Analysis of the K ordered odds ratio parameters, namely the analysis of 3-way interaction in the 2×2×K contingency table is a very common problem in the epidemiology and also in the clinical trial. Recently Hirotsu et al.(2001) proposed the max accumulatedx² statistic for a 2×J×K table related with the association analysis of disease and bivariate allele frequencies, which includes the 2×2×K table as its important special case. The purpose of the present paper is to reformulate the max accumulated statistic as useful specifically for the 2×2×K table and compare its power with the restricted likelihood ratio test proposed by Barmi(1997). It is shown that the behavior is rather similar but the max accumulated x² is easier to handle giving an exact algorithm for the probability calculation for the moderate sample size.

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A nonparametric method for the estimation of effective doses by kernel smoothing is proposed. The estimator of the dose and its asymptotic confidence interval are given. The estimation is based on the asymptotic properties of the proposed kernel estimator of dose response curves. The proposed method is compared with methods based on other kernel estimators and the parametric method via a simulation study, and is illustrated by applications to real data sets.

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The Bayesian cohort model was introduced by Takashi Nakamura in 1982. His model succeeded in overcoming the identification problem in cohort analysis by setting up an assumption that successive parameters change gradually. Subsequently, he incorporated age-by-period interaction effects into his original model. This paper presents the Bayesian cohort models with different types of interaction effects, said to be difficult to realize, such as age-by-cohort, cohort-by-age, period-by-cohort and cohort-by-period as well as period-by-age. These new models are applied to analysis of liquor consumption in Japan. In addition, this paper shows interactions with other factors are also among candidates for components of appropriate models, taking up a life-stage cohort model as an example. The life-stage cohort analysis proposed in this paper is to make a study of household cohorts classified according to the birth year of the eldest child, regarded as aging as the eldest child grows older. The study reveals that interaction effects between age of the eldest child and number of children living together are essential to analyze a share of seafood in food consumption.

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