Correcting for non‐compliance of repeated binary outcomes in randomized clinical trials: randomized analysis approach

Abstract

We develop the randomized analysis for repeated binary outcomes with non-compliance. A break randomization-based semi-parametric estimation procedure for both the causal risk difference and the causal risk ratio is proposed for repeated binary data. Although we assume the simple structural models for potential outcomes, we choose to avoid making any assumptions about comparability beyond those implied by randomization at time zero. The proposed methods can incorporate non-compliance information, while preserving the validity of the test of the null hypothesis, and even in the presence of non-random non-compliance can give the estimate of the causal effect that treatment would have if all individuals complied with their assigned treatment. The methods are applied to data from a randomized clinical trial for reduction of febrile neutropenia events among acute myeloid leukaemia patients, in which a prophylactic use of macrophage colony-stimulating factor (M-CSF) was compared to placebo during the courses of intensive chemotherapies.

Interval estimation of the risk difference in non‐compliance randomized trials with repeated binary measurements

“…, J ), the patient would receive the assigned treatment if he/she accepted, or receive the other, otherwise. As considered by Sato [11] and Matsuyama [14], we focus our discussion on the situation in which each patient will receive exactly one of the two treatments under comparison at each time point. When patients drop out due to declining either treatment, we can regard the observations on these patients as missing values.…”

“…Similarly, let Z i jg denote the random variable of received treatment status for the corresponding patient, and Z i jg = 1 if patient i at time point j assigned to treatment g actually received the experimental treatment, and = 0, otherwise. As assumed elsewhere [10,11,14], we assume that the probability P(Y i jg = 1|Z i jg ) = p i jg + Z i jg , where p i jg denotes the basic probability of positive response when patient i is assumed to receive the placebo; and represents the excess effect due to the experimental treatment over the placebo. In other words, patient i would have the probability p i jg + of positive response at time point j if he/she took the experimental treatment, or the probability p i jg of positive response if he/she took the placebo.…”

“…In a double-blind RCT, neither physicians nor patients know what the treatment a patient actually receives. Thus, the SUTVA and exclusion restriction assumption are generally plausible [11,14]. Since we randomly assign patients to receive one of the two treatments, the expectations of positive response for patients when they are all assumed to receive the placebo between two comparison groups are equal (i.e.…”

“…Based on the above model assumptions, the underlying characteristics of a patient can have the direct effect on the probability of response at time point j through the parameter p i jg and the indirect effect through his/her previous response on selecting the treatment, which in turn affects his/her probability of response at time point j. Furthermore, we make the stable unit treatment value assumption (SUTVA) and the exclusion restriction assumption [11,12,14]. The former is to assume that the response of a given patient is unrelated to the received treatment status of other patients, and the latter is to assume that the response is not directly affected by the treatment assigned, but rather by the treatment actually received.…”

Five Interval Estimators for Proportion Ratio under a Stratified Randomized Clinical Trial with Noncompliance

“…Similarly, let Z igk denote the random variable of treatment status, and Z igk ¼ 1 if patient i assigned to treatment g in stratum k actually received the experimental treatment (g ¼ 1), and ¼ 0, otherwise. Based on the simple multiplicative risk model suggested elsewhere (Sato, 2001;Matsuyama, 2002), we assume that the conditional probability of positive response for a given patient i assigned to treatment g in stratum k with the treatment status Z igk is given by…”