Weighted Quantile Sum (WQS) Permutation Test

The goal of wqspt is to implement a permutation test method for the weighted quantile sum (WQS) regression.

Weighted quantile sum regression is a statistical technique to evaluate the effect of complex exposure mixtures on an outcome (Carrico et al. 2015). It is a single-index method which estimates a combined mixture sum effect as well as weights determining each individual mixture component’s contributions to the sum effect. However, the model features a statistical power and Type I error (i.e., false positive) rate tradeoff, as there is a machine learning step to determine the weights that optimize the linear model fit. If the full data is used to estimate both the mixture component weights and the regression coefficients, there is high power but also a high false positive rate since coefficient p-values are calculated for a weighted mixture independent variable calculated using weights that have already been optimized to find a large effect.

This package provides an alternative method based on a permutation test that should reliably allow for both high power and low false positive rate when utilizing the WQSr. The permutation test is a method of obtaining a p-value by simulating the null distribution through permutations of the data. The permutation test algorithm is described more in detail and validated in Day et al. 2022. The version of this permutation test used for a continuous outcome variable has been applied in Loftus et al. 2021, Day et al. 2021, Wallace et al. 2022, Barrett et al. 2022, and Freije et al. 2022. Another version of the permutation test adapted for logistic WQSr with a binary outcome variable is applied in Loftus et al. 2022.


You can install the development version of wqspt from GitHub with:

# install.packages("devtools")


Here is a brief tutorial vignette on how to use the wqspt package.