  Frailty models are often the model of choice for heterogeneous survival data.
A frailty model contains both random effects and fixed effects, with the random
effects accommodating for the correlation in the data. Different estimation
procedures have been proposed for the fixed effects and the variances of and
covariances between the random effects. Especially with an unspecified baseline
hazard, i.e., the Cox model, the few available methods deal only with a
specific correlation structure. In this paper, an estimation procedure, based
on the integrated partial likelihood, is introduced, which can generally deal
with any kind of correlation structure. The new approach, namely the
maximisation of the integrated partial likelihood, combined with a stochastic
estimation procedure allows also for a wide choice of distributions for the
random effects. First, we demonstrate the almost sure convergence of the
stochastic algorithm towards a critical point of the integrated partial
likelihood. Second, numerical convergence properties are evaluated by
simulation. Third, the advantage of using an unspecified baseline hazard is
demonstrated through application on cancer clinical trial data.
