Adjusting for bias in randomized cluster trials

The randomized cluster design is typical in studies where the unit of randomization is a cluster of individuals rather than the individual. Evaluating various intervention strategies across medical care providers at either an institutional level or at a physician group practice level fits the randomized cluster model. Clearly, the analytical approach to such studies must take the unit of randomization and accompanying intraclass correlation into consideration. We review alternative methods to the typical Pearson's chi-square analysis and illustrate these alternatives. We have written and tested a Fortran program that produces the statistics outlined in this paper. The program, in an executable format is available from the author on request.     

Covariate adjustment for randomized controlled trials revisited

Covariate adjustment for the estimation of treatment effect for randomized controlled trials (RCT) is a simple approach with a long history, hence, its pros and cons have been well‐investigated and published in the literature. It is worthwhile to revisit this topic since recently there has been significant investigation and development on model assumptions, robustness to model mis‐specification, in particular, regarding the Neyman‐Rubin model and the average treatment effect estimand. This paper discusses key results of the investigation and development and their practical implication on pharmaceutical statistics. Accordingly, we recommend that appropriate covariate adjustment should be more widely used for RCTs for both hypothesis testing and estimation.     

Median treatment effect in randomized trials

For two response variables y _t and y _c corresponding to two treatments for two policies) T and C , we wish to learn about quantiles of y _t− y _c from the marginal quantiles of y _t and y _c; only one of y _t and y _c is observed for an individual. We find that, in general, this is difficult for quantiles other than the median unless strong assumptions are imposed on how y _t is related to y _c. For the median, we present conditions under which the sign of the median treatment effect is identified.     

An analytic method for randomized trials with informative censoring: Part 1

Consider a randomized trial in which time to the occurrence of a particular disease, say pneumocystis pneumonia in an AIDS trial or breast cancer in a mammographic screening trial, is the failure time of primary interest. Suppose that time to disease is subject to informative censoring by the minimum of time to death, loss to and end of follow-up. In such a trial, the censoring time is observed for all study subjects, including failures. In the presence of informative censoring, it is not possible to consistently estimate the effect of treatment on time to disease without imposing additional non-identifiable assumptions. The goals of this paper are to specify two non-identifiable assumptions that allow one to test for and estimate an effect of treatment on time to disease in the presence of informative censoring. In a companion paper (Robins, 1995), we provide consistent and reasonably efficient semiparametric estimators for the treatment effect under these assumptions. In this paper we largely restrict attention to testing. We propose tests that, like standard weighted-log-rank tests, are asymptotically distribution-free -level tests under the null hypothesis of no causal effect of treatment on time to disease whenever the censoring and failure distributions are conditionally independent given treatment arm. However, our tests remain asymptotically distribution-free -level tests in the presence of informative censoring provided either of our assumptions are true. In contrast, a weighted log-rank test will be an -level test in the presence of informative censoring only if (1) one of our two non-identifiable assumptions hold, and (2) the distribution of time to censoring is the same in the two treatment arms. We also extend our methods to studies of the effect of a treatment on the evolution over time of the mean of a repeated measures outcome, such as CD-4 count.     

An analytic method for randomized trials with informative censoring: Part II

Consider a randomized trial in which time to the occurrence of a particular disease, say pneumocystic pneumonia in an AIDS trial or breast cancer in a mammographic screening trial, is the failure time of primary interest. Suppose that time to disease is subject to informative censoring by the minimum of time to death, loss to and end of follow-up. In such a trial, the potential censoring time is observed for all study subjects, including failures. In the presence of informative censoring, it is not possible to consistently estimate the effect of treatment on time to disease without imposing additional non-identifiable assumptions. Robins (1995) specified two non-identifiable assumptions that allow one to test for and estimate an effect of treatment on time to disease in the presence of informative censoring. The goal of this paper is to provide a class of consistent and reasonably efficient semiparametric tests and estimators for the treatment effect under these assumptions. The tests in our class, like standard weighted-log-rank tests, are asymptotically distribution-free -level tests under the null hypothesis of no causal effect of treatment on time to disease whenever the censoring and failure distributions are conditionally independent given treatment arm. However, our tests remain asymptotically distribution-free -level tests in the presence of informative censoring provided either of our assumptions are true. In contrast, a weighted log-rank test will be an -level test in the presence of informative censoring only if (1) one of our two non-identifiable assumptions hold, and (2) the distribution of time to censoring is the same in the two treatment arms. We also study the estimation, in the presence of informative censoring, of the effect of treatment on the evolution over time of the mean of repeated measures outcome such as CD4 count.     

