Attrition in heterogeneous cohorts - James Vaupel; Zhen Zhang (Demographic Research, 2010)
In a heterogeneous cohort, the change with age in the force of mortality or some other kind of hazard or intensity of attrition depends on how the hazard changes with age for the individuals in the cohort and on how the composition of the cohort changes due to the loss of those most vulnerable to attrition. Here we prove that the change with age for the cohort equals the average of the change in the hazard for the individuals in the cohort minus the variance in the hazard across individuals. The variance captures the compositional change. This very general and remarkably elegant relationship can be applied to understand and to analyze changes with age in many kinds of demographic hazards, including, e.g., the lifetable aging rate or the intensity of first births.