510 Mathematik
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A semiparametric approach for meta-analysis of diagnostic accuracy studies with multiple cut-offs
(2022)
The accuracy of a diagnostic test is often expressed using a pair of measures: sensitivity (proportion of test positives among all individuals with target condition) and specificity (proportion of test negatives among all individuals without targetcondition). If the outcome of a diagnostic test is binary, results from different studies can easily be summarized in a meta-analysis. However, if the diagnostic test is based on a discrete or continuous measure (e.g., a biomarker), several cut-offs within one study as well as among different studies are published. Instead of taking all information of the cut-offs into account in the meta-analysis, a single cut-off per study is often selected arbitrarily for the analysis, even though there are statistical methods for the incorporation of several cut-offs. For these methods, distributional assumptions have to be met and/or the models may not converge when specific data structures occur. We propose a semiparametric approach to overcome both problems. Our simulation study shows that the diagnostic accuracy is underestimated, although this underestimation in sensitivity and specificity is relatively small. The comparative approach of Steinhauser et al. is better in terms of coverage probability, but may lead to convergence problems. In addition to the simulation results, we illustrate the application of the semiparametric approach using a published meta-analysis for a diagnostic test differentiating between bacterial and viral meningitis in children.
Methods for standard meta-analysis of diagnostic test accuracy studies are well established and understood. For the more complex case in which studies report test accuracy across multiple thresholds, several approaches have recently been proposed. These are based on similar ideas, but make different assumptions. In this article, we apply four different approaches to data from a recent systematic review in the area of nephrology and compare the results. The four approaches use: a linear mixed effects model, a Bayesian multinomial random effects model, a time-to-event model and a nonparametric model, respectively. In the case study data, the accuracy of neutrophil gelatinase-associated lipocalin for the diagnosis of acute kidney injury was assessed in different scenarios, with sensitivity and specificity estimates available for three thresholds in each primary study. All approaches led to plausible and mostly similar summary results. However, we found considerable differences in results for some scenarios, for example, differences in the area under the receiver operating characteristic curve (AUC) of up to 0.13. The Bayesian approach tended to lead to the highest values of the AUC, and the nonparametric approach tended to produce the lowest values across the different scenarios. Though we recommend using these approaches, our findings motivate the need for a simulation study to explore optimal choice of method in various scenarios.
Background: In many research areas it is necessary to find differences between treatment groups with several variables. For example, studies of microarray data seek to find a significant difference in location parameters from zero or one for ratios thereof for each variable. However, in some studies a significant deviation of the difference in locations from zero (or 1 in terms of the ratio) is biologically meaningless. A relevant difference or ratio is sought in such cases.
Results: This article addresses the use of relevance-shifted tests on ratios for a multivariate parallel two-sample group design. Two empirical procedures are proposed which embed the relevanceshifted test on ratios. As both procedures test a hypothesis for each variable, the resulting multiple testing problem has to be considered. Hence, the procedures include a multiplicity correction. Both procedures are extensions of available procedures for point null hypotheses achieving exact control of the familywise error rate. Whereas the shift of the null hypothesis alone would give straight-forward solutions, the problems that are the reason for the empirical considerations discussed here arise by the fact that the shift is considered in both directions and the whole parameter space in between these two limits has to be accepted as null hypothesis.
Conclusion: The first algorithm to be discussed uses a permutation algorithm, and is appropriate for designs with a moderately large number of observations. However, many experiments have limited sample sizes. Then the second procedure might be more appropriate, where multiplicity is corrected according to a concept of data-driven order of hypotheses.