---
title: 'Shazam: Quantification of selection pressure'
author: "Namita Gupta & Jason Anthony Vander Heiden & Julian Q. Zhou"
date: '`r Sys.Date()`'
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  %\VignetteIndexEntry{Selection quantification} 
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---

BASELINe quantifies selection pressure by calculating the posterior probability 
density function (PDF) based on observed mutations compared to expected 
mutation rates derived from an underlying SHM targeting model. Selection is 
quantified via the following steps:

1. Calculate the selection scores for individual sequences.
2. Group by relevant fields for comparison and convolve individual selection PDFs.
4. Plot and compare selection scores of different groups of sequences.

## Example data

A small example AIRR Rearrangement database is included in the `alakazam` package. 
The example dataset consists of a subset of Ig sequencing data from an 
influenza vaccination study (Laserson and Vigneault et al., PNAS, 2014). The 
data include sequences from multiple time-points before and after the subject 
received an influenza vaccination. Quantifying selection requires the following 
fields (columns) to be present in the table: 

* `sequence_id`
* `sequence_alignment`
* `germline_alignment_d_mask`

```{r, eval=TRUE, warning=FALSE, message=FALSE}
# Load example data
library(shazam)
data(ExampleDb, package="alakazam")
```

## Calculate selection PDFs for individual sequences

Selection scores are calculated with the `calcBaseline` function. This can
be performed with a single call to `calcBaseline`, which performs all 
required steps. Alternatively, one can perform each step separately for
greater control over the analysis parameters.

### Constructing clonal consensus sequences

Individual sequences within clonal groups are not, strictly speaking, 
independent events and it is generally appropriate to only analyze selection
pressures on an effective sequence for each clonal group. The `collapseClones`
function provides one strategy for generating an effective sequences for 
each clone. It reduces the input database to one row per clone and appends 
`clonal_sequence` and `clonal_germline` columns which contain the 
consensus sequences for each clone.

```{r, eval=TRUE, warning=FALSE, results="hide"}
# Collapse clonal groups into single sequences
clones <- collapseClones(ExampleDb, cloneColumn="clone_id", 
                         sequenceColumn="sequence_alignment", 
                         germlineColumn="germline_alignment_d_mask", 
                         regionDefinition=IMGT_V, 
                         method="thresholdedFreq", minimumFrequency=0.6,
                         includeAmbiguous=FALSE, breakTiesStochastic=FALSE, 
                         nproc=1)
```

### Calculating selection in multiple steps

Following construction of an effective sequence for each clone, the observed
and expected mutation counts are calculated for each sequence in the 
`clonal_sequence` column relative to the `clonal_germline`. `observedMutations` 
is used to calculate the number of observed mutations and 
`expectedMutations` calculates the expected frequency of mutations. 
The underlying targeting model for calculating expectations can be specified 
using the `targetingModel` parameter. In the example below, the default 
`HH_S5F` is used. Column names for sequence and germline sequence may
also be passed in as parameters if they differ from the Change-O defaults. 

Mutations are counted by these functions separately for complementarity 
determining (CDR) and framework (FWR) regions. The `regionDefinition` 
argument defines whether these regions are handled separately, and where
the boundaries lie. There are two built-in region definitions 
in the `shazam` package, both dependent upon the V segment
being IMGT-gapped:

*  `IMGT_V`: All regions in the V segment, excluding CDR3, grouped as 
    either CDR or FWR.
*  `IMGT_V_BY_REGIONS`: The CDR1, CDR2, CDR3, FWR1, FWR and FWR3 regions 
    in the V segment (no CDR3) treated as individual regions.

Users may define other region sets and boundaries by creating a custom
`RegionDefinition` object.

```{r, eval=TRUE, warning=FALSE, results="hide"}
# Count observed mutations and append mu_count columns to the output
observed <- observedMutations(clones, 
                              sequenceColumn="clonal_sequence",
                              germlineColumn="clonal_germline",
                              regionDefinition=IMGT_V, nproc=1)
# Count expected mutations and append mu_exptected columns to the output
expected <- expectedMutations(observed, 
                              sequenceColumn="clonal_sequence",
                              germlineColumn="clonal_germline",
                              targetingModel=HH_S5F,
                              regionDefinition=IMGT_V, nproc=1)
```

The counts of observed and expected mutations can be combined to test for selection 
using `calcBaseline`. The statistical framework used to test for selection based 
on mutation counts can be specified using the `testStatistic` parameter. 


```{r, eval=TRUE, warning=FALSE, results="hide"}
# Calculate selection scores using the output from expectedMutations
baseline <- calcBaseline(expected, testStatistic="focused", 
                         regionDefinition=IMGT_V, nproc=1)
```

