Flexible template matching for observational study design.

Matching is a popular design for inferring causal effect with observational data. Unlike model-based approaches, it is a nonparametric method to group treated and control subjects with similar characteristics together, hence to re-create a randomization-like scenario. The application of matched design for real world data may be limited by: (1) the causal estimand of interest; (2) the sample size of different treatment arms. We propose a flexible design of matching, based on the idea of template matching, to overcome these challenges. It first identifies the template group which is representative of the target population, then match subjects from the original data to this template group and make inference. We provide theoretical justification on how it unbiasedly estimates the average treatment effect using matched pairs and the average treatment effect on the treated when the treatment group has a bigger sample size. We also propose using the triplet matching algorithm to improve matching quality and devise a practical strategy to select the template size. One major advantage of matched design is that it allows both randomization-based or model-based inference, with the former being more robust. For the commonly used binary outcome in medical research, we adopt a randomization inference framework of attributable effects in matched data, which allows heterogeneous effects and can incorporate sensitivity analysis for unmeasured confounding. We apply our design and analytical strategy to a trauma care evaluation study.