Frailty models with applications in medical research : observed and simulated data

Abstract

Multivariate or cluster failure time data are common in survival analysis and nding an appropriate method to model the correlation among the observations is a very important issue for valid and reliable statistical inference. The primary objective of this project was to review various models for clustered survival data with focus on frailty models and their properties. Semi parametric Cox marginal and frailty models were used to analyze observed right censored data from a multicenter clinical trial. A simulation study was conducted to assess the impact of frailty distribution mis-speci cation on parameters estimates. Di erent settings in terms of the number of centers and true heterogeneity parameter were considered. From the observed data, the estimated heterogeneity parameters were small yielding insigni cant center e ect. From the simulation study, the regression coe cient was less a ected by mis-speci cation of the frailty distribution and initial simulation settings compared to the heterogeneity parameter. In conclusion, in the absence of center e ect, event times were homogenous between and within the centers. From simulation study, gamma frailty model would be a practical choice in real data analysis with time to event endpoint when the regression parameters are of primary interest and when the choice of frailty distribution is not straightforward. Key