     1 
attr(,"se")
standard error 
             0 


$waldman$cis

	Normal asymptotic test for 2x2 contingency tables based on the
	Sorensen-Dice dissimilarity

data:  tab
(d - d0) / se = 4.9573, p-value = 1
alternative hypothesis: true equivalence limit d0 is less than 0.4444444
95 percent confidence interval:
 0.0000000 0.6529946
sample estimates:
Sorensen dissimilarity 
             0.6010363 
attr(,"se")
standard error 
    0.03158842 


$waldman$miscellaneous

	Normal asymptotic test for 2x2 contingency tables based on the
	Sorensen-Dice dissimilarity

data:  tab
(d - d0) / se = -11.029, p-value < 2.2e-16
alternative hypothesis: true equivalence limit d0 is less than 0.4444444
95 percent confidence interval:
 0.0000000 0.2553636
sample estimates:
Sorensen dissimilarity 
             0.2222222 
attr(,"se")
standard error 
    0.02014852 


$waldman$sanger

	Normal asymptotic test for 2x2 contingency tables based on the
	Sorensen-Dice dissimilarity

data:  tab
(d - d0) / se = -5.1402, p-value = 1.372e-07
alternative hypothesis: true equivalence limit d0 is less than 0.4444444
95 percent confidence interval:
 0.0000000 0.3629683
sample estimates:
Sorensen dissimilarity 
             0.3246269 
attr(,"se")
standard error 
    0.02330993 


$waldman$Vogelstein

	Normal asymptotic test for 2x2 contingency tables based on the
	Sorensen-Dice dissimilarity

data:  tab
(d - d0) / se = -6.0739, p-value = 6.243e-10
alternative hypothesis: true equivalence limit d0 is less than 0.4444444
95 percent confidence interval:
 0.000000 0.345029
sample estimates:
Sorensen dissimilarity 
             0.3081081 
attr(,"se")
standard error 
    0.02244631 



attr(,"class")
[1] "equivSDhtestList" "list"            
> class(allTests)
[1] "equivSDhtestList" "list"            
> set.seed(123)
> allBootTests <- equivTestSorensen(allTabsBP.4, boot = TRUE)
> allBootTests
$cangenes
$cangenes$atlas

	No test performed due not finite (d - d0) / se statistic

data:  tab
(d - d0) / se = Inf, p-value = NA
alternative hypothesis: true equivalence limit d0 is less than 0.4444444
95 percent confidence interval:
   0 NaN
sample estimates:
Sorensen dissimilarity 
                     1 
attr(,"se")
standard error 
             0 



$cis
$cis$atlas

	Bootstrap test for 2x2 contingency tables based on the Sorensen-Dice
	dissimilarity (10000 bootstrap replicates)

data:  tab
(d - d0) / se = 8.807, p-value = 1
alternative hypothesis: true equivalence limit d0 is less than 0.4444444
95 percent confidence interval:
 0.000000 0.725535
sample estimates:
Sorensen dissimilarity 
             0.6819085 
attr(,"se")
standard error 
    0.02696312 


$cis$cangenes

	No test performed due not finite (d - d0) / se statistic

data:  tab
(d - d0) / se = Inf, p-value = NA
alternative hypothesis: true equivalence limit d0 is less than 0.4444444
95 percent confidence interval:
   0 NaN
sample estimates:
Sorensen dissimilarity 
                     1 
attr(,"se")
standard error 
             0 



$miscellaneous
$miscellaneous$atlas

	Bootstrap test for 2x2 contingency tables based on the Sorensen-Dice
	dissimilarity (10000 bootstrap replicates)

data:  tab
(d - d0) / se = -2.8406, p-value = 0.004
alternative hypothesis: true equivalence limit d0 is less than 0.4444444
95 percent confidence interval:
 0.000000 0.418077
sample estimates:
Sorensen dissimilarity 
             0.3802817 
attr(,"se")
standard error 
    0.02258792 


$miscellaneous$cangenes

	No test performed due not finite (d - d0) / se statistic

data:  tab
(d - d0) / se = Inf, p-value = NA
alternative hypothesis: true equivalence limit d0 is less than 0.4444444
95 percent confidence interval:
   0 NaN
sample estimates:
Sorensen dissimilarity 
                     1 
attr(,"se")
standard error 
             0 


$miscellaneous$cis

	Bootstrap test for 2x2 contingency tables based on the Sorensen-Dice
	dissimilarity (10000 bootstrap replicates)

data:  tab
(d - d0) / se = 2.5804, p-value = 0.9933
alternative hypothesis: true equivalence limit d0 is less than 0.4444444
95 percent confidence interval:
 0.000000 0.595412
sample estimates:
Sorensen dissimilarity 
             0.5364238 
attr(,"se")
standard error 
    0.03564549 



