Constrained confidence intervals in time series studies of mortality and air pollution

This paper focuses on constrained confidence intervals in the context of environmental time series studies where one seeks to ascertain the effects of ambient air pollution on human mortality. If the regression parameter representing such effects is non-negative, corresponding to a belief that more pollution cannot be beneficial, a desirable goal is to produce a constrained confidence interval for the parameter which is entirely non-negative. We show how this goal can be achieved using the method of tail functions. The proposed methodology is illustrated by the application to an environmental study of 100 cities in the United States involving regressions of mortality counts on levels of particulate matter air pollution. The large number of constrained CIs that contain zero is an indication that for the majority of the 100 cities there is not enough evidence to conclude a positive association between air pollution and mortality.