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Abstract Background An adaptive design allows modifying the design based on accumulated data while maintaining trial validity and integrity. The final sample size may be unknown when designing an adaptive trial. It is therefore important to consider what sample size is used in the planning of the study and how that is communicated to add transparency to the understanding of the trial design and facilitate robust planning. In this paper, we reviewed trial protocols and grant applications on the sample size reporting for randomised adaptive trials. Method We searched protocols of randomised trials with comparative objectives on ClinicalTrials.gov (01/01/2010 to 31/12/2022). Contemporary eligible grant applications accessed from UK publicly funded researchers were also included. Suitable records of adaptive designs were reviewed, and key information was extracted and descriptively analysed. Results We identified 439 records, and 265 trials were eligible. Of these, 164 (61.9%) and 101 (38.1%) were sponsored by industry and public sectors, respectively, with 169 (63.8%) of all trials using a group sequential design although trial adaptations used were diverse. The maximum and minimum sample sizes were the most reported or directly inferred (n = 199, 75.1%). The sample size assuming no adaptation would be triggered was usually set as the estimated target sample size in the protocol. However, of the 152 completed trials, 15 (9.9%) and 33 (21.7%) had their sample size increased or reduced triggered by trial adaptations, respectively. The sample size calculation process was generally well reported in most cases (n = 216, 81.5%); however, the justification for the sample size calculation parameters was missing in 116 (43.8%) trials. Less than half gave sufficient information on the study design operating characteristics (n = 119, 44.9%). Conclusion Although the reporting of sample sizes varied, the maximum and minimum sample sizes were usually reported. Most of the trials were planned for estimated enrolment assuming no adaptation would be triggered. This is despite the fact a third of reported trials changed their sample size. The sample size calculation was generally well reported, but the justification of sample size calculation parameters and the reporting of the statistical behaviour of the adaptive design could still be improved.

An adequately powered sample is essential for accurate parameter estimation and meaningful significance testing. It is important to balance sample size with practical considerations such as cost and feasibility. Sample size calculation is guided by key factors such as effect size, variability, power, and significance levels. While complex formulas and software aid precision, practical rules of thumb and strategies can also be used effectively. Transparent documentation of the rationale and methods used for sample size calculation is vital for ensuring reproducibility.

ABSTRACT An informed estimate of subject‐level variance is a key determinate for accurate estimation of the required sample size for clinical trials. Evaluating completed adult Type 2 diabetes studies submitted to the FDA for accuracy of the variance estimate at the planning stage provides insights to inform the sample size requirements for future studies. From the U.S. Food and Drug Administration (FDA) database of new drug applications containing 14,106 subjects from 26 phase 3 randomized studies submitted to the FDA in support of drug approvals in adult type 2 diabetes studies reviewed between 2013 and 2017, we obtained estimates of subject‐level variance for the primary endpoint—change in glycated hemoglobin (HbA1c) from baseline to 6 months. In addition, we used nine additional studies to examine the impact of clinically meaningful covariates on residual standard deviation and sample size re‐estimation. Our analyses show that reduced sample sizes can be used without interfering with the validity of efficacy results for adult type 2 diabetes drug trials. This finding has implications for future research involving the adult type 2 diabetes population, including the potential to reduce recruitment period length and improve the timeliness of results. Furthermore, our findings could be utilized in the design of future endocrinology clinical trials. [ABSTRACT FROM AUTHOR]

