Dose-scale pharmacodynamic bioequivalence is recommended for evaluating the consistency of generic and innovator formulations of certain locally acting drugs, such as orlistat. This study aimed to investigate the standard methodology for sample size determination and the impact of study design on dose-scale pharmacodynamic bioequivalence using orlistat as the model drug. A population pharmacodynamic model of orlistat was developed using NONMEM 7.5.1 and utilized for subsequent simulations. Three different study designs were evaluated across various predefined relative bioavailability ratios of test/reference (T/R) formulations. These designs included Study Design 1 (2×1 crossover with T1 60 mg, R1 60 mg, and R2 120 mg), Study Design 2 (2×1 crossover with T2 120 mg, R1 60 mg, and R2 120 mg), and Study Design 3 (2×2 crossover with T1 60 mg, T2 120 mg, R1 60 mg, and R2 120 mg). Sample sizes were determined using a stochastic simulation and estimation approach. Under the same T/R ratio and power, Study Design 3 required the minimum sample size for bioequivalence, followed by Study Design 1, while Study Design 2 performed the worst. For Study Designs 1 and 3, a larger sample size was needed on the T/R ratio < 1.0 side for the same power compared to that on the T/R ratio > 1.0 side. The opposite asymmetry was observed for Study Design 2. We demonstrated that Study Design 3 is most effective for reducing the sample size for orlistat bioequivalence studies, and the impact of T/R ratio on sample size shows asymmetry.

OBJECTIVE: While statistical analysis plays a crucial role in medical science, some published studies might have utilized suboptimal analysis methods, potentially undermining the credibility of their findings. Critically appraising analytical approaches can help elevate the standard of evidence and ensure clinicians and other stakeholders have trustworthy results on which to base decisions. The aim of the present study was to examine the statistical characteristics of original articles published in Peruvian medical journals in 2021-2022.
METHODS: We performed a methodological study of articles published between 2021 and 2022 from nine medical journals indexed in SciELO-Peru, Scopus, and Medline. We included original articles that conducted analytical analyses (i.e., association between variables). The statistical variables assessed were: statistical software used for analysis, sample size, and statistical methods employed (measures of effect), controlling for confounders, and the method employed for confounder control or epidemiological approaches.
RESULTS: We included 313 articles (ranging from 11 to 77 across journals), of which 67.7% were cross-sectional studies. While 90.7% of articles specified the statistical software used, 78.3% omitted details on sample size calculation. Descriptive and bivariate statistics were commonly employed, whereas measures of association were less common. Only 13.4% of articles (ranging from 0% to 39% across journals) presented measures of effect controlling for confounding and explained the criteria for selecting such confounders.
CONCLUSIONS: This study revealed important statistical deficiencies within analytical studies published in Peruvian journals, including inadequate reporting of sample sizes, absence of measures of association and confounding control, and suboptimal explanations regarding the methodologies employed for adjusted analyses. These findings highlight the need for better statistical reporting and researcher-editor collaboration to improve the quality of research production and dissemination in Peruvian journals.

UNASSIGNED: To describe and demonstrate sample size and power calculation for ophthalmic studies with a binary outcome from one or both eyes.
UNASSIGNED: We describe sample size and power calculation for four commonly used eye designs: (1) one-eye design or person-design: one eye per subject or outcome is at person-level; (2) paired design: two eyes per subject and two eyes are in different treatment groups; (3) two-eye design: two eyes per subject and both eyes are in the same treatment group; and (4) mixture design: mixture of one eye and two eyes per subject. For each design, we demonstrate sample size and power calculations in real ophthalmic studies.
UNASSIGNED: Using formulas and commercial or free statistical packages including SAS, STATA, R, and PS, we calculated sample size and power. We demonstrated that different statistical packages require different parameters and provide similar, yet not identical, results. We emphasize that studies using data from two eyes of a subject need to account for the intereye correlation for appropriate sample size and power calculations. We demonstrate the gain in efficiency in designs that include two eyes of a subject compared to one-eye designs.
UNASSIGNED: Ophthalmic studies use different eye designs that include one or both eyes in the same or different treatment groups. Appropriate sample size and power calculations depend on the eye design and should account for intereye correlation when two eyes from some or all subjects are included in a study. Calculations can be executed using formulas and commercial or free statistical packages.

