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Authors' reply: Letter to the Editor: Preference option randomized design (PORD) for comparative effectiveness research: Statistical power for testing comparative effect, preference effect, selection effect, intent-to-treat effect, and overall effect (SMMR, Vol. 28, Issue 2, 2019).

We appreciate Dr. Walter and his colleagues’ pointing out a limitation concerning (A2) assumption. In short, we adopted the A2 assumption because in preference option randomized design (PORD), there are no participants who prefer treatment B in AS (even though there are participants who prefer treatment B in RA, that is BA), or those who prefer treatment A in BS (even though there are participants who prefer treatment A in RB, that is AB). In theory, however, it might have been more reasonable to assume that P(AAjAS)1⁄4P(ABjBR[AB)1⁄4P(ABjRB)/ (1 P(BBjRB))1⁄4P(ABjRB)/(1 P(BAjRA)), this equation holding by a strict NSBR (no selection bias from randomization) assumption, and likewise P(BBjBS)1⁄4P(BAjRA)/(1 P(ABjRB)). However, these assumptions are restricted by the following conditions: P(ABjRB) 1 P(BAjRA)1⁄4P(ASjRA) and P(BAjRA) 1 P(ABjRB)1⁄4 P(BSjRA) so that P(AAjAS) 1 and P(BBjBS) 1. Therefore, the A2 assumption, albeit limited, might be necessary so that such a restriction can be avoided. Although Walter and his colleagues asserted in their letter that ‘‘. . . a valid analysis for this type of study is already available’’ and ‘‘. . . applies to the PORD design in particular,’’ we find that their approach based on post hoc preference analyses of parallel randomized trials is invalid by implicitly assuming that marginal or global probabilities are the same as conditional probabilities on treatment arms. Furthermore, their approach does not have anything to do with power analysis of preference trials. Specifically, their Table 1 (Box 1) classified study subjects into five mutually exclusive and exhaustive groups, and they assigned probabilities p1 to p5 to Groups 1 to 5, respectively. The probabilities p1 to p5 are all marginal or global probabilities, but not conditional probabilities on treatment arms, so that the sum of p1 to p5 is one, that is