Data description is the first step for understanding the nature of the problem at hand. Usually, it is a simple task that does not require any particular assumption. However, the interpretation of the used descriptive measures can be a source of confusion and misunderstanding. The incidence rate is the quotient between the number of observed events and the sum of time that the studied population was at risk of having this event (person-time). Despite this apparently simple definition, its interpretation is not free of complexity. In this piece of research, we revisit the incidence rate estimator under right-censorship. We analyze the effect that the censoring time distribution can have on the observed results, and its relevance in the comparison of two or more incidence rates. We propose a solution for limiting the impact that the data collection process can have on the results of the hypothesis testing. We explore the finite-sample behavior of the considered estimators from Monte Carlo simulations. Two examples based on synthetic data illustrate the considered problem. The R code and data used are provided as Supplementary Material.

To compare two or more survival distributions with interval-censored data, various nonparametric tests have been proposed. Some are based on the G ρ $$ {G}^{\\rho } $$ -family introduced by Harrington and Fleming (1991) that allows flexibility for situations in which the hazard ratio decreases monotonically to unity. However, it is unclear how to choose the appropriate value of the parameter ρ $$ \\rho $$ . In this work, we propose a novel linear rank-type test for analyzing interval-censored data that derived from a proportional reversed hazard model. We show its relationship with decreasing hazard ratio. This test statistic provides an alternative to the G ρ $$ {G}^{\\rho } $$ -based test statistics by bypassing the choice of the ρ $$ \\rho $$ parameter. Simulation results show its good behavior. Two studies on breast cancer and drug users illustrate its practical uses and highlight findings that would have been overlooked if other tests had been used. The test is easy to implement with standard software and can be used for a wide range of situations with interval-censored data to test the equality of survival distributions between two or more independent groups.

This article proposes a powerful method to compare two samples. The proposed method handles comparison of data by drawing inference from ROC curve model parameters. The method estimates parameters from a linear model framework on the empirical sensitivities and specificities. The consistent ROC parameters are then used to give a more powerful test than existing methods in several situations. In addition, we present a comprehensive statistic based on the Cauchy combination, which works well in all scenarios considered in this article. We also offer an efficient one-layer wild permutation procedure to calculate the P-value of our statistic. The method is particularly useful when the underlying continuous biomarker results are non-normal. We illustrate the proposed methods in a neonatal audiology diagnostic example.