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The accuracy of a screening test is often measured by the area under the receiver characteristic (ROC) curve (AUC) of a screening test. Two-phase designs have been widely used in diagnostic studies for estimating one single AUC and comparing two AUCs where the screening test results are measured for a large sample (Phase one sample) while the disease status is only verified for a subset of Phase one sample (Phase two sample) by a gold standard. In this paper, we consider the optimal two-phase sampling design for comparing the performance of two ordinal screening tests in classifying disease status. Specifically, we derive an analytical variance formula for the AUC difference estimator and use it to find the optimal sampling probabilities that minimize the variance formula for the AUC difference estimator. According to the proposed optimal two-phase design, the strata with the levels of two tests far apart from each other should be over-sampled while the strata with the levels of two tests close to each other should be under-sampled. Simulation results indicate that two-phase sampling under optimal allocation (OA) achieves a substantial amount of variance reduction, compared with two-phase sampling under proportional allocation (PA). Furthermore, in comparison with a one-phase random sampling, two-phase sampling under OA or PA has a clear advantage in reducing the variance of AUC difference estimator when the variances of the two screening test results in the disease population differ greatly from their counterparts in non-disease population. [ABSTRACT FROM AUTHOR]

Statistical methods have been well developed for comparing the predictive values of two binary diagnostic tests under a paired design. However, existing methods do not make allowance for incomplete data. Although maximum likelihood based method can be used to deal with incomplete data, it requires iterative algorithm for implementation. A simple and easily implemented statistical method is therefore needed. Simple methods exist for comparing two sensitivities or specificities with incomplete data but such simple methods are not available for comparing two predictive values with incomplete data. In this paper, we propose two simple methods for comparing two predictive values with incomplete data. The test statistics derived by these two methods are simple to compute, only involving some minor modification of the existing weighted generalized score statistics with complete data. Simulation results demonstrate that the proposed methods are more efficient than the ad-hoc method that only uses the subjects wit complete data. As an illustration, the proposed methods are applied to an observational study comparing two non-invasive methods in detecting endometriosis. [ABSTRACT FROM AUTHOR]

Positive and negative predictive values are important measures of the clinical accuracy of a diagnostic test. Various test statistics have been proposed to compare positive predictive values or negative predictive values of two binary diagnostic tests separately. However, such separate comparisons do not present a complete picture of the relative accuracy of the two diagnostic tests. In this paper, we propose an extension of McNemar's test for the joint comparison of predictive values of multiple diagnostic tests. The proposed extended McNemar's test is intuitive and simple to compute, only involving cell counts of discordant pairs from multiple 2 × 2 tables. Furthermore, we also propose a re-formulation of an existing Wald test statistic so that it can be implemented more easily than its original form. Simulations demonstrate that the proposed extended McNemar's test statistic preserves type one error much better than the existing Wald test statistic. Thus, we believe that the proposed extended McNemar's test statistic is the preferred statistic to simultaneously compare the predictive values of multiple binary diagnostic tests. [ABSTRACT FROM AUTHOR]

Root uptake strategies are associated with the strength of negative plant–soil feedback (PSF) induced by soil pathogens. Given the intensified effect of pathogen richness in fine roots on the strength of negative PSF through the synergistic effects of multiple pathogens, researchers have proposed a trade‐off between nutrient acquisition and pathogen defence in roots. However, empirical evidence is lacking. In addition, because the interaction between pathogens and fine roots depends on the mycorrhizal types of tree species, both fine root traits and mycorrhizal types should be incorporated to reveal covariation in pathogen richness and the strength of negative PSF. In this study, we selected 50 arbuscular mycorrhizal (AM) tree species and 7 ectomycorrhizal (ECM) tree species in a subtropical forest to investigate the relationships between fine root traits and pathogen richness in fine roots and determined whether their relationships depended on plant mycorrhizal types. Our results showed that pathogen richness was negatively correlated with fine root diameter but was positively correlated with specific root length for the AM‐associated species, while for the ECM‐associated species, the pathogen richness was only found to have a significant negative relationship with the relative abundance of ECM fungi. These findings highlight the difference between AM‐ and ECM‐associated species in pathogen defence and bridge the gap between root traits and pathogen richness, which is significant for improving our understanding of the potential factors mediating the strength of PSF and thus maintaining tree species diversity. [ABSTRACT FROM AUTHOR]

The case-control design is known for its efficiency at a fixed sample size when the disease under study is rare. Such a design is usually carried out for the inference of disease odds ratio in the context of independent data. In this paper, we consider its extension to clustered data set-ups for the comparison of diagnostic likelihood ratios of two binary tests and explore its efficiency gain in estimating relative diagnostic likelihood ratio (the ratio of two diagnostic likelihood ratios). The confidence interval and region formulas are derived for the comparison of two positive or negative diagnostic likelihood ratios separately and jointly. The proposed confidence interval and region formulas are simple to compute and can be used for both population-based and case-control clustered data. Simulation results show that case-control clustered data are substantially efficient than the population-based. The proposed methods are applied to a real data set from the identification of neonatal hearing impairment (INHI) study. [ABSTRACT FROM AUTHOR]

