The accuracy of a diagnostic test is often evaluated with the measures of sensitivity and specificity, and the joint dependence between these two measures is captured by receiver operating characteristic (ROC) curve. To combine multiple testing results from studies that are assumed to follow the same underlying probability law, a smooth summary receiver operating characteristic (SROC) curve can be fitted. Moses, Shapiro, and Littenberg (1993) proposed a least-squares approach to fit the smooth SROC curve, and the variances of the estimated parameters were derived by ignoring the variance of the independent variable. Since the independent variable was in fact random, the variances were likely underestimated. Hence we propose another way to estimate the variances of the statistics of interest, and use a real example to demonstrate the differences. We also perform a simulation study to examine these two approaches. The results suggest that the least squares estimates of the coefficients are biased, and that the averaged confidence coverage is not equal to its nominal level, regardless of the methods. While Moses et al.'s method tends to underestimate the confidence interval, our method sometimes overestimates the interval, depending on the ratio of the intra-study variation over the inter-study variation. Our estimation of the variances appears to be slightly better than the method proposed by Moses et al. because the coverage probability of the confidence interval is closer to the nominal level.
Fan, Ming-Yu and Zhou, Xiao-Hua, "Constructing Confidence Intervals of the Summary Statistics in the Least-Squares SROC Model" (March 2005). UW Biostatistics Working Paper Series. Working Paper 248.