Article first published online: 22 AUG 2012
Copyright © 2012 John Wiley & Sons, Ltd.
Statistics in Medicine
Volume 32, Issue 6, pages 964–977, 15 March 2013
How to Cite
Kosinski, A. S. (2013), A weighted generalized score statistic for comparison of predictive values of diagnostic tests. Statist. Med., 32: 964–977. doi: 10.1002/sim.5587
- Issue published online: 14 FEB 2013
- Article first published online: 22 AUG 2012
- Manuscript Accepted: 6 AUG 2012
- Manuscript Received: 17 APR 2012
- correlated data;
- diagnostic test;
- paired design;
- positive and negative predictive values;
- score statistic
Positive and negative predictive values are important measures of a medical diagnostic test performance. We consider testing equality of two positive or two negative predictive values within a paired design in which all patients receive two diagnostic tests. The existing statistical tests for testing equality of predictive values are either Wald tests based on the multinomial distribution or the empirical Wald and generalized score tests within the generalized estimating equations (GEE) framework. As presented in the literature, these test statistics have considerably complex formulas without clear intuitive insight. We propose their re-formulations that are mathematically equivalent but algebraically simple and intuitive. As is clearly seen with a new re-formulation we presented, the generalized score statistic does not always reduce to the commonly used score statistic in the independent samples case. To alleviate this, we introduce a weighted generalized score (WGS) test statistic that incorporates empirical covariance matrix with newly proposed weights. This statistic is simple to compute, always reduces to the score statistic in the independent samples situation, and preserves type I error better than the other statistics as demonstrated by simulations. Thus, we believe that the proposed WGS statistic is the preferred statistic for testing equality of two predictive values and for corresponding sample size computations. The new formulas of the Wald statistics may be useful for easy computation of confidence intervals for difference of predictive values. The introduced concepts have potential to lead to development of the WGS test statistic in a general GEE setting. Copyright © 2012 John Wiley & Sons, Ltd.