A new time-series methodology for estimating relationships between elderly frailty, remaining life expectancy, and...

Many publications estimate short-term air pollution-mortality risks, but few estimate the associated changes in life-expectancies.

We present a new methodology for analyzing time series of health effects, in which prior frailty is assumed to precede short-term elderly nontraumatic mortality. The model is based on a subpopulation of frail individuals whose entries and exits (deaths) are functions of daily and lagged environmental conditions: ambient temperature/season, airborne particles, and ozone. This frail susceptible population is unknown; its fluctuations cannot be observed but are estimated using maximum-likelihood methods with the Kalman filter. We used an existing 14-y set of daily data to illustrate the model and then tested the assumption of prior frailty with a new generalized model that estimates the portion of the daily death count allocated to nonfrail individuals.

In this demonstration dataset, new entries into the high-risk pool are associated with lower ambient temperatures and higher concentrations of particulate matter and ozone. Accounting for these effects on antecedent frailty reduces this at-risk population, yielding frail life expectancies of 5-7 days. Associations between environmental factors and entries to the at-risk pool are about twice as strong as for mortality. Nonfrail elderly deaths are seen to make only small contributions.

This new model predicts a small short-lived frail population-at-risk that is stable over a wide range of environmental conditions. The predicted effects of pollution on new entries and deaths are robust and consistent with conventional morbidity/mortality times-series studies. We recommend model verification using other suitable datasets.