Abstract
This analysis uses the concept of mixed populations—that is, ones among whose members the probability of loss varies, either in its baseline value or in its response to an intervention. Losses from such heterogeneous populations will be skewed in a systematic manner; members with high loss probabilities will be disproportionately represented among early dropouts. Similarly, such populations will respond to an intervention designed to postpone losses in a manner that reflects any differential in benefits afforded members at varying risk levels.
Traditional assessments of interventions are systematically biased, for they fail to take adequate account of variability in risk among members of a population. A general methodology is developed here for inferring the structure of a mixed population to the extent possible, for predicting accurately its response to an intervention and for extending existing models of mortality. The methodology is applied to data drawn from a number of health-related examples. For hernia recurrence, an outstanding fit is achieved when individuals at the 10th percentile are assigned 100 times the 5-yr recurrence risk of those at the 90th percentile. A blood pressure control example shows that traditional assessments overstate mortality reductions at age 75 by 16%. Cross-population comparisons of life expectancy (by nation and by race) exhibit crossovers in remaining life expectancy with increasing age.
The mixed-population approach can be useful whenever there are heterogeneous populations with dropouts. Whether the populations at issue consist of college students, satisfactory housing units, reformed criminals or patients receiving hernia repairs, attention to the variability of risk among individuals will strengthen our understanding of the dynamic processes at work, thereby enhancing our predictive powers.