On composite likelihood in bivariate meta-analysis of diagnostic test accuracy studies

Vine copula mixed models for meta-analysis of diagnostic accuracy studies without a gold standard

Numerous statistical models have been proposed for conducting meta-analysis of diagnostic accuracy studies when a gold standard is available. However, in real-world scenarios, the gold standard test may not be perfect due to several factors such as measurement error, non-availability, invasiveness, or high cost. A generalized linear mixed model (GLMM) is currently recommended to account for an imperfect reference test. We propose vine copula mixed models for meta-analysis of diagnostic test accuracy studies with an imperfect reference standard. Our general models include the GLMM as a special case, can have arbitrary univariate distributions for the random effects, and can provide tail dependencies and asymmetries. Our general methodology is demonstrated with an extensive simulation study and illustrated by insightfully re-analyzing the data of a meta-analysis of the Papanicolaou test that diagnoses cervical neoplasia. Our study suggests that there can be an improvement on GLMM and makes the argument for moving to vine copula random effects models.

Joint meta-analysis of two diagnostic tests accounting for within and between studies dependence

There is an extensive literature on methods for meta-analysis of diagnostic test accuracy, but it mainly focuses on a single test. A multinomial generalised linear mixed model was recently proposed for the joint meta-analysis of studies comparing two tests on the same participants in a paired tests design with a gold standard. In this setting, we propose a novel model for joint meta-analysis of studies comparing two diagnostic tests which assumes independent multinomial distributions for the counts of each combination of test results in diseased and non-diseased patients, conditional on the latent vector of probabilities of each combination of test results in diseased and non-diseased patients. For the random effects distribution of the latent proportions, we employ a one-truncated D-vine copula that can provide tail dependence or asymmetry. The proposed model includes the multinomial generalised linear mixed model as a special case, accounts for the within-study dependence induced because the tests are applied to the same participants, allows for between-studies dependence, and can also operate on the original scale of the latent proportions. The latter enables the derivation of summary receiver operating characteristic curves. Our methodology is demonstrated with simulation studies and a meta-analysis of screening for Down's syndrome with two tests: shortened humerus and shortened femur.

A pseudo-likelihood approach for multivariate meta-analysis of test accuracy studies with multiple thresholds

Multivariate meta-analysis of test accuracy studies when tests are evaluated in terms of sensitivity and specificity at more than one threshold represents an effective way to synthesize results by fully exploiting the data, if compared to univariate meta-analyses performed at each threshold independently. The approximation of logit transformations of sensitivities and specificities at different thresholds through a normal multivariate random-effects model is a recent proposal that straightforwardly extends the bivariate models well recommended for the one threshold case. However, drawbacks of the approach, such as poor estimation of the within-study correlations between sensitivities and between specificities, and severe computational issues can make it unappealing. We propose an alternative method for inference on common diagnostic measures using a pseudo-likelihood constructed under a working independence assumption between sensitivities and between specificities at different thresholds in the same study. The method does not require within-study correlations, overcomes the convergence issues and can be effortlessly implemented. Simulation studies highlight a satisfactory performance of the method, remarkably improving the results from the multivariate normal counterpart under different scenarios. The pseudo-likelihood approach is illustrated in the evaluation of a test used for diagnosis of preeclampsia as a cause of maternal and perinatal morbidity and mortality.

An extended trivariate vine copula mixed model for meta-analysis of diagnostic studies in the presence of non-evaluable outcomes

A recent paper proposed an extended trivariate generalized linear mixed model (TGLMM) for synthesis of diagnostic test accuracy studies in the presence of non-evaluable index test results. Inspired by the aforementioned model we propose an extended trivariate vine copula mixed model that includes the TGLMM as special case, but can also operate on the original scale of sensitivity, specificity, and disease prevalence. The performance of the proposed vine copula mixed model is examined by extensive simulation studies in comparison with the TGLMM. Simulation studies showed that the TGLMM leads to biased meta-analytic estimates of sensitivity, specificity, and prevalence when the univariate random effects are misspecified. The vine copula mixed model gives nearly unbiased estimates of test accuracy indices and disease prevalence. Our general methodology is illustrated by meta-analysing coronary CT angiography studies.

Using Copula Functions to Estimate The AUC for Two Dependent Diagnostic Tests

When performing validation studies on diagnostic classification procedures, one or more biomarkers are typically measured in individuals. Some of these biomarkers may provide better information; moreover, more than one biomarker may be significant and may exhibit dependence between them. This proposal intends to estimate the Area Under the Receiver Operating  Characteristic Curve  (AUC)  for classifying individuals in a screening study. We analyze the dependence between the results of the tests by means of copula-type dependence (using FGM and Gumbel-Barnett copula functions), and studying the respective AUC under this type of dependence. Three different dependence-level values were evaluated for each copula function considered. In most of the reviewed literature, the authors assume a normal model to represent the performance of the biomarkers used for clinical diagnosis. There are situations in which assuming normality is not possible because that model is not suitable for one or both biomarkers. The proposed statistical model does not depend on some distributional assumption for the biomarkers used for diagnosis procedure, and additionally, it is not necessary to observe a strong or moderate linear dependence between them.

A multinomial quadrivariate D-vine copula mixed model for meta-analysis of diagnostic studies in the presence of non-evaluable subjects

Diagnostic test accuracy studies observe the result of a gold standard procedure that defines the presence or absence of a disease and the result of a diagnostic test. They typically report the number of true positives, false positives, true negatives and false negatives. However, diagnostic test outcomes can also be either non-evaluable positives or non-evaluable negatives. We propose a novel model for the meta-analysis of diagnostic studies in the presence of non-evaluable outcomes, which assumes independent multinomial distributions for the true and non-evaluable positives, and, the true and non-evaluable negatives, conditional on the latent sensitivity, specificity, probability of non-evaluable positives and probability of non-evaluable negatives in each study. For the random effects distribution of the latent proportions, we employ a drawable vine copula that can successively model the dependence in the joint tails. Our methodology is demonstrated with an extensive simulation study and applied to data from diagnostic accuracy studies of coronary computed tomography angiography for the detection of coronary artery disease. The comparison of our method with the existing approaches yields findings in the real data application that change the current conclusions.

A D-vine copula mixed model for joint meta-analysis and comparison of diagnostic tests

For a particular disease, there may be two diagnostic tests developed, where each of the tests is subject to several studies. A quadrivariate generalised linear mixed model (GLMM) has been recently proposed to joint meta-analyse and compare two diagnostic tests. We propose a D-vine copula mixed model for joint meta-analysis and comparison of two diagnostic tests. Our general model includes the quadrivariate GLMM as a special case and can also operate on the original scale of sensitivities and specificities. The method allows the direct calculation of sensitivity and specificity for each test, as well as the parameters of the summary receiver operator characteristic (SROC) curve, along with a comparison between the SROCs of each test. Our methodology is demonstrated with an extensive simulation study and illustrated by meta-analysing two examples where two tests for the diagnosis of a particular disease are compared. Our study suggests that there can be an improvement on GLMM in fit to data since our model can also provide tail dependencies and asymmetries.