Statistics Seminars: Inference issues for True-Class Fractions in 2D and 3D ROC analysis
10 December 2015 14:15 in Elvet Hill House, room EH113
The three-class approach is used for progressive disorders when clinicians and researchers want to diagnose or classify subjects as members of one of three ordered categories based on a continuous diagnostic marker. The decision thresholds or optimal cut-off points required for this classification are often chosen to maximize the generalized Youden index (Nakas et al., Stat Med 2013; 32: 995–1003). The effectiveness of these chosen cut-off points can be evaluated by estimating their corresponding true class fractions and their associated confidence regions. Recently, in the two-class case, parametric and non- parametric methods were investigated for the construction of confidence regions for the pair of the Youden-index-based optimal sensitivity and specificity fractions that can take into account the correlation introduced between sensitivity and specificity when the optimal cut-off point is estimated from the data (Bantis et al., Biomet 2014; 70: 212–223). A parametric approach based on the Box–Cox transformation to normality often works well while for markers having more complex distributions a non-parametric procedure using logspline density estimation can be used instead. The true class fractions that correspond to the optimal cut-off points estimated by the generalized Youden index are correlated similarly to the two-class case. We present pitfalls in the assumptions of correlation between true-class fractions in the 2-class case and a generalisation of the methods in Bantis et al. (2014) to the three-class case, where ROC surface methodology can be employed for the evaluation of the discriminatory capacity of a diagnostic marker. We obtain three-dimensional joint confidence regions for the optimal true class fractions.
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