Joint work with Alessandra Meddis and Paul Blanche
Considerable research has focused on the development of new biomarkers. The first step in developing a clinically useful biomarker is to identify its ability in discriminating patients at high risk of dying within the next t-years (e.g. 5-years) from those who will not. The standard methodology to quantify the discrimination performance of a biomarker, with right censored data, is to estimate time dependent ROC curves, ROC(t). In presence of clustered failure times, the common strategy is to ignore heterogeneity in the phase of evaluation of the performance of a candidate biomarker, but to confirm its discriminatory capacity, it is important to account for heterogeneity while adjusting for clinical covariates. The usefulness of our approach is illustrated on our motivating example, which consists in the first meta-analysis on individual data of more than 2000 patients from 15 centers with non metastatic breast cancer. Its objective was to quantify the clinical usefulness of circulating tumor cells (CTCs) count as a prognostic marker of survival.
ROC(t) allows to study the capacity of a biomarker Y to discriminate between patients who experience event prior time t (cumulative cases) from those who do not up to time t (dynamic controls). The current methodol- ogy does not account for heterogeneity while estimating ROC(t). In this work, we fill this gap by proposing an extension to clustered data of the Song & Zhou method (Statistica Sinica, 2008). To estimate the covariate- specific time dependent ROC curve we consider a joint model: (i) shared frailty model which links the covariates and the biomarker to the time-to-event, (ii) location scale model to link the covariates to the biomarker. We evaluate the performance of the proposed method in a simulation study. We demonstrate an application of the estimator to data derived from a meta-analysis on individual patient data with non metastatic breast cancer where the goal is to understand the clinical usefulness of CTCs count for this scenario. In particular, we estimate the covariate-specific ROC curves that quantify the discrimination performance of CTCs count within subgroups of patients having the same tumor stage at time of diagnosis, since subjects with inflammatory tumor show a higher number of CTCs and a poorer prognosis. A bootstrap method is proposed for calculating confidence intervals.
The estimator is computationally simple and the simulation results highlighted the robustness of the method at varying of censoring with negligible bias (≈ 10−3). Moreover, we provide the results for the motivating example with the time dependent ROC curves and respective AUCs for different tumor stage. The wide confidence intervals highlighted that having inflammatory tumor does not influence the discrimination of the CTCs count.
In presence of clustered failure times it is important to take into account heterogeneity. In fact, the introduction of a random effect (frailty) is needed to estimate the performance of the biomarker in the general population. In this scenario, the covariate-specific time dependent ROC curve can be easily estimated with the proposed approach.