Latent Outcome Measures in Causal Inference with Doubly Robust Estimator Using Propensity Scores

In a non-randomized study, a propensity score is the probability of an individual case being in the treatment group, given the other covariates that confound the treatment assignment. Propensity scores can be used to equate the treatment and control groups which are otherwise unbalanced on the confounders to produce unbiased estimate of the average treatment effect. Doubly robust estimator is a method that involves the use of both propensity scores and one other group equating method, where either method, if correct, will lead to unbiased causal effect estimation. To date, the doubly robust estimators were applied to situations where the outcome variable is measured directly. This study focuses on application of the doubly robust estimator to latent outcomes that are measured by multiple indicators. A method of transforming the weighted residual bias corrections, a doubly robust causal effect estimator, into latent outcome application is proposed and tested on simulated datasets. The proposed method produces unbiased estimates of the average treatment effect under certain conditions