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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.

Positivity of anti-thyroglobulin antibody (TgAb) is one of the markers of chronic thyroiditis (Hashimoto disease). From 2000 to 2003, a thyroid disease prevalence study was conducted at the Radiation Effects Research Foundation, in Hiroshima and Nagasaki. Utilizing the study's results, we show that via EM algorithm log-transformed TgAb level is compatible with a two-component mixture normal distribution, with the smaller normal distribution corresponding to the TgAb negative group but the larger distribution not necessarily corresponding to the TgAb positive group. A subject is determined to be TgAb positive if TgAb level is greater than a given cutoff. We compared the cutoff values from population-based methods and the laboratory method. The population-based methods consist of a simple method, a receiver operating characteristic (ROC) curve method, and a minimum misclassification rate (MMR) method. The simple method is used to determine positivity from only TgAb negative populations. Since the ROC curve and MMR methods are valid only when TgAb positivity and negativity are known but the simple method is valid only when TgAb negativity is known, the simple method was deemed useful for determining the cutoff in our data. In comparison with the simple, population-based method, we show that the cutoff from the laboratory method is appropriate and that the TgAb positive rates from various methods are approximately equal. With the two-component mixture normal distribution in TgAb level, our simple population-based method for determination of cutoff is another more practical example of handling the clinical measurement than the method given in Thompson et al. (Applied Statistics 1998).

In epidemiological studies there are numerous challenges to finding an appropriate experimental design for studying the relationship between an exposure and a disease. A number of designs for observational studies have been investigated; the cohort study and the standard case-control study are the primary types. The nested case-control study design combines features of both. In the nested case-control study some information is available for all cohort members and additional information is obtained using a case-control design based on incidence density sampling rather than cumulative prevalence sampling. To get higher efficiency, it is important to effectively use the information already available on cohort members when we choose the controls. The counter-matched design is one such method, which chooses the controls based on exposure status or a surrogate measure of the exposure. It has high efficiency to estimate the effect of the exposure or interaction between the exposure and another risk factor. Unfortunately, there are few examples of application of this design to real situations. To encourage use of the counter-matched design, we describe the basic concept and statistical methods underlying the method. Some examples are presented to illustrate how to implement the design. We also propose some extensions to provide a more flexible sampling design.