$sanger
$sanger$atlas

	Bootstrap test for 2x2 contingency tables based on the Sorensen-Dice
	dissimilarity (10000 bootstrap replicates)

data:  tab
(d - d0) / se = -3.8566, p-value = 3e-04
alternative hypothesis: true equivalence limit d0 is less than 0.4444444
95 percent confidence interval:
 0.0000000 0.3960626
sample estimates:
Sorensen dissimilarity 
             0.3598775 
attr(,"se")
standard error 
    0.02192764 


$sanger$cangenes

	No test performed due not finite (d - d0) / se statistic

data:  tab
(d - d0) / se = Inf, p-value = NA
alternative hypothesis: true equivalence limit d0 is less than 0.4444444
95 percent confidence interval:
   0 NaN
sample estimates:
Sorensen dissimilarity 
                     1 
attr(,"se")
standard error 
             0 


$sanger$cis

	Bootstrap test for 2x2 contingency tables based on the Sorensen-Dice
	dissimilarity (10000 bootstrap replicates)

data:  tab
(d - d0) / se = 3.5799, p-value = 0.9996
alternative hypothesis: true equivalence limit d0 is less than 0.4444444
95 percent confidence interval:
 0.0000000 0.6278561
sample estimates:
Sorensen dissimilarity 
             0.5696203 
attr(,"se")
standard error 
    0.03496631 


$sanger$miscellaneous

	Bootstrap test for 2x2 contingency tables based on the Sorensen-Dice
	dissimilarity (10000 bootstrap replicates)

data:  tab
(d - d0) / se = -4.3974, p-value = 2e-04
alternative hypothesis: true equivalence limit d0 is less than 0.4444444
95 percent confidence interval:
 0.0000000 0.3765829
sample estimates:
Sorensen dissimilarity 
             0.3318584 
attr(,"se")
standard error 
    0.02560313 



$Vogelstein
$Vogelstein$atlas

	Bootstrap test for 2x2 contingency tables based on the Sorensen-Dice
	dissimilarity (10000 bootstrap replicates)

data:  tab
(d - d0) / se = -4.6585, p-value = 2e-04
alternative hypothesis: true equivalence limit d0 is less than 0.4444444
95 percent confidence interval:
 0.0000000 0.3809169
sample estimates:
Sorensen dissimilarity 
             0.3452381 
attr(,"se")
standard error 
    0.02129595 


$Vogelstein$cangenes

	No test performed due not finite (d - d0) / se statistic

data:  tab
(d - d0) / se = Inf, p-value = NA
alternative hypothesis: true equivalence limit d0 is less than 0.4444444
95 percent confidence interval:
   0 NaN
sample estimates:
Sorensen dissimilarity 
                     1 
attr(,"se")
standard error 
             0 


$Vogelstein$cis

	Bootstrap test for 2x2 contingency tables based on the Sorensen-Dice
	dissimilarity (10000 bootstrap replicates)

data:  tab
(d - d0) / se = 4.4076, p-value = 1
alternative hypothesis: true equivalence limit d0 is less than 0.4444444
95 percent confidence interval:
 0.0000000 0.6489965
sample estimates:
Sorensen dissimilarity 
             0.5940299 
attr(,"se")
standard error 
    0.03393844 


$Vogelstein$miscellaneous

	Bootstrap test for 2x2 contingency tables based on the Sorensen-Dice
	dissimilarity (10000 bootstrap replicates)

data:  tab
(d - d0) / se = -4.2339, p-value = 9.999e-05
alternative hypothesis: true equivalence limit d0 is less than 0.4444444
95 percent confidence interval:
 0.0000000 0.3796934
sample estimates:
Sorensen dissimilarity 
             0.3375796 
attr(,"se")
standard error 
    0.02524032 


$Vogelstein$sanger

	Bootstrap test for 2x2 contingency tables based on the Sorensen-Dice
	dissimilarity (10000 bootstrap replicates)

data:  tab
(d - d0) / se = -23.128, p-value = 9.999e-05
alternative hypothesis: true equivalence limit d0 is less than 0.4444444
95 percent confidence interval:
 0.0000000 0.1312585
sample estimates:
Sorensen dissimilarity 
             0.1051546 
attr(,"se")
standard error 
    0.01467036 



$waldman
$waldman$atlas

	Bootstrap test for 2x2 contingency tables based on the Sorensen-Dice
	dissimilarity (10000 bootstrap replicates)

data:  tab
(d - d0) / se = -9.3848, p-value = 9.999e-05
alternative hypothesis: true equivalence limit d0 is less than 0.4444444
95 percent confidence interval:
 0.0000000 0.3006583
sample estimates:
Sorensen dissimilarity 
             0.2697095 
attr(,"se")
standard error 
    0.01861884 