Background: An adaptive design allows modifying the design based on accumulated data while maintaining trial validity and integrity. The final sample size may be unknown when designing an adaptive trial. It is therefore important to consider what sample size is used in the planning of the study and how that is communicated to add transparency to the understanding of the trial design and facilitate robust planning. In this paper, we reviewed trial protocols and grant applications on the sample size reporting for randomised adaptive trials. Method: We searched protocols of randomised trials with comparative objectives on ClinicalTrials.gov (01/01/2010 to 31/12/2022). Contemporary eligible grant applications accessed from UK publicly funded researchers were also included. Suitable records of adaptive designs were reviewed, and key information was extracted and descriptively analysed. Results: We identified 439 records, and 265 trials were eligible. Of these, 164 (61.9%) and 101 (38.1%) were sponsored by industry and public sectors, respectively, with 169 (63.8%) of all trials using a group sequential design although trial adaptations used were diverse. The maximum and minimum sample sizes were the most reported or directly inferred (n = 199, 75.1%). The sample size assuming no adaptation would be triggered was usually set as the estimated target sample size in the protocol. However, of the 152 completed trials, 15 (9.9%) and 33 (21.7%) had their sample size increased or reduced triggered by trial adaptations, respectively. The sample size calculation process was generally well reported in most cases (n = 216, 81.5%); however, the justification for the sample size calculation parameters was missing in 116 (43.8%) trials. Less than half gave sufficient information on the study design operating characteristics (n = 119, 44.9%). Conclusion: Although the reporting of sample sizes varied, the maximum and minimum sample sizes were usually reported. Most of the trials were planned for estimated enrolment assuming no adaptation would be triggered. This is despite the fact a third of reported trials changed their sample size. The sample size calculation was generally well reported, but the justification of sample size calculation parameters and the reporting of the statistical behaviour of the adaptive design could still be improved. [ABSTRACT FROM AUTHOR]

In psychiatry clinical trials, an instrument or questionnaire with rating scale is often used to access safety and efficacy of a test treatment under investigation. Statistical analysis based on the collected rating scale is then performed a determine whether there is an improvement in endpoint change from baseline mean scale. This approach needs on absolute change, however, may not actually reflect the performance of the test treatment under study because the change, which may be considered of clinically importance, may fall within the same category in terms of disease severity such as mild, moderate, and severe. In this case, it is suggested, in addition to absolute change approach, a categorical shift analysis be considered to determine whether the endpoint change from baseline has resulted in an improvement in categorical shift, in terms of disease severity shift e.g., from severe to mild or moderate. In this article, we explore the relationship between absolute change approach and categorical shift analysis based on rating scales for assessment of test treatment under study. [ABSTRACT FROM AUTHOR]

Background: Knowing the predictive factors of the variation in a center-level continuous outcome of interest is valuable in the design and analysis of parallel-arm cluster randomized trials. The symbolic two-step method for sample size planning that we present incorporates this knowledge while simultaneously accounting for patient-level characteristics. Our approach is illustrated through application to cluster randomized trials in cancer care delivery research. The required number of centers (clusters) depends on the between- and within-center variance; the within-center variance is a function of estimates obtained by regressing the log within-center variance on predictive factors. Obtaining accurate estimates of the components needed to characterize the within-center variation is challenging. Methods: Using our previously derived sample size formula, our objective in the current research is to directly account for the imprecision in these estimates, using a Bayesian approach, to safeguard against designing an underpowered study when using the symbolic two-step method. Using estimates of the required components, including the number of centers that contribute to those estimates, we make formal allowance for the imprecision in these estimates on which a sample size will be based. Results: The mean of the distribution for power is consistently smaller than the single point estimate that the sample size formula yields. The reduction in power is more pronounced in the presence of increased uncertainty about the estimates with the reduction becoming more attenuated with increased numbers of centers that contribute to the estimates. Conclusions: Accounting for imprecision in the estimates of the components required for sample size estimation using the symbolic two-step method in the design of a cluster randomized trial yields conservative estimates of power. [ABSTRACT FROM AUTHOR]

Background: Many randomized trials measure a continuous outcome simultaneously at baseline and after taking the drug. For a single continuous post-treatment outcome, the sample size calculation is simple, but if there are assessments at multiple time points post-treatment then this longitudinal data may give more insights by analyzing the data using the repeated measures method. Also, if the sample size is calculated using the single time-point method for longitudinal data, it may lead to a larger than required sample size, increasing the cost and time. Methods: In this research, an effort is made to determine the size of the sample for repeated measures case and then compared with the single post-baseline case. The sample sizes were examined under different scenarios for the continuous type of response variable. Under Mean contrast and Diff contrast the sample sizes were calculated with different correlations. These two scenarios were again examined under compound symmetry as well as Auto regressive of order 1 type of correlation structure in longitudinal data. The graphical presentation is given for better visualization of the scenarios. Results: Sample size required for highly correlated longitudinal data using multi timepoint sample size derivation method led to much smaller sample size requirement as compared to single timepoint sample size calculation method. Conclusions: This study will help researchers to make better decisions in choosing the right method for sample size determination which may reduce the time and cost of carrying out the experiment. Also, we must carefully assess which method to go with when the correlation is weak. More complex correlation structures are not studied in this article but can be studied in the same fashion.

