Receiver operating characteristic surfaces in the presence of verification bias

Diagnostic test evaluation methodology: A systematic review of methods employed to evaluate diagnostic tests in the absence of gold standard - An update

OBJECTIVE

To systematically review methods developed and employed to evaluate the diagnostic accuracy of medical test when there is a missing or no gold standard.

STUDY DESIGN AND SETTINGS

Articles that proposed or applied any methods to evaluate the diagnostic accuracy of medical test(s) in the absence of gold standard were reviewed. The protocol for this review was registered in PROSPERO (CRD42018089349).

RESULTS

Identified methods were classified into four main groups: methods employed when there is a missing gold standard; correction methods (which make adjustment for an imperfect reference standard with known diagnostic accuracy measures); methods employed to evaluate a medical test using multiple imperfect reference standards; and other methods, like agreement studies, and a mixed group of alternative study designs. Fifty-one statistical methods were identified from the review that were developed to evaluate medical test(s) when the true disease status of some participants is unverified with the gold standard. Seven correction methods were identified and four methods were identified to evaluate medical test(s) using multiple imperfect reference standards. Flow-diagrams were developed to guide the selection of appropriate methods.

CONCLUSION

Various methods have been proposed to evaluate medical test(s) in the absence of a gold standard for some or all participants in a diagnostic accuracy study. These methods depend on the availability of the gold standard, its' application to the participants in the study and the availability of alternative reference standard(s). The clinical application of some of these methods, especially methods developed when there is missing gold standard is however limited. This may be due to the complexity of these methods and/or a disconnection between the fields of expertise of those who develop (e.g. mathematicians) and those who employ the methods (e.g. clinical researchers). This review aims to help close this gap with our classification and guidance tools.

Bayesian nonparametric estimation of ROC surface under verification bias

The receiver operating characteristic (ROC) surface, as a generalization of the ROC curve, has been widely used to assess the accuracy of a diagnostic test for three categories. A common problem is verification bias, referring to the situation where not all subjects have their true classes verified. In this paper, we consider the problem of estimating the ROC surface under verification bias. We adopt a Bayesian nonparametric approach by directly modeling the underlying distributions of the three categories by Dirichlet process mixture priors. We propose a robust computing algorithm by only imposing a missing at random assumption for the verification process but no assumption on the distributions. The method can also accommodate covariates information in estimating the ROC surface, which can lead to a more comprehensive understanding of the diagnostic accuracy. It can be adapted and hugely simplified in the case where there is no verification bias, and very fast computation is possible through the Bayesian bootstrap process. The proposed method is compared with other commonly used methods by extensive simulations. We find that the proposed method generally outperforms other approaches. Applying the method to two real datasets, the key findings are as follows: (1) human epididymis protein 4 has a slightly better diagnosis ability compared to CA125 in discriminating healthy, early stage, and late stage patients of epithelial ovarian cancer. (2) Serum albumin has a prognostic ability in distinguishing different stages of hepatocellular carcinoma.

A Bayesian semiparametric approach to correlated ROC surfaces with stochastic order constraints

In application of diagnostic accuracy, it is possible that a priori information may exist regarding the test score distributions, either between different disease populations for a single test or between multiple correlated tests. Few have considered constrained diagnostic accuracy analysis when the true disease status is binary; almost none when the disease status is ordinal. Motivated by a study on diagnosing endometriosis, we propose an approach to estimating diagnostic accuracy measures that can incorporate different stochastic order constraints on the test scores when an ordinal true disease status is in consideration. We show that the Dirichlet process mixture provides a convenient framework to both flexibly model the test score distributions and embed the a priori ordering constraints. We also utilize the Dirichlet process mixture to model the correlation between multiple tests. In taking a Bayesian perspective to inference, we develop an efficient Markov chain Monte Carlo algorithm to sample from the posterior distribution and provide posterior estimates of the receiver operating characteristic surfaces and the associated summary measures. The proposed approach is evaluated with extensive simulation studies, and is demonstrated with an application to the endometriosis study.

Estimation of the volume under the receiver-operating characteristic surface adjusting for non-ignorable verification bias

The receiver-operating characteristic surface is frequently used for presenting the accuracy of a diagnostic test for three-category classification problems. One common problem that can complicate the estimation of the volume under receiver-operating characteristic surface is that not all subjects receive the verification of the true disease status. Estimation based only on data from subjects with verified disease status may be biased, which is referred to as verification bias. In this article, we propose new verification bias correction methods to estimate the volume under receiver-operating characteristic surface for a continuous diagnostic test. We assume the verification process is missing not at random, which means the missingness might be related to unobserved clinical characteristics. Three classes of estimators are proposed, namely, inverse probability weighted, imputation-based, and doubly robust estimators. A jackknife estimator of variance is derived for all the proposed volume under receiver-operating characteristic surface estimators. The finite sample properties of the new estimators are examined via simulation studies. We illustrate our methods with data collected from Alzheimer's disease research.

Inverse probability weighting estimation of the volume under the ROC surface in the presence of verification bias

In diagnostic medicine, the volume under the receiver operating characteristic (ROC) surface (VUS) is a commonly used index to quantify the ability of a continuous diagnostic test to discriminate between three disease states. In practice, verification of the true disease status may be performed only for a subset of subjects under study since the verification procedure is invasive, risky, or expensive. The selection for disease examination might depend on the results of the diagnostic test and other clinical characteristics of the patients, which in turn can cause bias in estimates of the VUS. This bias is referred to as verification bias. Existing verification bias correction in three-way ROC analysis focuses on ordinal tests. We propose verification bias-correction methods to construct ROC surface and estimate the VUS for a continuous diagnostic test, based on inverse probability weighting. By applying U-statistics theory, we develop asymptotic properties for the estimator. A Jackknife estimator of variance is also derived. Extensive simulation studies are performed to evaluate the performance of the new estimators in terms of bias correction and variance. The proposed methods are used to assess the ability of a biomarker to accurately identify stages of Alzheimer's disease.