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We investigate estimation of causal effects of multiple competing (multi-valued) treatments in the absence of randomization. Our work is motivated by an intention-to-treat study of the relative cardiometabolic risk of assignment to one of six commonly prescribed antipsychotic drugs in a cohort of nearly 39 000 adults with serious mental illnesses. Doubly-robust estimators, such as targeted minimum loss-based estimation (TMLE), require correct specification of either the treatment model or outcome model to ensure consistent estimation; however, common TMLE implementations estimate treatment probabilities using multiple binomial regressions rather than multinomial regression. We implement a TMLE estimator that uses multinomial treatment assignment and ensemble machine learning to estimate average treatment effects. Our multinomial implementation improves coverage, but does not necessarily reduce bias, relative to the binomial implementation in simulation experiments with varying treatment propensity overlap and event rates. Evaluating the causal effects of the antipsychotics on 3-year diabetes risk or death, we find a safety benefit of moving from a second-generation drug considered among the safest of the second-generation drugs to an infrequently prescribed first-generation drug known for having low cardiometabolic risk., (© 2024 John Wiley & Sons, Ltd.)