Principal stratification: All-or-none versus partial compliance

Abstract

I would like to add another perspective to that in Shrier et al [1] on the application of principal stratification [2] to all-or-none versus partial compliance. With all-or-none compliance in randomized trials [3] or all-or-none changes in availability in the paired availability design [4, 5], the assumptions needed for identifiability of the principal stratification model are often reasonable. Consider a binary outcome and suppose participants are randomized to either group 0 (assigned T0) or group 1 (assigned T1). The principal strata partition participants into pairs defined by (treatment received if in group 0, treatment received if in group 1), namely (T0,T0), (T0,T1), (T1,T0), and (T1,T1). Assuming rational decision making so no (T1,T0), persons receiving T0 in group 0 are a mixture of (T0,T0) and (T0,T1); persons receiving T1 in group 0 are (T1,T1); persons receiving T0 in group 1 are (T0,T0); and persons receiving T1 in group 1 are a mixture of (T0,T1) and (T1,T1). With the additional assumption that probabilities of outcome not depend on group for (T0, T0) and (T1, T1), one can estimate the effect of receipt of T0 versus T1 (treatment efficacy) in the principal stratum (T0,T1) for compliers, a result which can be elucidated graphically [5, 6]. In essence, this estimation peels away the irrelevant (T0,T0) and (T1,T1) strata [7] to obtain a more informative estimate of treatment efficacy (if the assumptions hold) than an intent-to-treat estimate. This identifiability of treatment efficacy in principal stratification under all-or-none compliance extends to missing binary outcomes [7, 8] and survival outcomes [9].