wqs_pt {wqspt}

WQS permutation test

Description

wqs_pt takes a gwqs object as an input and runs the permutation test (Day et al. 2022) to obtain an estimate for the p-value significance for the WQS coefficient.

Usage

wqs_pt(
  model,
  niter = 200,
  boots = NULL,
  b1_pos = TRUE,
  b1_constr = FALSE,
  rs = FALSE,
  plan_strategy = "multicore",
  seed = NULL
)

Arguments

model

A gwqs object as generated from the gWQS package.

niter

Number of permutation test iterations.

boots

Number of bootstrap samples for each permutation test WQS regression iteration. If boots is not specified, then we will use the same bootstrap count for each permutation test WQS regression iteration as that specified in the main WQS regression run.

b1_pos

A logical value that indicates whether beta values should be positive or negative.

b1_constr

Logical value that determines whether to apply positive or negative constraints in the optimization function for the weight optimization.

rs

A logical value indicating whether random subset implementation should be performed.

plan_strategy

Evaluation strategy for the plan function. You can choose among "sequential", "transparent", "multisession", "multicore", "multiprocess", "cluster" and "remote." See future::plan documentation for full details.

seed

(optional) Random seed for the permutation test WQS reference run. This should be the same random seed as used for the main WQS regression run. This seed will be saved in the "gwqs_perm" object as "gwqs_perm$seed".

Details

To use wqs_pt, we first need to run an initial WQS regression run while setting validation = 0. We will use this gwqs object as the model argument for the wqs_pt function. Note that permutation test has so far only been validated for linear WQS regression (i.e., family = "gaussian") or logistic WQS regression (i.e., family = binomial(link = "logit")), though the permutation test algorithm should also work for all WQS GLMs. Therefore, this function accepts gwqs objects made with the following families: "gaussian" or gaussian(link = "identity"), "binomial" or binomial() with any accepted link function (e.g., "logit" or "probit"), "poisson" or poisson(link="log"), "negbin" for negative binomial, and "quasipoisson" or quasipoisson(link="log"). This function cannot currently accommodate gwqs objects made with the "multinomial" family, and it is not currently able to accommodate stratified weights or WQS interaction terms (e.g., y ~ wqs * sex).

The argument boots is the number of bootstraps for the WQS regression run in each permutation test iteration. Note that we may elect a bootstrap count boots lower than that specified in the model object for the sake of efficiency. If boots is not specified, then we will use the same bootstrap count in the permutation test WQS regression runs as that specified in the model argument.

The arguments b1_pos and rs should be consistent with the inputs chosen in the model object. The seed should ideally be consistent with the seed set in the model object for consistency, though this is not required.

Value

wqs_pt returns an object of class wqs_pt, which contains:

perm_test

List containing: (1) pval: permutation test p-value, (2) (linear WQS regression only) testbeta1: reference WQS coefficient beta1 value, (3) (linear WQS regression only) betas: Vector of beta values from each permutation test run, (4) (WQS GLM only) testpval: test reference p-value, (5) (WQS GLM only) permpvals: p-values from the null models.

gwqs_main

Main gWQS object (same as model input).

gwqs_perm

Permutation test reference gWQS object (NULL if model family != "gaussian" or if same number of bootstraps are used in permutation test WQS regression runs as in the main run).

References

Day, D. B., Sathyanarayana, S., LeWinn, K. Z., Karr, C. J., Mason, W. A., & Szpiro, A. A. (2022). A permutation test-based approach to strengthening inference on the effects of environmental mixtures: comparison between single index analytic methods. Environmental Health Perspectives, 130(8).

Day, D. B., Collett, B. R., Barrett, E. S., Bush, N. R., Swan, S. H., Nguyen, R. H., ... & Sathyanarayana, S. (2021). Phthalate mixtures in pregnancy, autistic traits, and adverse childhood behavioral outcomes. Environment International, 147, 106330.

Loftus, C. T., Bush, N. R., Day, D. B., Ni, Y., Tylavsky, F. A., Karr, C. J., ... & LeWinn, K. Z. (2021). Exposure to prenatal phthalate mixtures and neurodevelopment in the Conditions Affecting Neurocognitive Development and Learning in Early childhood (CANDLE) study. Environment International, 150, 106409.

Examples

library(gWQS)

# mixture names
PCBs <- names(wqs_data)[1:17] #half of the original 34 for quick computation

# create reference wqs object with 5 bootstraps
wqs_main <- gwqs(yLBX ~ wqs, mix_name = PCBs, data = wqs_data, q = 10, 
                 validation = 0, b = 5, b1_pos = TRUE, b1_constr = FALSE,
                 plan_strategy = "multicore", family = "gaussian", seed = 16)
# Note: We recommend niter = 1000 for the main WQS regression. This example
# has a lower number of bootstraps to serve as a shorter test run.

# run permutation test

perm_test_res <- wqs_pt(wqs_main, niter = 3, b1_pos = TRUE)


# Note: The default value of niter = 200 is the recommended parameter value. 
# This example has a lower niter in order to serve as a shorter test run.