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

Abstract

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.

On calibrated inverse probability weighting and generalized boosting propensity score models for mean estimation with incomplete survey data

“…The driving motivation in IPW is to weight the multivariate covariate probability distribution for the observed data P XjR ¼ 1 ð Þ to make it approximate the multivariate covariate probability distribution for all the data P X ð Þ. Ridgeway et al (2015) and Kang et al (2020) used this notion of balancing in causal inference for survey-weighted data and latent class exposures, respectively. The following definition clarifies the notion by weights w.…”

“…The driving motivation in IPW is to weight the multivariate covariate probability distribution for the observed data to make it approximate the multivariate covariate probability distribution for all the data . Ridgeway et al (2015) and Kang et al (2020) used this notion of balancing in causal inference for survey‐weighted data and latent class exposures, respectively. The following definition clarifies the notion by weights .Definition The multivariate balancing condition for is defined as That is, there is a that can adjust the multivariate covariate distribution for the observed data to equal the multivariate covariate distribution for the full data.…”