[Criteria for degrees of a smoothing method applied to mortality rates].
OBJECTIVE
Age-period-specific mortality rates are smoothed by methods to clarify their characteristics and trends. In the present study a procedure to determine appropriate iteration times for weighted averages was devised, and examined by application to mortality data.


METHODS
Mortality data for leukemia, solid neoplasms, and traffic accidents caused by cars in Japan were employed. The smoothing method was iterating weighted averages over age-period-specific death rates and their four nearest neighbors in age-period data tables. The primary condition, which the iteration times should satisfy, was that the differences between crude data and smoothed ones were not significantly large, i.e., smoothed mortality data should be within 95% confidence intervals of crude rates. Therefore, the following steps were adopted to determine appropriate times: (1) estimation of 95% confidence intervals for crude age-period-specific mortality rates. (2) determination of iteration times under the primary condition that the proportion of cells left out of the confidence intervals should be around 5%. In cases where the proportion of cells outside of confidence intervals was still below 5% even with 10 or more times of iteration, an index of convergence of smoothing was introduced and used to determine appropriate iteration times.


RESULTS
For solid neoplasms, appropriate times of iteration was three. With leukemia, the proportion of cells left out of their confidence intervals remained within 5% with iteration 27 times. Therefore, an index of convergence for the smoothing process was used to avoid over-smoothing. As a result, a value of five was obtained. In the case of car traffic accidents, even only a single smoothing did not fulfill the primary condition, because mortality rates increased very rapidly from age classes of 10-14 to 15-19, the mortality rates for the latter being about ten times larger. To deal with this, the proportion of cells left out of their confidence intervals was calculated excluding these age classes. As a result, five times was found to be appropriate.


CONCLUSIONS
The smoothing method in this study is simple and easy to apply to mortality data. And procedure to determine appropriate iteration times is based on an inferential statistical method. Applying the method to three kinds of mortality data, it was found to be practical and useful for clarification of their characteristics and trends.
Negishi
S
S
Department of Medical Information Science, Jichi Medical School.
Yokoyama
H
H
D000063:Accidents, Traffic / Q000401:mortality*; D000367:Age Factors; D000368:Aged; D000369:Aged, 80 and over; D004812:Epidemiologic Methods; D006801:Humans; D007564:Japan / Q000453:epidemiology; D007938:Leukemia / Q000401:mortality*; D008297:Male; D008875:Middle Aged; D009369:Neoplasms / Q000401:mortality*