In biomedical research, the simultaneous inference of multiple binary endpoints may be of interest. In such cases, an appropriate multiplicity adjustment is required that controls the family-wise error rate, which represents the probability of making incorrect test decisions. In this paper, we investigate two approaches that perform single-step p $p$ -value adjustments that also take into account the possible correlation between endpoints. A rather novel and flexible approach known as multiple marginal models is considered, which is based on stacking of the parameter estimates of the marginal models and deriving their joint asymptotic distribution. We also investigate a nonparametric vector-based resampling approach, and we compare both approaches with the Bonferroni method by examining the family-wise error rate and power for different parameter settings, including low proportions and small sample sizes. The results show that the resampling-based approach consistently outperforms the other methods in terms of power, while still controlling the family-wise error rate. The multiple marginal models approach, on the other hand, shows a more conservative behavior. However, it offers more versatility in application, allowing for more complex models or straightforward computation of simultaneous confidence intervals. The practical application of the methods is demonstrated using a toxicological dataset from the National Toxicology Program.

Structural neuroimaging data have been used to compute an estimate of the biological age of the brain (brain-age) which has been associated with other biologically and behaviorally meaningful measures of brain development and aging. The ongoing research interest in brain-age has highlighted the need for robust and publicly available brain-age models pre-trained on data from large samples of healthy individuals. To address this need we have previously released a developmental brain-age model. Here we expand this work to develop, empirically validate, and disseminate a pre-trained brain-age model to cover most of the human lifespan. To achieve this, we selected the best-performing model after systematically examining the impact of seven site harmonization strategies, age range, and sample size on brain-age prediction in a discovery sample of brain morphometric measures from 35,683 healthy individuals (age range: 5-90 years; 53.59% female). The pre-trained models were tested for cross-dataset generalizability in an independent sample comprising 2101 healthy individuals (age range: 8-80 years; 55.35% female) and for longitudinal consistency in a further sample comprising 377 healthy individuals (age range: 9-25 years; 49.87% female). This empirical examination yielded the following findings: (1) the accuracy of age prediction from morphometry data was higher when no site harmonization was applied; (2) dividing the discovery sample into two age-bins (5-40 and 40-90 years) provided a better balance between model accuracy and explained age variance than other alternatives; (3) model accuracy for brain-age prediction plateaued at a sample size exceeding 1600 participants. These findings have been incorporated into CentileBrain (https://centilebrain.org/#/brainAGE2), an open-science, web-based platform for individualized neuroimaging metrics.

BACKGROUND: Longitudinal ordinal data are commonly analyzed using a marginal proportional odds model for relating ordinal outcomes to covariates in the biomedical and health sciences. The generalized estimating equation (GEE) consistently estimates the regression parameters of marginal models even if the working covariance structure is misspecified. For small-sample longitudinal binary data, recent studies have shown that the bias of regression parameters may result from the GEE and have addressed the issue by applying Firth\'s adjustment for the likelihood score equation to the GEE as if generalized estimating functions were likelihood score functions. In this manuscript, for the proportional odds model for longitudinal ordinal data, the small-sample properties of the GEE were investigated, and a bias-reduced GEE (BR-GEE) was derived.
METHODS: By applying the adjusted function originally derived for the likelihood score function of the proportional odds model to the GEE, we produced the BR-GEE. We investigated the small-sample properties of both GEE and BR-GEE through simulation and applied them to a clinical study dataset.
RESULTS: In simulation studies, the BR-GEE had a bias closer to zero, smaller root mean square error than the GEE with coverage probability of confidence interval near or above the nominal level. The simulation also showed that BR-GEE maintained a type I error rate near or below the nominal level.
CONCLUSIONS: For the analysis of longitudinal ordinal data involving a small number of subjects, the BR-GEE is advantageous for obtaining estimates of the regression parameters of marginal proportional odds models.

