Sequential Hypothesis Tests for Identifying the Minimum Dose with a Threshold Effect

We propose a procedure to identify a lowest dose having greater effect than a threshold dose under the assumption of monotonicity of dose mean response in dose response test. So, we use statistics based on contrasts among sample means and apply a group sequential procedure to our procedure to identify effectively the dose. If we can identify the dose at an early step in the sequential test, since we can terminate the procedure with a few observations, the procedure is useful from an economical point of view. In a simulation studies, we compare the superiority among these procedures based on three contrasts.     

How U.S. and Japanese CEO's spend their time

Managing Directors (CEOs) in a number of large U.S. and Japanese corporations were asked to write a detailed diary of a typical working day, and they were asked what kind of information was useful for certain kinds of decisions. Some of the results of the survey are described in this article. It was found that the average age of the CEOs in the two countries was about the same—60 years old, but CEOs in the United States stayed longer in the position than Japanese CEOs because they were promoted at a younger age. CEOs in the United States worked a longer day than the Japanese. American chief executives spent about 3 hours longer in meetings than their Japanese counterparts. In Japanese corporations the information is distributed and the negotiating is done beforehand, so meetings tend to be shorter. In America contacts with businessmen outside the company were important sources of information, for strategic decisions in particular.     

Group sequential x2 statistic for testing the difference of two mean vectors in clinical trials

In this study we discuss the group sequential procedures for comparing two treatments based on multivariate observations in clinical trials. Also we suppose that a response vector on each of two treatments has a multivariate normal distribution with unknown covariance matrix. Then we propose a group sequential x² statistic in order to carry out repeated significance test for hypothesis of no difference between two population mean vectors. In order to realize the group sequential test where average sample number is reduced, we propose another modified group sequential x² statistic by extension of Jennison and Turnbull ( 1991 ). After construction of repeated confidence boundaries for making the repeated significance test, we compare two group sequential procedures based on two statistics regarding the average sample number and the power of the test in the simulations.     

Maximal Domain for Strategy-proof Rules in Allotment Economies

We consider the problem of allocating an amount of a perfectly divisible good among a group of n agents. We study how large a preference domain can be to allow for the existence of strategy-proof, symmetric and efficient allocation rules when the amount of the good is a variable. This question is qualified by an additional requirement that a domain should include a minimally rich domain. We first characterize the uniform rule (Bennasy in The economics of market disequilibrium, Academic, New York, 1982) as the unique strategy-proof, symmetric, and efficient rule on a minimally rich domain when the amount of the good is fixed. Then, exploiting this characterization, we establish the following: there is a unique maximal domain that includes a minimally rich domain and allows for the existence of strategy-proof, symmetric, and efficient rules when the amount of good is a variable. It is the single-plateaueddomain.     

Measuring World Better Life Frontier: A Composite Indicator for OECD Better Life Index

The OECD Better Life initiative recently released a comprehensive set of 11 indicators of well-being covering a group of countries. Each individual indicator corresponds to a key topic that is essential to well-being. However, the problem of aggregating them is left to users of this dataset. Using these as individual indicators, we propose a composite indicator of overall well-being, which is intended to measure the performance of each country in terms of providing well-being to its people. The ‘benefit of the doubt’ approach (BOD), a well-known aggregation tool based on a weighed sum, assigns the most favourable weights for each entity under investigation. BOD may also be considered to evaluate the performance of each entity in terms of its efficiency. Regarding individual indicators as outputs, it constructs the benchmark production frontier from observed individual indicators. A composite indicator based on BOD equals the distance between each entity’s individual indicator and the production frontier, indicating its efficiency. It is widely considered that the well-being of a country’s people stems from its productive base, which is characterized by capital assets and social infrastructures. Thus, the productive base can be considered the input used to produce well-being, which is reflected by individual indicators. Therefore, when we apply BOD to aggregate individual well-being indicators across countries, we implicitly assume that all countries have the same productive base, as BOD addresses only the output and neglects the input. This inaccurate assumption leads to a distorted performance measure. Data envelopment analysis (DEA), in which BOD has its roots, is a tool to measure the efficiency of each entity by allowing for differences in inputs as well as outputs across entities. DEA also measures efficiency by using the distance to the production frontier; however, unlike BOD, DEA constructs the production frontier more accurately by utilizing the information of inputs as well as outputs, leading to a better performance measure. We apply DEA to aggregate 11 individual well-being indicators into a composite indicator using the World Bank’s estimates of each country’s productive base. The composite indicator based on BOD is distributed similarly to and is highly correlated with the existing Human Development Indicator (HDI). It is also positively correlated with GDP per capita. On the other hand, we show that the composite indicator based on DEA is negatively correlated with HDI as well as GDP per capita.     

Procedure for determining sample size at each stage in group sequential test

The purpose of our study is to propose a. procedure for determining the sample size at each stage of the repeated group significance, tests intended to compare the efficacy of two treatments when a response variable is normal. It is necessary to devise a procedure for reducing the maximum sample size because a large number of sample size are often used in group sequential test. In order to reduce the sample size at each stage, we construct the repeated confidence boundaries which enable us to find which of the two treatments is the more effective at an early stage. Thus we use the recursive formulae of numerical integrations to determine the sample size at the intermediate stage. We compare our procedure with Pocock's in terms of maximum sample size and average sample size in the simulations.     

Development of Adaptive Group Sequential Procedure for Changing Sample Size

In this study, we propose a group sequential procedure that allows the change of necessary sample size at intermediary stage in sequential test. In the procedure, we formulate the conditional power to judge the necessity of the change of sample size in decision rules. Furthermore, we present an integral formula of the power of the test and show how to change the necessary sample size by using the power of the test. In simulation studies, we investigate the characteristics of the change of sample size and the pattern of decision across all stages based on generated normal random numbers.