BACKGROUND: Mediation analysis, often completed as secondary analysis to estimating the main treatment effect, investigates situations where an exposure may affect an outcome both directly and indirectly through intervening mediator variables. Although there has been much research on power in mediation analyses, most of this has focused on the power to detect indirect effects. Little consideration has been given to the extent to which the strength of the mediation pathways, i.e., the intervention-mediator path and the mediator-outcome path respectively, may affect the power to detect the total effect, which would correspond to the intention-to-treat effect in a randomized trial.
METHODS: We conduct a simulation study to evaluate the relation between the mediation pathways and the power of testing the total treatment effect, i.e., the intention-to-treat effect. Consider a sample size that is computed based on the usual formula for testing the total effect in a two-arm trial. We generate data for a continuous mediator and a normal outcome using the conventional mediation models. We estimate the total effect using simple linear regression and evaluate the power of a two-sided test. We explore multiple data generating scenarios by varying the magnitude of the mediation paths whilst keeping the total effect constant.
RESULTS: Simulations show the estimated total effect is unbiased across the considered scenarios as expected, but the mean of its standard error increases with the magnitude of the mediator-outcome path and the variability in the residual error of the mediator, respectively. Consequently, this affects the power of testing the total effect, which is always lower than planned when the mediator-outcome path is non-trivial and a naive sample size was employed. Analytical explanation confirms that the intervention-mediator path does not affect the power of testing the total effect but the mediator-outcome path. The usual effect size consideration can be adjusted to account for the magnitude of the mediator-outcome path and its residual error.
CONCLUSIONS: The sample size calculation for studies with efficacy and mechanism evaluation should account for the mediator-outcome association or risk the power to detect the total effect/intention-to-treat effect being lower than planned.

It is not uncommon for a substantial proportion of patients to be cured (or survive long-term) in clinical trials with time-to-event endpoints, such as the endometrial cancer trial. When designing a clinical trial, a mixture cure model should be used to fully consider the cure fraction. Previously, mixture cure model sample size calculations were based on the proportional hazards assumption of latency distribution between groups, and the log-rank test was used for deriving sample size formulas. In real studies, the latency distributions of the two groups often do not satisfy the proportional hazards assumptions. This article has derived a sample size calculation formula for a mixture cure model with restricted mean survival time as the primary endpoint, and did simulation and example studies. The restricted mean survival time test is not subject to proportional hazards assumptions, and the difference in treatment effect obtained can be quantified as the number of years (or months) increased or decreased in survival time, making it very convenient for clinical patient-physician communication. The simulation results showed that the sample sizes estimated by the restricted mean survival time test for the mixture cure model were accurate regardless of whether the proportional hazards assumptions were satisfied and were smaller than the sample sizes estimated by the log-rank test in most cases for the scenarios in which the proportional hazards assumptions were violated.

Pilots are small-scale initial experiments that are intended to guide the design of future, larger studies, with a view to increasing their effectiveness. In this statistical primer we highlight five common mistakes that limit the utility of pilot studies and provide practical guidance to avoid such errors and increase their effectiveness. The common thread connecting these mistakes is insufficient planning and over-interpretation of the results. This approach compromises the ultimate goals of the research programme and the future experimental cascade. In support of our view that over-interpretation is an error, we present a simple simulation to demonstrate that pilots will generally generate an inaccurate estimate of the variability of the biological endpoint under study and that frequent under-estimation will lead to inconclusive and unethical subsequent experiments. We argue that well planned pilots are an important part of the research cascade and still need to be implemented to a high standard.

In the individual stepped-wedge randomized trial (ISW-RT), subjects are allocated to sequences, each sequence being defined by a control period followed by an experimental period. The total follow-up time is the same for all sequences, but the duration of the control and experimental periods varies among sequences. To our knowledge, there is no validated sample size calculation formula for ISW-RTs unlike stepped-wedge cluster randomized trials (SW-CRTs). The objective of this study was to adapt the formula used for SW-CRTs to the case of individual randomization and to validate this adaptation using a Monte Carlo simulation study. The proposed sample size calculation formula for an ISW-RT design yielded satisfactory empirical power for most scenarios except scenarios with operating characteristic values near the boundary (i.e., smallest possible number of periods, very high or very low autocorrelation coefficient). Overall, the results provide useful insights into the sample size calculation for ISW-RTs.

This research introduces a systematic framework for calculating sample size in studies focusing on enteric methane (CH4, g/kg of DMI) yield reduction in dairy cows. Adhering to the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines, we conducted a comprehensive search across the Web of Science, Scopus, and PubMed Central databases for studies published from 2012 to 2023. The inclusion criteria were: studies reporting CH4 yield and its variability in dairy cows, employing specific experimental designs (Latin Square Design (LSD), Crossover Design, Randomized Complete Block Design (RCBD), and Repeated Measures Design) and measurement methods (Open-circuit respirometry chambers (RC), the GreenFeed system, and the sulfur hexafluoride tracer technique), conducted in Canada, the United States and Europe. A total of 150 studies, which included 177 reports, met our criteria and were included in the database. Our methodology for using the database for sample size calculations began by defining 6 CH4 yield reduction levels (5, 10, 15, 20, 30, and 50%). Utilizing an adjusted Cohen\'s f formula and a power analysis we calculated the sample sizes required for these reductions in balanced LSD and RCBD reports from studies involving 3 or 4 treatments. The results indicate that within-subject studies (i.e., LSD) require smaller sample sizes to detect CH4 yield reductions compared with between-subject studies (i.e., RCBD). Although experiments using RC typically require fewer individuals due to their higher accuracy, our results demonstrate that this expected advantage is not evident in reports from RCBD studies with 4 treatments. A key innovation of this research is the development of a web-based tool that simplifies the process of sample size calculation (samplesizecalculator.ucdavis.edu). Developed using Python, this tool leverages the extensive database to provide tailored sample size recommendations for specific experimental scenarios. It ensures that experiments are adequately powered to detect meaningful differences in CH4 emissions, thereby contributing to the scientific rigor of studies in this critical area of environmental and agricultural research. With its user-friendly interface and robust backend calculations, this tool represents a significant advancement in the methodology for planning and executing CH4 emission studies in dairy cows, aligning with global efforts toward sustainable agricultural practices and environmental conservation.

