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Extensions of cox model for non-proportional hazards purpose

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Borucka J.
Econometrics. Ekonometria. Advances in Applied Data Analytics
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2014
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issue 3(45)
85-101
EN
Cox proportional hazard model is one of the most common methods used in time to event analysis. The idea of the model is to define a hazard level as a dependent variable which is explained by the time-related component (so-called baseline hazard) and the covariates- related component. The model is based on several restrictive assumptions one of which is the assumption of proportional hazard. However, if this assumption is violated, this does not necessarily prevent an analyst from using Cox model. The current paper presents two ways of model modification in the case of non-proportional hazards: introducing interactions of selected covariates with function of time and stratification model. Calculations performed give the evidence that both methods result in better model fit as compared with the original model. Additionally, they allow interpreting the parameters estimates more precisely, taking into account the effect of the covariate at the hazard level that is changing over time. The choice of the appropriate method of tied events handling however is not straightforward and should be adjusted to the particular analysis purpose.
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The modified Lunn-McNeil model in the assessment of intensity of exiting from the unemployment

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Bieszk-Stolorz B.
Econometrics. Ekonometria. Advances in Applied Data Analytics
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2019
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issue vol. 23 no. 1
77-89
EN
The goal of the article is the assessment of the relative intensity of exiting from unemployment of long-term unemployed people with relation to their characteristics: gender, age, education, seniority and the number of subsequent registrations. The modified Lunn-McNeil model for various types of competing events: accepting the job, refusal and remaining causes of deregistration was used in the research. The modification consisted of the application of the stratified Cox model of non-proportional hazard, which allowed to assess the relative hazard after entering the state of long-term unemployment. The individual data of persons registered in the County [Powiat] Labour Office in Szczecin were used in the research. Age had the greatest impact on the change in relative hazard at the transition to long-term unemployment, while the level of education had no significant impact. The research made it possible to identify groups of people taking up work with the least intensity and refusing to take up jobs with the greatest intensity. These people should be taken into consideration during the process of creating the labour market policy.
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