An exact test for comparing two predictive values in small‐size clinical trials

Positive and negative predictive values describe the performance of a diagnostic test. There are several methods to test the equality of predictive values in paired designs. However, these methods were premised on large sample theory, and they may not be suitable for small‐size clinical trials because of inflation of the type 1 error rate. In this study, we propose an exact test to control the type 1 error rate strictly for conducting a small‐size clinical trial that investigates the equality of predictive values in paired designs. In addition, we execute simulation studies to evaluate the performance of the proposed exact test and existing methods in small‐size clinical trials. The proposed test can calculate the exact P value, and as a result of simulations, the empirical type 1 error rate for the proposed test did not exceed the significance level regardless of the setting, and the empirical power for the proposed test is not much different from the other methods based on large‐sample theory. Therefore, it is considered that the proposed exact test is useful when the type 1 error rate needs to be controlled strictly.     

Production planning and inventory control in a company manufacturing PC parts: A case study

In this paper, we present a case study on the production planning and inventory system in a company manufacturing personal computer (PC) parts. In the case study, the targets are specified for developing a system for production planning and inventory control. The current state of the company is analysed for clarifying the points necessary to achieve the targets. Also, a system based on the analysis is proposed and its effects are estimated.     

The Complex Road to Happiness: The Influence of Human Development, a Healthy Environment and a Free Press

Happiness is considered one of the goals of individuals and nations. Thus, many interdisciplinary efforts have attempted to determine the factors that lead to happiness. However, most of these efforts have ignored some important but less tangible factors, such as having a free press and a healthy environment. In this study, we argue that press freedom—a measure of social capital—along with human and built capital, and natural capital, predicts levels of life satisfaction across nations. Using data from 161 countries, our study provides empirical support to our theoretical model that forms of capital do not influence life satisfaction separately but are actually situated in a web of interrelationships. This is consistent with the assumptions that the road to happiness is not direct. It is a complex path where different forms of capital influence one another before leading to a happy life.     

Recursive Methods in Discounted Stochastic Games: An Algorithm for δ→ 1 and a Folk Theorem

We present an algorithm to compute the set of perfect public equilibrium payoffs as the discount factor tends to 1 for stochastic games with observable states and public (but not necessarily perfect) monitoring when the limiting set of (long‐run players') equilibrium payoffs is independent of the initial state. This is the case, for instance, if the Markov chain induced by any Markov strategy profile is irreducible. We then provide conditions under which a folk theorem obtains: if in each state the joint distribution over the public signal and next period's state satisfies some rank condition, every feasible payoff vector above the minmax payoff is sustained by a perfect public equilibrium with low discounting.     

On Measuring Uncertainty of Benchmarked Predictors with Application to Disease Risk Estimate

Empirical Bayes (EB) estimates in general linear mixed models are useful for the small area estimation in the sense of increasing precision of estimation of small area means. However, one potential difficulty of EB is that the overall estimate for a larger geographical area based on a (weighted) sum of EB estimates is not necessarily identical to the corresponding direct estimate such as the overall sample mean. Another difficulty is that EB estimates yield over‐shrinking, which results in the sampling variance smaller than the posterior variance. One way to fix these problems is the benchmarking approach based on the constrained empirical Bayes (CEB) estimators, which satisfy the constraints that the aggregated mean and variance are identical to the requested values of mean and variance. In this paper, we treat the general mixed models, derive asymptotic approximations of the mean squared error (MSE) of CEB and provide second‐order unbiased estimators of MSE based on the parametric bootstrap method. These results are applied to natural exponential families with quadratic variance functions. As a specific example, the Poisson‐gamma model is dealt with, and it is illustrated that the CEB estimates and their MSE estimates work well through real mortality data.     

Generation carryover of a fraction of population members as an animal adaptation to unstable environmental conditions

A heterogeneous life cycle of individuals in a population was examined on its adaptive significance to an unstable environmental condition. The trend of population growth was simulated by a simple mathematical model in which a part of population in a certain generation was carried over to the next generation without participating in the reproduction. With the increase of the rate of carryover of individuals to the next generation the population fluctuation tended to be stabilized. A minute fraction of population is carried over, the effect is very large to prevent the population decline at a sequence of adverse environmental conditions. The population level increased greatly depending upon the extent of environmental change as far as the rate of carryover took an intermediate value. The optimum proportion of members to be carried over to the next generation was determined by the extent of environmental change and its frequency of occurrence.