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Summary Step change-point and slope change-point models in the independent Poisson sequence are developed based on accumulated and doubly-accumulated statistics. The method for the step change-point model developed in Section 2 is an alternative to the likelihood ratio test of Worsley (1986) and the algorithm for p-value calculation based on the first-order Markov property is the same as that given there. Different algorithms for the non-null distribution and inference on the change-point itself are, however, newly developed and a Pascal program is given in the Appendix. These methods are extended to the slope change-point model in Section 3. The approach is essentially the same as that of Section 2 but the algorithm is now based on the second-order Markov property and becomes a little more complicated. The Pascal program related to the slope change-point model is supported on the website, URL: https://corec.meisei-u.ac.jp/labs/hirotsu/.

A unifying approach to the shape and change-point hypotheses is extended generally to a discrete univariate exponential family. The maximal contrast type tests are newly proposed for the convexity and sigmoidicity hypotheses based on the complete class lemma of tests for the restricted alternatives. Those tests are also efficient score tests for the slope change-point and inflection point models, respectively. For each of those tests the successive component statistics are the doubly- and triply-accumulated statistics. They have nice Markov properties for the exact and efficient recursion formulae for calculating the p -value. Further the sum of squares of the component statistics are developed as the cumulative chi-squared statistics for the directional goodness-of-fit tests of the dose-response model. Therefore the interesting applications will be in monitoring of spontaneous reporting of the adverse drug events and the directional goodness-of-fit tests.

In a phase II clinical trial it is simultaneously required to prove a drug is truly effective by showing a monotone dose-response relationship and also to obtain information on the recommended dose for the ordinary clinical treatments. Then the multiple comparisons of the interested dose-response patterns are more preferable than an overall testing of the null hypothesis or a fitting of a particular parametric model. In this article the maximal accumulated t statistic (max acc. t-test) proposed for the monotone hypothesis testing is compared with other maximal contrast type tests and shown to be useful also for estimating the dose-response pattern. It is even remarkable that the effect of adding other monotone contrasts to the basic contrasts of max acc. t is so small. The simultaneous lower bounds obtained by the inversion of max acc. t is also shown to be useful for this purpose and has some advantage in giving the lower confidence bound for the mean difference of the estimated optimal dose against the ...

棚瀬，松田論文(2006)は分割表における多重比較法とその評価という表題の下に，実際は行の対比較の問題のみを扱っている.ところが，その第4.1節で ‘広津(1992)のScheffe法’ と紹介されているのが実は1983年の旧版であり，また，確率計算の近似法や検出力の評価についても，不正確な表現や不適切な取り扱いが見られる．そこで，この覚書では正確を期すために，２元配置分散分析において交互作用多重比較のために提案された方法(Hirotsu, 1991)を，改めて２次元分割表解析に定式化して具体的に示すと共に，確率近似精度の新しい評価結果について報告する．また，Scheffe法と要因分析を目的とする多重比較法との考え方の違いについても言及する．

Two approaches of multiple decision processes are proposed for unifying the non-inferiority, equivalence and superiority tests in a comparative clinical trial for a new drug against an active control. One is a method of confidence set with confidence coefficient 0.95 improving the conventional 0.95 confidence interval in the producer's risk and also the consumer's risk in some cases. It requires to include 0 within the region as well as to clear the non-inferiority margin so that a trial with somewhat large number of subjects and inappropriately large non-inferiority margin for proving non-inferiority of a drug that is actually inferior should be unsuccessful. The other is the closed testing procedure which combines the one- and two-sided tests by applying the partitioning principle and justifies the switching procedure by unifying the non-inferiority, equivalence and superiority tests. In particular regarding the non-inferiority, the proposed method justifies simultaneously the old Japanese Statistical Guideline (one-sided 0.05 test) and the International Guideline ICH E9 (one-sided 0.025 test). The method is particularly attractive, changing the strength of the evidence of relative efficacy of the test drug against a control at five levels according to the achievement of the clinical trial. The meaning of the non-inferiority test and also the rationale of switching from it to superiority test will be discussed. Copyright © 2007 John Wiley & Sons, Ltd.

