  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 three-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.
