---
title: "Introduction to PhILR"
author: "Justin Silverman"
date: "`r Sys.Date()`"
bibliography: philr.bib
output: BiocStyle::html_document
vignette: >
  %\VignetteIndexEntry{Introduction to PhILR}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

# Introduction
PhILR is short for "Phylogenetic Isometric Log-Ratio Transform".
This package provides functions for the analysis of [compositional data](https://en.wikipedia.org/wiki/Compositional_data) (e.g., data representing proportions of different variables/parts). Specifically this package allows analysis of compositional data where the parts can be related through a phylogenetic tree (as is common in microbiota survey data) and makes available the Isometric Log Ratio transform built from the phylogenetic tree and utilizing a weighted reference measure [@egozcue2016]. 

# Overview of PhILR Analysis
The goal of PhILR is to transform compositional data into an orthogonal unconstrained space (real space) with phylogenetic / evolutionary interpretation while preserving all information contained in the original composition. Unlike in the original compositional space, in the transformed real space, standard statistical tools may be applied. For a given set of samples consisting of measurements of  taxa, we transform data into a new space of  samples and  orthonormal coordinates termed ‘balances’. Each balance  is associated with a single internal node  of a phylogenetic tree with the taxa as leaves. The balance represents the log-ratio of the geometric mean abundance of the two groups of taxa that descend from the given internal node. 

# Loading and Preprocessing Dataset
Here we will demonstrate PhILR analysis using the Global Patterns dataset that
was originally published by @caporaso2011. This dataset is provided with the 
`phyloseq` package [@mcmurdie2013] and our analysis follows, in part, that of the authors 
[GitHub Tutorial](http://joey711.github.io/phyloseq/preprocess.html).

```{r, echo=TRUE, message=FALSE}
library(philr); packageVersion("philr")
library(phyloseq); packageVersion("phyloseq")
library(ape); packageVersion("ape")
library(ggplot2); packageVersion("ggplot2")

data(GlobalPatterns)
```

## Filter Extreemly Low Abundance OTUs
Taxa that were not seen with more than 3 counts in at least 20% of samples are filtered.
Subsequently, those witha coefficient of variation ≤ 3 are filtered. These steps follow 
those of [@mcmurdie2013]. Finally we add a pseudocount of 1 to the remaining OTUs to avoid 
calculating log-ratios involving zeros. Alternatively other replacement methods 
(multiplicative replacement etc...) may be used instead if desired; the 
subsequent taxa weighting procedure we will describe complements a variety of 
zero replacement methods. 

```{r, message=FALSE, warning=FALSE}
GP <-  filter_taxa(GlobalPatterns, function(x) sum(x > 3) > (0.2*length(x)), TRUE)
GP <-  filter_taxa(GP, function(x) sd(x)/mean(x) > 3.0, TRUE)
GP <- transform_sample_counts(GP, function(x) x+1)
```

With these two commands we have removed the filtered taxa from the OTU table, 
pruned the phylogenetic tree, and subset the taxa table. 
Here is the result of those filtering steps
```{r, echo=FALSE}
GP
```

## Process Phylogenetic Tree
Next we check that the tree is rooted and binary (all multichotomies have been resolved). 
```{r, message=FALSE, warning=FALSE}
is.rooted(phy_tree(GP)) # Is the tree Rooted?
is.binary.tree(phy_tree(GP)) # All multichotomies resolved?
```

Note that if the tree is not binary, the function `multi2di` from the `ape` package
can be used to replace multichotomies with a series of dichotomies with one (or several)
branch(es) of zero length . 

