On the aggregation of published prognostic scores for causal inference in observational studies

As real world evidence on drug efficacy involves nonrandomized studies, statistical methods adjusting for confounding are needed. In this context, prognostic score (PGS) analysis has recently been proposed as a method for causal inference. It aims to restore balance across the different treatment groups by identifying subjects with a similar prognosis for a given reference exposure ("control"). This requires the development of a multivariable prognostic model in the control arm of the study sample, which is then extrapolated to the different treatment arms. Unfortunately, large cohorts for developing prognostic models are not always available. Prognostic models are therefore subject to a dilemma between overfitting and parsimony; the latter being prone to a violation of the assumption of no unmeasured confounders when important covariates are ignored. Although it is possible to limit overfitting by using penalization strategies, an alternative approach is to adopt evidence synthesis. Aggregating previously published prognostic models may improve the generalizability of PGS, while taking account of a large set of covariates-even when limited individual participant data are available. In this article, we extend a method for prediction model aggregation to PGS analysis in nonrandomized studies. We conduct extensive simulations to assess the validity of model aggregation, compared with other methods of PGS analysis for estimating marginal treatment effects. We show that aggregating existing PGS into a "meta-score" is robust to misspecification, even when elementary scores wrongfully omit confounders or focus on different outcomes. We illustrate our methods in a setting of treatments for asthma.