epiGWAS (version 1.0.2)

modified_outcome: Implements the modified outcome approach

Description

In the modified outcome approach, we estimate the risk difference \(E\left[Y| A=1,X\right]-E\left[Y| A=0,X\right]\). The risk difference measures the synergy between A and the set of covariates in X. For genome-wide association studies, it can be interpreted as a pure epistatic term. However, for a single sample, we only observe one of the two possibilities A=1 or A=0, making the direct estimate of the risk difference impossible. Through propensity scores, modified outcome was proposed as a solution to this problem. The risk difference is recovered by constructing a modified outcome that combines A, Y and the propensity score \(\pi(A| X)\): \(Y \times \left[\frac{A}{\pi(A=1| X)} - \frac{1-A}{1-\pi(A=1| X)} \right]\). The use of stabilityGLM or stabilityBIG for the modified outcome regression allows us to recover the interacting components within X.

Usage

modified_outcome(A, X, Y, propensity, parallel = FALSE, ...)

Arguments

A

target variant

X

rest of the genotype

Y

phenotype

propensity

propensity scores vector/matrix. If given as a matrix, the first column is \(\pi(A = 0| X)\) while the second is \(\pi(A = 1| X)\)

parallel

whether to perform support estimation in a parallelized fashion with the stabilityBIG function

...

additional arguments to be passed to stabilityGLM or stabilityBIG

Value

a vector containing the area under the stability selection path for each variable in X

References

Rosenbaum, Paul R., and Donald B. Rubin. 'The central role of the propensity score in observational studies for causal effects.' Biometrika 70.1 (1983): 41-55.

Examples

# NOT RUN {
n <- 30
p <- 10
X <- matrix((runif(n * p) < 0.5) + (runif(n * p) < 0.5), ncol = p, nrow = n)
A <- (runif(n, min = 0, max = 1) < 0.3)
propensity <- runif(n, min = 0.4, max = 0.8)
Y <- runif(n) < 1/ (1 + exp(- 2 * X[, 5, drop = FALSE]))
auc_scores <- modified_outcome(A, X, Y, propensity,
                               ncores = 1, parallel = TRUE, n_subsample = 1)

# }