Causal inference of latent classes in complex survey data with the estimating equation framework

Latent class analysis (LCA) has been effectively used to cluster multiple survey items. However, causal inference with an exposure variable, identified by an LCA model, is challenging because (1) the exposure variable is unobserved and harbors the uncertainty of estimating parameters in the LCA model and (2) confounding bias adjustments need to be done with the unobserved LCA-driven exposure variable. In addition to these challenges, complex survey design features and survey weights must be accounted for if they are present. Our solutions to these issues are to (1) assess point estimates with the expected estimating function approach and (2) modify the survey design weights with LCA-based propensity scores. This paper aims to introduce a statistical procedure to apply the estimating equation approach to assessing the effects of LCA-driven cause in complex survey data using an example of the National Health and Nutrition Examination Survey.