This paper presents an asymptotic method of power calculations for likelihood ratio tests in the nested case-control designs with a randomly sampled control per case. It is an extension of the approach described in Self et al. (1992) for proportional hazards models. Our approach here focuses on a simple scenario with 1 : 1 case-control ratio, simple random sampling design, and two independent dichotomous covariates with no interaction effects. The approximation of the noncentrality of the noncentral chi-square distribution for the likelihood ratio statistic is provided. Simulation studies are conducted to examine the accuracy for several parameter values and data configurations. Overall the results suggest that estimates of power using our proposed method are consistent with those of actual power from Monte Carlo simulation. Therefore, the proposed approach can be practically useful in assessing the statistical power for the simple nested case-control design.
Ranking significant genes based on the P-value in multiple testing is a simple and common practice in microarray data analysis, and its theoretical optimality is of particular interest. McLachlan et al. (Bioinformatics 2006; 22: 1608-1615) presented a method for calculating the local FDR under normal mixture models and provided a theoretical optimality of the local FDR as a ranking statistic. In this article, we show that the optimal gene ranking based on the local FDR calculated by the McLachlan et al.'s method perfectly accords with that based on P-value under certain conditions. We argue that these conditions are generally satisfied for significant genes with small P-values. We demonstrate it using several real examples.
Surrogate endpoints, which represent a compromise in the conflict between measurability and clinical relevance of endpoints, have considerable advantage in rapid drug approvals compared to true endpoints in confirmatory clinical trials dealing with life-threatening diseases, such as cancer or AIDS. However, past experiences have shown the risk of relying too heavily on surrogate endpoints. In this paper, we review statistical criteria for evaluating surrogate endpoints and the past examples properly evaluated the surrogacy, taking into consideration relevant clinical and statistical issues.