KNOTTY KNOTS

Abstract

Rational for the Study Once calculation concerns with Generalized Additive Models emerged during 2002, the number and placement of knots to smooth variables using natural splines became a prominent methodological issue when estimating health effects of ambient air particles. Methods Using data from at least seven different cities in the United States (additional cities are currently being added to the analysis already performed), the paper compares the estimated effect of various ambient air particles by the number and placement of knots for variables smoothed in the non-linear models. Graphs and charts compare the estimated effects, by city, for nine different combinations of knots for smoothing time and four different combinations of knots for weather measures. The appropriateness of the number and placement of knots are compared using Akaike's Information Criterion, standard error of the estimates, patterns in residuals, and characteristics of the health and ambient air particle data. Results of the Study In general, the number of knots tends to influence the estimated effects more than the placement of the knots. Cities with greater fluctuation in weather or health endpoints tend require more knots for smoothing than those with less fluctuation. The less frequent the health endpoints (daily mortality, hospital admissions, etc.) the relatively fewer number of knots appear reasonable. For example, estimating the health effects of ambient air particles in Boston, Massachusetts, in general, requires many more knots than in Atlanta, GA. The average and standard deviation in the daily health endpoints affects the general findings, as well as the number of air particles estimated simultaneously. Conclusions The less cyclical the ambient air particle data or health endpoints, the fewer number of knots appear necessary. When multiple pollutants are included in one model, when estimating effects and comparing them across multiple cities, etc. the “best” number of knots for each individual particulate measure might not be the best overall strategy. When presenting results, more than one scenario may be most appropriate to illustrate the sensitivity of the estimated effects as a function of the number/placement of knots.