  The preponderance of large-scale healthcare databases provide abundant
opportunities for comparative effectiveness research. Evidence necessary to
making informed treatment decisions often relies on comparing effectiveness of
multiple treatment options on outcomes of interest observed in a small number
of individuals. Causal inference with multiple treatments and rare outcomes is
a subject that has been treated sparingly in the literature. This paper designs
three sets of simulations, representative of the structure of our healthcare
database study, and propose causal analysis strategies for such settings. We
investigate and compare the operating characteristics of three types of methods
and their variants: Bayesian Additive Regression Trees (BART), regression
adjustment on multivariate spline of generalized propensity scores (RAMS) and
inverse probability of treatment weighting (IPTW) with multinomial logistic
regression or generalized boosted models. Our results suggest that BART and
RAMS provide lower bias and mean squared error, and the widely used IPTW
methods deliver unfavorable operating characteristics. We illustrate the
methods using a case study evaluating the comparative effectiveness of
robotic-assisted surgery, video-assisted thoracoscopic surgery and open
thoracotomy for treating non-small cell lung cancer.
