Penalized estimation for competing risks regression with applications to high-dimensional covariates

High-dimensional regression has become an increasingly important topic for many research fields. For example, biomedical research generates an increasing amount of data to characterize patients' bio-profiles (e.g. from a genomic high-throughput assay). The increasing complexity in the characterization of patients' bio-profiles is added to the complexity related to the prolonged follow-up of patients with the registration of the occurrence of possible adverse events. This information may offer useful insight into disease dynamics and in identifying subset of patients with worse prognosis and better response to the therapy. Although in the last years the number of contributions for coping with high and ultra-high-dimensional data in standard survival analysis have increased (Witten and Tibshirani, 2010. Survival analysis with high-dimensional covariates. Statistical Methods in Medical Research 19(1), 29-51), the research regarding competing risks is less developed (Binder and others, 2009. Boosting for high-dimensional time-to-event data with competing risks. Bioinformatics 25(7), 890-896). The aim of this work is to consider how to do penalized regression in the presence of competing events. The direct binomial regression model of Scheike and others (2008. Predicting cumulative incidence probability by direct binomial regression. Biometrika 95(1), 205-220) is reformulated in a penalized framework to possibly fit a sparse regression model. The developed approach is easily implementable using existing high-performance software to do penalized regression. Results from simulation studies are presented together with an application to genomic data when the endpoint is progression-free survival. An R function is provided to perform regularized competing risks regression according to the binomial model in the package timereg (Scheike and Martinussen, 2006. Dynamic Regression models for survival data. New York: Springer), available through CRAN

Efficient Estimation of Semiparametric Transformation Models for Two-Phase Cohort Studies

Under two-phase cohort designs, such as case-cohort and nested case-control sampling, information on observed event times, event indicators, and inexpensive covariates is collected in the first phase, and the first-phase information is used to select subjects for measurements of expensive covariates in the second phase; inexpensive covariates are also used in the data analysis to control for confounding and to evaluate interactions. This paper provides efficient estimation of semiparametric transformation models for such designs, accommodating both discrete and continuous covariates and allowing inexpensive and expensive covariates to be correlated. The estimation is based on the maximization of a modified nonparametric likelihood function through a generalization of the expectation-maximization algorithm. The resulting estimators are shown to be consistent, asymptotically normal and asymptotically efficient with easily estimated variances. Simulation studies demonstrate that the asymptotic approximations are accurate in practical situations. Empirical data from Wilms’ tumor studies and the Atherosclerosis Risk in Communities (ARIC) study are presented

Additive risk model with case-cohort sampled current status data

additive risk model, current status data, two phase sampling,

Buckley–James-type of estimators under the classical case cohort design

Case-cohort study, Buckley–James estimator, Right-censorship, Linear regression model, Self-consistent algorithm, Survival data,