Letter From the Editor

Abstract

We congratulate Harbord and others (2007) for identifying the very closely related and sometimes identical relationship between the hierarchical summary receiver operating characteristic (HSROC) model (Rutter and Gatsonis, 2001) and the bivariate random-effects meta-analysis (Van Houwelingen and others , 2002; Macaskill, 2004; Reitsma and others , 2005; Chu and Cole, 2006) from a meta-analysis of diagnostic accuracy studies. However, the formulas for constructing the summary receiver operating characteristic (SROC) curve from the HSROC model presented in equation (5.1) by Harbord and others (2007), in p. 2870 by Rutter and Gatsonis (2001), and in p. 927 by Macaskill (2004) are incorrect and potentially misleading.Tosimplify the discussion, we focus on models without any covariates. Let n i 11 , n i 00 , n i 01 , and n i 10 be the number of true positives, true negatives, false positives, and false negatives and n i 1 · and n i 0 · be the number of diseased and nondiseased patients in the i th diagnostic accuracy studies from a meta-analysis, respectively. Conditional on the number of diseased and nondiseased patients in each study, the bivariate random-effects meta-analysis model assumes the following: n i 00 ∼ Binomial ( n i 0 · , Sp i ) , n i 11 ∼ Binomial ( n i 1 · , Se i ) , logit ( Se i ) = +