Analysis of Repeated Markers Used toPredict Progression

We consider methods for evaluating repeated markers to be used as a substitute for a clinical examination or to predict an outcome, in our case progression of breast cancer. We propose a deenition of speciicity and sensitivity for this setting and describe nonparametric estimators for these parameters. We then derive the theory required to obtain conndence intervals for the speciicity and sensitivity of a marker and to deene an asymptotically normal statistic for comparing the sensitivities of two markers at a xed speciicity. The theory allows for correlations introduced by the fact that markers may be obtained from the same patient at multiple visits and that both markers being compared may be obtained from the same patient. The work allows for an approach that compliments the frequently used time dependent Cox model which, we believe, will facilitate clinical interpretation of marker data. 2