Although randomized studies have high internal validity, generalizability of the estimated causal effect from randomized clinical trials to real-world clinical or educational practice may be limited. We consider the implication of randomized assignment to treatment, as compared with choice of preferred treatment as it occurs in real-world conditions. Compliance, engagement, or motivation may be better with a preferred treatment, and this can complicate the generalizability of results from randomized trials. The doubly randomized preference trial (DRPT) is a hybrid randomized and nonrandomized design that allows for estimation of the causal effect of randomization versus treatment preference. In the DRPT, individuals are first randomized to either randomized assignment or choice assignment. Those in the randomized assignment group are then randomized to treatment or control, and those in the choice group receive their preference of treatment versus control. Using the potential outcomes framework, we apply the algebra of conditional independence to show how the DRPT can be used to derive an unbiased estimate of the causal effect of randomization versus preference for each of the treatment and comparison conditions. Also, we show how these results can be implemented using full matching on the propensity score. The methodology is illustrated with a DRPT of introductory psychology students who were randomized to randomized assignment or preference of mathematics versus vocabulary training. We found a small to moderate benefit of preference versus randomization with respect to the mathematics outcome for those who received mathematics training.
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