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Abstract Bayesian statistics plays a pivotal role in advancing medical science by enabling healthcare companies, regulators, and stakeholders to assess the safety and efficacy of new treatments, interventions, and medical procedures. The Bayesian framework offers a unique advantage over the classical framework, especially when incorporating prior information into a new trial with quality external data, such as historical data or another source of co-data. In recent years, there has been a significant increase in regulatory submissions using Bayesian statistics due to its flexibility and ability to provide valuable insights for decision-making, addressing the modern complexity of clinical trials where frequentist trials are inadequate. For regulatory submissions, companies often need to consider the frequentist operating characteristics of the Bayesian analysis strategy, regardless of the design complexity. In particular, the focus is on the frequentist type I error rate and power for all realistic alternatives. This tutorial review aims to provide a comprehensive overview of the use of Bayesian statistics in sample size determination, control of type I error rate, multiplicity adjustments, external data borrowing, etc., in the regulatory environment of clinical trials. Fundamental concepts of Bayesian sample size determination and illustrative examples are provided to serve as a valuable resource for researchers, clinicians, and statisticians seeking to develop more complex and innovative designs.

Randomized selection trials are frequently used to compare experimental treatments that have the potential to be beneficial, but they often do not include a control group. While time-to-event endpoints are commonly applied in clinical investigations, methodologies for determining the required sample size for such endpoints, except exponential distribution, are lacking. In recent times, there has been a shift in clinical trials, with a growing emphasis on progression-free survival as a primary endpoint. However, the utilization of this measure has typically been restricted to specific time points for both sample size determination and analysis. This alteration in approach could wield a substantial influence on the clinical trial process, potentially diminishing the capacity to discern variances between treatment groups. In the calculation of sample sizes for randomized trials, this investigation operates under the assumption that the time-to-event endpoint conforms to either an exponential, Weibull, or generalized exponential distribution.

Abstract Background Bayesian methods are increasing in popularity in clinical research. The design of Bayesian clinical trials requires a prior distribution, which can be elicited from experts. In diseases with international differences in management, the elicitation exercise should recruit internationally, making a face-to-face elicitation session expensive and more logistically challenging. Thus, we used a remote, real-time elicitation exercise to construct prior distributions. These elicited distributions were then used to determine the sample size of the Bronchiolitis in Infants with Placebo Versus Epinephrine and Dexamethasone (BIPED) study, an international randomised controlled trial in the Pediatric Emergency Research Network (PERN). The BIPED study aims to determine whether the combination of epinephrine and dexamethasone, compared to placebo, is effective in reducing hospital admission for infants presenting with bronchiolitis to the emergency department. Methods We developed a Web-based tool to support the elicitation of the probability of hospitalisation for infants with bronchiolitis. Experts participated in online workshops to specify their individual prior distributions, which were aggregated using the equal-weighted linear pooling method. Experts were then invited to provide their comments on the aggregated distribution. The average length criterion determined the BIPED sample size. Results Fifteen paediatric emergency medicine clinicians from Canada, the USA, Australia and New Zealand participated in three workshops to provide their elicited prior distributions. The mean elicited probability of admission for infants with bronchiolitis was slightly lower for those receiving epinephrine and dexamethasone compared to supportive care in the aggregate distribution. There were substantial differences in the individual beliefs but limited differences between North America and Australasia. From this aggregate distribution, a sample size of 410 patients per arm results in an average 95% credible interval length of less than 9% and a relative predictive power of 90%. Conclusion Remote, real-time expert elicitation is a feasible, useful and practical tool to determine a prior distribution for international randomised controlled trials. Bayesian methods can then determine the trial sample size using these elicited prior distributions. The ease and low cost of remote expert elicitation mean that this approach is suitable for future international randomised controlled trials. Trial registration ClinicalTrials.gov NCT03567473

Abstract Background Sample size planning for longitudinal data is crucial when designing mediation studies because sufficient statistical power is not only required in grant applications and peer-reviewed publications, but is essential to reliable research results. However, sample size determination is not straightforward for mediation analysis of longitudinal design. Methods To facilitate planning the sample size for longitudinal mediation studies with a multilevel mediation model, this article provides the sample size required to achieve 80% power by simulations under various sizes of the mediation effect, within-subject correlations and numbers of repeated measures. The sample size calculation is based on three commonly used mediation tests: Sobel’s method, distribution of product method and the bootstrap method. Results Among the three methods of testing the mediation effects, Sobel’s method required the largest sample size to achieve 80% power. Bootstrapping and the distribution of the product method performed similarly and were more powerful than Sobel’s method, as reflected by the relatively smaller sample sizes. For all three methods, the sample size required to achieve 80% power depended on the value of the ICC (i.e., within-subject correlation). A larger value of ICC typically required a larger sample size to achieve 80% power. Simulation results also illustrated the advantage of the longitudinal study design. The sample size tables for most encountered scenarios in practice have also been published for convenient use. Conclusions Extensive simulations study showed that the distribution of the product method and bootstrapping method have superior performance to the Sobel’s method, but the product method was recommended to use in practice in terms of less computation time load compared to the bootstrapping method. A R package has been developed for the product method of sample size determination in mediation longitudinal study design.