Bennett (Statistics in Medicine4 (1985), 535-539) proposed a goodness-of-fit statistic to compare two predictive values in an attempt to improve upon its earlier version he derived in 1976. However, this new version of Bennett's goodness-of-fit statistic was not presented correctly, and more importantly, its validity has been questioned by several authors in the literature as it did not involve the disease prevalence, a part of the two Predictive Values to be compared. To shed some light on this classical test statistic, in this paper, we first obtain the corrected version of Bennett's goodness-of-fit statistic. We then compare the corrected version with its recent Wald counterpart proposed by Wang (Statistics in Medicine25(2006), 2215-2229) and show that the two statistics are asymptotically equivalent. The validity of the corrected Bennett's goodness-of-fit statistic is further supported by a simulation study which indicates that Bennett's goodness-of-fit statistic with correction has similar finite sample performance to its Wald counterpart. In conclusion, the corrected Bennett's goodness-of-fit statistic is a competitive statistic for testing equality of two predictive values. [ABSTRACT FROM AUTHOR]

Nonparametric inference of the area under ROC curve (AUC) has been well developed either in the presence of verification bias or clustering. However, current nonparametric methods are not able to handle cases where both verification bias and clustering are present. Such a case arises when a two-phase study design is applied to a cohort of subjects (verification bias) where each subject might have multiple test results (clustering). In such cases, the inference of AUC must account for both verification bias and intra-cluster correlation. In the present paper, we propose an IPW AUC estimator that corrects for verification bias and derive a variance formula to account for intra-cluster correlations between disease status and test results. Results of a simulation study indicate that the method that assumes independence underestimates the true variance of the IPW AUC estimator in the presence of intra-cluster correlations. The proposed method, on the other hand, provides a consistent variance estimate for the IPW AUC estimator by appropriately accounting for correlations between true disease statuses and between test results. [ABSTRACT FROM AUTHOR]

Predictive values of a binary diagnostic test are often evaluated under a random sample design. When the disease is rare, however, such a design might not be as efficient as a nested case–control design where the cases are oversampled from a large existing cohort. Under a nested case–control design, direct proportion estimators of predictive values are biased because cases are oversampled. Consistent estimates of predictive values can be easily obtained by inverse probability weighting (IPW) method. The only difficulty with these IPW estimators has been the absence of expressions for their variances. To fill this gap, in the current paper, we obtain the asymptotic variance formulas for the IPW estimators of predictive values. Unlike their counterparts from weighted logistic regression, our variance formulas take into account the variance of the estimated weights in the IPW estimators of predictive values. We further use the proposed variance formulas to examine the gain in efficiency under a nested case–control design compared with a simple random sampling design. Our results clearly show that when the disease is rare, a nested case–control design can achieve a substantial amount of variance reduction by oversampling cases, compared with a random sample design. Finally, we compare via simulation the accuracy of the proposed variance formulas with the existing methods and illustrate the proposed method by a real data example evaluating the accuracy of D-dimer test. [ABSTRACT FROM AUTHOR]

Eliasziw and Donner (1991) proposed an adjusted McNemar test that can be used to compare two proportions estimated from paired clustered binary data. The adjustment factor they proposed is formulated in terms of an intra-cluster correlation. They considered two estimators for the intra-cluster correlation. However, both estimators presented estimation issues; the first estimator cannot be calculated when the number of discordant pairs is small while the second estimator is not consistent when the Dirichlet-multinomial distribution assumption is violated. To overcome the two estimation issues, we propose an alternative adjustment factor that is formulated in terms of a different intra-cluster correlation, which can be estimated consistently using both discordant and accordant pairs. The consistency of our estimator of the new intra-cluster correlation is guaranteed even when the Dirichlet-multinomial distribution assumption is violated. In addition, we show that the proposed adjusted McNemar test performs as well as Eliasziw and Donner's adjusted McNemar test in terms of size and power. [ABSTRACT FROM AUTHOR]

Statistical methods are well developed for estimating the area under the receiver operating characteristic curve (AUC) based on a random sample where the gold standard is available for every subject in the sample, or a two-phase sample where the gold standard is ascertained only at the second phase for a subset of subjects sampled using fixed sampling probabilities. However, the methods based on a two-phase sample do not attempt to optimize the sampling probabilities to minimize the variance of AUC estimator. In this paper, we consider the optimal two-phase sampling design for evaluating the performance of an ordinal test in classifying disease status. We derived the analytic variance formula for the AUC estimator and used it to obtain the optimal sampling probabilities. The efficiency of the two-phase sampling under the optimal sampling probabilities (OA) is evaluated by a simulation study, which indicates that two-phase sampling under OA achieves a substantial amount of variance reduction with an over-sample of subjects with low and high ordinal levels, compared with two-phase sampling under proportional allocation (PA). Furthermore, in comparison with an one-phase random sampling, two-phase sampling under OA or PA have a clear advantage in reducing the variance of AUC estimator when the variance of diagnostic test results in the disease population is small relative to its counterpart in nondisease population. Finally, we applied the optimal two-phase sampling design to a real-world example to evaluate the performance of a questionnaire score in screening for childhood asthma. [ABSTRACT FROM AUTHOR]

In diagnostic trials, clustered data are obtained when several subunits of the same patient are observed. Intracluster correlations need to be taken into account when analyzing such clustered data. A nonparametric method has been proposed by Obuchowski (1997) to estimate the Receiver Operating Characteristic curve area (AUC) for such clustered data. However, Obuchowski's estimator is not efficient as it gives equal weight to all pairwise rankings within and between cluster. In this paper, we propose a more efficient nonparametric AUC estimator with two sets of optimal weights. Simulation results show that the loss of efficiency of Obuchowski's estimator for a single AUC or the AUC difference can be substantial when there is a moderate intracluster test correlation and the cluster size is large. The efficiency gain of our weighted AUC estimator for a single AUC or the AUC difference is further illustrated using the data from a study of screening tests for neonatal hearing. [ABSTRACT FROM AUTHOR]