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A New Logistic Regression Approach for the Evaluation of Diagnostic Test Results

Center for Clinical Decision Sciences, Department of Public Health, Erasmus MC, the Netherlands, a.janssens{at}erasmusmc.nl

Yazhong Deng, MSc

Center for Clinical Decision Sciences, Department of Public Health, Erasmus MC, the Netherlands

Gerard J. J. M. Borsboom, MSc

Center for Clinical Decision Sciences, Department of Public Health, Erasmus MC, the Netherlands

Marinus J. C. Eijkemans, PhD

Center for Clinical Decision Sciences, Department of Public Health, Erasmus MC, the Netherlands

J. Dik. F. Habbema, PhD

Center for Clinical Decision Sciences, Department of Public Health, Erasmus MC, the Netherlands

Ewout W. Steyerberg, PhD

Center for Clinical Decision Sciences, Department of Public Health, Erasmus MC, the Netherlands

The value of a dichotomous diagnostic test is often described in terms of sensitivity, specificity, and likelihood ratios (LRs). Although it is known that these test characteristics vary between subgroups of patients, they are generally interpreted, on average, without considering information on patient characteristics, such as clinical signs and symptoms, or on previous test results. This article presents a reformulation of the logistic regression model that allows to calculate the LRs of diagnostic test results conditional on these covariates. The proposed method starts with estimating logistic regression models for the prior and posterior odds of disease. The regression model for the prior odds is based on patient characteristics, whereas the regression model for the posterior odds also includes the diagnostic test of interest. Following the Bayes theorem, the authors demontsrate that the regression model for the LR can be derived from taking the differences between the regression coefficients of the 2 models. In a clinical example, they demonstrate that the LRs of positive and negative test results and the sensitivity and specificity of the diagnostic test varied considerably between patients with different risk profiles, even when a constant odds ratio was assumed. The proposed logistic regression approach proves an efficient method to determine the performance of tests at the level of the individual patient risk profile and to examine the effect of patient characteristics on diagnostic test characteristics.

Key Words: logistic regression • likelihood ratio • prior probability • risk profile • diagnostic test • Bayes theorem • multiple testing

Medical Decision Making, Vol. 25, No. 2, 168-177 (2005)
DOI: 10.1177/0272989X05275154


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