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

Abstract

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

Objective and methods: 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.

Results: 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.

Conclusions: 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.

Keywords::

• Time-series analysis
• daily mortality
• morbidity
• frailty
• life expectancy
• Kalman filter

Acknowledgments

The authors gratefully acknowledge the support and guidance of Dr. Ronald E. Wyzga during the performance of this project. They thank Rebecca Klemm and Eddie Thomas for the generalized linear model regression runs used in Supplementary Appendix D and the reviewers for their insightful comments.

Declaration of interest

This research was supported by the Electric Power Research Institute; the conclusions are those of the authors alone.