Problems of clinical trials associated with human beings are discussed. They are characterized by very inhomogeneous and limited numbers of samples, and by periods of observation too short to allow efficacy and safety to be evaluated. Avoiding human error associated with subjective measures and ensuring the generalizability of the result of a limited trial to the true target population are crucial. The regulatory science is therefore an important factor in making appropriate decisions and gaining maximal benefit from insufficient information.

2×2×K分割表におけるオッズ比の単調仮説は応用例が多く,これまでにも尤度比検定,累積x2検定などが提案されている.一方,Hirotsu et al.(2001)で提案された2×J×K分割表での2次元傾向性仮説に対する最大対比型の正確検定も2×2×K分割表の場合にはオッズ比の単調仮説の検定に帰着する.そこで本論文ではこの最大対比型正確検定を2×2×K分割表の場合に特化し,使い易く定式化するとともに,新たに対立仮説のもとでの検出力の正確な計算方法を与える.また本論文の設定では比較的セル頻度の多い分割表が対象となることも考慮し,正規近似によるP値についても考察する.さらに,代表的な対立仮説パターンを取り上げて最大対比型正確検定の検出力を計算するとともに,マルコフ連鎖・モンテカルロ法による経験分布から得られる尤度比検定との比較を行った.

There are a lot of papers discussing the testing and estimation problems on the parameters under order restrictions. They are, however, mostly for the balanced case and there are only a few papers dealing with the design problems. The purpose of the present paper is to note that the favorite tests for the balanced case are not necessarily good for the extremely unbalanced case where a simple minimax test or a linear trend test behaves better.

The association analysis between the disease and genetic alleles is one of the simple methods for localizing the susceptibility locus in the genes. For revealing the association, several statistical tests have been proposed without discussing explicitly the alternative hypotheses. We therefore specify two types of alternative hypotheses (i.e., there is only one susceptibility allele in the locus, and there is an extension or shortening of alleles associated with the disease) and derive exact tests for the respective hypotheses. We also propose to combine these two tests when the prior knowledge is not sufficient enough to specify one of these two hypotheses. In particular, these ideas are extended to the haplotype analysis of three-way association between the disease and bivariate allele frequencies at two closely linked loci. As a by-product, a factorization of the probability distribution of the three-way cell frequencies under the null hypothesis of no three-way interaction is obtained.

Simultaneous lower bounds (SLB) for the isotonic contrasts in normal means are obtained. In particular a SLB for the range is given. These SLBs are obtained from the one-sided max t test. It is then generalized to obtain simultaneous upper bounds for the responses at lower levels. Under the assumption of the convexity of the response curve at lower levels the upper bounds are further improved. The method compares very well with other available methods numerically as well as in real examples.

summary Exact null and alternative distributions of the two-way maximally selected x2 for interaction between the ordered rows and columns are derived for each of the normal and Poisson models, respectively. The method is one of the multiple comparison procedures for ordered parameters and is useful for defining a block interaction or a two-way change-point model as a simple alternative to the two-way additive model. The construction of a confidence region for the two-way change-point is then described. An important application is found in a dose-response clinical trial with ordered categorical responses, where detecting the dose level which gives significantly higher responses than the lower doses can be formulated as a problem of detecting a change in the interaction effects.

臨床試験第III相では新たな被験薬を標準薬と比較し,有効率が劣らないという非劣等性の検証を求められることが多い.それは通常の仮説検定の論理では扱えず,ハンディキャップ検定方式や信頼区間方式が提案されている(例えば,広津(1986, 1995)参照).本論文ではとくに2項比率差に関し歪度修正信頼区間計算プログラムを得,その統計的特性を素朴な信頼区間方式,及びハンディキャップ検定方式と比較した結果を報告する.さらに簡便な例数設計方式の結果を,この信頼区間方式に適用した場合に,所与の検出力が実用上十分な精度で実現されることをシミュレーションにより確認したので報告する.