Sample size formulas have been proposed for comparing two sensitivities (specificities) in the presence of verification bias under a paired design. However, the existing sample size formulas involve lengthy calculations of derivatives and are too complicated to implement. In this paper, we propose alternative sample size formulas for each of three existing tests, two Wald tests and one weighted McNemar\'s test. The proposed sample size formulas are more intuitive and simpler to implement than their existing counterparts. Furthermore, by comparing the sample sizes calculated based on the three tests, we can show that the three tests have similar sample sizes even though the weighted McNemar\'s test only use the data from discordant pairs whereas the two Wald tests also use the additional data from accordant pairs.

In randomised controlled trials, the outcome of interest could be recurrent events, such as hospitalisations for heart failure. If mortality rates are non-negligible, both recurrent events and competing terminal events need to be addressed when formulating the estimand and statistical analysis is no longer trivial. In order to design future trials with primary recurrent event endpoints with competing risks, it is necessary to be able to perform power calculations to determine sample sizes. This paper introduces a simulation-based approach for power estimation based on a proportional means model for recurrent events and a proportional hazards model for terminal events. The simulation procedure is presented along with a discussion of what the user needs to specify to use the approach. The method is flexible and based on marginal quantities which are easy to specify. However, the method introduces a lack of a certain type of dependence. This is explored in a sensitivity analysis which suggests that the power is robust in spite of that. Data from a randomised controlled trial, LEADER, is used as the basis for generating data for a future trial. Finally, potential power gains of recurrent event methods as opposed to first event methods are discussed.

Cluster randomized trials are an essential design in public health and medical research, when individual randomization is infeasible or undesirable for scientific or logistical reasons. However, the correlation among observations within clusters leads to a decrease in statistical power compared to an individually randomised trial with the same total sample size. This correlation - often quantified using the intra-cluster correlation coefficient - must be accounted for in the sample size calculation to ensure that the trial is adequately powered. In this paper, we first describe the principles of sample size calculation for parallel-arm CRTs, and explain how these calculations can be extended to CRTs with cross-over designs, with a baseline measurement and stepped-wedge designs. We introduce tools to guide researchers with their sample size calculation and discuss methods to inform the choice of the a priori estimate of the intra-cluster correlation coefficient for the calculation. We also include additional considerations with respect to anticipated attrition, a small number of clusters, and use of covariates in the randomisation process and in the analysis.

There is an increasing number of potential quantitative biomarkers that could allow for early assessment of treatment response or disease progression. However, measurements of such biomarkers are subject to random variability. Hence, differences of a biomarker in longitudinal measurements do not necessarily represent real change but might be caused by this random measurement variability. Before utilizing a quantitative biomarker in longitudinal studies, it is therefore essential to assess the measurement repeatability. Measurement repeatability obtained from test-retest studies can be quantified by the repeatability coefficient, which is then used in the subsequent longitudinal study to determine if a measured difference represents real change or is within the range of expected random measurement variability. The quality of the point estimate of the repeatability coefficient, therefore, directly governs the assessment quality of the longitudinal study. Repeatability coefficient estimation accuracy depends on the case number in the test-retest study, but despite its pivotal role, no comprehensive framework for sample size calculation of test-retest studies exists. To address this issue, we have established such a framework, which allows for flexible sample size calculation of test-retest studies, based upon newly introduced criteria concerning assessment quality in the longitudinal study. This also permits retrospective assessment of prior test-retest studies.

Count outcomes are collected in clinical trials for new drug development in several therapeutic areas and the event rate is commonly used as a single primary endpoint. Count outcomes that are greater than the mean value are termed overdispersion; thus, count outcomes are assumed to have a negative binomial distribution. However, in clinical trials for treating asthma and chronic obstructive pulmonary disease (COPD), a regulatory agency has suggested that a continuous endpoint related to lung function must be evaluated as a primary endpoint in addition to the event rate. The two co-primary endpoints that need to be evaluated include overdispersed count and continuous outcomes. Some researchers have proposed sample size calculation methods in the context of co-primary endpoints for various outcome types. However, methodologies for sample size calculation in trials with two co-primary endpoints, including overdispersed count and continuous outcomes, required when planning clinical trials for treating asthma and COPD, remain to be proposed. In this study, we aimed to develop a hypothesis-testing method and a corresponding sample size calculation method with two co-primary endpoints including overdispersed count and continuous outcomes. In a simulation, we demonstrated that the proposed sample size calculation method has adequate power accuracy. In addition, we illustrated an application of the proposed sample size calculation method to a placebo-controlled Phase 3 trial for patients with COPD.