Analysis of time-to-event data including frailty modeling.
There are several methods of analysing time-to-event data. These include nonparametric approaches such as Kaplan-Meier estimation and parametric approaches such as regression modeling. Parametric regression modeling involves specifying the distribution of the survival time of the individuals, which are commonly chosen to be either exponential, Weibull, log- normal, log-logistic or gamma distributed. Another well known model that does not require assumptions about the hazard function to be made is the Cox proportional hazards model. However, there may be deviations from proportional hazards which may be explained by unaccounted random heterogeneity. In the early 1980s, a series of studies showed concern with the possible bias in the estimated treatment e®ect when important covariates are omitted. Other problems may be encountered with the traditional proportional hazards model when there is a possibility of correlated data, for instance when there is clustering. A method of handling these types of problems is by making use of frailty modeling. Frailty modeling is a method whereby a random e®ect is incorporated in the Cox pro- portional hazards model. While this concept is fairly simple to understand, the method of estimation of the ¯xed and random e®ects becomes complicated. Various methods have been explored by several authors, including the Expectation-Maximisation (EM) algorithm, pe- nalized partial likelihood approach, Markov Chain Monte Carlo (MCMC) methods, Monte Carlo EM approach and di®erent methods using Laplace approximation. The lack of available software is problematic for ¯tting frailty models. These models are usually computationally extensive and may have long processing times. However, frailty modeling is an important aspect to consider, particularly if the Cox proportional hazards model does not adequately describe the distribution of survival time.