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The prognostic score, or disease risk score (DRS), is a summary score that is used to control for confounding in non-experimental studies. While the DRS has been shown to effectively control for measured confounders, unmeasured confounding continues to be a fundamental obstacle in non-experimental research. Both theory and simulations have shown that in the presence of unmeasured confounding, controlling for variables that affect treatment (both instrumental variables and measured confounders) amplifies the bias caused by unmeasured confounders. In this paper, we use causal diagrams and path analysis to review and illustrate the process of bias amplification. We show that traditional estimation strategies for the DRS do not avoid bias amplification when controlling for predictors of treatment. We then discuss estimation strategies for the DRS that can potentially reduce bias amplification that is caused by controlling both instrumental variables and measured confounders. We show that under certain assumptions, estimating the DRS in populations outside the defined study cohort where treatment has not been introduced, or in outside populations with reduced treatment prevalence, can control for the confounding effects of measured confounders while at the same time reduce bias amplification.

Reducing Bias Amplification in the Presence of Unmeasured Confounding through Out-of-Sample Estimation Strategies for the Disease Risk Score