This article is concerned with sample size determination methodology for prediction models. We propose to combine the individual calculations via learning‐type curves. We suggest two distinct ways of doing so, a deterministic skeleton of a learning curve and a Gaussian process centered upon its deterministic counterpart. We employ several learning algorithms for modeling the primary endpoint and distinct measures for trial efficacy. We find that the performance may vary with the sample size, but borrowing information across sample size universally improves the performance of such calculations. The Gaussian process‐based learning curve appears more robust and statistically efficient, while computational efficiency is comparable. We suggest that anchoring against historical evidence when extrapolating sample sizes should be adopted when such data are available. The methods are illustrated on binary and survival endpoints. [ABSTRACT FROM AUTHOR]

Cluster randomization trials with survival endpoint are predominantly used in drug development and clinical care research when drug treatments or interventions are delivered at a group level. Unlike conventional cluster randomization design, stratified cluster randomization design is generally considered more effective in reducing the impacts of imbalanced baseline prognostic factors and varying cluster sizes between groups when these stratification factors are adopted in the design. Failure to account for stratification and cluster size variability may lead to underpowered analysis and inaccurate sample size estimation. Apart from the sample size estimation in unstratified cluster randomization trials, there are no development of an explicit sample size formula for survival endpoint when a stratified cluster randomization design is employed. In this article, we present a closed-form sample size formula based on the stratified cluster log-rank statistics for stratified cluster randomization trials with survival endpoint. It provides an integrated solution for sample size estimation that account for cluster size variation, baseline hazard heterogeneity, and the estimated intracluster correlation coefficient based on the preliminary data. Simulation studies show that the proposed formula provides the appropriate sample size for achieving the desired statistical power under various parameter configurations. A real example of a stratified cluster randomization trial in the population with stable coronary heart disease is presented to illustrate our method. [ABSTRACT FROM AUTHOR]

In planning randomized clinical trials (RCTs) for diseases such as Alzheimer's disease (AD), researchers frequently rely on the use of existing data obtained from only two time points to estimate sample size via the subtraction of baseline from follow-up measurements in each subject. However, the inadequacy of this method has not been reported. The aim of this study is to discuss the limitation of sample size estimation based on the subtraction of available data from only two time points for RCTs. Mathematical equations are derived to demonstrate the condition under which the obtained data pairs with variable time intervals could be used to adequately estimate sample size. The MRI-based hippocampal volume measurements from the Alzheimer's Disease Neuroimaging Initiative (ADNI) and Monte Carlo simulations (MCS) were used to illustrate the existing bias and variability of estimates. MCS results support the theoretically derived condition under which the subtraction approach may work. MCS also show the systematically under- or over-estimated sample sizes by up to 32.27 % bias. Not used properly, such subtraction approach outputs the same sample size regardless of trial durations partly due to the way measurement errors are handled. Estimating sample size by subtracting two measurements should be treated with caution. Such estimates can be biased, the magnitude of which depends on the planned RCT duration. To estimate sample sizes, we recommend using more than two measurements and more comprehensive approaches such as linear mixed effect models.

In an individually randomized group treatment (IRGT) trial, participant outcomes can be positively correlated due to, for example, shared therapists in treatment delivery. Oftentimes, because of limited treatment resources or participants at one location, an IRGT trial can be carried out across multiple centers. This design can be subject to potential correlations in the participant outcomes between arms within the same center. While the design of a single‐center IRGT trial has been studied, little is known about the planning of a multicenter IRGT trial. To address this gap, this paper provides analytical sample size formulas for designing multicenter IRGT trials with a continuous endpoint under the linear mixed model framework. We found that accounting for the additional center‐level correlation at the design stage can lead to sample size reduction, and the magnitude of reduction depends on the amount of between‐therapist correlation. However, if the variance components of therapist‐level random effects are considered as input parameters in the design stage, accounting for the additional center‐level variance component has no impact on the sample size estimation. We presented our findings through numeric illustrations and performed simulation studies to validate our sample size procedures under different scenarios. Optimal design configurations under the multicenter IRGT trials have also been discussed, and two real‐world trial examples are drawn to illustrate the use of our method. [ABSTRACT FROM AUTHOR]