SUMMARY Multiple comparison procedures based on the maximal component of the cumulative chi-squared statistic are discussed. The Markov properties for the successive components of the cumulative chi-squared statistic are proved and applied for obtaining the p-value of the maximal component in each of the one-way and the two-way analysis of variance models and the two-way contingency table. The power of the multiple comparison procedure is compared with those for some well-known procedures in the setting of Williams (1971) for detecting the change point from the zero level.

SUMMARY A mixed effects model is assumed for comparing treatments based on repeated measurements. The covariance structure of the data is interpreted as some systematic inhomogeneity of individual profiles along the time axis, rather than as serial correlation. Then a method of comparing treatment effects is proposed as well as that of testing the homogeneity of individual profiles. A follow-up analysis of residuals for the resulting model is also mentioned.

The benefits of a systolic blood pressure (BP) below 150-160 mmHg are well established; whether a systolic BP of less than 140 mmHg provides additional benefits remains controversial. This study was designed to compare the 2-year effect of a strict treatment to maintain systolic BP below 140 mmHg (group A) and that of a mild treatment to maintain systolic BP at between 140 and below 160 mmHg (group B). The study design followed the Prospective Randomized Open Blinded End-point (PROBE) study. The subjects were elderly patients (65-85 years old) who consistently had a systolic BP of 160 mmHg or higher. The baseline drug was efonidipine hydrochloride (efonidipine), a long-acting dihydropiridine calcium antagonist. The primary endpoints were stroke, cardiac disease, vascular disease, and renal failure. After a run-in period of 2 to 4 weeks, 2,165 patients were assigned to group A and 2,155 patients to group B. There were no significant differences between the groups in sex, age, baseline BP, or other cardiovascular risk factors. The systolic BP was 7.2 mmHg lower (p0.0001) and the diastolic BP 2.4 mmHg lower (p0.0001) in group A than in group B after 12 months of treatment. As of this interim analysis, primary endpoints have occurred in 87 patients (stroke in 58 patients, cardiac disease in 27 patients, occlusive arterial disease in 1 patient, and renal failure in 1 patient). Five patients have died of stroke and 2 patients of myocardial infarction. The primary-endpoint-related morbidity rate was 20.9/1,000 patient-years, and the mortality rate was 1.7/1,000 patient-years. Currently available results indicate that this study, one of the largest randomized trials of antihypertensive therapy in elderly patients in Japan, was conducted safely. The final results are expected to provide important and practical information for the management of hypertension in elderly patients.

An overview of the analytical methods for interaction is given with particular interest in the row- and/or column-wise multiple comparison procedures for the case where there is a natural ordering in the rows and/or columns. The methods are useful not only for the analysis of variance model, but also for two-way contingency tables. In particular, a new approach is introduced to classifying rows according to their convex, flat or concave response patterns along the columns. A real example of classifying 147 subjects based on their 24 hours blood pressure measurements is also given.

This article evaluates the impact of the ICH E9 guideline Statistical Principles for Clinical Trials on the conduct of clinical trials in Japan. In particular, the following Japanese practices in the conduct of clinical trials are discussed in detail from the ethical, statistical, and logical viewpoints: 1. Conducting only one phase 3 multicenter trial with many centers and few subjects per center; 2. Seeking to show noninferiority to an active control rather than superiority to placebo; and 3. Choosing a global assessment variable with a subjective component as the primary endpoint. The influence of public health insurance and the potential number of patients in Japan on various aspects of a trial are discussed. Problems requiring further research are mentioned and points requiring clarification are highlighted. © 2003, Drug Information Association. All rights reserved.

