Copula Link-Based Additive Models for Right-Censored Event Time Data

Flexible parametric copula modeling approaches for clustered survival data

Copula-based survival regression models, which consist of a copula function and marginal distribution (i.e., marginal survival function), have been widely used for analyzing clustered multivariate survival data. Archimedean copula functions are useful for modeling such dependence. For the likelihood inference, one-stage and two-stage estimation methods have been usually used. The two-stage procedure can give inefficient estimation results because of separate estimation of the marginal and copula's dependence parameters. The more efficient one-stage procedure has been mainly developed under a restrictive parametric assumption of marginal distribution due to complexity of the full likelihood with unknown marginal baseline hazard functions. In this paper, we propose a flexible parametric Archimedean copula modeling approach using a one-stage likelihood procedure. In order to reduce the complexity of the full likelihood, the unknown marginal baseline hazards are modeled based on a cubic M-spline basis function that does not require a specific parametric form. Simulation results demonstrate that the proposed one-stage estimation method gives a consistent estimator and also provides more efficient results over existing one- and two-stage methods. The new method is illustrated with three clinical data sets. The Appendix provides an R function so that the proposed method becomes directly accessible to interested readers.

Single- and Multiple-Group Penalized Factor Analysis: A Trust-Region Algorithm Approach with Integrated Automatic Multiple Tuning Parameter Selection

Penalized factor analysis is an efficient technique that produces a factor loading matrix with many zero elements thanks to the introduction of sparsity-inducing penalties within the estimation process. However, sparse solutions and stable model selection procedures are only possible if the employed penalty is non-differentiable, which poses certain theoretical and computational challenges. This article proposes a general penalized likelihood-based estimation approach for single- and multiple-group factor analysis models. The framework builds upon differentiable approximations of non-differentiable penalties, a theoretically founded definition of degrees of freedom, and an algorithm with integrated automatic multiple tuning parameter selection that exploits second-order analytical derivative information. The proposed approach is evaluated in two simulation studies and illustrated using a real data set. All the necessary routines are integrated into the R package penfa.