Power Calculation for Likelihood Ratio Tests in the Nested Case-control Designs with a Randomly Sampled Control Per Case

Abstract

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.