BACKGROUND: Clinical studies are often limited by resources available, which results in constraints on sample size. We use simulated data to illustrate study implications when the sample size is too small.
RESULTS: Using 2 theoretical populations each with N = 1000, we randomly sample 10 from each population and conduct a statistical comparison, to help make a conclusion about whether the 2 populations are different. This exercise is repeated for a total of 4 studies: 2 concluded that the 2 populations are statistically significantly different, while 2 showed no statistically significant difference.
CONCLUSIONS: Our simulated examples demonstrate that sample sizes play important roles in clinical research. The results and conclusions, in terms of estimates of means, medians, Pearson correlations, chi-square test, and P values, are unreliable with small samples.

The sample size is just about the most common question in the minds of many medical researchers. This size determines the reliability of the results and helps to detect a medically important effect when present. Some studies miss an important effect due to inappropriate sample size. Many postgraduate students and established researchers often contact a statistician to help them determine an appropriate sample size for their study. More than 80 formulas are available to calculate sample size for different settings and the choice requires some expertise. Their use is even more difficult because most exact formulas are quite complex. An added difficulty is that different books, software, and websites use different formulas for the same problem. Such discrepancy in the published formulas confounds a biostatistician also. The objective of this communication is to present uniformly looking formulas for many situations together at one place in their simple but correct form, along with the setting where they are applicable. This will help in choosing an appropriate formula for the kind of research one is proposing to do and use it with confidence. This communication is restricted to the sample size required to detect a medically important effect when present - known to the statisticians as the test of hypothesis situation. Such a collection is not available anywhere, not even in any book. The sample size formulas for estimation are different and not discussed here.

OBJECTIVE: Temporomandibular disorder (TMD) is the term used to describe a pathology (dysfunction and pain) in the masticatory muscles and temporomandibular joint (TMJ). There is an apparent upward trend in the publication of dental research and a need to continually improve the quality of research. Therefore, this study was conducted to analyse the use of sample size and effect size calculations in a TMD randomised controlled trial.
METHODS: The period was restricted to the full 5 years, i.e., papers published in 2019, 2020, 2021, 2022, and 2023. The filter article type-\"Randomized Controlled Trial\" was used. The studies were graded on a two-level scale: 0-1. In the case of 1, sample size (SS) and effect size (ES) were calculated.
RESULTS: In the entire study sample, SS was used in 58% of studies, while ES was used in 15% of studies.
CONCLUSIONS: Quality should improve as research increases. One factor that influences quality is the level of statistics. SS and ES calculations provide a basis for understanding the results obtained by the authors. Access to formulas, online calculators and software facilitates these analyses. High-quality trials provide a solid foundation for medical progress, fostering the development of personalized therapies that provide more precise and effective treatment and increase patients\' chances of recovery. Improving the quality of TMD research, and medical research in general, helps to increase public confidence in medical advances and raises the standard of patient care.

Pragmatic trials aim to assess intervention efficacy in usual patient care settings, contrasting with explanatory trials conducted under controlled conditions. In aging research, pragmatic trials are important designs for obtaining real-world evidence in elderly populations, which are often underrepresented in trials. In this review, we discuss statistical considerations from a frequentist approach for the design and analysis of pragmatic trials. When choosing the dependent variable, it is essential to use an outcome that is highly relevant to usual medical care while also providing sufficient statistical power. Besides traditionally used binary outcomes, ordinal outcomes can provide pragmatic answers with gains in statistical power. Cluster randomization requires careful consideration of sample size calculation and analysis methods, especially regarding missing data and outcome variables. Mixed effects models and generalized estimating equations (GEEs) are recommended for analysis to account for center effects, with tools available for sample size estimation. Multi-arm studies pose challenges in sample size calculation, requiring adjustment for design effects and consideration of multiple comparison correction methods. Secondary analyses are common but require caution due to the risk of reduced statistical power and false-discovery rates. Safety data collection methods should balance pragmatism and data quality. Overall, understanding statistical considerations is crucial for designing rigorous pragmatic trials that evaluate interventions in elderly populations under real-world conditions. In conclusion, this review focuses on various statistical topics of interest to those designing a pragmatic clinical trial, with consideration of aspects of relevance in the aging research field.