A Compound Model of Multiple Treatment Selection with Applications to Marginal Structural Modeling

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 model 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. It is applicable if the treatment set is finite, treatments are given at one time point, and the outcome is observed at a fixed time point. This representation can reduce bias when not all treatments are available to all patients. 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. ### Competing Interest Statement Dr. Amin is PI or CoPI of clinical trials sponsored by NIH/NIAID, NeuroRX Pharma, Pulmotect, Blade Therapeutics, Novartis, Takeda, Humanigen, Eli Lilly PTC Therapeutics, OctaPharma, Fulcrum Therapeutics, and Alexion. This work is not related to this manuscript. Dr. Webb has received a grant from Regeneron. ### Funding Statement This study was supported wholly or in part with federal funds from the Administration for Strategic Preparedness and Response, Biomedical Advanced Research and Development Authority, under Contract Number 75FCMC18D0047, Task Order 75A50121F80012, awarded to The MITRE Corporation. ### Author Declarations I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained. Yes The details of the IRB/oversight body that provided approval or exemption for the research described are given below: IRB of Houston Methodist gave approval for this work. IRB of UC Irvine gave approval for this work. IRB of The Mayo Clinic gave approval for this work. IRB of Intermountain Healthcare gave approval for this work. I confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the research group so cannot be used to identify individuals. Yes I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance). Yes I have followed all appropriate research reporting guidelines and uploaded the relevant EQUATOR Network research reporting checklist(s) and other pertinent material as supplementary files, if applicable. Yes All data have been deposited with the National Covid Cohort Collaborative.