Copula inference under censoring

This paper discusses copula model selection procedures and goodness-of-fit tests under censoring. The proposed methodology is based on a comparison of nonparametric and model-based estimators of the probability integral transformation, K. New weighted estimators for K are introduced. The resulting tests are compared to an existing approach by simulation and illustrated with an example involving bleeding changes in a woman's reproductive history. Copyright 2010, Oxford University Press.

Modeling of Successive Cancer Risks in Lynch Syndrome Families in the Presence of Competing Risks Using Copulas

In this article, we propose an association model to estimate the penetrance (risk) of successive cancers in the presence of competing risks. The association between the successive events is modeled via a copula and a proportional hazards model is specified for each competing event. This work is motivated by the analysis of successive cancers for people with Lynch Syndrome in the presence of competing risks. The proposed inference procedure is adapted to handle missing genetic covariates and selection bias, induced by the data collection protocol of the data at hand. The performance of the proposed estimation procedure is evaluated by simulations and its use is illustrated with data from the Colon Cancer Family Registry (Colon CFR)

Robust Estimation of Mean Functions and Treatment Effects for Recurrent Events Under Event-Dependent Censoring and Termination: Application to Skeletal Complications in Cancer Metastatic to Bone

In clinical trials featuring recurrent clinical events, the definition and estimation of treatment effects involves a number of interesting issues, especially when loss to follow-up may be eventrelated and when terminal events such as death preclude the occurrence of further events. This paper discusses a clinical trial of breast cancer patients with bone metastases where the recurrent events are skeletal complications, and where patients may die during the trial. We argue that treatment effects should be based on marginal rate and mean functions. When recurrent event data are subject to event-dependent censoring, however, ordinary marginal methods may yield inconsistent estimates. Incorporating correctly specified inverse probability of censoring weights into analyses can protect against dependent censoring and yield consistent estimates of marginal features. An alternative approach is to obtain estimates of rate and mean functions from models that involve some conditioning to render censoring conditionally independent. We consider three methods of estimating mean functions of recurrent event processes and examine the bias and efficiency of unweighted and inverse probability weighted versions of the methods with and without a terminating event. We compare the methods via simulation and use them to analyse the data from the breast cancer trial.Natural Sciences and Engineering Research Council of Canada (RJC RGPIN 155849, JFL RGPIN 8597); Canadian Institutes for Health Research (FRN 13887); Canada Research Chair (Tier 1) – CIHR funded (950-226626

Risks of Colorectal Cancer and Cancer-Related Mortality in Familial Colorectal Cancer Type X and Lynch Syndrome Families

BACKGROUND: The risk of cancers is well characterized in Lynch syndrome (LS) families but has been less studied in familial colorectal cancer type X (FCCTX) families. METHODS: In this article, we compare the risk estimates of first and second colorectal cancers (CRCs) in 168 FCTTX and 780 LS families recruited through the Colon Cancer Family Registry as well as the risk of cancer-related deaths and disease-free survival (DFS) after a first CRC. Our methodology is based on a survival analysis approach, developed specifically to model the occurrence of successive cancers (ie, first and second CRCs) in the presence of competing risk events (ie, death from any causes). RESULTS: We found an excess risk of first and second CRC in individuals with LS compared to FCCTX family members. However, for an average age at first CRC of 60 years in FCCTX families and 50 years in LS families, the DFS rates were comparable in men but lower in women from FCCTX vs LS families, eg , 75.1% (95% confidence interval [CI] = 69.0% to 80.9%) vs 78.9% (95% CI = 76.3% to 81.3%) for the 10-year DFS. The 10-year risk of cancer-related death was higher in FCCTX families vs LS families, eg, 15.4% in men (95% CI = 10.9% to 19.8%) and 19.3% in women (95% CI = 13.6% to 24.7%) vs 8.9% (95% CI = 7.5% to 11.4%) and 8.7% (95% CI = 7.1% to 10.8%), respectively. CONCLUSIONS: Individuals with CRCs arising in the context of FCCTX do not experience the same improved DFS and overall survival of those with LS, and that difference may be relevant in management decisions