Once this is done, we name the internal nodes of the tree so they 
are easier to work with. We prefix the node number with `n` and thus the root 
is named `n1`. 

```{r, message=FALSE, warning=FALSE}
phy_tree(GP) <- makeNodeLabel(phy_tree(GP), method="number", prefix='n')
```

We note that the tree is already rooted with Archea as the outgroup and 
no multichotomies are present. This uses the function `name.balance` from the `philr` 
package. This function uses a simple voting scheme to find a consensus naming
for the two clades that descend from a given balance. Specifically for a
balance named `x/y`, `x` refers to the consensus name of the clade in the numerator
of the log-ratio and `y` refers to the denominator. 
```{r}
name.balance(phy_tree(GP), tax_table(GP), 'n1')
```

## Investigate Dataset Components
Finally we transpose the OTU table (`philr` uses the conventions of the `compositions` 
package for compositional data analysis in R, taxa are columns, samples are rows). 
Then we will take a look at part of the dataset in more detail
```{r}
otu.table <- t(otu_table(GP))
tree <- phy_tree(GP)
metadata <- sample_data(GP)
tax <- tax_table(GP)

otu.table[1:2,1:2] # OTU Table
tree # Phylogenetic Tree
head(metadata,2) # Metadata
head(tax,2) # taxonomy table
```


# Transform Data using PhILR
The function `philr::philr()` implements a user friendly wrapper for the key 
steps in the philr transform. 

1. Convert the phylogenetic tree to its sequential binary partition (SBP) representation
using the function `philr::phylo2sbp()`
2. Calculate the weighting of the taxa (aka parts) or use the user specified weights
3. Built the contrast matrix from the SBP and taxa weights using the function 
`philr::buildilrBasep()`
4. Convert OTU table to relative abundance (using `philr::miniclo()`) and 
'shift' dataset using the weightings [@egozcue2016] using the function `philr::shiftp()`.
5. Transform the data to PhILR space using the function `philr::ilrp()`
6. (Optional) Weight the resulting PhILR space using phylogenetic distance. These
weights are either provided by the user or can be calculated by the function 
`philr::calculate.blw()`. 

Note: The preprocessed OTU table should be passed
to the function `philr::philr()` before it is closed (normalized) to relative abundances, as
some of the preset weightings of the taxa use the original count data to down weight low 
abundance taxa. 

Here we will use the same weightings as we used in the main paper.

```{r}
gp.philr <- philr(otu.table, tree, 
                  part.weights='enorm.x.gm.counts', 
                  ilr.weights='blw.sqrt')
gp.philr[1:5,1:5]
```

Now the transformed data is represented in terms of balances and since 
each balance is associated with a single internal node of the tree, we denote the balances
using the same names we assigned to the internal nodes (e.g., `n1`). 

# Ordination in PhILR Space
Euclidean distance in PhILR space can be used for ordination analysis. We 
do this ordination using tools from the `phyloseq` package. 

```{r}
gp.dist <- dist(gp.philr, method="euclidean")
gp.pcoa <- ordinate(GP, 'PCoA', distance=gp.dist)
plot_ordination(GP, gp.pcoa, color='SampleType') + geom_point(size=4)
```

# Identify Balances that Distinguish Human/Non-Human
More than just ordination analysis, PhILR provides an entire coordinate system 
in which standard multivariate tools can be used. Here we will make use of sparse
logistic regression (from the `glmnet` pacakge) to identify a small number of 
balances that best distinguish human from non-human samples. 

First we will make a new variable distinguishing human/non-human
```{r, message=FALSE, warning=FALSE}
sample_data(GP)$human <- factor(get_variable(GP, "SampleType") %in% c("Feces", "Mock", "Skin", "Tongue"))
```

Now we will fit a sparse logistic regression model (logistic regression with $l_1$ penalty)
```{r, message=FALSE, warning=FALSE}
library(glmnet); packageVersion('glmnet')
glmmod <- glmnet(gp.philr, sample_data(GP)$human, alpha=1, family="binomial")
```

We will use a hard-threshold for the $l_1$ penalty of $\lambda = 0.2526$ which 
we choose so that the resulting number of non-zero coefficients is $\approx 5$ 
(for easy of visualization in this tutorial). 

```{r}
top.coords <- as.matrix(coefficients(glmmod, s=0.2526))
top.coords <- rownames(top.coords)[which(top.coords != 0)]
(top.coords <- top.coords[2:length(top.coords)]) # remove the intercept as a coordinate
```