In a clinical trial there arise a variety of multiplicity problems which might cause the bias and need to be considered carefully in analyzing and interpreting the data. We first introduce those problems frequently encountered in practice and then discuss some statistical approaches to overcome the difficulty.

A training system for statistical methods in Total Quality Control or Total Quality Management is discussed and we suggest what and how to teach. It is stated that we have no department of statistics in the universities in Japan and stressed that applied statistics is most efficiently taught to those who have their own problems and motivations to apply these statistical methods. It is then essential for a company to have their own training systems for the TQM researchers although some extra company training courses may also be efficiently utilised. As an example we introduce in some detail the seminars provided by JUSE as well as in-company training systems of Toyota Motor Corporation and Takenaka Corporation.

The row-wise and/or the column-wise multiple comparison procedure is introduced for analysing twoway tables. It leads to a block interaction model and is particularly useful when one factor is indicative or variational in the usual analysis of variance model. The procedure is also useful for comparing multinomials or detecting a change point in the sequence of multinomials, where the row-wise and/or the colum-wise comparisons are essential. A two-way change point model is newly introduced when there are natural orderings in both of rows and columns.

Clinical trials often have special features that require other methods of analysis besides the usual analysis of variance techniques. For example, data are usually not normally distributed and frequently are in the form of rank data or ordered categorical data. The cumulative chi-squared statistic and its maximal component are proposed as nonparametric tests for analyzing such data. They offer not only robustness of validity but also that of efficiency. These two statistics are useful generally for modelling and analyzing data in situations where there is an ordering in the parameters. The cumulative chi-squared statistic is applied to the profile analysis of repeated measures that require taking the natural ordering along the time axis into account. The maximal component statistic is applied to a dose finding experiment where a particular multiple comparison procedure is required for ordered parameters corresponding to dose levels. Other problems addressed in the paper include various kinds of multiplicity problems and the proving equivalence of a test drug to the standard which require a quite different approach from the usual significance tests.

The problem of testing hypotheses against ordered alternatives for treatment effects in a one-way layout is discussed by many authors; see, for example, Bartholomew (1959a, b; 1961). For interaction effects in a two-way layout, it is required to specify the ordered alternatives appropriate to practical situations and then to establish the test procedures. James (1961) defined an ordered alternative for a simple case. In the present paper several types of ordered alternatives are defined for the case of the two-factor interaction with one factor A indicating the treatments and the other factor B expressing the stages or degrees of the effects of A. For these ordered alternatives, appropriate methods for testing the null hypothesis are proposed. The powers of these test procedures are examined numerically for the seven different patterns of the alternatives. One real example from a drug experiment is shown as an illustration.

A method is given to classify rows and columns into subgroups so that additivity holds within each of the subtables made of the grouped rows or the grouped columns. The least squares estimators of the cell means are easily obtained for the resulting linear model together with their variances. An estimator of the error varianceσ2 is given when there is only one observation per cell. A treatment of an ordered table is also given.

On caracterise le khi-deux cumule, dans l'analyse de variance a un critere, comme la somme ponderee de variables khi-deux independantes a un degre de liberte

Summary The optimal allocation of observations when there is a natural ordering in the k normal population means is discussed. It is shown that the design which minimizes the total mean square error of the maximum likelihood estimators in the null case allocates half the observations to each of the two extreme populations. The design is obviously optimal for testing the homogeneity of means against the simple ordered alternative. It is, however, hardly acceptable for the estimation in the nonnull case. It is, therefore, shown that the observations could be allocated to the non-extreme populations according to weights which are proportional to the absolute values of the Abelson and Tukey scores at the same time keeping the minimum local power for testing the simple ordered alternative to be maximal. The design gives also the maximum minimum power, not local, for the alternative in the class of linear tests. It, of course, suffers from a small loss of efficiency for the estimation under the null case but is much better under the nonnull case than the extreme design which allocates half the observations to each of the two extreme populations. Some numerical comparisons of the mean square errors are given.