Figure 4 contains a rectangle that shows the 1.96–standard-error confidence region of the joint distribution of the means for the true-positive rate (TPR, or sensitivity) and false-positive rate (FPR, or one minus specificity) of the shortened humerus for detecting trisomy 21 for the 11 meta-analyzed studies when TPR and FPR are analyzed independently. The plot is on the logit scale. The coordinates of the summary point are −2.97 and −0.56. With separate meta-analyses the 1.96–standard-error confidence region is a rectangle, as the correlation between the logit TPR and logit FPR is explicitly ignored. The 95% confidence intervals for the mean logit TPR are −0.92 to −0.20 and for the sumary FPR are −3.36 to −2.58.

Figure 41.96-standard-error confidence region (rectangle) for independent meta-analyses of sensitivity and specificity (shortened humerus only)

The area of the 1.96-standard-error region is 0.5587

FPR = false-positive rate (1-specificity); TPR = true-positive rate (sensitivity).

Note: The plot is on the logit scale. The black dot represents the coordinates of the mean of logit-transformed sensitivity and false-positive rate for shortened humerus. The red horizontal lines represent the 95% confidence interval on the margin of the summary logit true-positive rate, and the red vertical lines represent the corresponding 95% confidence intervals of the summary logit false-positive rate. The rectangle is the 1.96-standard-error confidence region of the joint distribution of the two means, which have been obtained from separate univariate random effects meta-analyses with REML. The coordinates of the summary point in this figure come from separate meta-analyses, and are slightly different from Figure 3.

From: Analysis of the Example

Cover of Evaluating Practices and Developing Tools for Comparative Effectiveness Reviews of Diagnostic Test Accuracy
Evaluating Practices and Developing Tools for Comparative Effectiveness Reviews of Diagnostic Test Accuracy: Methods for the Joint Meta-Analysis of Multiple Tests [Internet].
Trikalinos TA, Hoaglin DC, Small KM, et al.

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