Instrumental variable (IV) methods are widely applied in biometrics and related fields, offering potential solutions to problems associated with unmeasured confounders. Particularly, Mendelian randomization (MR), which uses single nucleotide polymorphisms (SNPs) as IVs, has garnered significant attention in recent years. In this review, we introduce MR and the statistical methods used, categorizing them into two types: one-sample MR and two-sample MR, with some illustrative examples. In onesample MR, the two-stage least squares (2SLS) estimator is commonly applied, while in two-sample MR, the inverse-variance weighted method is used. We also explore the relationship between these methods. Additionally, we discuss unique problems of MR, such as the weak instrument problem and the issue of invalid IVs, and present some current solutions. Furthermore, we address biometrics-specific topics applicable to binary outcomes and concerns regarding the applicability of 2SLS.

A cluster randomised trial is a trial design in which randomisation is carried out by grouping areas, facilities, schools, etc., into a single unit (i.e. a cluster). It is used when adopting an individual randomised trial in which the intervention is allocated to individual subjects within the same cluster is impossible or inappropriate. Cluster randomised trials have specific issues that differ from individual randomised trials in terms of implementation and statistical methodology. In particular, about the statistical aspects, it is essential to consider intracluster correlation in sample size calculation and statistical analysis. In addition, although the basic design of cluster randomised trials is a parallel group, different trial designs (e.g., stepped wedge cluster randomised trials and cluster randomised crossover trials) may be adopted mainly from the perspective of practicality and efficiency. In this paper, we will explain the situations in which cluster randomised trials are applied, points to note, frequently used sample size calculation and statistical analysis methods, and derivative designs, with examples of their practical application in the medical field.

To ensure the safety of drugs, developing a risk management plan (RMP) is required to manage a series of risks in drug development, including the important identified risks, important potential risks, and important missing information for predicting the post-marketing safety of the drug. Few methods to assess data from a singlearm study conducted as a post-marketing surveillance (PMS) about the magnitude of risks identified before the surveillance, however, have been established. We propose a novel method for evaluating the identified risks using a statistical inference framework based on the relative belief ratio (RB ratio), a ratio of the posterior distribution to the prior distribution. In our context, the RB ratio is defined as the ratio of a prior distribution based on the incidence of adverse drug reactions identified as a rate of risk at the time of RMP development and the number of events calculated from the total person-time of PMS observations to a posterior distribution updated after the PMS data are available. We illustrate our method to apply real data from the published RMP and its PMS report of a drug, and show the usefulness of our method.