A compound representation of the multiple treatment propensity score with applications to marginal structural modeling

• Published in: Epidemiologic methods Vol. 13; no. 2
• Main Authors: Stein, David, D’Arinzo, Lauren, Gaspar, Fraser, Oliver, Max, Fitzgerald, Kristin, Lu, Di, Piantadosi, Steven, Amin, Alpesh, Webb, Brandon
• Format: Journal Article
• Language: English
• Published: Berlin De Gruyter 06.11.2024; Walter de Gruyter GmbH
• Subjects: Bias; Clinical trials; Coronaviruses; COVID-19; Estimates; marginal structural models; multiple treatment propensity score; Observational studies; Pandemics; Regression analysis; Severe acute respiratory syndrome
• ISSN: 2161-962X; 2194-9263; 2161-962X
• DOI: 10.1515/em-2023-0005

Methods of causal inference are used to estimate treatment effectiveness for non-randomized study designs. The propensity score (i.e., the probability that a subject receives the study treatment conditioned on a set of variables related to treatment and/or outcome) is often used with matching or sample weighting techniques to, ideally, eliminate bias in the estimates of treatment effect due to treatment decisions. If multiple treatments are available, the propensity score is a function of the adjustment set and the set of possible treatments. This paper develops a compound representation that separates the treatment decision into a binary decision: treat or don't treat, and a potential treatment decision: choose the treatment that would be given if the subject is treated.The compound representation was derived from Robin's definition of the propensity score, and a second proof is derived from importance sampling. A simulation study illustrates the use of the method.Multiple treatment stabilized marginal structural weights were calculated with this approach, and the method was applied to an observational study to evaluate the effectiveness of different neutralizing monoclonal antibodies to treat infection with various severe acute respiratory syndrome coronavirus 2 variants.The method can greatly simplify the computation of multiple treatment propensity scores and reduce bias in comparison with improperly used logistic regression.