Proportional hazards models are among the most popular regression models in survival analysis. Multi-state models generalise them in the sense of jointly considering different types of events along with their interrelations, whereas frailty models introduce random effects to account for unobserved risk factors, possibly shared by groups of subjects.
The integration of frailty and multi-state methodology is interesting to control for unobserved heterogeneity in presence of complex event history structures, particularly appealing in multicenter clinical trials applications.
In the present thesis we propose the incorporation of nested frailties in the transition-specific hazard function; then, we develop and evaluate both parametric and semi-parametric inference. Simulation studies, performed thanks to an innovative method for generating dependent multi-state survival data, show that parametric inference is correct but extremely imprecise, whilst semiparametric methods are very competitive to evaluate the effect of covariates.
Two case studies are presented, relative to cancer multicenter clinical trials. The multi-state nature of the models allows to study the treatment effect taking into account intermediate events, while the presence of frailties reduces the attenuation effect due to clustering.
Finally, we present two new software tools, one to fit parametric frailty models
with up to twenty possible combinations of baseline and frailty distributions, and one implementing semiparametric inference for multilevel frailty models, essential to fit the new nested frailty multi-state models
