Sample size planning of two‐arm superiority and noninferiority survival studies with discrete follow‐up

In clinical trials using lifetime as primary outcome variable, it is more the rule than the exception that even for patients who are failing in the course of the study, survival time does not become known exactly since follow‐up takes place according to a restricted schedule with fixed, possibly long intervals between successive visits. In practice, the discreteness of the data obtained under such circumstances is plainly ignored both in data analysis and in sample size planning of survival time studies. As a framework for analyzing the impact of making no difference between continuous and discrete recording of failure times, we use a scenario in which the partially observed times are assigned to the points of the grid of inspection times in the natural way. Evaluating the treatment effect in a two‐arm trial fitting into this framework by means of ordinary methods based on Cox's relative risk model is shown to produce biased estimates and/or confidence bounds whose actual coverage exhibits marked discrepancies from the nominal confidence level. Not surprisingly, the amount of these distorting effects turns out to be the larger the coarser the grid of inspection times has been chosen. As a promising approach to correctly analyzing and planning studies generating discretely recorded failure times, we use large‐sample likelihood theory for parametric models accommodating the key features of the scenario under consideration. The main result is an easily implementable representation of the expected information and hence of the asymptotic covariance matrix of the maximum likelihood estimators of all parameters contained in such a model. In two real examples of large‐scale clinical trials, sample size calculation based on this result is contrasted with the traditional approach, which consists of applying the usual methods for exactly observed failure times. Copyright © 2017 John Wiley & Sons, Ltd.     

A general approach for sample size calculation for the three‐arm ‘gold standard’ non‐inferiority design

In the three‐arm ‘gold standard’ non‐inferiority design, an experimental treatment, an active reference, and a placebo are compared. This design is becoming increasingly popular, and it is, whenever feasible, recommended for use by regulatory guidelines. We provide a general method to calculate the required sample size for clinical trials performed in this design. As special cases, the situations of continuous, binary, and Poisson distributed outcomes are explored. Taking into account the correlation structure of the involved test statistics, the proposed approach leads to considerable savings in sample size as compared with application of ad hoc methods for all three scale levels. Furthermore, optimal sample size allocation ratios are determined that result in markedly smaller total sample sizes as compared with equal assignment. As optimal allocation makes the active treatment groups larger than the placebo group, implementation of the proposed approach is also desirable from an ethical viewpoint. Copyright © 2012 John Wiley & Sons, Ltd.     

Optimal auxiliary‐covariate‐based two‐phase sampling design for semiparametric efficient estimation of a mean or mean difference,with application to clinical trials

To address the objective in a clinical trial to estimate the mean or mean difference of an expensive endpoint Y, one approach employs a two‐phase sampling design, wherein inexpensive auxiliary variables W predictive of Y are measured in everyone, Y is measured in a random sample, and the semiparametric efficient estimator is applied. This approach is made efficient by specifying the phase two selection probabilities as optimal functions of the auxiliary variables and measurement costs. While this approach is familiar to survey samplers, it apparently has seldom been used in clinical trials, and several novel results practicable for clinical trials are developed. We perform simulations to identify settings where the optimal approach significantly improves efficiency compared to approaches in current practice. We provide proofs and R code. The optimality results are developed to design an HIV vaccine trial, with objective to compare the mean ‘importance‐weighted’ breadth (Y) of the T‐cell response between randomized vaccine groups. The trial collects an auxiliary response (W) highly predictive of Y and measures Y in the optimal subset. We show that the optimal design‐estimation approach can confer anywhere between absent and large efficiency gain (up to 24 % in the examples) compared to the approach with the same efficient estimator but simple random sampling, where greater variability in the cost‐standardized conditional variance of Y given W yields greater efficiency gains. Accurate estimation of E[Y | W] is important for realizing the efficiency gain, which is aided by an ample phase two sample and by using a robust fitting method. Copyright © 2013 John Wiley & Sons, Ltd.     

Two-sample density-based empirical likelihood ratio tests based on paired data, with application to a treatment study of attention-deficit/hyperactivity disorder and severe mood dysregulation

It is a common practice to conduct medical trials to compare a new therapy with a standard-of-care based on paired data consisted of pre- and post-treatment measurements. In such cases, a great interest often lies in identifying treatment effects within each therapy group and detecting a between-group difference. In this article, we propose exact nonparametric tests for composite hypotheses related to treatment effects to provide efficient tools that compare study groups utilizing paired data. When correctly specified, parametric likelihood ratios can be applied, in an optimal manner, to detect a difference in distributions of two samples based on paired data. The recent statistical literature introduces density-based empirical likelihood methods to derive efficient nonparametric tests that approximate most powerful Neyman-Pearson decision rules. We adapt and extend these methods to deal with various testing scenarios involved in the two-sample comparisons based on paired data. We show that the proposed procedures outperform classical approaches. An extensive Monte Carlo study confirms that the proposed approach is powerful and can be easily applied to a variety of testing problems in practice. The proposed technique is applied for comparing two therapy strategies to treat children's attention deficit/hyperactivity disorder and severe mood dysregulation.