Choice of Degree of Smoothing in Fitting Nonparametric Regression Models for Temperature-mortality Relation in Japan Based on a Priori Knowledge

抄録

The objectives of this study were to determine the extent of smoothness for some selected nonparametric models, and to examine the suitability of the default method for evaluating temperature-mortality relation in Japan. Our analysis was conducted for Japanese aged 65 and older, from 1972 to 1994. The models we selected were smoothing spline and locally-weighted scatterplot smoothing (LOWESS/LOESS). Firstly, we determined the degrees of smoothness by an “a priori” approach. After exhaustively drawing curves of the relation between daily maximum temperature and sex-specific mortality rate for each prefecture using a wide range of smoothing parameters, we selected the degrees of smoothing for each prefecture, based on a priori knowledge. This assumes that we a priori know that the relation between temperature and mortality is V-shaped, i.e., between two temperature extremes the curve should have a minimum mortality rate at a certain temperature (optimum temperature=OT), which is an absolute minimum with no local extremes. For the cases in which no OT was observed for any of the degree of smoothing, we did not assign an OT. Among selected degrees of smoothing, we further selected “best” degrees of smoothing for the models such that the degrees of smoothing yielded OTs for all the prefectures (except for those with non-OT). Next, based on the “best” degrees of smoothing, we examined the generalized cross-validation (GCV) method, which is one of the most successful “default” methods for selecting a smoothing parameter, and which is a default method in R statistical language. For most of the prefectures, the relation between daily maximum temperatures and mortality rates were V-shaped. The OTs varied among prefectures and tended to be higher for southern prefectures. Some of the estimates based on GCV method, in particular for the LOESS models, yielded non-OT type relations even when the “a priori” approach yielded OTs. LOESS model showed more sensitivity to the value of span (the parameter of smoothness); an average difference in OT levels within the “best” selected range of spans was 0.5°C, while that for the smoothing spline model was 0.3°C. This study suggests that, for evaluating the relation between daily mortality and temperature, the smoothing spline model with degree of freedom being 6-7.5 was the most appropriate model for the Japanese data, and that blind use of the default method was problematic in this case.