---
title: "Overview of shiftR Package"
date: "`r Sys.Date()`"
output:
    html_document:
        theme: readable
        toc: true # table of content true
vignette: >
    %\VignetteIndexEntry{Overview of shiftR package}
    %\VignetteEngine{knitr::rmarkdown}
---

```{r loadKnitr, echo=FALSE}
library("knitr")
# opts_chunk$set(eval=FALSE)
library(pander)
panderOptions("digits", 3)
set.seed(18090212)
library(shiftR)
```

# Overview

This package is designed for fast enrichment analysis of 
locally correlated statistics via circular permutations.
Circular permutations are used to preserve local dependence of test statistics.
This allows the permutation analysis 
to produce correct p-values when alternatives (like Fisher's exact test)
would produce inflated test statistics (next chapter provides an example).

# Permutation analysis on matched binary data sets {#binary}

First, for the introduction, 
let us consider two data sets with binary measurements across
the same set of conditions. 

* Both data sets are binary (e.g. 0/1, success/failure outcomes).
* The values in one data set are matched to the values in the other,
  i.e. the values are available for the same location / time.

A practical example of such pair of data sets would be
a set of daily weather measurements in two cities,
with binary values 0/1 indicating if it was raining
in the given city on a particular day.
The values within each data set are clearly locally correlated,
as the weather today depends on the weather yesterday.

Our goal is to test if the occurences of rain
in the two cities are statistically dependent.

Note that Fisher's exact test should NOT be applied here
because it requires independence of measurements within each data set.

With the following code we generate
a pair of **independent** data sets with high local dependence (`cor = 0.99`)
and perform testing for dependence with `shiftR` contrast it 
with Fisher's exact test.
The local dependence causes Fisher's Exact test 
to produce unreasonably small p-value < 10^-19^,
wrongly suggesting strong dependence between data sets,
while permutation testing by `shiftR` 
does not detect any dependence (p-value > 0.1).

```{r generateData}
n = 1e6

sim = simulateBinary(n, corWithin = 0.99, corAcross = 0)

offsets = getOffsetsUniform(n = n, npermute = 10e3)
perm = shiftrPermBinary( sim$data1, sim$data2, offsets)

message("Fisher exact test p-value: ", perm$fisherTest$p.value)
message("Permutation p-value: ", perm$permPV)
```

# Enrichment testing for two sets of p-values \
(Permutation analysis on matched numeric data sets)

Consider the following scenario.
We have performed two genome-wide (or methylome-wide) association studies.
Our goal is to test whether the top genomic locations indicated by one study
are enriched with top locations indicated by another study.
For simplicity, we first assume the studies were testing 
the same set of genomic locations.

As in previous example, 
the p-values produced by each study are locally dependent
(due to linkage disequilibrium).

Let `sim` contain two simulated sets of p-values
from the aforementioned studies.

```{r seed2, echo=FALSE}
set.seed(18090212)
```

```{r genPV}
n = 1e6
sim = simulatePValues(n, corWithin = 0.99, corAcross = 0)
```

The dependence of p-values within each study
causes Fisher's exact test to indicate strong dependence
between top results (using 0.10 p-value threshold).

```{r pvfish}
fisher.test(sim$data1 < 0.10, sim$data2 < 0.10)$p.value
```

## Enrichment testing with shiftR

The function `enrichmentAnalysis` in our package
conducts enrichment testing on two sets of locally correlated
set of p-values (or other types of values, smaller being better).

The code below test for enrichment between the p-value data sets
using 10,000 circular permutations.
The first data set is thresholded at 0.01, 0.05, and 0.10 percentiles,
as is the second.

```{r enr}
enr = enrichmentAnalysis(
    sim$data1,
    sim$data2,
    percentiles1 = c(0.01, 0.05, 0.10),
    percentiles2 = c(0.01, 0.05, 0.10),
    npermute = 10e3,
    threads = 2)

message('Enrichment p-value is: ', enr$overallPV[2])
```
Note that unlike Fisher's exact test,
circular permutation analysis is robust to local correlation of 
the tests in each data set.


The enrichment testing is performed for each
pair of percentile thresholds as descripbed in [Section 2](#binary).

The overall testing (detailed below) tests across all thresholds
and does not require additional correction for multiple testing.
The overall testing is conducted as follows.
For each permutation and each threshold,
we calculate the overlap of top genomic sites
and calculate the Cramer's V score for the overlap.
Then, the maximim V score (maxV) across possible thresholds is
calculated the permutation. The distribution of maxV 
under permutation is then compared to the maxV for the original data
and the overall permutation p-value for enrichment is calculated.
For overall test of depletion, minV equal to minimum V score is used.
The overall two-sided test used maximum absolute value of V score.

# Matching data sets by location

In practice, the genomic locations at
which the data in the data sets is available differs.
This can happen, for example, it one data set has gene-wise information
and the other has p-value for methylation sites.

Genomic data sets can be easily matched by location with the
`matchDatasets` function.