Correcting for non-compliance in randomized trials using structural nested mean models

In a randomized trial designed to study the effect of a treatment of interest on the evolution of the mean of a time-dependent outcome variable, subjects are assigned to a treatment regime, or, equivalently, a treatment protocol. Unfortunately, subjects often fail to comply with their assigned regime. From a public health point of view, the causal parameter of interest will often be a function of the treatment differences that would have been observed hadcontrary to fact, all subjects remained on protocol. This paper considers the identification and estimation of these treatment differences based on a new class of structural models, the multivariate structural nested mean models, when reliable estimates of each subject's actual treatment are available. Estimates of “actual treatment” might, for example, be obtained by measuring the amount of “active drug” in the subject's blood or urine at each follow-up visit or by pill counting techniques. In addition, we discuss a natural extension of our methods to observational studies.     

SPIRIT: A seamless phase I/II randomized design for immunotherapy trials

Immunotherapy—treatments that enlist the immune system to battle tumors—has received widespread attention in cancer research. Due to its unique features and mechanisms for treating cancer, immunotherapy requires novel clinical trial designs. We propose a Bayesian seamless phase I/II randomized design for immunotherapy trials (SPIRIT) to find the optimal biological dose (OBD) defined in terms of the restricted mean survival time. We jointly model progression‐free survival and the immune response. Progression‐free survival is used as the primary endpoint to determine the OBD, and the immune response is used as an ancillary endpoint to quickly screen out futile doses. Toxicity is monitored throughout the trial. The design consists of two seamlessly connected stages. The first stage identifies a set of safe doses. The second stage adaptively randomizes patients to the safe doses identified and uses their progression‐free survival and immune response to find the OBD. The simulation study shows that the SPIRIT has desirable operating characteristics and outperforms the conventional design.     

Non-parametric group sequential designs in randomized clinical trials

This paper examines some non‐parametric group sequential designs applicable for randomized clinical trials, for comparing two continuous treatment effects taking the observations in matched pairs, or applicable in event‐based analysis. Two inverse binomial sampling schemes are considered, of which the second one is an adaptive data‐dependent design. These designs are compared with some fixed sample size competitors. Power and expected sample sizes are calculated for the proposed procedures.     

The need for research into the effectiveness of international statistical systems and standards

Conclusion In this brief and highly selective examination of the adequacy of ISSS, it is suggested that statistical and economic research is essential if we are to ensure that these systems are fit for their intended purposes. It is too readily assumed that the statistical infrastructure is either adequate or, if not, of little significance in dealing with the major problems faced by the world today. This is far from being so and, if the necessary research were carried out, the results could make an invaluable contribution to resolving many of those problems.     

Analysing direct effects in randomized trials with secondary interventions: an application to human immunodeficiency virus prevention trials

Summary.  The 'Methods for improving reproductive health in Africa' trial is a recently completed randomized trial that investigated the effect of diaphragm and lubricant gel use in reducing infection by the human immunodeficiency virus (HIV) among susceptible women. 5045 women were randomly assigned to either the active treatment arm or not. Additionally, all subjects in both arms received intensive condom counselling and provision, the 'gold standard' HIV prevention barrier method. There was much lower reported use of condoms in the intervention arm than in the control arm, making it difficult to answer important public health questions based solely on the intention-to-treat analysis. We adapt an analysis technique from causal inference to estimate the 'direct effects' of assignment to the diaphragm arm, adjusting for use of condoms in an appropriate sense. Issues raised in the trial apply to other trials of HIV prevention methods, some of which are currently being conducted or designed.     

Multistate modeling of clinical hold in randomized clinical trials

A clinical hold order by the Food and Drug Administration (FDA) to the sponsor of a clinical trial is a measure to delay a proposed or to suspend an ongoing clinical investigation. The phase III clinical trial START serves as motivating data example to explore implications and potential statistical approaches for a trial continuing after a clinical hold is lifted. In spite of a modified intention‐to‐treat (ITT) analysis introduced to account for the clinical hold by excluding patients potentially affected most by the clinical hold, results of the trial did not show a significant improvement of overall survival duration, and the question remains whether the negative result was an effect of the clinical hold. In this paper, we propose a multistate model incorporating the clinical hold as well as disease progression as intermediate events to investigate the impact of the clinical hold on the treatment effect. Moreover, we consider a simple counterfactual censoring approach as alternative strategy to the modified ITT analysis to deal with a clinical hold. Using a realistic simulation study informed by the START data and with a design based on our multistate model, we show that the modified ITT analysis used in the START trial was reasonable. However, the censoring approach will be shown to have some benefits in terms of power and flexibility.     

