International Biometric Society Focussed Model Selection for Frailty Models

In survival analysis recurrent event times are often observed on the same subject. These event times may be correlated and Cox’s (1972) proportional hazards (PH) model has been extended by the inclusion of frailty (or random effect) terms to model this correlation. Typically, in such a model we deal with three unknown structures in the conditional hazard λij(t;xi, ui) = λ0(t) exp(x′ijβ).ui (1) where i = 1,...,m independent subjects and j = 1,..., ni indexes the recurrent survival times on the ith subject whence n = Σni. Formally, λ0(t) is an unknown function of possi-bly large dimension, β is a regression parameter of fixed dimension p and we may choose ui = exp(ziν) where zi is the ith row of a partitioned model matrix, ν = (ν1;...; νk)T is a par-titioned vector of k distinct vector frailty components, each following a different distribution eg νr ∼ Nqr(0; Σr), r = 1,..., k. We assume there are maximally d frailty dispersion parameters depending on how the Σr are parametrized in terms of a vector α ′ = (α1,..., αk), where dim (α) = d. With these arrangements, our interest lies in developing model selection criteria to identif