Extended Hazard Regression for Censored Survival Data with Covariates: A Spline Approximation for the Baseline Hazard Function

Biometrics ◽  
1987 ◽  
Vol 43 (1) ◽  
pp. 181 ◽  
Author(s):  
Jamshid Etezadi-Amoli ◽  
Antonio Ciampi
Keyword(s):  
Survival Data ◽  
Hazard Function ◽  
Spline Approximation ◽  
Hazard Regression ◽  
Censored Survival Data ◽  
Baseline Hazard ◽  
Baseline Hazard Function

B-spline approximation for the baseline hazard function

1991 ◽  
Vol 2 (3) ◽  
pp. 323-339 ◽  
Author(s):  
James Angelos ◽  
Carl M.-S. Lee ◽  
Karan P. Singh
Keyword(s):  
Hazard Function ◽  
Spline Approximation ◽  
B Spline ◽  
Baseline Hazard ◽  
Baseline Hazard Function

Simulating Duration Data for the Cox Model

2018 ◽  
Vol 7 (04) ◽  
pp. 921-928 ◽  
Author(s):  
Jeffrey J. Harden ◽  
Jonathan Kropko
Keyword(s):  
Hazard Function ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Cox Model ◽  
Cox Proportional Hazards ◽  
Cox Proportional Hazards Model ◽  
Simulation Studies ◽  
Baseline Hazard ◽  
Baseline Hazard Function ◽  
Time Varying Covariates

The Cox proportional hazards model is a popular method for duration analysis that is frequently the subject of simulation studies. However, no standard method exists for simulating durations directly from its data generating process because it does not assume a distributional form for the baseline hazard function. Instead, simulation studies typically rely on parametric survival distributions, which contradicts the primary motivation for employing the Cox model. We propose a method that generates a baseline hazard function at random by fitting a cubic spline to randomly drawn points. Durations drawn from this function match the Cox model’s inherent flexibility and improve the simulation’s generalizability. The method can be extended to include time-varying covariates and non-proportional hazards.

scholarly journals Nonparametric Bayes estimators for hazard functions based on right censored data

2002 ◽  
Vol 33 (2) ◽  
pp. 173-190 ◽  
Author(s):  
I. W. McKeague ◽  
M. Tighiouart
Keyword(s):  
Survival Data ◽  
Hazard Rate ◽  
Markov Random Fields ◽  
Hazard Function ◽  
Right Censored Data ◽  
Hazard Functions ◽  
Censored Survival Data ◽  
Step Functions ◽  
Sample Paths ◽  
The Mean

In this article, we analyse right censored survival data by modelling their common hazard function nonparametrically. The hazard rate is assumed to be a stochastic process, with sample paths taking the form of step functions. This process jumps at times that form a time-homogeneous Poisson process, and a class of Markov random fields is used to model the values of these sample paths. Features of the posterior distribution, such as the mean hazard rate and survival probabilities, are evaluated using the Metropolis--Hastings--Green algorithm. We illustrate our methodology by simulation examples.

Proportional hazard model for cutting tool recovery in machining

2019 ◽  
Vol 234 (2) ◽  
pp. 322-332
Author(s):  
Abdoulaye Diamoutene ◽  
Farid Noureddine ◽  
Rachid Noureddine ◽  
Bernard Kamsu-Foguem ◽  
Diakarya Barro
Keyword(s):  
Hazard Function ◽  
Cutting Tool ◽  
Hazard Model ◽  
Value Theory ◽  
Extreme Value ◽  
Operating Conditions ◽  
Proportional Hazard ◽  
Proportional Hazard Model ◽  
Baseline Hazard ◽  
Baseline Hazard Function

The proportional hazard model is a statistical method capable of including information on environmental and operating conditions. In machining, in the reliability field of a cutting tool, the interest of using proportional hazard model is highlighted. On one hand, the environmental and operating conditions are described and taken into account as explanatory variables. Three covariates are considered, namely, the vibration signal, the hardness material, and the lubrication/cooling. On the other hand, a new baseline hazard function is designed according to phenomena of tiny tool breakage followed by a self-sharpening process. This latter phenomenon, which can be considered as a rare event, prompted us to study extreme value theory to propose an adequate baseline hazard function. The newly obtained baseline hazard function will be named generalized extreme value proportional hazard model. This function is obtained thanks to the Gumbel function and has the property to be non-monotonic, an increasing then decreasing function. An alternative option as a baseline hazard function, based on the flexible Weibull distributions, is also proposed. Results produced in this article show the impact of all these variables on the surface roughness of the machined parts. According to reliability studies, the premature replacement of the cutting tool implying financial losses can be delayed. This may be of particular significance and benefit, in terms of sustainable development, in the case of mass production, by limiting the frequency of tool replacement.

Simultaneous monitoring for regression coefficients and baseline hazard profile in Cox modeling of time-to-event data

Biostatistics ◽  
2020 ◽  
Author(s):  
Yishu Xue ◽  
Jun Yan ◽  
Elizabeth D Schifano
Keyword(s):  
Control Chart ◽  
Hazard Function ◽  
Cox Model ◽  
Regression Coefficients ◽  
Event Data ◽  
Time To Event ◽  
Baseline Hazard ◽  
Baseline Hazard Function ◽  
Time To Event Data ◽  
Profile Control

Summary The Cox model is the most popular tool for analyzing time-to-event data. The nonparametric baseline hazard function can be as important as the regression coefficients in practice, especially when prediction is needed. In the context of stochastic process control, we propose a simultaneous monitoring method that combines a multivariate control chart for the regression coefficients and a profile control chart for the cumulative baseline hazard function that allows for data blocks of possibly different censoring rates and sample sizes. The method can detect changes in either the parametric or the nonparametric part of the Cox model. In simulation studies, the proposed method maintains its size and has substantial power in detecting changes in either part of the Cox model. An application in lymphoma survival analysis in which patients were enrolled by 2-month intervals in the Surveillance, Epidemiology, and End Results program identifies data blocks with structural model changes.

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