Interval estimation of relative risks for combined unilateral and bilateral correlated data.

Measurements are generally collected as unilateral or bilateral data in clinical trials, epidemiology, or observational studies. For example, in ophthalmology studies, the primary outcome is often obtained from one eye or both eyes of an individual. In medical studies, the relative risk is usually the parameter of interest and is commonly used. In this article, we develop three confidence intervals for the relative risk for combined unilateral and bilateral correlated data under the equal dependence assumption. The proposed confidence intervals are based on maximum likelihood estimates of parameters derived using the Fisher scoring method. Simulation studies are conducted to evaluate the performance of proposed confidence intervals with respect to the empirical coverage probability, the mean interval width, and the ratio of mesial non-coverage probability to the distal non-coverage probability. We also compare the proposed methods with the confidence interval based on the method of variance estimates recovery and the confidence interval obtained from the modified Poisson regression model with correlated binary data. We recommend the score confidence interval for general applications because it best controls converge probabilities at the 95% level with reasonable mean interval width. We illustrate the methods with a real-world example.

Interval estimation for operating characteristic of continuous biomarkers with controlled sensitivity or specificity.

The receiver operating characteristic (ROC) curve provides a comprehensive performance assessment of a continuous biomarker over the full threshold spectrum. Nevertheless, a medical test often dictates to operate at a certain high level of sensitivity or specificity. A diagnostic accuracy metric directly targeting the clinical utility is specificity at the controlled sensitivity level, or vice versa. While the empirical point estimation is readily adopted in practice, the nonparametric interval estimation is challenged by the fact that the variance involves density functions due to estimated threshold. In addition, even with a fixed threshold, many standard confidence intervals including the Wald interval for binomial proportion could have erratic behaviors. In this article, we are motivated by the superior performance of the score interval for binomial proportion and propose a novel extension for the biomarker problem. Meanwhile, we develop exact bootstrap and establish consistency of the bootstrap variance estimator. Both single-biomarker evaluation and two-biomarker comparison are investigated. Extensive simulation studies were conducted, demonstrating competitive performance of our proposals. An illustration with aggressive prostate cancer diagnosis is provided.