# Name Balances
To find the taxonomic labels that correspond to these balances we can use the function
`philr::name.balance()`. This funciton uses a simple voting scheme to name
the two descendent clades of a given balance separately. For a given clade, 
the taxonomy table is subset to only contain taxa from that clade. Starting 
at the finest taxonomic rank (e.g., species) the subset taxonomy table is checked to see
if any label (e.g., species name) represents ≥ threshold (default 95%) of
the table entries at that taxonomic rank. If no consensus identifier is found, the table is checked at the next-most specific taxonomic rank (etc...). 

```{r}
tc.names <- sapply(top.coords, function(x) name.balance(tree, tax, x))
tc.names
```

We can also get more information on what goes into the naming by viewing the votes 
directly.

```{r}
votes <- name.balance(tree, tax, 'n730', return.votes = c('up', 'down'))

votes[[c('up.votes', 'Family')]] # Numerator at Family Level
votes[[c('down.votes', 'Family')]] # Denominator at Family Level
```


# Visualize Results

```{r, message=FALSE, warning=FALSE}
library(ggtree); packageVersion("ggtree")
library(dplyr); packageVersion('dplyr')
```

Above we found the top 5 coordinates (balances) that distinguish whether a 
sample is from a human or non-human source. Now using the `ggtree` [@yu2016] package we 
can visualize these balances on the tree using the `geom_balance` object. 
To use these functions we need to know the acctual node number (not just the names we have given) of these balances
on the tree. To convert between node number and name, we have added the functions
`philr::name.to.nn()` and `philr::nn.to.name()`.  
In addition, it is important that we know which clade of the balance is in the 
numerator (+) and which is in the denominator (-) of the log-ratio. To help us keep track
we have created the function `philr::annotate_balance()` which allows us to easily
label these two clades. 

```{r, message=FALSE, warning=FALSE}
tc.nn <- name.to.nn(tree, top.coords)
tc.colors <- c('#a6cee3', '#1f78b4', '#b2df8a', '#33a02c', '#fb9a99')
p <- ggtree(tree, layout='fan') +
  geom_balance(node=tc.nn[1], fill=tc.colors[1], alpha=0.6) +
  geom_balance(node=tc.nn[2], fill=tc.colors[2], alpha=0.6) +
  geom_balance(node=tc.nn[3], fill=tc.colors[3], alpha=0.6) +
  geom_balance(node=tc.nn[4], fill=tc.colors[4], alpha=0.6) +
  geom_balance(node=tc.nn[5], fill=tc.colors[5], alpha=0.6)
p <- annotate_balance(tree, 'n16', p=p, labels = c('n16+', 'n16-'),
                 offset.text=0.15, bar=FALSE)
annotate_balance(tree, 'n730', p=p, labels = c('n730+', 'n730-'),
                 offset.text=0.15, bar=FALSE)
```

We can also view the distribution of these 5 balances for human/non-human sources.
In order to plot with `ggplot2` we first need to convert the PhILR transformed
data to long format. We have included a function `philr::convert_to_long()` for
this purpose. 

```{r}
gp.philr.long <- convert_to_long(gp.philr, get_variable(GP, 'human')) %>%
  filter(coord %in% top.coords)

ggplot(gp.philr.long, aes(x=labels, y=value)) +
  geom_boxplot(fill='lightgrey') +
  facet_grid(.~coord, scales='free_x') +
  xlab('Human') + ylab('Balance Value') +
  theme_bw()
```

# Use Balances for Dimention Reduction
Lets just look at balance n16 vs. balance n730 (the ones we annotated in the above tree). 
```{r, message=FALSE, warning=FALSE}
library(tidyr); packageVersion('tidyr')

gp.philr.long %>%
  rename(Human=labels) %>%
  filter(coord %in% c('n16', 'n730')) %>%
  spread(coord, value) %>%
  ggplot(aes(x=n16, y=n730, color=Human)) +
  geom_point(size=4) +
  xlab(tc.names['n16']) + ylab(tc.names['n730']) +
  theme_bw()
```


# References