Germán Rodríguez

Survival Analysis
Princeton University
The figure below shows age-specific mortality rates for black and white males using U.S. data from 2002. You will notice that the population-average hazard is higher for blacks fror every age up to 87, but then the curves cross over.

To illustrate how this type of pattern could be the result of unobserved heterogeneity I will treat these synthetic-cohort rates as if they applied to real heterogeneous cohorts where frailty has a gamma distribution. The initial curves use homogeneous cohorts, but using the slider you can change the variance of heterogeneity from 0 to 1.

You will notice that increasing heterogeneity eventually leads to the subject-specific hazard curves to uncross, showing that the observed pattern could result from black males experiencing more selection as a result of higher mortality rates. However, the variance needed to remove the crossover is very high. An alternative explanation may lie in age misreporting.

Code for the underlying calculations in Stata or R may be found here.