Matched case-control design is a type of stratification for the control of confounding at the design stage. One of basic premises is a 1:M matched case-control study, where each case is matched with one or multiple controls on a number of variables. The goal is to test the equality of K odds ratios stemming from K+1 distinct matching scenarios. In the literature, conditional likelihood approach is used for calculating sample size for detecting specific departures from the null hypothesis of no association with a given power (See Sinha and Mukherjee 2006). In this research proposal, we use the full likelihood for calculating sample sizes. Comparisons are made between the two approaches.
The second study proposed is the calculation of sample sizes to detect departures from the null hypothesis of no association with a given power in unmatched case-control studies when an unknown number of controls are cases. The focus is on 2×2 case-control unmatched studies, in which the cases (those with the disease) are genuine but the controls may contain patients with disease due to misclassification in disease screening. We systemically examine the effect of such contamination on odds ratio and data analysis. We will provide sample size formulas using two different procedures by taking into account the contamination ratio, one procedure is by testing equivalence of two sample proportions and the other using log odds ratio test. The misclassification problem arose when planning a study to identify factors causing sleep apnea.