While the two-stage randomized design allows us to unbiasedly evaluate the impact of patients' treatment preference on the outcome of interest, it may not always be practical to implement in clinical practice; patients with a strong preference may not be willing to be randomized. The more pragmatic, partially randomized preference design (PRPD) allows patients who are unwilling to be randomized, but willing to state their preference, to receive their preferred treatment in lieu of the first-stage randomization in the two-stage design, at the cost of potentially introducing bias in estimating the effects of interest. In this article, we consider the application of propensity score stratification (PSS) in a PRPD to recreate a conditional first-stage randomization based on observed covariates, enabling the estimation and inference of the overall treatment, selection and preference effects with minimum bias. We additionally derive a set of closed-form sample size formulas for detecting all three effects of interest in a PSS-PRPD. Simulation studies demonstrate the bias reduction properties of the PSS-PRPD, and validate the accuracy of the proposed sample size formulas. Our results show that 5 to 10 propensity score strata may be needed to correct for biases in effect estimates, and the exact number of strata needed to achieve the best match between the empirical power and formula prediction may depend on the degree of effect heterogeneity. Finally, we demonstrate our proposed formulas by estimating the required sample sizes to detect treatment, selection and preference effects in the context of the Harapan Study.
Keywords: Patient preference; partially randomized preference design; power; propensity score; sample size; stratified design.