Author: Tabitha Peter

# Getting started with plmmr

#### Tabitha Peter

    library(plmmr)
    #> Loading required package: bigalgebra
    #> Loading required package: bigmemory

## Introduction

`plmmr` is a package for fitting Penalized Linear Mixed Models in R. This package was created for the purpose of fitting penalized regression models to high dimensional data in which the observations are correlated. For instance, this kind of data arises often in the context of genetics (e.g., GWAS in which there is population structure and/or family grouping).

The novelties of `plmmr` are:

1. Integration: `plmmr` combines the functionality of several packages in order to do quality control, model fitting/analysis, and data visualization all in one package. For example, if you have GWAS data, `plmmr` will take you from PLINK files all the way to a list of SNPs for downstream analysis.

2. Accessibility: `plmmr` can be run from an `R` session on a typical desktop or laptop computer. The user does not need access to a supercomputer or have experience with the command line in order to fit models using `plmmr`.

3. Handling correlation: `plmmr` uses a transformation that (1) measures correlation among samples and (2) uses this correlation measurement to improve predictions (via the best linear unbiased predictor, or BLUP). This means that in `plmm()`, there’s no need to filter data down to a ‘maximum subset of unrelated samples.’

## Minimal example

Below is a minimal reproducible example of how `plmmr` can be used:

    # library(plmmr)
    fit <- plmm(admix$X, admix$y) # admix data ships with package
    plot(fit)

    cvfit <- cv_plmm(admix$X, admix$y)
    plot(cvfit)

    summary(cvfit)
    #> lasso-penalized model with n=197 and p=101
    #> At minimum cross-validation error (lambda=0.2454):
    #> -------------------------------------------------
    #>   Nonzero coefficients: 5
    #>   Cross-validation error (deviance): 2.18
    #>   Scale estimate (sigma): 1.477

## Computational capability

### File-backing

In many applications of high dimensional data analysis, the dataset is too large to read into R – the session will crash for lack of memory. This is particularly common when analyzing data from genome-wide association studies (GWAS). To analyze such large datasets, `plmmr` is equipped to analyze data using filebacking - a strategy that lets R ‘point’ to a file on disk, rather than reading the file into the R session. Many other packages use this technique - bigstatsr and biglasso are two such examples. The package that `plmmr` uses to create and store filebacked objects is bigmemory. The filebacked computation relies on the biglasso package by Yaohui Zeng et al. and on bigalgebra by Michael Kane et al. For processing PLINK files, we use methods from the `bigsnpr` package by Florian Privé.

### Numeric outcomes only

At this time, the package is designed for linear regression only – that is, we are considering only continuous (numeric) outcomes. We maintain that treating binary outcomes as numeric values is appropriate in some contexts, as described by Hastie et al. in the Elements of Statistical Learning, chapter 4. In the future, we would like to extend this package to handle dichotomous outcomes via logistic regression; the theoretical work underlying this is an open problem.

### 3 types of penalization

Since we are focused on penalized regression in this package, `plmmr` offers 3 choices of penalty: the minimax concave (MCP), the smoothly clipped absolute deviation (SCAD), and the least absolute shrinkage and selection operator (LASSO). The implementation of these penalties is built on the concepts/techniques provided in the ncvreg package.

### Data size and dimensionality

We distinguish between the data attributes ‘big’ and ‘high dimensional.’ ‘Big’ describes the amount of space data takes up on a computer, while ‘high dimensional’ describes a context where the ratio of features (also called ‘variables’ or ‘predictors’) to observations (e.g., samples) is high. For instance, data with 100 samples and 100 variables is high dimensional, but not big. By contrast, data with 10 million observations and 100 variables is big, but not high dimensional.

`plmmr` is optimized for data that are high dimensional – the methods we are using to estimate relatedness among observations perform best when there are a high number of features relative to the number of observations.

`plmmr` is also designed to accommodate data that is too large to analyze in-memory. We accommodate such data through file-backing (as described above). Our current analysis pipeline works well for data files up to about 40 Gb in size. In practice, this means that `plmmr` is equipped to analyze GWAS data, but not biobank-sized data.

## Data input types

`plmmr` currently works with three types of data input:

1. Data that is stored in-memory as a matrix or data frame

2. Data that is stored in PLINK files

3. Data that is stored in delimited files

### Example data sets

`plmmr` currently includes three example data sets, one for each type of data input.

- The `admix` data is our example of matrix input data. `admix` is a small data set (197 observations, 100 SNPs) that describes individuals of different ancestry groups. The outcome of `admix` is simulated to include population structure effects (i.e. race/ethnicity have an impact on the SNP associations). This data set is available whenever `library(plmmr)` is called. An example analysis with the `admix` data is available in `vignette('matrix_data', package = "plmmr")`.

- The `penncath_lite` data is our example of PLINK input data. `penncath_lite` (data on coronary artery disease from the PennCath study) is a high dimensional data set (1401 observations, 4217 SNPs) with several health outcomes as well as age and sex information. The features in this data set represent a small subset of a much larger GWAS data set (the original data has over 800K SNPs). For information on this data set, refer to the original publication. An example analysis with the `penncath_lite` data is available in `vignette('plink_files', package = "plmmr")`.

- The `colon2` data is our example of delimited-file input data. `colon2` is a variation of the `colon` data included in the biglasso package. `colon2` has 62 observations and 2001 features representing a study of colon disease. 2000 features are original to the data, and the ‘sex’ feature is simulated. An example analysis with the `colon2` data is available in `vignette('delim_files', package = "plmmr")`.