Comparison of diagnostic likelihood ratios of two binary tests with case-control clustered data

The case-control design is known for its efficiency at a fixed sample size when the disease under study is rare. Such a design is usually carried out for the inference of disease odds ratio in the context of independent data. In this paper, we consider its extension to clustered data set-ups for the comparison of diagnostic likelihood ratios of two binary tests and explore its efficiency gain in estimating relative diagnostic likelihood ratio (the ratio of two diagnostic likelihood ratios). The confidence interval and region formulas are derived for the comparison of two positive or negative diagnostic likelihood ratios separately and jointly. The proposed confidence interval and region formulas are simple to compute and can be used for both population-based and case-control clustered data. Simulation results show that case-control clustered data are substantially efficient than the population-based. The proposed methods are applied to a real data set from the identification of neonatal hearing impairment (INHI) study.