Enhanced doubly robust estimation with concave link functions for estimands in clinical trials

For observational studies or clinical trials not fully randomised, the baseline covariates are often not balanced between the treatment and control groups. In this case, the traditional estimates of treatment effects are biased, and causal inference method is needed to get unbiased estimate. The doubly robust estimator (DRE) is a recent popular development in casual inference. However, the unbiasedness of DRE relies on the correct specification of either propensity score or outcome models, which is hardly guaranteed. To overcome this issue, Yuan et al. [(2021), 'Enhanced Doubly Robust Procedure for Causal Inference', Statistics in Bioscience, 13(3), 454-478. https://doi.org/10.1007/s12561-021-09300-y.] proposed an enhanced doubly robust estimator which utilises semiparametric models and nonparametric monotone link functions for both propensity score and outcome models. In this article, we further develop an enhanced doubly robust estimator with concave link functions for both propensity score and outcome models. The asymptotic properties of the enhanced doubly robust estimator are studied. Simulation studies are conducted to evaluate the proposed method. A clinical trial data analysis is used to illustrate the method.