Prognostic score-based model averaging approach for propensity score estimation

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BackgroundPropensity scores (PS) are typically evaluated using balance metrics that focus on covariate balance, often without considering their predictive power for the outcome. This approach may not always result in optimal bias reduction in the treatment effect estimate. To address this issue, evaluating covariate balance through prognostic scores, which account for the relationship between covariates and the outcome, has been proposed. Similarly, using a typical model averaging approach for PS estimation that minimizes prediction error for treatment status and covariate imbalance does not necessarily optimize PS-based confounding adjustment. As an alternative approach, using the averaged PS model that minimizes inter-group differences in the prognostic score may further reduce bias in the treatment effect estimate. Moreover, since the prognostic score is also an estimated quantity, model averaging in the prognostic scores can help identify a better prognostic score model. Utilizing the model-averaged prognostic scores as the balance metric for constructing the averaged PS model can contribute to further decreasing bias in treatment effect estimates. This paper demonstrates the effectiveness of the PS model averaging approach based on prognostic score balance and proposes a method that uses the model-averaged prognostic score as a balance metric, evaluating its performance through simulations and empirical analysis.MethodsWe conduct a series of simulations alongside an analysis of empirical observational data to compare the performances of weighted treatment effect estimates using the proposed and existing approaches. In our examination, we separately provid four candidate estimates for the PS and prognostic score models using traditional regression and machine learning methods. The model averaging of PS based on these candidate estimators is performed to either maximize the prediction accuracy of the treatment or to minimize intergroup differences in covariate distributions or prognostic scores. We also utilize not only the prognostic scores from each candidate model but also an averaged score that best predicted the outcome, for the balance assessment.ResultsThe simulation and empirical data analysis reveal that our proposed model-averaging approaches for PS estimation consistently yield lower bias and less variability in treatment effect estimates across various scenarios compared to existing methods. Specifically, using the optimally averaged prognostic scores as a balance metric significantly improves the robustness of the weighted treatment effect estimates.DiscussionThe prognostic score-based model averaging approach for estimating PS can outperform existing model averaging methods. In particular, the estimator using the model averaging prognostic score as a balance metric can produce more robust estimates. Since our results are obtained under relatively simple conditions, applying them to real data analysis requires adjustments to obtain accurate estimates according to the complexity and dimensionality of the data.ConclusionsUsing the prognostic score as the balance metric for the PS model averaging enhances the performance of the treatment effect estimator, which can be recommended for a wide variety of situations. When applying the proposed method to real-world data, it is important to use it in conjunction with techniques that mitigate issues arising from the complexity and high dimensionality of the data.