<p> 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 the 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 et al. (1993) proposed a least squares approach to fit the smooth SROC curve. </p> <p> In this thesis we overview the summary measures for the ROC curve in single study data as well as the summary statistics for the SROC curves in meta-analysis. These summary statistics include, the area under the curve (AUC), Q* statistic, area swept under the curve (ASC) and the partial area under the curve (pAUC). </p> <p> Our focus, however is mainly on the partial area under the SROC curve as it is being used frequently in meta-analysis of diagnostic testing. The appeal to use the pAUC instead of the full AUC is that the partial area can be used to focus on a clinically relevant region of the SROC curve where false positive rate (FPR) is small. Simulations and considerations for the use of the summary indices of the ROC and SROC curves are presented here. </p> / Thesis / Master of Science (MSc)

In this study, meta-analysis of diagnostic tests, Summary Receiver Operating Characteristic (SROC) curve, bivariate random effects and Hierarchical Summary Receiver Operating Characteristic (HSROC) curve theories have been discussed and accuracy in literature of Fine Needle Aspiration (FNA) biopsy that is used in the diagnosis of masses in breast cancer (malignant or benign) has been analyzed. FNA Cytological (FNAC) examination in breast tumor is, easy, effective, effortless, and does not require special training for clinicians. Because of the uncertainty related to FNAC&lsquo / s accurate usage in publications, 25 FNAC studies have been gathered in the meta-analysis. In the plotting of the summary ROC curve, the logit difference and sums of the true positive rates and the false positive rates included in the meta-analysis&lsquo / s codes have been generated by SAS. The formula of the bivariate random effects model and hierarchical summary ROC curve is presented in context with the literature. Then bivariate random effects implementation with the new SAS PROC GLIMMIX is generated. Moreover, HSROC implementation is generated by SAS PROC HSROC NLMIXED. Curves are plotted with RevMan Version 5 (2008). It has been stated that the meta-analytic results of bivariate random effects are nearly identical to the results from the HSROC approach. The results achieved through both random effects meta-analytic methods prove that FNA Cytology is a diagnostic test with a high level of distinguish over breast tumor.