Arbeitspapier
Generating survival times to simulate Cox proportional hazards models
This paper discusses techniques to generate survival times for simulation studies regarding Cox proportional hazards models. In linear regression models, the response variable is directly connected with the considered covariates, the regression coefficients and the simulated random errors. Thus, the response variable can be generated from the regression function, once the regression coefficients and the error distribution are specified. However, in the Cox model, which is formulated via the hazard function, the effect of the covariates have to be translated from the hazards to the survival times, because the usual software packages for estimation of Cox models require the individual survival time data. A general formula describing the relation between the hazard and the corresponding survival time of the Cox model is derived. It is shown how the exponential, the Weibull and the Gompertz distribution can be used to generate appropriate survival times for simulation studies. Additionally, the general relation between hazard and survival time can be used to develop own distributions for special situations and to handle flexibly parameterized proportional hazards models. The use of other distributions than the exponential distribution only is indispensable to investigate the characteristics of the Cox proportional hazards model, especially in non-standard situations, where the partial likelihood depends on the baseline hazard.
- Language
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Englisch
- Bibliographic citation
-
Series: Discussion Paper ; No. 338
- Subject
-
Cox proportional hazards model
exponential distribution
Gompertz distribution
simulation
survival times
Weibull distribution
- Event
-
Geistige Schöpfung
- (who)
-
Bender, Ralf
Augustin, Thomas
Blettner, Maria
- Event
-
Veröffentlichung
- (who)
-
Ludwig-Maximilians-Universität München, Sonderforschungsbereich 386 - Statistische Analyse diskreter Strukturen
- (where)
-
München
- (when)
-
2003
- DOI
-
doi:10.5282/ubm/epub.1716
- Handle
- URN
-
urn:nbn:de:bvb:19-epub-1716-2
- Last update
-
10.03.2025, 11:43 AM CET
Data provider
ZBW - Deutsche Zentralbibliothek für Wirtschaftswissenschaften - Leibniz-Informationszentrum Wirtschaft. If you have any questions about the object, please contact the data provider.
Object type
- Arbeitspapier
Associated
- Bender, Ralf
- Augustin, Thomas
- Blettner, Maria
- Ludwig-Maximilians-Universität München, Sonderforschungsbereich 386 - Statistische Analyse diskreter Strukturen
Time of origin
- 2003
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Erweiterung des Cox-Proportional-Hazards-Modells um latente Faktoren und latente Klassen
Cox-McFadden Partial and Marginal Likelihoods for the Proportional Hazard Model with Random Effects
Cox-McFadden Partial and Marginal Likelihoods for the Proportional Hazard Model with Random Effects
simPH: An R Package for Illustrating Estimates from Cox Proportional Hazard Models Including for Interactive and Nonlinear Effects
Model-based recursive partitioning with adjustment for measurement error : applied to the Cox’s proportional hazards and Weibull model
Lagged Duration Dependence in Mixed Proportional Hazard Models
Lagged duration dependence in mixed proportional hazard models
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The Multivariate Mixed Proportional Hazard Model: Applications and Extensions
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Reliability prediction using the Cox proportional hazards model
Erweiterung des Cox-Proportional-Hazards-Modells um latente Faktoren und latente Klassen
Cox-McFadden Partial and Marginal Likelihoods for the Proportional Hazard Model with Random Effects
Cox-McFadden Partial and Marginal Likelihoods for the Proportional Hazard Model with Random Effects
simPH: An R Package for Illustrating Estimates from Cox Proportional Hazard Models Including for Interactive and Nonlinear Effects
Model-based recursive partitioning with adjustment for measurement error : applied to the Cox’s proportional hazards and Weibull model
Lagged Duration Dependence in Mixed Proportional Hazard Models
Lagged duration dependence in mixed proportional hazard models
Determinants of Inter-Trade Durations and Hazard Rates Using Proportional Hazard ARMA Model
The Multivariate Mixed Proportional Hazard Model: Applications and Extensions
The multivariate mixed proportional hazard model : applications and extensions