The diagnostic odds ratio: a single indicator of test performance

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Abstract

Diagnostic testing can be used to discriminate subjects with a target disorder from subjects without it. Several indicators of diagnostic performance have been proposed, such as sensitivity and specificity. Using paired indicators can be a disadvantage in comparing the performance of competing tests, especially if one test does not outperform the other on both indicators. Here we propose the use of the odds ratio as a single indicator of diagnostic performance. The diagnostic odds ratio is closely linked to existing indicators, it facilitates formal meta-analysis of studies on diagnostic test performance, and it is derived from logistic models, which allow for the inclusion of additional variables to correct for heterogeneity. A disadvantage is the impossibility of weighing the true positive and false positive rate separately. In this article the application of the diagnostic odds ratio in test evaluation is illustrated.

Introduction

In an era of evidence-based medicine, decision makers need high-quality data to support decisions about whether or not to use a diagnostic test in a specific clinical situation and, if so, which test. Many quantitative indicators of test performance have been introduced, comprising sensitivity and specificity, predictive values, chance-corrected measures of agreement, likelihood ratios, area under the receiver operating characteristic curve, and many more. All are quantitative indicators of the test's ability to discriminate patients with the target condition (usually the disease of interest) from those without it, resulting from a comparison of the test's results with those from the reference standard in a series of representative patients. In most applications, the reference standard is the best available method to decide on the presence or absence of the target condition. Less well known is the odds ratio as a single indicator of test performance. The odds ratio is a familiar statistic in epidemiology, expressing the strength of association between exposure and disease. As such it also can be applied to express the strength of the association between test result and disease.

This article offers an introduction to the understanding and use of the odds ratio in diagnostic applications. In brief, we will refer to it as the diagnostic odds ratio (DOR). First, we will point out the usefulness of the odds ratio in dichotomous and polychotomous tests. We will then discuss the use of the DOR in meta-analysis and the application of conditional logistic regression techniques to enhance the information resulting from such analysis.

Section snippets

Dichotomous test outcomes

Although most diagnostic tests have multiple or continuous outcomes, either grouping of categories or application of a cutoff value is frequently applied to classify results into positive or negative. Such a dichotomization enables one to represent the comparison between a diagnostic test and its reference standard in one 2×2 contingency table, as depicted in Table 1. Common indicators of test performance derived from such a 2×2 table are the sensitivity of the test, its specificity, the

Polychotomous and continuous test outcomes

The performance of a test for which several cutoffs are available can be expressed by means of ROC analysis [14], [15]. A receiver operating characteristic (ROC) curve plots the true positive rate on the Y-axis as a function of the false positive rate on the X-axis for all possible cutoff values of the test under evaluation. The area under the curve obtained (AUC) can subsequently be calculated as an alternative single indicator of test performance [16].

The AUC takes values between 0 and 1,

The DOR in meta-analysis

The DOR offers considerable advantages in meta-analysis of diagnostic studies that combines results from different studies into summary estimates with increased precision. Meta-analysis of diagnostic tests offers statistical challenges, because of the bivariate nature of the conventional expressions of test performance. Simple pooling of sensitivity and specificity usually is inappropriate, as this approach ignores threshold differences [11], [18]. In addition, heterogeneity may lead to an

Logistic regression

The DOR offers advantages when logistic regression is used with diagnostic problems. Logistic regression can be used to construct decision rules, reflecting the combined diagnostic value of a number of diagnostic variables [25]. Another application is the study of the added value of diagnostic tests [26]. With a single dichotomous test the logistic regression equation reads:P(D|x)=11+exp−(α+βx)where x stands for the test result and the coefficients α and β have to be estimated. If a positive

Discussion

The diagnostic odds ratio as a measure of test performance combines the strengths of sensitivity and specificity, as prevalence independent indicators, with the advantage of accuracy as a single indicator. These characteristics lend the DOR particularly useful for comparing tests whenever the balance between false negative and false positive rates is not of immediate importance. These features are also highly convenient in systematic reviews and meta-analyses.

In decisions on the introduction of

Acknowledgements

The authors thank Dr. Guus Hart for critically reviewing and giving useful suggestions on earlier drafts.

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