Graphical approach provides a useful framework for multiplicity adjustment in clinical trials with multiple endpoints. When designing a graphical approach, initial weight and transition probability for the endpoints are often assigned based on clinical importance. For example, practitioners may prefer putting more weights on some primary endpoints. The clinical preference can be formulated as a constrain in the sample size optimization problem. However, there has been a lack of theoretical guidance on how to specify initial weight and transition probability in a graphical approach to meet the clinical preference but at the same time to minimize the sample size needed for a power requirement. To fill this gap, we propose statistical methods to optimize sample size over initial weight and transition probability in a graphical approach under a common setting, which is to use marginal power for each endpoint in a trial design. Importantly, we prove that some of the commonly used graphical approaches such as putting all initial weights on one endpoint are suboptimal. Our methods are flexible, which can be used for both single‐arm trials and randomized controlled trials with either continuous or binary or mixed types of endpoints. Additionally, we prove the existence of optimal solution where all marginal powers are placed exactly at the prespecified values, assuming continuity. Two hypothetical clinical trial designs are presented to illustrate the application of our methods under different scenarios. Results are first presented for a design with two endpoints and are further generalized to three or more endpoints. Our findings are helpful to guide the design of a graphical approach and the sample size calculation in clinical trials. [ABSTRACT FROM AUTHOR]

Biomechanical experiments help link tissue morphology with load-deformation characteristics. A tissue-dependent minimum sample number is indispensable to obtain accurate material properties. Stress-strain properties were retrieved from human dura mater and scalp skin, exemplifying two distinct soft tissues. Minimum sample sizes necessary for a stable estimation of material properties were obtained in a simulation study. One-thousand random samples were sequentially drawn for calculating the point at which a majority of the estimators settled within a corridor of stability at given tolerance levels around a 'complete' reference for the mean, median and coefficient of variation. Stable estimations of means and medians can be achieved below sample sizes of 30 at a ± 20%-tolerance within 80%-conformity for scalp skin and dura. Lower tolerance levels or higher conformity dramatically increase the required sample size. Conformity was barely ever reached for the coefficient of variation. The parameter type appears decisive for achieving conformity. Biomechanical trials utilizing human tissues are needed to obtain material properties for surgical repair, tissue engineering and modeling purposes. Linking tissue mechanics with morphology helps elucidate form-function relationships, the 'morpho-mechanical link'. For material properties to be accurate, it is vital to examine a minimum number of samples. This number may vary between tissues, and the effects of intrinsic tissue characteristics on data accuracy are unclear to date. This study used data obtained from human dura and skin to compute minimum sample sizes required for estimating material properties at a stable level. It was shown that stable estimations are possible at a ± 20%-tolerance within 80%-conformity below sample sizes of 30. Higher accuracy warrants much higher sample sizes for most material properties. [Display omitted] [ABSTRACT FROM AUTHOR]

Dynamic treatment regimens (DTRs), also known as treatment algorithms or adaptive interventions, play an increasingly important role in many health domains. DTRs are motivated to address the unique and changing needs of individuals by delivering the type of treatment needed, when needed, while minimizing unnecessary treatment. Practically, a DTR is a sequence of decision rules that specify, for each of several points in time, how available information about the individual's status and progress should be used in practice to decide which treatment (e.g. type or intensity) to deliver. The sequential multiple assignment randomized trial (SMART) is an experimental design widely used to empirically inform the development of DTRs. Sample size planning resources for SMARTs have been developed for continuous, binary, and survival outcomes. However, an important gap exists in sample size estimation methodology for SMARTs with longitudinal count outcomes. Furthermore, in many health domains, count data are overdispersed —having variance greater than their mean. We propose a Monte Carlo-based approach to sample size estimation applicable to many types of longitudinal outcomes and provide a case study with longitudinal overdispersed count outcomes. A SMART for engaging alcohol and cocaine-dependent patients in treatment is used as motivation. [ABSTRACT FROM AUTHOR]

