The identification of duration dependence in hazard models remains a highly-debated topic, see Machin and Manning (1999).
Cox's (1972) regression model for censored survival data was applied to our data to study the dependence of hazard of death on the explanatory variables, taking account of potential confounders.
The comparison between the data and normative model prediction of the dependence on hazard rate (session) used an analogous normalized measure: d i s = (K i s, f a s t − K i s, s l o w ) / (K i s, f a s t + K i s, s l o w ) where 'fast' and 'slow' indicate the 2 Hz and 0.1 Hz sessions respectively.
The analysis confirms a time dependence of the hazard ratio by HR status in HER2+ patients, indicating that the fixed hazard ratio of 0.72 over 10 years underestimates the difference between the HR+ and HR- groups in the first years after diagnosis.
The parameter δ 2 t 2 is a time-specific intercept term measuring duration dependence in the hazard rate out of the employment, and the coefficient ϵ2 measures the unobserved effects in the hazard rate.
The duration dependence of the hazard rate is captured in two ways.
The parameter δ 1 j t 1 ; j = 1, 2, 3 are time-specific intercept terms measuring duration dependence in the hazard rate to work, and ϵ1j are destination specific unobserved random effects.
The results are also highly robust as long as the number of support points remains between two and three.23 This may imply that the information content in the data relating to the distribution of the unobserved heterogeneity term is sufficient to ensure robust identification of the structural duration dependence in the hazard rates, as well as the effects of benefits on spell duration.
Furthermore, time dependence of the hazard ratio did not become significant (p > 0.05).
Concerning the isolated local recurrence of breast cancer, the dependence of the hazard function after the ILRR on the sojourn time is analysed.
In order to know if the function exp (- t - d)), based only on expert knowledge and describing the dependence of the hazard function on the time since recurrence (t - d), accords with reality, FPs were applied on this time-varying covariate.