$waldman$cangenes

	No test performed due not finite (d - d0) / se statistic

data:  tab
(d - d0) / se = Inf, p-value = NA
alternative hypothesis: true equivalence limit d0 is less than 0.4444444
95 percent confidence interval:
   0 NaN
sample estimates:
Sorensen dissimilarity 
                     1 
attr(,"se")
standard error 
             0 


$waldman$cis

	Bootstrap test for 2x2 contingency tables based on the Sorensen-Dice
	dissimilarity (10000 bootstrap replicates)

data:  tab
(d - d0) / se = 4.9573, p-value = 1
alternative hypothesis: true equivalence limit d0 is less than 0.4444444
95 percent confidence interval:
 0.0000000 0.6525683
sample estimates:
Sorensen dissimilarity 
             0.6010363 
attr(,"se")
standard error 
    0.03158842 


$waldman$miscellaneous

	Bootstrap test for 2x2 contingency tables based on the Sorensen-Dice
	dissimilarity (10000 bootstrap replicates)

data:  tab
(d - d0) / se = -11.029, p-value = 9.999e-05
alternative hypothesis: true equivalence limit d0 is less than 0.4444444
95 percent confidence interval:
 0.0000000 0.2577849
sample estimates:
Sorensen dissimilarity 
             0.2222222 
attr(,"se")
standard error 
    0.02014852 


$waldman$sanger

	Bootstrap test for 2x2 contingency tables based on the Sorensen-Dice
	dissimilarity (10000 bootstrap replicates)

data:  tab
(d - d0) / se = -5.1402, p-value = 9.999e-05
alternative hypothesis: true equivalence limit d0 is less than 0.4444444
95 percent confidence interval:
 0.0000000 0.3639666
sample estimates:
Sorensen dissimilarity 
             0.3246269 
attr(,"se")
standard error 
    0.02330993 


$waldman$Vogelstein

	Bootstrap test for 2x2 contingency tables based on the Sorensen-Dice
	dissimilarity (10000 bootstrap replicates)

data:  tab
(d - d0) / se = -6.0739, p-value = 9.999e-05
alternative hypothesis: true equivalence limit d0 is less than 0.4444444
95 percent confidence interval:
 0.0000000 0.3470915
sample estimates:
Sorensen dissimilarity 
             0.3081081 
attr(,"se")
standard error 
    0.02244631 



