Pseudo full likelihood estimation for prospective survival analysis with a general semiparametric shared frailty model: asymptotic theory

General Semiparametric Shared Frailty Model Estimation and Simulation with frailtySurv

The R package frailtySurv for simulating and fitting semi-parametric shared frailty models is introduced. Package frailtySurv implements semi-parametric consistent estimators for a variety of frailty distributions, including gamma, log-normal, inverse Gaussian and power variance function, and provides consistent estimators of the standard errors of the parameters' estimators. The parameters' estimators are asymptotically normally distributed, and therefore statistical inference based on the results of this package, such as hypothesis testing and confidence intervals, can be performed using the…

通过 h-似然构建用于半参数脆弱模型的深度神经网络

Deep Neural Networks for Semiparametric Frailty Models via H-likelihood

本文提出 DNN-FM，用负剖面 h-似然训练 gamma 脆弱模型，实现成组生存数据预测，并在实验和真实数据中优于现有方法及 DNN-Cox。

Prospective survival analysis with a general semiparametric shared frailty model - a pseudo full likelihood approach

In this work we provide a simple estimation procedure for a general frailty model for analysis of prospective correlated failure times. Rigorous large-sample theory for the proposed estimators of both the regression coefficient vector and the dependence parameter is given, including consistent variance estimators. In a simulation study under the widely used gamma frailty model, our proposed approach was found to have essentially the same efficiency as the EM-based estimator considered by other authors, with negligible difference between the standard errors of the two estimators. The proposed a…

Case-Control Survival Analysis with a General Semiparametric Shared Frailty Model - a Pseudo Full Likelihood Approach

In this work we deal with correlated failure time (age at onset) data arising from population-based case-control studies, where case and control probands are selected by population-based sampling and an array of risk factor measures is collected for both cases and controls and their relatives. Parameters of interest are effects of risk factors on the hazard function of failure times and within-family dependencies of failure times after adjusting for the risk factors. Due to the retrospective nature of sampling, a large sample theory for existing methods has not been established. We develop a n…

Exponent dependence measures of survival functions and correlated frailty models

The present article studies survival analytic aspects of semiparametric copula dependence models with arbitrary univariate marginals. The underlying survival functions admit a representation via exponent measures which have an interpretation within the context of hazard functions. In particular, correlated frailty survival models are linked to copulas. Additionally, the relation to exponent measures of minumum-infinitely divisible distributions as well as to the Lévy measure of the Lévy-Khintchine formula is pointed out. The semiparametric character of the current analyses and the construction…

Robust Inference for Univariate Proportional Hazards Frailty Regression Models

We consider a class of semiparametric regression models which are one-parameter extensions of the Cox [J. Roy. Statist. Soc. Ser. B 34 (1972) 187-220] model for right-censored univariate failure times. These models assume that the hazard given the covariates and a random frailty unique to each individual has the proportional hazards form multiplied by the frailty. The frailty is assumed to have mean 1 within a known one-parameter family of distributions. Inference is based on a nonparametric likelihood. The behavior of the likelihood maximizer is studied under general conditions where the fitt…