Am J Epidemiol 2003; 158:93-94.
Copyright © 2003 by Johns
Hopkins Bloomberg School of Public Health
LETTERS TO THE EDITOR |
RE: "ON THE USE OF GENERALIZED ADDITIVE MODELS IN TIME-SERIES STUDIES OF AIR POLLUTION AND HEALTH" AND "TEMPERATURE AND MORTALITY IN 11 CITIES OF THE EASTERN UNITED STATES"
1 Department of Biostatistics, Johns Hopkins Bloomberg School of Public Health, Johns Hopkins University, Baltimore, MD.
2 Department of Epidemiology, Johns Hopkins Bloomberg School of Public Health, Johns Hopkins University, Baltimore, MD.
Recently, Dominici et al. (1) reported on the potential biases incurred when using S-Plus software (Insightful Corporation, Seattle, Washington) with default convergence criteria to fit generalized additive models. In the article by Curriero et al. (2), we used a generalized additive model with S-Plus software default convergence to describe the temperature-mortality relation in 11 US cities. These analyses have now been updated using natural splines. Although results changed quantitatively, interpretations remained qualitatively similar.
The specific model we now use has the form:
log expected mortality(t) = ns(t, 176) + ns(D0, 6) + ns(adj T1–3, 6) + ns(adj D1–3, 6) + ns(T0, 6).
The variables t, T0, D0, adj T1–3, and adj D1–3 represent, respectively, calendar time, same day temperature and dew point, adjusted average temperature, and adjusted dew point over the preceding 3-day lag (see Curriero et al. (2) for details), and ns(•, 
) represents a smooth relative risk function parameterized as a natural cubic spline with degrees of freedom for the variable indicated. The corresponding temperature relative risk curves for the 11 cities are shown in figure 1. Still apparent is the J-shaped relation between temperature and relative risk mortality (see figure 1 of Curriero et al. (2) for comparison); however, there appears to be a greater range of temperatures where the relative risk of mortality remains flat.
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Based on the mortality relative risk curves in figure 1, model 1 was reparameterized, substituting the same day temperature smooth relative risk effect ns(T0, 6) with the following series of piecewise log-linear effects:
log expected mortality(t) = ns(t, 176) + ns(D0, 6) + ns(adj T1–3, 6) + ns(adj D1–3, 6) + ß1T0 + ß2(T0 – t1)I1 + ß3(T0 – t2)I2,
where t1 < t2 are temperature values selected to represent the range at which relative risk mortality remains flat, and I1 and I2 are indicator variables defined, respectively, to be 1 when T0 ≥ t1 and T0 ≥ t2 and 0 otherwise. The results from fitting model 2 are shown together with results from model 1 in figure 1. Cold slopes and hot slopes are now estimated simultaneously from model 2 as ß1 and ß1 + ß2 + ß3, respectively (table 1). The temperature values t1 and t2 were chosen by visual inspection of the city-specific mortality relative risk curves from model 1 with emphasis on capturing the cold and hot sloped portions of the curve.
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Analysis of the variation in relative risk curves for temperature across cities proceeded as described by Curriero et al. (2), excluding the quantity minimum mortality temperature. Parameter uncertainty estimates from model 2 were used to directly estimate variances for cold and hot slopes. As previously reported, the percentage of poverty and the percentage of households with air conditioners were statistically significant predictors of the hot slope. Previously, we reported that the percentage of the population aged 65 years or more significantly predicted cold slope (table 3 of Curriero et al. (2)). It is no longer significantly associated using the updated regression methods. In addition, the dependence of the temperature-mortality relation on latitude has diminished.
REFERENCES
Editor’s note: In accordance with Journal policy, Dr. Dominici was asked if the authors wished to respond to the letter by Curriero et al. but chose not to do so.
REFERENCES
- Dominici F, McDermott A, Zeger SL, et al. On the use of generalized additive models in time-series studies of air pollution and health. Am J Epidemiol 2002;156:193–203.
[Abstract/Free Full Text] - Curriero FC, Heiner KS, Samet JM, et al. Temperature and mortality in 11 cities of the eastern United States. Am J Epidemiol 2002;155:80–7.
[Abstract/Free Full Text]
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