Multiple comparison methods such as the Williams’ test are used to adjust for multiplicity of multiple doses in many confirmatory pharmacology studies. The existing Williams test is not suitable for paired data such as experiments using human cells. We constructed a test statistic of the Williams’ test that can be applied to individual-paired data, following the method of constructing the test statistic of existing Williams’ test and using the unbiased estimator of the error variance and the degrees of freedom in the ANOVA table for a two-factor linear model. Critical values were obtained by evaluating the distribution of the test statistic under the null hypothesis. Simulation studies confirmed the validity of the critical value and that the actual significance level were maintained at the nominal level. Furthermore, the Williams’ test extended for paired data, was found to have higher power than the Dunnett’s test and the fixed sequence test in the mid-saturation dose-response relationship often seen in confirmatory pharmacology studies. And it was shown that the analysis extended for paired data is necessary when analyze the paired data. Thus, the Williams’ test extended to paired data is appropriate and is superior to other multiple comparison methods in terms of power.

Consistency is an important assumption to justify evidence synthesis in network meta-analysis. Sidesplitting is a representative method used to evaluate inconsistency; it decomposes the overall estimate of network meta-analysis on a specific treatment pair to those of direct and indirect comparisons and assesses their concordance. A relevant issue in sidesplitting is that adequate adjustments are needed in multi-arm trials (≥3 arms) to prevent biases. In existing methods, sidesplitting requires several restrictions on model parameters or additional parameter modeling and the computations are complicated. In this article, we show that sidesplitting involving the adjustments of multi-arm trials can be uniformly treated within a network meta-regression framework, especially via the modeling method of Noma et al. (2017; Stat Med 36:917-927), which introduces additional free parameters to adjust the biases caused by multi-arm trials. The proposed approach can be interpreted as a specific version of the design-by-treatment interaction model, and any inference methods for the network meta-regression can be applied involving higher-order asymptotic approximations. The proposed method is applied to two network meta-analyses of hypertensive drugs.

The contrast-based approach is one of the primary approaches in network meta-analysis. For statistical modeling in network meta-analysis and meta-regression models, within-study covariance estimates are needed to adequately address the correlations among the multivariate outcomes. In this computational note, we present the formulas of covariance estimators for standard effect measures used in modern meta-analysis practice: risk difference, risk ratio, odds ratio, mean difference, and standardized mean difference (Cohen’s d and Hedge’s g).

Epidemiology is the study of health-related states or events in specific populations and their determinants, with the aim of controlling health problems. It encompasses various research fields, such as cancer epidemiology, infectious disease epidemiology, and social epidemiology, molecular epidemiology, environmental epidemiology, genetic epidemiology, clinical epidemiology, pharmacoepidemiology, spatial epidemiology, and theoretical epidemiology, among others, and is closely related to statistics and biometrics. In analytical epidemiological studies, data is collected from study populations using appropriate study designs, and statistical methods are applied to understand disease occurrence and its causes, particularly establishing causal relationships between interventions or exposures and disease outcomes. This paper focuses on five topics in epidemiology, including infectious disease control through spatial epidemiology, cancer epidemiology using cancer registry data, research about long-term health effects, targeted learning in observational studies, and that in randomized controlled trials. This paper provides the latest insights from experts in each field and offers a prospect for the future development of quantitative methods in epidemiology.