In comparative effectiveness studies, researchers typically use propensity score methods. However, propensity score methods have known limitations in real-world scenarios, when the true data generating mechanism is unknown. Targeted maximum likelihood estimation (TMLE) is an alternative estimation method with a number of desirable statistical properties. It is a doubly robust method, making use of both the outcome model and propensity score model to generate an unbiased estimate as long as at least one of the models is correctly specified. TMLE also enables the integration of machine learning approaches. Despite the fact that this method has been shown to perform better than propensity score methods in a variety of scenarios, it is not widely used in medical research as the implementation details of this approach are generally not well understood.

This article introduces and implements the framework of propensity score method from Dehejia and Wahba (1999) "Causal Effects in Non-Experimental Studies: Reevaluating the Evaluation of Training Programs," Journal of the American Statistical Association, Vol. I will briefly go over the theories and then walk through how I implemented the stratification matching step by step. The full Python code is provided at the end of the article. The intuition of propensity score method is: instead of conditioning on the full vector of covariates Xᵢ, which can get difficult when there are many pre-treatment variables and when the treatment and comparison groups are very different, we try to condition on the propensity score estimated with Xᵢ. Propensity score matching works in the same way as covariate matching except that we match on the score instead of the covariates directly.