A composite likelihood approach to multivariate survival data (Q2739866)

The author considers multisample survival times analysis with dependent samples. To describe the dependence between the survival times the shared frailty model is used in which the considered survival times, say \(T_1\) and \(T_2\), depend on an unobserved frailty variable \(Z\). Conditional hazard functions of \(T_i\) given \(Z\) are \(Z\alpha_i(t)\) for baseline hazard functions \(\alpha_i\). E.g., if \(Z\) has gamma distribution with \({\mathbf E}Z=0\), \(\text{Var} Z=\vartheta\), then the joint survival function is NEWLINE\[NEWLINE\Pr\{T_1>t, T_2>t\}=(1+\vartheta \{A_1(t)+A_2(t)\})^{-\vartheta^{-1}}, NEWLINE\]NEWLINE where \(A_i(t)=\int_0^t\alpha_i(s)ds\). In the multisample case, many frailty variables can be used to describe real dependencies of the samples. The standard likelihood approach to such models fails since the likelihood ratio is unbounded.NEWLINENEWLINENEWLINEThe author develops a composite likelihood approach which is based on the use of a weighted product of parewise likelihoods contributions. This technique is applied to data on survival times of adopted children and their adoptive and biological parents.