Lower Confidence Limits on the Generalized Exponential Distribution Percentiles Under Progressive Type-I Interval Censoring

In industrial life test and survival analysis, the percentile estimation is always a practical issue with lower confidence bound required for maintenance purpose. Sampling distributions for the maximum likelihood estimators of percentiles are usually unknown. Bootstrap procedures are common ways to estimate the unknown sampling distributions. Five parametric bootstrap procedures are proposed to estimate the confidence lower bounds on maximum likelihood estimators for the generalized exponential (GE) distribution percentiles under progressive type-I interval censoring. An intensive simulation is conducted to evaluate the performances of proposed procedures. Finally, an example of 112 patients with plasma cell myeloma is given for illustration.     

Robustness of the shrinkage estimator for the relative potency in the combination of multivariate bioassays

ABSTRACT

This article investigates the robustness of the shrinkage Bayesian estimator for the relative potency parameter in the combinations of multivariate bioassays proposed in Chen et al. (1999 Chen, D.G., Carter, E.M., Hubert, J.J., Kim, P.T. (1999). Empirical Bayesian estimation for combinations of multivariate bioassays. Biometrics 55(4):1035–1043. [Google Scholar]), which incorporated prior information on the model parameters based on Jeffreys’ rules. This investigation is carried out for the families of t-distribution and Cauchy-distribution based on the characteristics of bioassay theory since the t-distribution approaches the normal distribution which is the most commonly used distribution in the applications of bioassay as the degrees of freedom increases and the t-distribution approaches the Cauchy-distribution as the degrees of freedom approaches 1 which is also an important distribution in bioassay. A real data is used to illustrate the application of this investigation. This analysis further supports the application of the shrinkage Bayesian estimator to the theory of bioassay along with the empirical Bayesian estimator.     

From statistical power to statistical assurance: It's time for a paradigm change in clinical trial design

A well-designed clinical trial requires an appropriate sample size with adequate statistical power to address trial objectives. The statistical power is traditionally defined as the probability of rejecting the null hypothesis with a pre-specified true clinical treatment effect. This power is a conditional probability conditioned on the true but actually unknown effect. In practice, however, this true effect is never a fixed value. Thus, we discuss a newly proposed alternative to this conventional statistical power: statistical assurance, defined as the unconditional probability of rejecting the null hypothesis. This kind of assurance can then be obtained as an expected power where the expectation is based on the prior probability distribution of the unknown treatment effect, which leads to the Bayesian paradigm. In this article, we outline the transition from conventional statistical power to the newly developed assurance and discuss the computations of assurance using Monte Carlo simulation-based approach.     

Weighted Multiple Testing Correction for Correlated Binary Endpoints

Multiple binary endpoints often occur in clinical trials and are usually correlated. Many multiple testing adjustment methods have been proposed to control familywise type I error rates. However, most of them disregard the correlation among the endpoints, for example, the commonly used Bonferroni correction, Bonferroni fixed-sequence (BFS) procedure, and its extension, the alpha-exhaustive fallback (AEF). Extending BFS by taking into account correlations among endpoints, Huque and Alosh proposed a flexible fixed-sequence (FFS) testing method, but this FFS method faces computational difficulty when there are four or more endpoints and the power of the first hypothesis does not depend on the correlations among endpoints. In dealing with these issues, Xie proposed a weighted multiple testing correction (WMTC) for correlated continuous endpoints and showed that the proposed method can easily handle hundreds of endpoints by using the R package and has higher power for testing the first hypothesis compared with the FFS and AEF methods. Since WMTC depends on the joint distribution of the endpoints, it is not clear whether WMTC still keeps those advantages when correlated binary endpoints are used. In this article, we evaluated the statistical power of WMTC method for correlated binary endpoints in comparison with the FFS, the AEF, the prospective alpha allocation scheme (PAAS), and the weighted Holm-Bonferroni methods. Furthermore the WMTC method and others are illustrated on a real dataset examining the circumstance of homicide in New York City.