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

Abstract

In a randomized clinical trial (RCT), we often encounter non-compliance with the treatment protocol for a subset of patients. The intention-to-treat (ITT) analysis is probably the most commonly used method in a RCT with non-compliance. However, the ITT analysis estimates 'the programmatic effectiveness' rather than 'the biological efficacy'. In this paper, we focus attention on the latter index and consider use of the risk difference (RD) to measure the effect of a treatment. Based on a simple additive risk model proposed elsewhere, we develop four asymptotic interval estimators of the RD for repeated binary measurements in a RCT with non-compliance. We apply Monte Carlo simulation to evaluate and compare the finite-sample performance of these interval estimators in a variety of situations. We find that all interval estimators considered here can perform well with respect to the coverage probability. We further find that the interval estimator using a tanh(-1)(x) transformation is probably more precise than the others, while the interval estimator derived from a randomization-based approach may cause a slight loss of precision. When the number of patients per treatment is large and the probability of compliance to an assigned treatment is high, we find that all interval estimators discussed here are essentially equivalent. Finally, we illustrate use of these interval estimators with data simulated from a trial of using macrophage colony-stimulating factor to reduce febrile neutropenia incidence in acute myeloid leukaemia patients.

Five Interval Estimators of the Risk Difference Under Stratified Randomized Clinical Trials with Noncompliance and Repeated Measurements

“…Note also thatˆ C k in equation (3) is an extension of the instrumental variable estimator (Angrist et al, 1996) to accommodate repeated binary measurements (Sato, 2001). Using the delta method, we can show that an asymptotic variance ofˆ C k in equation (3) is given by (Lui, 2007a)…”

“…Note that the risk difference (RD) C k actually represents the complier average causal effect (CACE) in stratum k under model (1). For a given single stratum k, model (1) includes the constant risk additive model assumed elsewhere (Sato, 2000(Sato, , 2001Matsuyama, 2002;Lui, 2007a) as a special case when C k = A k = N k . Because patients are randomly assigned to one of two treatments within each stratum k, the expected number of positive responses over J k time points for a randomly selected patient i from the assigned experimental treatment and that for a randomly selected patient i from the assigned standard treatment (or placebo) will be expected to equal each other in a given stratum k if all participated patients are assumed to receive the standard treatment (or placebo); that is, E p…”

“…However, these papers generally focused attention on the situation in which there were no confounders, and the discussions on estimation of treatment effect under stratified analysis were limited. Furthermore, because compliers and noncompliers to a treatment can have quite different prognostic conditions, the constant risk models, which assume the same treatment effect on compliers and noncompliers considered elsewhere (Sato, 2001;Matsuyama, 2002;Lui, 2007aLui, , 2008a, are likely too restricted and debatable (Lui, 2007b(Lui, , 2011.…”

“…An analysis by simply pooling data together for all patients with varying health conditions from trials can lead us to obtain a possibly biased conclusion. Based on constant risk models, a few recent publications (Sato, 2001;Matsuyama, 2002;Lui, 2007aLui, , 2008a discussed estimation of treatment effect in repeated binary data for an RCT with noncompliance. However, these papers generally focused attention on the situation in which there were no confounders, and the discussions on estimation of treatment effect under stratified analysis were limited.…”

“…Three courses of intensive and different combinations of chemotherapies were planned after one or two courses of the remission induction chemotherapy (Ohno et al, 1997). Thus, statistical methods for analyzing such a kind of repeated binary measurements for an RCT with noncompliance should be of practical use and interest (Sato, 2001;Matsuyama, 2002;Lui, 2007aLui, , 2008a.…”