An Assessment of the Cox Proportional Hazards Regression Model for Epidemiologic Studies : Assessment of the Cox Proportional Hazards Regression Model

Time-series, cross-sectional, and prospective cohort studies have observed associations between mortality and particulate air pollution but have been limited by ecologic design or small number of subjects or study areas. The present study evaluates effects of particulate air pollution on mortality using data from a large cohort drawn from many study areas. We linked ambient air pollution data from 151 U.S. metropolitan areas in 1980 with individual risk factor on 552,138 adults who resided in these areas when enrolled in a prospective study in 1982. Deaths were ascertained through December, 1989. Exposure to sulfate and fine particulate air pollution, which is primarily from fossil fuel combustion, was estimated from national data bases. The relationships of air pollution to all-cause, lung cancer, and cardiopulmonary mortality was examined using multivariate analysis which controlled for smoking, education, and other risk factors. Although small compared with cigarette smoking, an association between mortality and particulate air pollution was observed. Adjusted relative risk ratios (and 95% confidence intervals) of all-cause mortality for the most polluted areas compared with the least polluted equaled 1.15 (1.09 to 1.22) and 1.17 (1.09 to 1.26) when using sulfate and fine particulate measures respectively. Particulate air pollution was associated with cardiopulmonary and lung cancer mortality but not with mortality due to other causes. Increased mortality is associated with sulfate and fine particulate air pollution at levels commonly found in U.S. cities. The increase in risk is not attributable to tobacco smoking, although other unmeasured correlates of pollution cannot be excluded with certainty.

Experiments in animals and two epidemiologic studies in humans suggest that aspirin and other nonsteroidal antiinflammatory drugs (NSAIDs) may be protective against colon cancer. We tested this hypothesis in a prospective mortality study of 662,424 adults who provided information in 1982 on the frequency and duration of their aspirin use. Death rates from colon cancer were measured through 1988. The possible influence of other risk factors for colon cancer was examined in multivariate analyses for 598 case patients and 3058 matched control subjects drawn from the cohort. Death rates from colon cancer decreased with more frequent aspirin use in both men and women. The relative risk among persons who used aspirin 16 or more times per month for at least one year was 0.60 in men (95 percent confidence interval, 0.40 to 0.89) and 0.58 in women (95 percent confidence interval, 0.37 to 0.90). The risk estimates were unaffected when we excluded persons who reported at entry into the study that they had cancer, heart disease, stroke, or another condition that might influence both their aspirin use and their mortality. Adjustment for dietary factors, obesity, physical activity, and family history did not alter the findings significantly. No association was found between the use of acetaminophen and the risk of colon cancer. Regular aspirin use at low doses may reduce the risk of fatal colon cancer. Whether this is due to a direct effect of aspirin, perhaps mediated by the inhibition of prostaglandin synthesis, or to other factors indirectly associated with aspirin use is unclear.

The widely used generalized additive models (GAM) method is a flexible and effective technique for conducting nonlinear regression analysis in time-series studies of the health effects of air pollution. When the data to which the GAM are being applied have two characteristics--1) the estimated regression coefficients are small and 2) there exist confounding factors that are modeled using at least two nonparametric smooth functions--the default settings in the gam function of the S-Plus software package (version 3.4) do not assure convergence of its iterative estimation procedure and can provide biased estimates of regression coefficients and standard errors. This phenomenon has occurred in time-series analyses of contemporary data on air pollution and mortality. To evaluate the impact of default implementation of the gam software on published analyses, the authors reanalyzed data from the National Morbidity, Mortality, and Air Pollution Study (NMMAPS) using three different methods: 1) Poisson regression with parametric nonlinear adjustments for confounding factors; 2) GAM with default convergence parameters; and 3) GAM with more stringent convergence parameters than the default settings. The authors found that pooled NMMAPS estimates were very similar under the first and third methods but were biased upward under the second method.