"The Statistical Principles for Clinical Trials" agreed in The International Conference on Har-monization (ICH) adopts a new principle for dealing with the treatment-by-centre interaction. It recommended that the efficacy of a new treatment might be confirmed by a hypothesis test based on an ANOVA model without treatment-by-centre interaction. This recommendation is not consistent with the conventional method, which preliminarily uses the test for interaction before testing the existence of the main effect on an ANOVA model.
This paper investigated the plausibility of this recommendation compared with the conventional method through the evaluation of the probability of approving the efficacy of the new treatment.
It quantitatively clarified that the recommended procedure highly suppressed the probability when the interaction existed, i.e., the difference of the probability between the two method was as large as 17% when 10 patients in each of two groups were recruited for each of five centres and the in-teraction effect was observable in spite of the existence of a fairy big main effect. The observed tendency was retained even if the number of patients allocated to each of two groups compared was not identical.
This indicates that the ICH recommendation is consistent with the strategy of ICH that the new treatment should not be approved without further examination on the physical implications of the interaction when it exists.

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Neural networks have received considerable attention as useful tools for analyzing data with complex structure. We consider the use of radial basis function networks in constructing nonlinear regression models.
Suppose that we have n observations {(y_i, x_i);i=1, ..., n}, where yi are independent random response variables and xi are vectors of d explanatory variables. Consider the regression model
y_i=u(x_i)+ε_i, i=1, ..., n,
where u(·) is an unknown smooth function and the errors εi are independently distributed n(0, σ²). Our aim is to estimate the function u(·) from the observed data, for which we use the radial basis function (RBF) network
u(x_i)= ∑ω_kφ_k(x_i)+ω₀
where φk(x) is the basis function given by
φ_k(x)=exp(-||x-c_k||²/2vs²_k), k=1, ..., M.
We introduce the Gaussian basis function with hyperparameter v that adjusts the amount of overlapping basis functions.
In the first stage the centres ck_kand scale factors s²_k of the basis functions are determined by using the k-means clustering algorithm based on the input data set {x_i;i=1, ..., n}. In the second stage we estimate the weights ω_k by the regularization method which maximizes the penalized log-likelihood
$sum;logf(y_i|x;ω, σ²)- λ/2 ω'Qψ,
where ω=(ω₀, ω₁, ..., ω_M)', λ is a smoothing parameter and Q is some fixed (M+1)×(M+1) nonnegative-definite matrix.
A crucial issue in the RBF network regression model is the choice of smoothing parameters v, λ and also the number of basis functions that control the smoothness of the fitted function by regularization. We present an information-theoretic criterion for evaluating the nonlinear regression model based on the RBF network. The information criterion proposed is applied to choose the smoothing parameters and the number of basis functions.
We use Monte Carlo experiments and a real data example to examine the performance of the RBF network nonlinear modeling. The simulation results show that our nonlinear modeling performs well in various situations, and that clear improvements are obtained for the use of the hyperparameter in the radial basis functions.

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We investigate structures to represent the quality of life (QOL) of elderly demented people by analyzing clinical data obtained in a ward. We find it inappropriate to argue the subjective QOL in terms of direct answers that might be given by the patients. We deal with the objective QOL on the basis of clinical data which indicate the attitudes and ways of behavior in their daily life in the ward.
Three sets of measurement items are designed. The first set consists of nine items about QOL, the second of nine items about the activities of daily living (ADL), and the third of a single item to assess the intellectual level in terms of Hasegawa's dementia scale-revised (HDS-R). Measurements were performed by the care staff, twice with an interval of six months.
Using procedures of multivariate analysis, we obtain the spatial and the cluster structures of the nineteen items. We then interpret the results from a medical point of view, and present new findings based on the cluster structure. Lastly, we discuss the significance and the limitations of our findings, and examine the validity and the reliability of our study. The present research may serve as a case study for further investigation on the QOL of elderly demented people.

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