Scaled Fisher consistency for the partial likelihood estimation in various extensions of the Cox model

Abstract The Cox proportional hazards model has become the most widely used procedure in survival analysis. theoretical basis of original been developed various extensions. In recent years, vital research undertaken involving incorporation random effects to models. this setting, effect is a variable ( frailty ) which embraces variation among individuals or groups cannot be explained by observable covariates. right choice distribution essential for an accurate description dependence structure present data. paper, we aim investigate accuracy inference based on primer existence unobserved heterogeneity, that is, when data generating mechanism more complex than presumed and described kind extension with undefined frailty. We show conventional partial likelihood estimator under considered Fisher-consistent up scaling factor, provided symmetry-type distributional assumptions also results simulation experiments reveal exemplary behaviour estimators.