### Calculating selection in one step

It is not required for `observedMutation` and `expectedMutations` to be run prior to 
`calcBaseline`. If the output of these two steps does not appear in the input 
data.frame, then `calcBaseline` will call the appropriate functions prior to 
calculating selection scores.

```{r, eval=TRUE, warning=FALSE, results="hide"}
# Calculate selection scores from scratch
baseline <- calcBaseline(clones, testStatistic="focused", 
                         regionDefinition=IMGT_V, nproc=1)
```

### Using alternative mutation definitions and models

The default behavior of `observedMutations` and `expectedMutations`, and
by extension `calcBaseline`, is to define a replacement mutation in the usual
way - any change in the amino acid of a codon is considered a replacement 
mutation. However, these functions have a `mutationDefinition` argument which 
allows these definitions to be changed by providing a `MutationDefinition` 
object that contains alternative replacement and silent criteria. `shazam` 
provides the following built-in MutationDefinitions:

* `CHARGE_MUTATIONS`: Amino acid mutations are defined by changes in side chain 
   charge class.
* `HYDROPATHY_MUTATIONS`: Amino acid mutations are defined by changes in side chain 
   hydrophobicitity class.
* `POLARITY_MUTATIONS`: Amino acid mutations are defined by changes in side chain 
   polarity class.
* `VOLUME_MUTATIONS`: Amino acid mutations are defined by changes in side chain 
   volume class.

The default behavior of `expectedMutations` is to use the human 5-mer mutation model,
`HH_S5F`. Alternative SHM targeting models can be provided using the 
`targetingModel` argument.

```{r, eval=FALSE, warning=FALSE, results="hide"}
# Calculate selection on charge class with the mouse 5-mer model
baseline <- calcBaseline(clones, testStatistic="focused", 
                         regionDefinition=IMGT_V, 
                         targetingModel=MK_RS5NF,
                         mutationDefinition=CHARGE_MUTATIONS,
                         nproc=1)
```

## Group and convolve individual selection distributions

To compare the selection scores of groups of sequences, the sequences must
be convolved into a single PDF representing each group. In the example dataset, 
the `sample_id` field corresponds to samples taken at different time points 
before and after an influenza vaccination and the `c_call` field specifies 
the isotype of the sequence. The `groupBaseline` function convolves the BASELINe 
PDFs of individual sequences/clones to get a combined PDF. The field(s) by 
which to group the sequences are specified with the `groupBy` parameter. 

The `groupBaseline` function automatically calls `summarizeBaseline` to 
generate summary statistics based on the requested groupings, and populates 
the `stats` slot of the input `Baseline` object with the number of sequences 
with observed mutations for each region, mean selection scores, 95% confidence 
intervals, and p-values with positive signs indicating the presence of positive 
selection and/or p-values with negative signs indicating the presence of negative 
selection. The magnitudes of the p-values (without the signs) should be 
interpreted as analagous to a t-test.

### Grouping by a single annotation

The following example generates a single selection PDF for each unique 
annotation in the `sample_id` column.

```{r, eval=TRUE, warning=FALSE, results="hide"}
# Combine selection scores by time-point
grouped_1 <- groupBaseline(baseline, groupBy="sample_id")
```

### Subsetting and grouping by multiple annotations

Grouping by multiple annotations follows the sample proceedure as a 
single annotation by simply adding columns to the `groupBy` argument. 
Subsetting the data can be performed before or 
after generating selection PDFs via `calcBaseline`. However, note 
that subsetting may impact the clonal representative sequences 
generated by `collapseClones`. In the following example subsetting 
precedes the collapsing of clonal groups.

```{r, eval=TRUE, warning=FALSE, results="hide"}
# Subset the original data to switched isotypes
db_sub <- subset(ExampleDb, c_call %in% c("IGHM", "IGHG"))

# Collapse clonal groups into single sequence
clones_sub <- collapseClones(db_sub, cloneColumn="clone_id",
                             sequenceColumn="sequence_alignment",
                             germlineColumn="germline_alignment_d_mask",
                             regionDefinition=IMGT_V, 
                             method="thresholdedFreq", minimumFrequency=0.6,
                             includeAmbiguous=FALSE, breakTiesStochastic=FALSE, 
                             nproc=1)

# Calculate selection scores from scratch
baseline_sub <- calcBaseline(clones_sub, testStatistic="focused", 
                             regionDefinition=IMGT_V, nproc=1)

# Combine selection scores by time-point and isotype
grouped_2 <- groupBaseline(baseline_sub, groupBy=c("sample_id", "c_call"))
```

