A nonparametric method for estimating interaction effect of age and period on mortality.

In this paper we introduce a new model and develop an estimation strategy to analyze mortality data. The model we dealt with has the specific structure E[log qij] = mu + alpha i + beta j + rho ij subject to the linear restrictions sigma i alpha i/sigma 2i = sigma j beta j = sigma i pij/sigma 2i = sigma j rho ij = 0 for any i and j; here, qij denotes the mortality for the jth period category and ith age category, mu denotes the overall mean, alpha i denotes the ith age effect in antichronological order, beta j the jth period effect, rho ij the general interaction effect; and sigma 2i is the common error variance of log qij for the ith age group. We propose a combined technique of ANOVA and nonparametric smoothing for estimating these parameters. The methods described are illustrated by mortality data on rectum cancer in Japanese males and females between 1950-1986.