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Influence of random effects on bivariate and trivariate survival models

We discuss the influence of univariate, bivariate and trivariate random effects on the hazard rate, survival function and other measures of dependence. When the existence of associated random effects is ignored, the hazard rate will be underestimated and the survival times are stochastically larger than expected. We also show that odds ratios and densities of L-measures for bivariate and trivariate survival times are functions of the conditional moments or cumulants of random effects given that the i-th life length is greater than t p for all i.