MSCCT: Multiple Survival Crossing Curves Tests

Description

Tests of comparison of two or more survival curves. Allows for comparison of more than two survival curves whether the proportional hazards hypothesis is verified or not.

Author(s)

Maintainer: Hugo MINA PASSI hugo.minapassi@gmail.com [copyright holder]

Authors:

• Olayidé BOUSSARI olayide.boussari@u-bourgogne.fr

See Also

Useful links:

• https://github.com/HMinP/MSCCT

• Report bugs at https://github.com/HMinP/MSCCT/issues

A simulation with three groups without the Proportional Hazards hypothesis

Description

This dataframe represents a simulation of a study where the three survival curves cross each other.

Usage

data_not_PH

Format

data_not_PH

A data frame with 600 rows and 3 columns:

time

Time of events in months with truncation at 60 months

status

Indicator of censorship. 1 denotes an event, 0 denotes a censor

arm

Integer from 0 to 2. Indicates the group the patient belongs to

A simulation with three groups under the Proportional Hazards hypothesis

Description

This dataframe represents a simulation of a study under the Proportional Hazards hypothesis. All three survival curves follows an exponential distribution with different parameters.

Usage

data_under_PH

Format

data_under_PH

A data frame with 600 rows and 3 columns:

time

Time of events in months with truncation at 60 months

status

Indicator of censorship. 1 denotes an event, 0 denotes a censor

arm

Integer from 0 to 2. Indicates the group the patient belongs to

(Weighted) Log-rank test for comparison of two or more survival curves.

Description

Performs a global log-rank test for comparing two or more survival curves.

Usage

multi_lr(df, weights, test = c("lr", "gw", "fh"), rho = 1, gamma = 0)

Arguments

Details

weights contains the chosen weights for the test. It must be a vector, a matrix or an object that can be coerced to a matrix, like a data frame (passed as argument to as.matrix). Can be omitted.

If not given (default), then perform either a log-rank test, a Gehan-Wilcoxon test or a Fleming-Harrington test depending on the choice of test.

If weights is a one-dimension vector, its length must be equal to the number of distinct time of event and throws an error if it is not true. In this case, multi_lr() performs a weighted log-rank test with the specified weights.

If weights is a matrix (or a two-dimension object), its number of rows must be equal to the number of distinct time of event and throws an error if it is not true. In this case, multi_lr() performs as many tests as the number of columns in weights. The first test is a weighted log-rank test with weights the first column of weights, the second test is a weighted log-rank test with weights the second column of weights, and so on.

Value

An object of class multi_lr containing:

• U : Statistics of tests;

• p : The corresponding p-values;

• degree : Degrees of freedom of the statistics of tests;

• The argument test, changed to "chosen" if weights are given.

Examples

  # Log-rank test
  multi_lr(data_not_PH)

  # Gehan-Wilcoxon test
  multi_lr(data_not_PH, test="gw")

  # It is possible to run several tests with different weights at a time
  evt_time = unique(data_not_PH$time[data_not_PH$status == 1])
  nb_evt_time = length(evt_time)
  weights = matrix(runif(nb_evt_time*3), ncol=3)
  multi_lr(data_not_PH, weights=weights)

Test of RMST for comparing two or more survival curves

Description

Performs the test of Restricted Mean Survival Time for two or more survival curves by comparing the difference of areas under survival curves.

Usage

multi_rmst(df, tau, method = p.adjust.methods, nboot = 500)

Arguments

Details

For each group, the Restricted Mean Survival Time at time tau (RMST(tau)) is computed as the area under the survival curve between time 0 and tau. The test of RMST is a pairwise multiple comparison test. For each pair of groups, it tests whether the difference between the RMST(tau) is zero or not. If the difference is not null, then the survival curves cannot be equal.

For exactly two groups, a single test is performed. For more than two survival curves, it compares each survival curve to every other curves and tests the global null hypothesis "all curves are equal" against the hypothesis "the curves are not all equal".

Value

An object of class multi_rmst containing :

• rmst_mat RMST estimation for each arm;

• results A matrix. Each row represents a comparison of two curves and contains the difference of RMST, its standard deviation, the p-value and the adjusted p-value;

• p The p-value of the global test;

• nb_tests The number of performed tests;

• The parameters tau, method and nboot.

References

Royston, P., & Parmar, M. K. (2013). Restricted mean survival time: an alternative to the hazard ratio for the design and analysis of randomized trials with a time-to-event outcome. BMC medical research methodology, 13, 1-15.

Examples

  multi_rmst(data_under_PH, tau = 36, nboot = 300)
  multi_rmst(data_not_PH, tau = 36, method = "BH", nboot = 300)

Two-staged test for comparison of two or more survival curves.

Description

Performs a two-stage test for each pair of survival curves and apply a correction in case of several comparisons.

Usage

multi_ts(df, method = p.adjust.methods, eps = 0.1, nboot = 100)

Arguments

Details

For a two-stage test, the first stage is a log-rank test. If the first test is significant, then the whole procedure stops and we conclude that the survival curves are different. If it is not significant, then the survival curves are either equal or crossing each other and the log-rank test can't conclude the difference. A second test is performed to distinguish these two cases.

For multiple curves comparison, the two-stage test is a pairwise test. A two-stage test is performed for each pair of curves.

Value

An object of class multi_ts containing:

• results : A matrix. Each row represents a comparison of two curves and contains the p-values for both stage, the global p-value and the adjusted global p-value;

• p : The p-value for the global test;

• nb_tests : The number of performed Two-Stage tests;

• the parameters eps, method and nboot.

References

• Qiu, P., & Sheng, J. (2008). A two-stage procedure for comparing hazard rate functions. Journal of the Royal Statistical Society Series B: Statistical Methodology, 70(1), 191-208. Chen, Zhongxue & Huang, Hanwen & Qiu, Peihua. (2017).

• Chen, Z., Huang, H., & Qiu, P. (2017). An improved two-stage procedure to compare hazard curves. Journal of Statistical Computation and Simulation, 87(9), 1877-1886.

Examples

  # test with a quarter of the data frame data_not_PH
  ind = c(1:100, 401:500, 801:900)
  multi_ts(data_not_PH[ind,], method = "BH", eps = 0.1, nboot = 10)

Print method for the multiple log-rank test

Description

Print method for the multiple log-rank test

Usage

## S3 method for class 'multi_lr'
print(x, ...)

Arguments

Value

None

Examples

  x = multi_lr(data_not_PH)
  print(x)

Print method for the multiple test of RMST

Description

Print method for the multiple test of RMST

Usage

## S3 method for class 'multi_rmst'
print(x, ...)

Arguments

Value

None

Examples

  x = multi_rmst(data_under_PH, tau = 36, nboot = 300)
  print(x)

Print method for the multiple Two-Stage test

Description

Print method for the multiple Two-Stage test

Usage

## S3 method for class 'multi_ts'
print(x, ...)

Arguments

Value

None

Examples

  # test with a quarter of the data frame data_not_PH
  ind = c(1:100, 401:500, 801:900)
  x = multi_ts(data_not_PH[ind,], method = "BH", eps = 0.1, nboot = 10)
  print(x)