Analysis of repeated markers used to predict progression of cancer.

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 definition of specificity and sensitivity for this setting and describe non-parametric estimators for these parameters. We then derive the theory required to obtain confidence intervals for the specificity and sensitivity of a marker and to define an asymptotically normal statistic for comparing the sensitivities of two markers at a fixed specificity. 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 complements the frequently used time dependent Cox model, which we believe, will facilitate clinical interpretation of marker data.