Meta‐analysis of full ROC curves using bivariate time‐to‐event models for interval‐censored data

Abstract

Systematic reviews and meta-analyses are the cornerstones of evidence-based medicine and inform treatment, diagnosis, or prevention of individual patients as well as policy decisions in health care. Statistical methods for the meta-analysis of intervention studies are well established today. Meta-analysis for diagnostic accuracy trials has also been a vivid research area in recent years, which is especially due to the increased complexity of their bivariate outcome of sensitivity and specificity. The situation is even more challenging when single studies report a full ROC curve with several pairs of sensitivity and specificity, each pair for a different threshold. Researchers frequently ignore this information and use only 1 pair of sensitivity and specificity from each study to arrive at meta-analytic estimates. Although methods to deal with the full information have been proposed, they have some disadvantages, eg, the numbers or values of thresholds have to be identical across studies, or the precise values of thresholds are ignored. We propose an approach for the meta-analysis of full ROC curves including the information from all thresholds by using bivariate time-to-event models for interval-censored data with random effects. This approach avoids the problems of previous methods and comes with the additional advantage that it allows for various distributions of the underlying continuous test values. The results from a small simulation study are given, which show that the approach works well in practice. Furthermore, we illustrate our new model using an example based on the population-based screening for type 2 diabetes mellitus.

Meta‐analysis of full ROC curves with flexible parametric distributions of diagnostic test values

“…Our recent approach for the meta‐analysis of full ROC curves is based on a bivariate time‐to‐event model for interval‐censored data …”

“…As we are interested in sensitivity and specificity, we have to keep diseased and non‐diseased participants apart and finally arrive at the close correspondence between an ROC curve and a bivariate time‐to‐event model for interval‐censored data. For modeling diagnostic test values in the two populations of diseased and non‐diseased, we used three different distributions, which are in the following given for the population of diseased ( D + ) and are defined analogously for the non‐diseased ( D − ): the Weibull distribution with density …”

“…Explicitly naming the analogy of our model to the class of time‐to‐event models, we consider the diagnostic test values as the “time” scale. Sensitivity is then the event probability in the population of diseased (or 1‐specificity in the population of non‐diseased), which can be interpreted, with the diagnostic test values on the x ‐axis, as a cohort life‐table estimator where sensitivity changes (in general, decreases) with increasing thresholds . In other words, each individual study participant contributes three pieces of information: its true disease status, the interval in which its diagnostic test value lies (and which is measured on our underlying “time” scale), and finally, the study from which it originates.…”

“…In the past, methods for the meta‐analysis of diagnostic studies frequently focused on summarizing only a selected single pair of sensitivity and specificity from each study that leads to a waste of the majority of observations. Methods for the meta‐analysis of full receiver operating characteristic (ROC) curves have been proposed; however, they come with several disadvantages . These are, for example, the need for an identical number of thresholds across single studies, ignoring concrete threshold values or applying two‐step approaches that partly neglect estimation uncertainty from the first step in the second step.…”

“…These are, for example, the need for an identical number of thresholds across single studies, ignoring concrete threshold values or applying two‐step approaches that partly neglect estimation uncertainty from the first step in the second step. As an alternative and to overcome these disadvantages, we proposed an approach based on bivariate time‐to‐event models for interval‐censored data . Thereby, we assume that the underlying diagnostic test values in the population of diseased and non‐diseased follow parametric distributions, such as the Weibull, log‐normal, or log‐logistic distribution.…”