attr(,"class")
[1] "equivSDhtestList" "list"            
> class(allBootTests)
[1] "equivSDhtestList" "list"            
> getPvalue(allBootTests, simplify = FALSE)
                   atlas cangenes       cis miscellaneous     sanger Vogelstein
atlas         0.00000000      NaN 1.0000000    0.00399960 0.00029997 0.00019998
cangenes             NaN        0       NaN           NaN        NaN        NaN
cis           1.00000000      NaN 0.0000000    0.99330067 0.99960004 1.00000000
miscellaneous 0.00399960      NaN 0.9933007    0.00000000 0.00019998 0.00009999
sanger        0.00029997      NaN 0.9996000    0.00019998 0.00000000 0.00009999
Vogelstein    0.00019998      NaN 1.0000000    0.00009999 0.00009999 0.00000000
waldman       0.00009999      NaN 1.0000000    0.00009999 0.00009999 0.00009999
                waldman
atlas         9.999e-05
cangenes            NaN
cis           1.000e+00
miscellaneous 9.999e-05
sanger        9.999e-05
Vogelstein    9.999e-05
waldman       0.000e+00
> getEffNboot(allBootTests)
          cangenes.atlas                cis.atlas             cis.cangenes 
                     NaN                    10000                      NaN 
     miscellaneous.atlas   miscellaneous.cangenes        miscellaneous.cis 
                   10000                      NaN                    10000 
            sanger.atlas          sanger.cangenes               sanger.cis 
                   10000                      NaN                    10000 
    sanger.miscellaneous         Vogelstein.atlas      Vogelstein.cangenes 
                   10000                    10000                      NaN 
          Vogelstein.cis Vogelstein.miscellaneous        Vogelstein.sanger 
                   10000                    10000                    10000 
           waldman.atlas         waldman.cangenes              waldman.cis 
                   10000                      NaN                    10000 
   waldman.miscellaneous           waldman.sanger       waldman.Vogelstein 
                   10000                    10000                    10000 
> 
> # To adjust for testing multiplicity:
> p.adjust(getPvalue(allBootTests), method = "holm")
          cangenes.atlas.p-value                cis.atlas.p-value 
                             NaN                       1.00000000 
            cis.cangenes.p-value      miscellaneous.atlas.p-value 
                             NaN                       0.02399760 
  miscellaneous.cangenes.p-value        miscellaneous.cis.p-value 
                             NaN                       1.00000000 
            sanger.atlas.p-value          sanger.cangenes.p-value 
                      0.00209979                              NaN 
              sanger.cis.p-value     sanger.miscellaneous.p-value 
                      1.00000000                       0.00179982 
        Vogelstein.atlas.p-value      Vogelstein.cangenes.p-value 
                      0.00179982                              NaN 
          Vogelstein.cis.p-value Vogelstein.miscellaneous.p-value 
                      1.00000000                       0.00149985 
       Vogelstein.sanger.p-value            waldman.atlas.p-value 
                      0.00149985                       0.00149985 
        waldman.cangenes.p-value              waldman.cis.p-value 
                             NaN                       1.00000000 
   waldman.miscellaneous.p-value           waldman.sanger.p-value 
                      0.00149985                       0.00149985 
      waldman.Vogelstein.p-value 
                      0.00149985 
> 
> # If only partial statistics are desired:
> dSorensen(allTabsBP.4)
                  atlas cangenes       cis miscellaneous    sanger Vogelstein
atlas         0.0000000        1 0.6819085     0.3802817 0.3598775  0.3452381
cangenes      1.0000000        0 1.0000000     1.0000000 1.0000000  1.0000000
cis           0.6819085        1 0.0000000     0.5364238 0.5696203  0.5940299
miscellaneous 0.3802817        1 0.5364238     0.0000000 0.3318584  0.3375796
sanger        0.3598775        1 0.5696203     0.3318584 0.0000000  0.1051546
Vogelstein    0.3452381        1 0.5940299     0.3375796 0.1051546  0.0000000
waldman       0.2697095        1 0.6010363     0.2222222 0.3246269  0.3081081
                waldman
atlas         0.2697095
cangenes      1.0000000
cis           0.6010363
miscellaneous 0.2222222
sanger        0.3246269
Vogelstein    0.3081081
waldman       0.0000000
> duppSorensen(allTabsBP.4)
                  atlas cangenes       cis miscellaneous    sanger Vogelstein
atlas         0.0000000      NaN 0.7262589     0.4174355 0.3959452  0.3802668
cangenes            NaN        0       NaN           NaN       NaN        NaN
cis           0.7262589      NaN 0.0000000     0.5950555 0.6271347  0.6498536
miscellaneous 0.4174355      NaN 0.5950555     0.0000000 0.3739718  0.3790962
sanger        0.3959452      NaN 0.6271347     0.3739718 0.0000000  0.1292852
Vogelstein    0.3802668      NaN 0.6498536     0.3790962 0.1292852  0.0000000
waldman       0.3003348      NaN 0.6529946     0.2553636 0.3629683  0.3450290
                waldman
atlas         0.3003348
cangenes            NaN
cis           0.6529946
miscellaneous 0.2553636
sanger        0.3629683
Vogelstein    0.3450290
waldman       0.0000000
> seSorensen(allTabsBP.4)
                   atlas cangenes        cis miscellaneous     sanger
atlas         0.00000000        0 0.02696312    0.02258792 0.02192764
cangenes      0.00000000        0 0.00000000    0.00000000 0.00000000
cis           0.02696312        0 0.00000000    0.03564549 0.03496631
miscellaneous 0.02258792        0 0.03564549    0.00000000 0.02560313
sanger        0.02192764        0 0.03496631    0.02560313 0.00000000
Vogelstein    0.02129595        0 0.03393844    0.02524032 0.01467036
waldman       0.01861884        0 0.03158842    0.02014852 0.02330993
              Vogelstein    waldman
atlas         0.02129595 0.01861884
cangenes      0.00000000 0.00000000
cis           0.03393844 0.03158842
miscellaneous 0.02524032 0.02014852
sanger        0.01467036 0.02330993
Vogelstein    0.00000000 0.02244631
waldman       0.02244631 0.00000000
> 
> 
> # Tipically, in a real study it would be interesting to scan tests
> # along some ontologies and levels inside these ontologies:
> # (which obviously will be a quite slow process)
> # gc()
> # set.seed(123)
> # allBootTests_BP_MF_lev4to8 <- allEquivTestSorensen(allOncoGeneLists,
> #                                                    boot = TRUE,
> #                                                    geneUniverse = humanEntrezIDs, orgPackg = "org.Hs.eg.db",
> #                                                    ontos = c("BP", "MF"), GOLevels = 4:8)
> # getPvalue(allBootTests_BP_MF_lev4to8)
> # getEffNboot(allBootTests_BP_MF_lev4to8)
> 
> proc.time()
   user  system elapsed 
148.941  25.044 185.709