\)   Nested models are compared using the likelihood ratio (LR) test. Under the null hypothesis that the models do not differ the likelihood test statistic approximately follows a χ2 distribution with m degrees of freedom where m is the number of additionally included covariates. The LR-test statistic is computed as two times the difference between the log likelihoods (LL): LR = 2 [LL(present model) – LL(reference model)]. The use of likelihood ratio tests is limited to nested models. In order to compare non-nested models we used the graphical methods described by Blossfeld and Rohwer (2002). We performed a non-parametric

estimation of a survivor function using the PND-1186 datasheet selleck screening library product limit estimation (Kaplan and Meier 1958). Then, given a parametric assumption, the survivor function is transformed so that the results become a linear function that can be plotted. If the model is appropriate, the resulting plot should be linear and the accuracy of the fit can be evaluated with the R 2 measure. The graphical check, however, is not possible for the Gompertz–Makeham model (unless a = 0 or c = 0). Pseudoresiduals were also computed to check the statistical fit of the parametric models (Cox and Snell 1968). If the model is appropriate, the pseudoresiduals should follow approximately a standard exponential distribution. Napabucasin concentration A plot of the logarithm of

the survivor function against the residuals should be a straight line that passes through the origin (Blossfeld and Rohwer 2002). Ethical approval Ethical approval was sought from the Medical Ethics Committee of the University Medical Center Groningen, who advised that according to Dutch law ethical clearance why was not required for this secondary study on sickness absence data. Results Between 1998 and 2001, 16,433 employees (30%) had a total of 22,159 long-term sickness absence episodes. The majority of workers (73%; 11,923) who were long-term absent had one episode; 21% (N = 3,495) had two episodes and 6% (N = 1,015) had three or more long-term

absence episodes. Onset of long-term sickness absence From the generalized gamma distributions with k = 1 it can be seen that the exponential model and the Weibull model give the best fit (see Table 1). The Weibull model does not have a better fit than the exponential model (LR(1) = 2, p = 0.157). The Gompertz–Makeham model does have a better fit than the exponential model: LR(2) = 10 (p = 0.007). The negative C-parameter of the Gompertz–Makeham model indicates a declining rate of long-term absence with increasing duration. In Fig. 2 the graphical checks are plotted. The plots of the exponential and the Gompertz–Makeham models show a straight line suggesting good fits. However, the exponential model is the simplest of the parametric alternatives, and seems a good choice because of that simplicity.