PurposeTo assess and compare the wetting kinetics of sheathed and unsheathed Schirmer's tear test (STT) strips, and to determine the repeatability of 5-minute wetted length (WL) and basal tear production rate (BTPR).MethodsSeventeen subjects underwent two sheathed and unsheathed STTs each for both eyes on four visits on separate days. After administration of topical anesthetic, WLs were measured every 30 seconds for 5 minutes, and BTPRs were calculated for sheathed strips. Limits of agreement (LoA), difference-versus-mean plots (DVM), and the coefficient of repeatability (CR) assessed WL and BTPR repeatabilities. Variance estimates were used to calculate sample sizes for future study.ResultsFor the unsheathed STT, the mean (SD) difference in WLs between visits was 0.74 (5.05) mm, LoA were [-9.17, 10.64], and CR was 9.17 mm; for the sheathed STT, the mean (SD) intervisit difference was 0.16 (5.94) mm, LoA were [-11.49, 11.8], and CR was 10.53 mm. Eight of 48 sheathed STTs and 20 of 44 unsheathed STTs showed constant WL for the final 90 seconds of the test. The mean (SD) difference between repeated visits for BTPR was approximately 0.0 μL/min, LoA were [-1.82, 1.82], and CR was 1.91 μL/min.ConclusionsRepeatability of sheathed and unsheathed 5-minute WL and BTPR is inadequate for measuring within-subject changes, but is sufficient for group studies with moderate sample sizes. Constant WL for the final 90 seconds with the eight sheathed STT measurements suggests varying BTPR, whereas constant WL with the unsheathed STT can be explained by balancing evaporation and BTPR.Translational relevanceRepeatability of the modified STT is evaluated clinically to establish quantitative BTPRs rather than inference from a strip WL.

Estimation of areas under receiver operating characteristic curves and their differences is a key task in diagnostic studies. Here we develop closed-form sample size formulas for such studies with a focus on estimation rather than hypothesis testing, by explicitly incorporating pre-specified precision and assurance, with precision denoted by the lower limit of confidence interval and assurance denoted by the probability of achieving that lower limit. For sample size estimation purposes, we introduce a normality-based variance function for valid estimation allowing for unequal variances of observations in the disease and non-disease groups. Simulation results demonstrate that the proposed formulas produce empirical assurance probability close to the pre-specified assurance probability and empirical coverage probability close to the nominal level. Compared with a frequently used existing variance function, the proposed function provides more accurate and efficient sample size estimates. For an illustration of the proposed formulas, we present real-world worked examples. To facilitate implementation, we have developed an online calculator openly available at https://dishu.page/calculator/. [ABSTRACT FROM AUTHOR]

Multivariate outcomes are common in pragmatic cluster randomized trials. While sample size calculation procedures for multivariate outcomes exist under parallel assignment, none have been developed for a stepped wedge design. In this article, we present computationally efficient power and sample size procedures for stepped wedge cluster randomized trials (SW‐CRTs) with multivariate outcomes that differentiate the within‐period and between‐period intracluster correlation coefficients (ICCs). Under a multivariate linear mixed model, we derive the joint distribution of the intervention test statistics which can be used for determining power under different hypotheses and provide an example using the commonly utilized intersection‐union test for co‐primary outcomes. Simplifications under a common treatment effect and common ICCs across endpoints and an extension to closed‐cohort designs are also provided. Finally, under the common ICC across endpoints assumption, we formally prove that the multivariate linear mixed model leads to a more efficient treatment effect estimator compared to the univariate linear mixed model, providing a rigorous justification on the use of the former with multivariate outcomes. We illustrate application of the proposed methods using data from an existing SW‐CRT and present extensive simulations to validate the methods. [ABSTRACT FROM AUTHOR]

