ABSTRACT
In this chapter, we discuss dierent method of estimation for shared frailty models which are used more often and they have a lot of applications. Frailties are usually viewed as unobserved covariates. This led to the use of the EM algorithm as an tool. However, the algorithm is slow, variance estimates require further computation. Penalized partial likelihood (PPL) approach provides an alternate approach. The frailty terms are treated as additional regression coecients which are constrained by a penalty function added to the loglikelihood. They are computationally similar to other shrinkage methods for penalized regression such as ridge regression, the lasso and smoothing splines. Standard algorithms for tting Cox semiparametric and parametric models can be simply extended to include penalty functions. These methods usually converge quickly and produce both point and variance estimates for model parameters. The EM algorithm and PPL approach give the same results in the case of the gamma frailty model. It is proved theoretically in Duchateau and Janssen (2008). That is why PPL approach can be safely used for the gamma frailty density.
