For the test of complete independence of a multi-way contingency table, we consider test statistics based on the 𝜙-divergence family. Members of the 𝜙-divergence family of statistics all have an equivalent chi-square limiting distribution under the null hypothesis. Taneichi and Sekiya (2024) considered a second-order correction term as an index for investigating whether the distribution of statistics is close to the chi-square limiting distribution, and by using the index, they derived a condition for selecting a 𝜙-divergence statistic when considering an asymptotic test in the case of data being sparse. They found that only Pearson’s X² statistic satisfies the condition among the power divergence family of statistics as well as among the family of statistics proposed by Rukhin (1994). In this paper, we present a new test statistic that satisfies the condition as does Pearson’s X² statistic. Furthermore, we numerically investigate whether the distribution of the new test statistic is close to the chi-square limiting distribution, and we show that the new statistic performs well.

The partial likelihood method for the Cox proportional hazards model is a successful method for estimating regression coefficients without considering the baseline hazard function. On the other hand, if one is interested in estimating both the regression coefficients and the baseline hazard function, parametric methods such as Weibull regression, piecewise exponential hazard regression, and spline hazard regression are useful. The purpose of this paper is to explain these regression methods and compare their statistical performance. We provide a detailed explanation of Poisson regression under piecewise exponential models and penalized maximum likelihood under spline hazard models, and discuss important considerations when analyzing medical data. Simulations are performed under various baseline hazard functions for the population, and a numerical comparison of the estimation accuracy of Cox regression (partial likelihood), Weibull regression, Poisson regression, and spline regression is conducted. Finally, we compare the results of these regression methods through a data example.

Due to the development of methodology of multivariate meta-analysis during the 2000s, the methods of meta-analyses of diagnostic test accuracy (DTA) studies have been established. The DTA meta-analysis has been gaining prominence in research for clinical epidemiology, health policy, and technology developments and has been used in many systematic reviews published in leading medical journals. In the DTA meta-analysis, multivariate statistical models that treat multiple diagnostic accuracy measures simultaneously (e.g., sensitivity and specificity) are used. Also, various multivariate heterogeneity measures (e.g., Q-statistics, I²-statistics) and summarizing methods such as the summary operating characteristics curve are adopted. In this article, we provide a tutorial for these methods with an illustrative example of a DTA meta-analysis for airway eosinophilia in asthma.

In medical research, the Mann-Whitney effect is often used to compare the survival distributions between two independent groups. It is given by the probability that a random subject from the treatment group survives longer than an independent random subject from the control group. In general, researchers examine whether the effect deviates from the null, 1/2. When two survival times are independent of each other, the Mann-Whitney effect can be estimated using Efron's classical method with marginal survival functions. However, under the independence assumption, the Mann-Whitney effect cannot be estimated using the Efron method. To address this, we use parametric copulas to model the bivariate survival function and review the computation procedure for the Mann-Whitney effect under the dependence assumption (Nakazono et al. (2024)). In this article, we introduce Nakazono et al. (2024) and re-examine the behavior of the Mann-Whitney effect estimator in correlated survival data by providing more detailed theoretical explanations and numerical evaluations, including an additional copula (the t-copula). Furthermore, we describe how to implement our proposed method in SAS and R and introduce our web application (https://nkosuke.shinyapps.io/shiny_survival/).

In public health, the rapid detection and response to diseases based on surveillance is one of the critical challenges. However, issues such as data incompleteness and reporting delays, which arise from prioritizing human lives, make statistical inference and accurate interpretation challenging, especially during the COVID-19 pandemic and in the face of imminent next pandemics. This study explains public health surveillance and statistical monitoring methods from a statistical perspective, using time-series data and sequential decision analysis. In particular, we elaborate on the Farrington algorithm and spatial scan statistics, which are globally used for the early detection of infectious disease outbreaks. Additionally, we describe methods to evaluate the statistical performance of surveillance, such as the probability of false alarms, detection delays, and detection success rates.

Logistic regression has been widely applied in clinical and epidemiological studies as a standard method for multivariate analysis of binary outcome data. However, the odds-ratio is not directly interpretable effect measure and only can be interpreted as an approximation of risk-ratio when the event frequency is low. Many recent reporting guidelines recommend using directly interpretable effect measures, and thus, the modified Poisson and least-squares regressions have been widely adopted in practice to address this issue. Using these methods, valid estimates of risk ratio and risk difference can be obtained through simply fitting Poisson and least-squares regressions to binary outcome data. In this article, we provide theoretical review of these methods and show why these regression analyses can provide consistent risk ratio and risk difference estimators within the framework of estimating equation theory. We also provide a tutorial for actual data analyses using these methods by R package “rqlm” released on CRAN. In addition, we review recent methodological studies concerning these regression methods for further analyses.

In this paper, we consider multivariate multiple comparison procedures among mean vectors when the population has a multivariate normal or an elliptical distribution. In particular, we give an approximate upper percentile of T_max² type statistic for constructing the simultaneous confidence intervals, and we introduce the multivariate Tukey-Kramer procedure. We also discuss the problem of estimating the kurtosis parameter in elliptical distributions, the problem of testing equality of mean components and an asymptotic expansion of the distribution for the test statistic on the mean vectors when missing observations are of monotone type. Finally, we deal with the multivariate normality test statistic based on the multivariate kurtosis and give its normalizing transformation statistic. This is a review of my several works.

A representation of a Markov chain gives useful algorithms. We show that discrete exponential families are associated with a system of hypergeometric partial differential equations, and that the Gröbner basis can guarantee that direct sampling of conditional distributions is possible in principle, and that there is no need to find the Gröbner basis if approximations are allowed.