We propose a modification of the pure random search algorithm for cases when the global optimum point can be located near the boundary of a feasible region. If the feasible region is cube-shaped, the worst case occurs when the global optimum point is located at the vertex of a cube. In these cases, the sample size for the pure random search should be increased significantly because the success probability of the single trial is decreased. The proposed modification is based on the virtual extension of the feasible region. The extended region contains ε -neighbourhoods of all points of the original region. All random points that fall outside the original feasible region are mapped to the nearest points on its boundary before the values of an objective function at these points are calculated. This extension of the feasible region also leads to an increase in the sample size due to the increased volume. We compare sample sizes required to hit into the neighbourhood of the global optimum point with a given probability for the proposed method and the original pure random search algorithm with a corrected sample size. We consider ball-shaped and cube-shaped feasible regions and find the sufficient conditions for the proposed algorithm to be more efficient. We offer a practical recommendation for cases, in which the feasible region is defined by a system of linear inequalities. [ABSTRACT FROM AUTHOR]

Estimating causal effects from randomized experiments is central to clinical research. Reducing the statistical uncertainty in these analyses is an important objective for statisticians. Registries, prior trials, and health records constitute a growing compendium of historical data on patients under standard-of-care that may be exploitable to this end. However, most methods for historical borrowing achieve reductions in variance by sacrificing strict type-I error rate control. Here, we propose a use of historical data that exploits linear covariate adjustment to improve the efficiency of trial analyses without incurring bias. Specifically, we train a prognostic model on the historical data, then estimate the treatment effect using a linear regression while adjusting for the trial subjects' predicted outcomes (their prognostic scores). We prove that, under certain conditions, this prognostic covariate adjustment procedure attains the minimum variance possible among a large class of estimators. When those conditions are not met, prognostic covariate adjustment is still more efficient than raw covariate adjustment and the gain in efficiency is proportional to a measure of the predictive accuracy of the prognostic model above and beyond the linear relationship with the raw covariates. We demonstrate the approach using simulations and a reanalysis of an Alzheimer's disease clinical trial and observe meaningful reductions in mean-squared error and the estimated variance. Lastly, we provide a simplified formula for asymptotic variance that enables power calculations that account for these gains. Sample size reductions between 10% and 30% are attainable when using prognostic models that explain a clinically realistic percentage of the outcome variance. [ABSTRACT FROM AUTHOR]

Background: Many randomized trials measure a continuous outcome simultaneously at baseline and after taking the drug. For a single continuous post-treatment outcome, the sample size calculation is simple, but if there are assessments at multiple time points post-treatment then this longitudinal data may give more insights by analyzing the data using the repeated measures method. Also, if the sample size is calculated using the single time-point method for longitudinal data, it may lead to a larger than required sample size, increasing the cost and time. Methods: In this research, an effort is made to determine the size of the sample for repeated measures case and then compared with the single post-baseline case. The sample sizes were examined under different scenarios for the continuous type of response variable. Under Mean contrast and Diff contrast the sample sizes were calculated with different correlations. These two scenarios were again examined under compound symmetry as well as Auto regressive of order 1 type of correlation structure in longitudinal data. The graphical presentation is given for better visualization of the scenarios. Results: Sample size required for highly correlated longitudinal data using multi timepoint sample size derivation method led to much smaller sample size requirement as compared to single timepoint sample size calculation method. Conclusions: This study will help researchers to make better decisions in choosing the right method for sample size determination which may reduce the time and cost of carrying out the experiment. Also, we must carefully assess which method to go with when the correlation is weak. More complex correlation structures are not studied in this article but can be studied in the same fashion.

Abstract Cellular heterogeneity underlies cancer evolution and metastasis. Advances in single-cell technologies such as single-cell RNA sequencing and mass cytometry have enabled interrogation of cell type-specific expression profiles and abundance across heterogeneous cancer samples obtained from clinical trials and preclinical studies. However, challenges remain in determining sample sizes needed for ascertaining changes in cell type abundances in a controlled study. To address this statistical challenge, we have developed a new approach, named Sensei, to determine the number of samples and the number of cells that are required to ascertain such changes between two groups of samples in single-cell studies. Sensei expands the t-test and models the cell abundances using a beta-binomial distribution. We evaluate the mathematical accuracy of Sensei and provide practical guidelines on over 20 cell types in over 30 cancer types based on knowledge acquired from the cancer cell atlas (TCGA) and prior single-cell studies. We provide a web application to enable user-friendly study design via https://kchen-lab.github.io/sensei/table_beta.html .

