  Propensity score (PS) based estimators are increasingly used for causal
inference in observational studies. However, model selection for PS estimation
in high-dimensional data has received little attention. In these settings, PS
models have traditionally been selected based on the goodness-of-fit for the
treatment mechanism itself, without consideration of the causal parameter of
interest. Collaborative minimum loss-based estimation (C-TMLE) is a novel
methodology for causal inference that takes into account information on the
causal parameter of interest when selecting a PS model. This "collaborative
learning" considers variable associations with both treatment and outcome when
selecting a PS model in order to minimize a bias-variance trade off in the
estimated treatment effect. In this study, we introduce a novel approach for
collaborative model selection when using the LASSO estimator for PS estimation
in high-dimensional covariate settings. To demonstrate the importance of
selecting the PS model collaboratively, we designed quasi-experiments based on
a real electronic healthcare database, where only the potential outcomes were
manually generated, and the treatment and baseline covariates remained
unchanged. Results showed that the C-TMLE algorithm outperformed other
competing estimators for both point estimation and confidence interval
coverage. In addition, the PS model selected by C-TMLE could be applied to
other PS-based estimators, which also resulted in substantive improvement for
both point estimation and confidence interval coverage. We illustrate the
discussed concepts through an empirical example comparing the effects of
non-selective nonsteroidal anti-inflammatory drugs with selective COX-2
inhibitors on gastrointestinal complications in a population of Medicare
beneficiaries.
