Adaptative Designs for Multi-Arm Clinical Trials: The Play-the-Winner Rule Revisited

Adaptative designs for clinical trials that are based on a generalization of the “play-the-winner” rule are considered as an alternative to previously developed models. Theoretical and numerical results show that these designs perform better for the usual criteria. Bayesian methods are proposed for the statistical analysis of these designs.     

On the Evaluation of the Kolmogorov Statistic

At least two computer program packages, SPSS and STRATA, use simulated Bernoulli trials to draw (without replacement) a random sample of records from a finite population of records. Therefore, the size of the sample is a random variable. Two estimators of a population total under this sampling procedure are compared with the usual estimator under simple random sampling. Conditions under which the Bernoulli sampling estimators have almost the same mean squared error as the simple random-sample estimator are illustrated.     

The Multicenter Clinical Trials Coordinating Center Statistician: “More than a Consultant”

Over the past several decades the employment of statisticians in the area of medical clinical trials in private industry, academic centers, and the federal government has increased significantly. This trend does not appear to be slowing, particularly in those organizations that have come to be termed coordinating centers. In this article we will describe the expanded role that statisticians employed in these centers are expected to be able to fill.     

Deriving Approximations in a Random Effects Model for Multicenter Clinical Trials with Binary Response

The design and analysis of multicenter trials based on a random effects model is well developed for a continuous response, but is less well developed for a binary response. Here we describe a random effects model for a binary response for two treatments and show how maximum likelihood estimates for the unknown treatment difference can be derived using a novel approximation to the likelihood. The suggested approximation is easy to use and seems to be better suited to the problem than the Laplace approximation and the approximation based on adaptive Gaussian quadratures. We also derive an approximation for the Fisher information matrix of the treatment parameters. The results extend those previously reviewed by Agresti and Hartzel (2000 Agresti , A. , Hartzel , J. ( 2000 ). Strategies for comparing treatments on a binary response with multi-centre data . Statist. Med. 19 : 1115 – 1139 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]).     

The Minimaxity of the Mid P-value under Linear and Squared Loss Functions

The mid-p is defined as the sum of the probabilities of all outcomes more extreme than an observed value, plus half of the probabilities of all outcomes exactly as extreme. On the one hand, it offers greater power than the standard p-value, but on the other, tests based on the mid-p statistic may have greater Type I error than their nominal level. This article investigates the mid p-value's properties under the estimated truth paradigm, which views p-values as estimators of the truth. The mid-p is shown to minimize the maximum risk for one-sided and two-sided tests.     

Bayesian Analysis of Randomized Response Sum Score Variables

The randomized-response (RR) technique is an effective survey method when collecting sensitive information. In this technique, a probability mechanism using randomization devices is commonly involved in answering to sensitive questions. In order to evaluate the survey at the most accurate extend, self-protection (SP) is introduced to describe the responses by participants who give the evasive answer without taking the result of the randomization device into account. In this study, we propose a Bayesian approach to modeling RR sum score variables under SP assumption. RR data from a Dutch survey on non-compliance with social security regulation in 2004 is used to demonstrate the proposed models.     

A stratified Tracy and Osahan's two-stage randomized response model

ABSTRACT

This paper proposes an alternative two-stage stratified randomized response model based on Tracy and Osahan (1999 Tracy, D.S., Osahan, S.S. (1999). An improved randomized response technique. Pak. J. Stat. 15(1):1–6. [Google Scholar]) model that has an optimal allocation and large gain in precision. It is also shown that the proposed model is more efficient than Kim and Warde (2004 Kim, J., Warde, W. (2004). A stratified Warner randomized response model. J. Stat. Plan. Infer. 120:155–165.[Crossref], [Web of Science ®] , [Google Scholar]) and Kim and Elam (2005 Kim, J.M., Elam, M.E. (2005). A two-stage stratified Warner's randomized response model using optimal allocation. Metrika 61:1–7.[Crossref], [Web of Science ®] , [Google Scholar]) stratified randomized response models under the conditions presented in both the cases of completely truthful reporting and that of not completely truthful reporting by the respondents. Numerical illustrations and graphs are also given in support of the present study.     

Comparison among non parametric prediction intervals of order statistics

Abstract

In this article, we are interested in conducting a comparison study between different non parametric prediction intervals of order statistics from a future sample based on an observed order statistics. Typically, coverage probabilities of well-known non parametric prediction intervals may not reach the preassigned probability levels. Moreover, prediction intervals for predicting future order statistics are no longer available in some cases. For this, we propose different methods involving random indices and fractional order statistics. In each case, we find the optimal prediction intervals. Numerical computations are presented to assess the performances of the so-obtained intervals. Finally, a real-life data set is presented and analyzed for illustrative purposes.     

Improved strategy to collect sensitive data by using geometric distribution as a randomization device

Abstract

In this article, we improvise Singh and Grewal (2013 Singh, S., and I. S. Grewal. 2013. Geometric distribution as a randomization device implemented in the Kuk’s model. International Journal of Contemporary Mathematical Sciences 8:243–8.[Crossref] , [Google Scholar]) and Hussain et al. (2016 Hussain, Z., J. Shabbir, Z. Pervez, S. F. Shah, and M. Khan. 2016. Generalized geometric distribution of order k: A flexible choice to randomize the response. Communications in Statistics: Simulation and Computation 46:4708–21.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) techniques by introducing a new two-stage randomization response process. Using the proposed new technique, we achieve better efficiency and increasing protection of privacy of respondents than the Kuk (1990 Kuk, A. Y. C. 1990. Asking sensitive questions indirectly. Biometrika 77 (2):436–8.[Crossref], [Web of Science ®] , [Google Scholar]), Singh and Grewal (2013 Singh, S., and I. S. Grewal. 2013. Geometric distribution as a randomization device implemented in the Kuk’s model. International Journal of Contemporary Mathematical Sciences 8:243–8.[Crossref] , [Google Scholar]) and Hussain et al. (2016 Hussain, Z., J. Shabbir, Z. Pervez, S. F. Shah, and M. Khan. 2016. Generalized geometric distribution of order k: A flexible choice to randomize the response. Communications in Statistics: Simulation and Computation 46:4708–21.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) models. The relative efficiency and protection of the respondents of the proposed two-stage randomization device have been investigated through simulation study, and the situations are reported where the proposed estimator performs better than its competitors. The SAS code used to investigate the performance of the proposed strategy are also provided.     

Analyzing survival data in conjunction with time-dependent surrogate endpoints in clinical trials

Current survival techniques do not provide a good method for handling clinical trials with a large percent of censored observations. This research proposes using time-dependent surrogates of survival as outcome variables, in conjunction with observed survival time, to improve the precision in comparing the relative effects of two treatments on the distribution of survival time. This is in contrast to the standard method used today which uses the marginal density of survival time, T. only, or the marginal density of a surrogate, X, only, therefore, ignoring some available information. The surrogate measure, X, may be a fixed value or a time-dependent variable, X(t). X is a summary measure of some of the covariates measured throughout the trial that provide additional information on a subject's survival time. It is possible to model these time-dependent covariate values and relate the parameters in the model to the parameters in the distribution of T given X. The result is that three new models are available for the analysis of clinical trials. All three models use the joint density of survival time and a surrogate measure. Given one of three different assumed mechanisms of the potential treatment effect, each of the three methods improves the precision of the treatment estimate.