Evidence of a threshold effect for TSP in the Philadelphia data set

The purpose of the present paper is to examine the complex set of questions about the PM-mortality exposure–response (E-R) relationship by looking at the practical and demonstrable consequences of time series model building and by considering alternate modelling methods.

Two questions are posed. The first is how to demonstrate goodness-of-fit for an exposure–response model and the effectiveness of a particular term in the model. The second is how to detect poor model fit associated with unusual relationships in the data, such as thresholds or other non-linear patterns. Suggested solutions are demonstrated using the Philadelphia data set used by Kelsall. These solutions are potentially applicable to other time series data analyses.

Examination of the example data indicate several findings. First, the addition of the pollution terms to a model which contains temporal and weather variables has a negligible change on the predictive ability of the model. While the statistical criteria are slightly improved the practical improvement in mortality prediction is minimal. Second, for these data, there is demonstrable evidence that there is a threshold effect for total suspended particulate (TSP) on predicted mortality. The threshold is also seen in the gaseous pollutants. Lastly, the inclusion of terms representing the day of the week statistically improves model fit to a greater extent than the pollution terms.

The results from this exercise suggest that several steps should be added to the traditional analysis and presentation of time-series data. These include visual and tabular presentation of results from each major model and analysis for a threshold at least for the criteria pollutant terms. The presentation elements allow the reader to independently assess model fit and the predictive capabilities of the model. Determination of a threshold allows objective determination of a no adverse effect level. Overall, application of these methods to time-series analyses provides more specificity for testing the predictive power of the model and for protecting health.Copyright © 1999 John Wiley & Sons, Ltd.