Non-parametric hazard versus non-parametric frailty distribution in modelling recurrence of breast-cancer.

In extending survival models to include frailty effects, the relative merits of parametric and nonparametric formulations are unclear. The epidemiological emphasis (Clayton, Statist. in Med. 7 (1988) 819–841) has been upon nonparametric specification of conditional effects while, within econometrics (Heckman and Singer, Longitudinal Analysis of Labor Market Data (Cambridge University Press, Cambridge, 1985) 39–110) there has been some concern with the nonparametric specification of residual heterogeneity. This paper illustrates and examines some of the issues that arise in applying frailty models to the recurrence of breast cancer. The results suggest marginal advantage for the ‘econometric’ approach provided that there is no interest per se in the frailty distribution. However, it is important to adopt a flexible parametric specification for the conditional hazard and to allow different shaped hazard functions for successive durations.