Doubly weighted mean score estimating functions with a partially observed effect modifier

Effect modification plays a central role in stratified medicine, of which the goal is often to find biomarker profiles that identify individuals who benefit from a treatment of interest. We consider the problem of causal inference regarding the effect modifying role of a biomarker, which is only available for some individuals in an observational study. We develop inverse probability weighted mean score estimating functions with one weight to account for confounding and a second weight for the missing data process. An iterative approach is described for solving the equations in the spirit of the expectation-maximization algorithm, and large sample properties of the resulting estimator are developed. Simulation studies are conducted to compare the proposed method with a doubly weighted complete case analysis and a propensity score weighted multiple imputation approach. An application to a study of the effect of a biologic therapy on inflammation in a rheumatology cohort is given for illustration.

Automated summary

We investigate causal inference for the effect modification of a biomarker in an observational study where the biomarker is only available for some individuals. We propose inverse probability weighted mean score estimating functions with two weights to account for confounding and missing data. An iterative approach is used to solve the equations and the large sample properties of the estimator are developed. Simulation studies compare the proposed method with other approaches, and an application to a rheumatology cohort illustrates the effect of a biologic therapy on inflammation.