Estimation of the cumulative incidence function under multiple dependent and independent censoring mechanisms

Competing risks occur in a time-to-event analysis in which a patient can experience one of several types of events. Traditional methods for handling competing risks data presuppose one censoring process, which is assumed to be independent. In a controlled clinical trial, censoring can occur for several reasons: some independent, others dependent. We propose an estimator of the cumulative incidence function in the presence of both independent and dependent censoring mechanisms. We rely on semi-parametric theory to derive an augmented inverse probability of censoring weighted (AIPCW) estimator. We demonstrate the efficiency gained when using the AIPCW estimator compared to a non-augmented estimator via simulations. We then apply our method to evaluate the safety and efficacy of three anti-HIV regimens in a randomized trial conducted by the AIDS Clinical Trial Group, ACTG A5095.     

Reweighted estimators for additive hazard model with censoring indicators missing at random

Survival data with missing censoring indicators are frequently encountered in biomedical studies. In this paper, we consider statistical inference for this type of data under the additive hazard model. Reweighting methods based on simple and augmented inverse probability are proposed. The asymptotic properties of the proposed estimators are established. Furthermore, we provide a numerical technique for checking adequacy of the fitted model with missing censoring indicators. Our simulation results show that the proposed estimators outperform the simple and augmented inverse probability weighted estimators without reweighting. The proposed methods are illustrated by analyzing a dataset from a breast cancer study.     

A regularized variable selection procedure in additive hazards model with stratified case-cohort design

Case-cohort designs are commonly used in large epidemiological studies to reduce the cost associated with covariate measurement. In many such studies the number of covariates is very large. An efficient variable selection method is needed for case-cohort studies where the covariates are only observed in a subset of the sample. Current literature on this topic has been focused on the proportional hazards model. However, in many studies the additive hazards model is preferred over the proportional hazards model either because the proportional hazards assumption is violated or the additive hazards model provides more relevent information to the research question. Motivated by one such study, the Atherosclerosis Risk in Communities (ARIC) study, we investigate the properties of a regularized variable selection procedure in stratified case-cohort design under an additive hazards model with a diverging number of parameters. We establish the consistency and asymptotic normality of the penalized estimator and prove its oracle property. Simulation studies are conducted to assess the finite sample performance of the proposed method with a modified cross-validation tuning parameter selection methods. We apply the variable selection procedure to the ARIC study to demonstrate its practical use.     

Discussion of “Nonparametric Bayesian Inference in Applications”: Bayesian nonparametric methods in econometrics

The use of Bayesian nonparametrics models has increased rapidly over the last few decades driven by increasing computational power and the development of efficient Markov chain Monte Carlo algorithms. We review some applications of these models in economic applications including: volatility modelling (using both stochastic volatility models and GARCH-type models) with Dirichlet process mixture models, uses in portfolio allocation problems, long memory models with flexible forms of time-dependence, flexible extension of the dynamic Nelson-Siegel model for interest rate yields and multivariate time series models used in macroeconometrics.     

A penalized likelihood method for nonseparable space–time generalized additive models

In this paper, we study space–time generalized additive models. We apply the penalyzed likelihood method to fit generalized additive models (GAMs) for nonseparable spatio-temporal correlated data in order to improve the estimation of the response and smooth terms of GAMs. The results show that our space–time generalized additive models estimated response and smooth terms reasonable well, and in addition, the mean squared error, mean absolute deviation and coverage intervals improved considerably compared to the classic GAM. An application on particulate matter concentration in the North-Italian region of Piemonte is also presented.     

A hierarchical model for ordinal matrix factorization

This paper proposes a hierarchical probabilistic model for ordinal matrix factorization. Unlike previous approaches, we model the ordinal nature of the data and take a principled approach to incorporating priors for the hidden variables. Two algorithms are presented for inference, one based on Gibbs sampling and one based on variational Bayes. Importantly, these algorithms may be implemented in the factorization of very large matrices with missing entries.     

Sequential Monte Carlo for rare event estimation

This paper discusses a novel strategy for simulating rare events and an associated Monte Carlo estimation of tail probabilities. Our method uses a system of interacting particles and exploits a Feynman-Kac representation of that system to analyze their fluctuations. Our precise analysis of the variance of a standard multilevel splitting algorithm reveals an opportunity for improvement. This leads to a novel method that relies on adaptive levels and produces, in the limit of an idealized version of the algorithm, estimates with optimal variance. The motivation for this theoretical work comes from problems occurring in watermarking and fingerprinting of digital contents, which represents a new field of applications of rare event simulation techniques. Some numerical results show performance close to the idealized version of our technique for these practical applications.