The restricted cubic spline as baseline hazard in the proportional hazards model with step function time-dependent covariables

1995 ◽  
Vol 14 (19) ◽  
pp. 2119-2129 ◽  
Author(s):  
James E. Herndon ◽  
Frank E. Harrell
Keyword(s):  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Cubic Spline ◽  
Step Function ◽  
Time Dependent ◽  
Baseline Hazard ◽  
Hazards Model ◽  
Function Time

Penalized likelihood estimation of the proportional hazards model for survival data with interval censoring

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Jun Ma ◽  
Dominique-Laurent Couturier ◽  
Stephane Heritier ◽  
Ian C. Marschner
Keyword(s):  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Penalized Likelihood ◽  
Interval Censoring ◽  
Basis Functions ◽  
Likelihood Method ◽  
Baseline Hazard ◽  
Computational Performance ◽  
Hazards Model ◽  
Study Results

Abstract This paper considers the problem of semi-parametric proportional hazards model fitting where observed survival times contain event times and also interval, left and right censoring times. Although this is not a new topic, many existing methods suffer from poor computational performance. In this paper, we adopt a more versatile penalized likelihood method to estimate the baseline hazard and the regression coefficients simultaneously. The baseline hazard is approximated using basis functions such as M-splines. A penalty is introduced to regularize the baseline hazard estimate and also to ease dependence of the estimates on the knots of the basis functions. We propose a Newton–MI (multiplicative iterative) algorithm to fit this model. We also present novel asymptotic properties of our estimates, allowing for the possibility that some parameters of the approximate baseline hazard may lie on the parameter space boundary. Comparisons of our method against other similar approaches are made through an intensive simulation study. Results demonstrate that our method is very stable and encounters virtually no numerical issues. A real data application involving melanoma recurrence is presented and an R package ‘survivalMPL’ implementing the method is available on R CRAN.

scholarly journals Testing Linear and Nonlinear Hypotheses in a Cox Proportional Hazards Model with Errors in Covariates

2019 ◽  
Vol 58 (1) ◽  
pp. 39-47
Author(s):  
Oksana Chernova ◽  
Alexander Kukush
Keyword(s):  
Measurement Errors ◽  
Hazard Rate ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Cox Proportional Hazards ◽  
Cox Proportional Hazards Model ◽  
Baseline Hazard ◽  
Hazards Model ◽  
Regression Parameters ◽  
Linear And Nonlinear

We investigate linear and nonlinear hypotheses testing in a Cox proportional hazards model for right-censored survival data when the covariates are subject to measurement errors. In Kukush and Chernova (2018) [Theor. Probability and Math. Statist. 96, 101–110], a consistent simultaneous estimator is introduced for the baseline hazard rate and the vector of regression parameters. Therein the baseline hazard rate belongs to an unbounded set of nonnegative Lipschitz functions, with fixed constant, and the vector of regression parameters belongs to a compact parameter set. Based on the estimator, we develop two procedures to test nonlinear and linear hypotheses about the vector of regression parameters: Wald-type and score-type tests. The latter is based on an unbiased estimating equation. The consistency of the tests is shown.

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