### Convolving variables at multiple levels

To make selection comparisons using two levels of variables, you
would need two iterations of groupings, where the first iteration of 
`groupBaseline` groups on both variables, and the second iteration groups
on the "outer" variable. For example, if a data set has both case and control 
subjects, annotated in `status` and `subject` columns, then
generating convolved PDFs for each status would be performed as:

```{r, eval=FALSE, warning=FALSE, results="hide"}
# First group by subject and status
subject_grouped <- groupBaseline(baseline, groupBy=c("status", "subject"))

# Then group the output by status
status_grouped <- groupBaseline(subject_grouped, groupBy="status")
```

### Testing the difference in selection PDFs between groups

The `testBaseline` function will perform signifance testing between two
grouped BASELINe PDFs, by region, and return a data.frame with the 
following information:

* `region`: The sequence region, such as `cdr` and `fwr`.
* `test`: The name of the two groups compared.
* `pvalue`: Two-sided p-value for the comparison.
* `fdr`: FDR corrected p-value.

```{r, eval=TRUE}
testBaseline(grouped_1, groupBy="sample_id")
```

## Plot and compare selection scores for groups

`plotBaselineSummary` plots the mean and confidence interval of selection scores 
for the given groups. The `idColumn` argument specifies the field that contains 
identifiers of the groups of sequences. If there is a secondary field by which 
the sequences are grouped, this can be specified using the `groupColumn`. This 
secondary grouping can have a user-defined color palette passed into 
`groupColors` or can be separated into facets by setting the `facetBy="group"`. 
The `subsetRegions` argument can be used to visualize selection of specific 
regions. Several examples utilizing these different parameters are provided 
below.

```{r, eval=TRUE, warning=FALSE}
# Set sample and isotype colors
sample_colors <- c("-1h"="seagreen", "+7d"="steelblue")
isotype_colors <- c("IGHM"="darkorchid", "IGHD"="firebrick", 
                    "IGHG"="seagreen", "IGHA"="steelblue")

# Plot mean and confidence interval by time-point
plotBaselineSummary(grouped_1, "sample_id")

# Plot selection scores by time-point and isotype for only CDR
plotBaselineSummary(grouped_2, "sample_id", "c_call", groupColors=isotype_colors,
                    subsetRegions="cdr")

# Group by CDR/FWR and facet by isotype
plotBaselineSummary(grouped_2, "sample_id", "c_call", facetBy="group")
```

`plotBaselineDensity` plots the full `Baseline` PDF of selection scores for the 
given groups. The parameters are the same as those for `plotBaselineSummary`.
However, rather than plotting the mean and confidence interval, the full density 
function is shown.

```{r, eval=TRUE, warning=FALSE}
# Plot selection PDFs for a subset of the data
plotBaselineDensity(grouped_2, "c_call", groupColumn="sample_id", colorElement="group", 
                    colorValues=sample_colors, sigmaLimits=c(-1, 1))
```


## Editing a field in a Baseline object

If, for any reason, one needs to edit the existing values in a field in a 
`Baseline` object, one can do so via `editBaseline`. In the following example,
we remove results related to IGHA in the relevant fields from `grouped_2`. 
When the input data is large and it takes a long time for `calcBaseline` to run,
`editBaseline` could become useful when, for instance, one would like to exclude
a certain sample or isotype, but would rather not re-run `calcBaseline` after 
removing that sample or isotype from the original input data.

```{r, eval=FALSE, warning=FALSE, results="hide"}
# Get indices of rows corresponding to IGHA in the field "db"
# These are the same indices also in the matrices in the fileds "numbOfSeqs", 
# "binomK", "binomN", "binomP", and "pdfs"
# In this example, there is one row of IGHA for each sample
dbIgMIndex <- which(grouped_2@db[["c_call"]] == "IGHA")

grouped_2 <- editBaseline(grouped_2, "db", grouped_2@db[-dbIgMIndex, ])
grouped_2 <- editBaseline(grouped_2, "numbOfSeqs", grouped_2@numbOfSeqs[-dbIgMIndex, ])
grouped_2 <- editBaseline(grouped_2, "binomK", grouped_2@binomK[-dbIgMIndex, ])
grouped_2 <- editBaseline(grouped_2, "binomN", grouped_2@binomN[-dbIgMIndex, ])
grouped_2 <- editBaseline(grouped_2, "binomP", grouped_2@binomP[-dbIgMIndex, ])
grouped_2 <- editBaseline(grouped_2, "pdfs", 
                          lapply(grouped_2@pdfs, function(pdfs) {pdfs[-dbIgMIndex, ]} ))

# The indices corresponding to IGHA are slightly different in the field "stats"
# In this example, there is one row of IGHA for each sample and for each region
grouped_2 <- editBaseline(grouped_2, "stats", 
                          grouped_2@stats[grouped_2@stats[["c_call"]] != "IGHA", ])
```

