In this paper, we consider a matrix consisting of longitudinal data as a frequency table for each individual at each observation time point, and apply a topic model based on Non-negative Matrix Factorization (NMF).Thus, it is possible for us to apply the soft clustering based on NMF and grasp the similar time-trend of longitudinal data.NMF also has an aspect of a regression model in which the observed data of each individual is approximated by a linear combination of several basis vectors.Two cases are illustrated, 1) the case where the number of observation time points is smaller than the number of individuals, 2) the case where the number of observation time points is larger than the number of individuals, which makes regression analysis difficult.From the results of the examples, varying coefficients were considered on the coefficient matrix of NMF.As a result, it is possible to predict the longitudinal data using the location information not included in the observation matrix.

Evidence-based medicine, nowadays, has become an indispensable rationale for clinical decision making and is based on a statistical analysis of the double-blind placebo controlled trial. For the analysis, in recent years, the Cox proportional hazards model has brought more precise interpretation of the differences in heterogeneity between participants of the trial. Nevertheless, when a statistically significant efficacy is gained, usually the intervention is widely carried out in practice for the similar patient group to the participants.

However, there remains the possibility that the significance is derived from the efficacy only to a part of the participants, that is, the existence of responders. Moreover, as heterogeneity is based on predictable risk factors and when the existence of responders is derived from an unknown confounder, the existence of the confounder is not elucidated by subgroup analysis.

In this issue, the way of estimating the presence or absence of the responders is proposed by means of Akaike information criterion (AIC), provided that a little ingenuity is needed to apply the AIC to the statistics composed of both the intervention and the placebo group data, as a pair.

The content of the lecture by Yasushi Nagata at “The Frontier Seminar of the Japanese Society of Applied Statistics, Past, Present and Future of Applied Statistics” held on January 29, 2022 is reported.

This paper describes the background of the decision to give the lecture on this theme, and then summarizes the basic concepts of the multiple comparison procedures from a historical point of view.

Statistics and data science have become very popular in these days, and the number of people involved in data analysis is rapidly increasing. So, it is now time to consider the most important topic in statistics that the distinction between “causation” and “correlation”. The topic will be discussed in the framework of regression analysis here. Also in recent years, the use of open data has become a hot topic. The characteristic feature of this type of data is that they are so-called aggregate data. Therefore, the ecological reference as a methodology for inferring individual behavior from aggregate data seems to be quite important. Familiar examples are taken up and the results of the analyses are critically discussed. The message here is that we should recognize that data are composed of numerical values and background information. Without background information, data analysis can easily fall into mere numerical analysis.

This paper will introduce the situation of statistical expert human resource development in the U.S. and the undergraduate and graduate education in data science at the University of California, Berkeley, and present the viewpoints necessary for the “statistical expert development project,” including the development of university statistical faculty, which was launched in Japan in 2021.