Correcting for non-compliance in randomized trials using rank preserving structural failure time models

We propose correcting for non-compliance in randomized trials by estimating the parameters of a class of semi-parametric failure time models, the rank preserving structural failure time models, using a class of rank estimators. These models are the structural or strong version of the “accelerated failure time model with time-dependent covariates” of Cox and Oakes (1984). In this paper we develop a large sample theory for these estimators, derive the optimal estimator within this class, and briefly consider the construction of “partially adaptive” estimators whose efficiency may approach that of the optimal estimator. We show that in the absence of censoring the optimal estimator attains the semiparametric efficiency bound for the model.     

Propensity score matched augmented controls in randomized clinical trials: A case study

Existing statutes in the United States and Europe require manufacturers to demonstrate evidence of effectiveness through the conduct of adequate and well‐controlled studies to obtain marketing approval of a therapeutic product. What constitutes adequate and well‐controlled studies is usually interpreted as randomized controlled trials (RCTs). However, these trials are sometimes unfeasible because of their size, duration, cost, patient preference, or in some cases, ethical concerns. For example, RCTs may not be fully powered in rare diseases or in infections caused by multidrug resistant pathogens because of the low number of enrollable patients. In this case, data available from external controls (including historical controls and observational studies or data registries) can complement information provided by RCT. Propensity score matching methods can be used to select or “borrow” additional patients from the external controls, for maintaining a one‐to‐one randomization between the treatment arm and active control, by matching the new treatment and control units based on a set of measured covariates, ie, model‐based pairing of treatment and control units that are similar in terms of their observable pretreatment characteristics. To this end, 2 matching schemes based on propensity scores are explored and applied to a real clinical data example with the objective of using historical or external observations to augment data in a trial where the randomization is disproportionate or asymmetric.     

Likelihood methods in randomized trials with noncompliance and subsequent nonresponse

This article considers likelihood methods for estimating the causal effect of treatment assignment for a two-armed randomized trial assuming all-or-none treatment noncompliance and allowing for subsequent nonresponse. We first derive the observed data likelihood function as a closed form expression of the parameter given the observed data where both response and compliance state are treated as variables with missing values. Then we describe an iterative procedure which maximizes the observed data likelihood function directly to compute a maximum likelihood estimator (MLE) of the causal effect of treatment assignment. Closed form expressions at each iterative step are provided. Finally we compare the MLE with an alternative estimator where the probability distribution of the compliance state is estimated independent of the response and its missingness mechanism. Our work indicates that direct maximum likelihood inference is straightforward for this problem. Extensive simulation studies are provided to examine the finite sample performance of the proposed methods.     

Estimands and inference in cluster‐randomized vaccine trials

Cluster‐randomized trials are often conducted to assess vaccine effects. Defining estimands of interest before conducting a trial is integral to the alignment between a study's objectives and the data to be collected and analyzed. This paper considers estimands and estimators for overall, indirect, and total vaccine effects in trials, where clusters of individuals are randomized to vaccine or control. The scenario is considered where individuals self‐select whether to participate in the trial, and the outcome of interest is measured on all individuals in each cluster. Unlike the overall, indirect, and total effects, the direct effect of vaccination is shown in general not to be estimable without further assumptions, such as no unmeasured confounding. An illustrative example motivated by a cluster‐randomized typhoid vaccine trial is provided.     

Bayesian randomized clinical trials: A decision‐theoretic sequential design

The authors propose a Bayesian decision‐theoretic framework justifying randomization in clinical trials. Noting that the decision maker is often unable or unwilling to specify a unique utility function, they develop a sequential myopic design that includes randomization justified by the consideration of a set of utility functions. Randomization is introduced over all nondominated treatments, allowing for interim removal of treatments and early stopping. The authors illustrate their approach in the context of a study to find the optimal dose of pegylated interferon for platinum resistant ovarian cancer. They also develop an algorithm to implement their methodology in a phase II clinical trial comparing several competing experimental treatments.