Inference and validation of prognostic marker for correlated survival data with application to cancer

Clustered data often arises in medical research. These are characterized by correlations between observations belonging to the same cluster. Here, we discuss some extension to clustered data in different contexts: evaluating the performance of a candidate biomarker, and assessing the treatment effect in an individual patient data (IPD) meta-analysis with competing risks. The former was motivated by the IMENEO study, an IPD meta-analysis where the prognostic validity of the Circulating Tumor Cells (CTCs) was of interest. Our objective was to determine how well CTCs discriminates patients that died from the one that did not within the t-years, comparing individuals with same tumor stage. Although the covariate-specific time dependent ROC curve has been widely used for biomarker's discrimination, there is no methodology that can handle clusteres censored data. We proposed an estimator for the covariate-specific time dependent ROC curves and area under the ROC curve when clustered failure times are detected. We considered a shared frailty model for modeling the effect of the covariates and the biomarker on the outcome in order to account for the cluster effect. A simulation study was conducted and it showed negligible bias for the proposed estimator and a nonparametric one based on inverse probability censoring weighting, while a semiparametric estimator, ignoring the clustering, is markedly biased.We further considered an IPD meta-analysis with competing risks to assess the benefit of the addition of chemotherapy to radiotherapy on each competing endpoint for patients with nasopharyngeal carcinoma. Recommendations for the analysis of competing risks in the context of randomized clinical trials are well established. Surprisingly, no formal guidelines have been yet proposed to conduct an IPD meta-analysis with competing risk endpoints. To fill this gap, this work detailed: how to handle the heterogeneity between trials via a stratified regression model for competing risks and it highlights that the usual metrics of inconsistency to assess heterogeneity can readily be employed. The typical issues that arise with meta-analyses and the advantages due to the availability of patient-level characteristics were underlined. We proposed a landmark approach for the cumulative incidence function to investigate the impact of follow up on the treatment effect.The assumption of non informative cluster size was made in both the analyses. The cluster size is said to be informative when the outcome depends on the size of the cluster conditional on a set of covariates. Intuitively, a meta-analysis would meet this assumption. However, non informative cluster size is commonly assumed even though it may be not true in some situations and it leads to incorrect results. Informative cluster size (ICS) is a challenging problem and its presence has an impact on the choice of the correct methodology. We discussed more in details interpretation of results and which quantities can be estimated under which conditions. We proposed a test for ICS with censored clustered data. To our knowledge, this is the first test on the context of survival analysis. A simulation study was conducted to assess the power of the test and some illustrative examples were provided.The implementation of each of these developments are available at https://github.com/AMeddis.