Propensity score mixed model for correcting non-compliance bias

Background The non-compliance problem is often encountered not only in the randomized controlled trials (RCTs) but also in observational studies, such as population-based screening program for the referral of screen-positive participants. Intentional-to-treat method often used for solving this problem in the RCTs may not be possibly applied when the follow-up outcome among the non-compliers is not available. Propensity score method is therefore proposed as an alternative by making use of information on the imbalance of baseline covariates between the two groups. In spite of its usefulness, the logics for balancing score function in relation to propensity score function based on strongly ignorable treatment assignment (SITA) are still elusive since it was proposed by Rosenbaum and Rubin. Objectives and methods The objectives of this thesis were to (1) develop philosophical logics of operational criteria using the balancing score given SITA to approximately estimate the true treatment effect; (2) demonstrate how a new propensity score mixed effect model can render the balancing score finer following (1); to approximate the true treatment effect through matching, stratification, and covariance adjustment based on one randomized controlled trial; (3) apply the PS-mixed effect model to two randomized controlled trials and also the referral of FIT (fecal immunochemical test) positive participants in nationwide population-based colorectal cancer screening. Results Based on the development of philosophical logics of operational criteria using balancing score given SITA, the simulated results using the randomized controlled trial data showed the proposed propensity score mixed-effect (PS-mixed) model rendered the estimates of efficacy closer to true treatment effect compared with the fix-effect model. The application of this propensity score mixed-effect model with the incorporation of random-effect also gave an unbiased estimate of true treatment effect by comparing the outcome of compliers in the experimental group with that of potential compliers in the control group. While the propensity score fixed-effect model was applied to colorectal cancer screening program, the efficacy of colonoscopy (the compliers (referral) versus the non-compliers(non-referral)) gave an estimate of relative rate (RR) of the risk for death from CRC of 0.60 (95% Confidence interval: 0.49 ~ 0.74), only slightly different from the crude estimate of 0.64 (95% Confidence interval: 0.52 ~ 0.78), but substantially different from the adjusted estimate of 0.49 (95% Confidence interval: 0.36 ~0.66) based on the application of the propensity score mixed-effect model. Conclusion In a nutshell, we developed philosophical logics for operational criteria pertaining to SITA and provided the analytical framework for the propensity score analysis. We then proposed the PS-mixed model to render balancing score function as fine as possible to make the estimate of treatment effect given the PS-mixed model as close as to the true treatment effect. The proposed PS-mixed model was successfully applied to the non-compliance problem encountered in the RCT while incomplete follow-up outcome is not available and also in the observational studies when the two treatment groups have the imbalance of baseline characteristics.