Conducting confirmatory clinical trials initiated and managed by nonpharmaceutical company researchers is often unfeasible because the calculated sample size is excessively large. We propose an alternative approach: conducting a pre-confirmatory clinical trial with a relatively high type I error rate and limited sample size. Our approach involves the use of a significance level calculated based on the conditional probability (P₂), which is the probability of having a true treatment effect, given that the statistical test shows statistical significance, and its application to sample size calculation for pre-confirmatory clinical trials.

We examined the performance and operational characteristics of our approach using a case study. For a confirmatory clinical trial that required 100 participants in each group, when our method was applied, a pre-confirmatory clinical trial required a considerably small number of participants. For example, for a P₂ of 80 %, with no prior information on the treatment effect, and a power of 80 %, the significance level of our approach was calculated as 20 %. Based on these values, the sample size in each group was 52. Although insufficient participant accrual during confirmatory clinical trials may affect the conclusion of the trials, our approach can ameliorate the situation.

In planning a multi-regional clinical trial including Japan, the sample size for Japanese subjects is often considered based on the probability of obtaining consistent results between Japanese subpopulation and the overall study population, as recommended in the Japanese guideline ‘Basic Principles on Global Clinical Trials.’ Some methods have been proposed for calculating the sample size for Japanese subjects in multi-regional clinical trials based on the guideline, but no such methods have been proposed for trials where nonparametric methods are used for comparing two treatments. In this paper, we propose a method for calculating the Japanese sample size for a study where a nonparametric method is used. The proposed method uses the area under the ROC curve (AUROC) as an effect-size measure. This idea is justified by the fact that the AUROC is equivalent to Mann-Whitney’s U statistics. The AUROC is subdivided into parts according to Japanese/non-Japanese subpopulations and their variance and covariances are derived to construct a formula for calculating the probability of obtaining consistent results between the overall study population and Japanese subpopulation. Investigation by simulation suggests that the accuracy of the method is sufficiently high for practical use.

Determination of the number of subjects to include in a clinical trial is a crucial aspect of experimental design. The standard methodology for sample size determination (SSD) has been established based on a frequentist perspective, while the literature addressing the SSD problem from a Bayesian perspective has increased for the last 20 years. In this paper I discuss the basic concept of Bayesian SSD, with specific focus on an inferential performance-based (non-decision theoretic) approach, using two distinct prior distributions: analysis prior and design prior. The analysis prior formalizes pre-trial information, and it is used to obtain posterior distributions, while the design prior describes a scenario and it is used to obtain prior predictive distributions. In practice, the specification of prior distributions is a key element of Bayesian inference. The prior information may be derived from either expert beliefs or relevant empirical data, and the subjective knowledge derived from an expert elicitation procedure may be useful to define a prior distribution when no or limited data from previous studies is available. In experimental design, the interplay between Bayesian and frequentist methodology is intrinsic. Whichever method is used in SSD, the distinction between demands as expressed in the range of equivalence, and their expectation or beliefs, as represented by the prior information is of paramount importance.

This review provides a comprehensive introduction to recent developments in agricultural statistics. Agricultural statistics, which began with Fisher’s design of experiments, has developed in various directions as the nature of the data it handles has changed. The ability to rapidly measure omics data, including DNA sequences, has led to methods such as genomic selection. It has become possible to comprehensively measure even the metabolites of living organisms, giving birth to a new field called metabolomics. The development of machine learning, including deep learning, has enabled the use of image data, which has been difficult to connect with agriculture and is creating new areas such as disease diagnosis of crops. In this review, we first refer to the statistics of Fisher’s era, recall the philosophy of science in statistics, and look at the prospects of modern agricultural statistics by taking a broad overview of new fields.