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 in some complex way. For instance, this kind of data arises often in the context of genetics (e.g., GWAS dealing with population structure/family structure).

For more information on the theoretical context of penalized regression, check out these online course notes; the section on ridge regression may be a good place to start.

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 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.’

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 examples of packages that use the filebacking technique. 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 as 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 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 2,001 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").