Abstract

The prognostic score (PGS) is a function of observed covariates that summarizes covariates’ association with potential responses. In the current study, we propose a full prognostic score (FPGS), an extension of the PGS that integrates individual prognostic scores to account for confounding adjustments in causal inference. Under effect modification, we demonstrate that FPGS meets the sufficiency condition for confounding adjustment. Consequently, the implemented FPGS is sufficient for estimating the average causal effect. To estimate PGS and FPGS, we apply linear regression, random forest regression, gradient boosting regression, and support vector machine. When estimating the average treatment effect, we incorporate FPGS into semi-parametric estimators, including regression imputation and targeted maximum likelihood estimation (TMLE). The finite sample properties of estimators are compared through three simulation studies. Based on the findings from FPGS estimators, the mean squared errors of the linear regression imputation estimator and TMLE estimator, which comprise linearly regressed PGS, are smaller than those of alternative estimators. In an empirical study, we analyze data from the National Health and Nutrition Examination Survey (NHANES, 2007-2008) to determine the effect of smoking on blood lead levels.