Specific plasma proteins serve as valuable markers for various diseases and are in many cases routinely measured in clinical laboratories by fully automated systems. For safe diagnostics and monitoring using these markers, it is important to ensure an analytical quality in line with clinical needs. For this purpose, information on the analytical and the biological variation of the measured plasma protein, also in the context of the discovery and validation of novel, disease protein biomarkers, is important, particularly in relation to for sample size calculations in clinical studies. Nevertheless, information on the biological variation of the majority of medium-to-high abundant plasma proteins is largely absent. In this study, we hypothesized that it is possible to generate data on inter-individual biological variation in combination with analytical variation of several hundred abundant plasma proteins, by applying LC-MS/MS in combination with relative quantification using isobaric tagging (10-plex TMT-labeling) to plasma samples. Using this analytical proteomic approach, we analyzed 42 plasma samples prepared in doublets, and estimated the technical, inter-individual biological, and total variation of 265 of the most abundant proteins present in human plasma thereby creating the prerequisites for power analysis and sample size determination in future clinical proteomics studies. Our results demonstrated that only five samples per group may provide sufficient statistical power for most of the analyzed proteins if relative changes in abundances >1.5-fold are expected. Seventeen of the measured proteins are present in the European Federation of Clinical Chemistry and Laboratory Medicine (EFLM) Biological Variation Database, and demonstrated remarkably similar biological CV’s to the corresponding CV’s listed in the EFLM database suggesting that the generated proteomic determined variation knowledge is useful for large-scale determination of plasma protein variations.

In anesthesia and intensive care, treatment benefits that were claimed on the basis of small or modest-sized trials have repeatedly failed to be confirmed in large randomized controlled trials. A well-designed small trial in a homogeneous patient population with high event rates could yield conclusive results; however, patient populations in anesthesia and intensive care are typically heterogeneous because of comorbidities. The size of the anticipated effects of therapeutic interventions is generally low in relation to relevant endpoints. For regulatory purposes, trials are required to demonstrate efficacy in clinically important endpoints, and therefore must be large because clinically important study endpoints such as death, sepsis, or pneumonia are dichotomous and infrequently occur. The rarer endpoint events occur in the study population; that is, the lower the signal-to-noise ratio, the larger the trials must be to prevent random events from being overemphasized. In addition to trial design, sample size determination on the basis of event rates, clinically meaningful risk ratio reductions and actual patient numbers studied are among the most important characteristics when interpreting study results. Trial size is a critical determinant of generalizability of study results to larger or general patient populations. Typical characteristics of small single-center studies responsible for their known fragility include low variability of outcome measures for surrogate parameters and selective publication and reporting. For anesthesiology and intensive care medicine, findings in volume resuscitation research on intravenous infusion of colloids exemplify this, since both the safety of albumin infusion and the adverse effects of the artificial colloid hydroxyethyl starch have been confirmed only in large-sized trials.

Average biosimilarity is investigated under a three-arm parallel design: one arm corresponds to the test drug T , and the other two arms correspond to two versions of the reference drug, say R1 and R2. The hypothesis of interest is the equivalence of the population average response for T with the mean of the population average responses for R_1 and R_2. The parameter of interest is formulated as the absolute difference of the above two averages, scaled by the absolute difference between the population means corresponding to R_1 and R_2. A difference parameter is also proposed. For the ratio parameter, a test can be derived using the asymptotic normality of an appropriate test statistic; however, the test is not satisfactory in terms of type I error probabilities. Improved tests are derived by applying a bootstrap calibration, and by using the idea of a generalized pivotal quantity (gpq). The tests are developed under equal variance and unequal variance scenarios. Sample size determination is also addressed. For the difference parameter, a satisfactory test is developed using the gpq idea. The proposed methods result in tests that are satisfactory in terms of type I error performance.

The purpose of this present study was to determine the right sample size in observational study which is focusing on medical or health sciences field. Sample size calculation is actually depends on the type of how the study is designed. For example different formulas are used to calculate the sample size in different type of the study. In this article, the formula of single proportion and two proportions is discussed and an example from medical research, which may contribute to the understanding of this problem, is presented

Some equivalence tests are based on two one-sided tests, where in many applications the test statistics are approximately normal. We define and find evidence for equivalence in Z-tests and then one- and two-sample binomial tests as well as for t-tests. Multivariate equivalence tests are typically based on statistics with non-central chi-squared or non-central F distributions in which the non-centrality parameter λ is a measure of heterogeneity of several groups. Classical tests of the null λ ≥ λ 0 versus the equivalence alternative λ < λ 0 are available, but simple formulae for power functions are not. In these tests, the equivalence limit λ 0 is typically chosen by context. We provide extensions of classical variance stabilizing transformations for the non-central chi-squared and F distributions that are easy to implement and which lead to indicators of evidence for equivalence. Approximate power functions are also obtained via simple expressions for the expected evidence in these equivalence tests.