Epidemiologists often study the associations between a set of exposures and multiple biologically relevant outcomes. However, the frequently used scale-and-context-dependent regression coefficients may not offer meaningful comparisons and could further complicate the interpretation if these outcomes do not have similar units. Additionally, when scaling up a hypothesis-driven study based on preliminary data, knowing how large to make the sample size is a major uncertainty for epidemiologists. Conventional p-value-based sample size calculations emphasize precision and might lead to a large sample size for small- to moderate-effect sizes. This asymmetry between precision and utility is costly and might lead to the detection of irrelevant effects. Here, we introduce the " δ -score" concept, by modifying Cohen's f 2 . δ -score is scale independent and circumvents the challenges of regression coefficients. Further, under a new hypothesis testing framework, it quantifies the maximum Cohen's f 2 with certain optimal properties. We also introduced "Sufficient sample size", which is the minimum sample size required to attain a δ -score. Finally, we used data on adults from a 2017–2018 U.S. National Health and Nutrition Examination Survey to demonstrate how the δ -score and sufficient sample size reduced the asymmetry between precision and utility by finding associations between mixtures of per-and polyfluoroalkyl substances and metals with serum high-density and low-density lipoprotein cholesterol. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of cost reduction of data collection procedures. To select an adequate regression or classification model, a sample set of minimum sufficient size must be collected. This sample set is modelled according to follow the data generation hypotheses. Namely, the generalised linear regression models assume the independent and identically distributed target variable. The paper analyses several numerical methods of sample size estimation and compared them in practical terms. It includes statistic, heuristic and Bayesian methods. The practical goal of a sample set collection is modelling, some methods involve analysis of the model parameters. The computational experiment includes widely-used sample sets. The open-source code and the software are provided for the practitioners to use in the data collection planning. [ABSTRACT FROM AUTHOR]

The Finkelstein and Schoenfeld (FS) test is a popular generalized pairwise comparison approach to analyze prioritized composite endpoints (eg, components are assessed in order of clinical importance). Power and sample size estimation for the FS test, however, are generally done via simulation studies. This simulation approach can be extremely computationally burdensome, compounded by increasing number of composite endpoints and with increasing sample size. Here we propose an analytical solution to calculate power and sample size for commonly encountered two‐component hierarchical composite endpoints. The power formulas are derived assuming underlying distributions in each of the component outcomes on the population level, which provide a computationally efficient and practical alternative to the standard simulation approach. Monte Carlo simulation results demonstrate that performance of the proposed power formulas are consistent with that of the simulation approach, and have generally desirable objective properties including robustness to mis‐specified distributional assumptions. We demonstrate the application of the proposed formulas by calculating power and sample size for the Transthyretin Amyloidosis Cardiomyopathy Clinical Trial. [ABSTRACT FROM AUTHOR]

This study aims to identify two critical components required for pharmaceutical cleaning verification when an FTIR is used: (a) the number of scans required per hard-to-clean location, and (b) the limit of quantification (LOQ) of the FTIR instrument when measuring the surface contamination. The current practice in pharmaceutical manufacturing does not require multiple samples as it is standard practice to collect a single swab sample from a 25 × 25 cm area from a difficult-to-reach area of the manufacturing equipment. However, since the FTIR will only scan a tiny portion of the surface compared to the swab, a sufficient number of samples (data points) are required to provide enough confidence to ensure that the measurement results are close to the true value with a maximum degree of certainty. Similarly, calculating the LOQ for a linear regression could be straightforward. However, complexity arises when the experimental data are complex; in this case, the complexity arises due to the nature of the measurement and the lack of the defined peak in the pre-processed spectra. Therefore, this study uses the practical approach of calculating the sample size and the LOQ. [ABSTRACT FROM AUTHOR]

Mixed outcome endpoints that combine multiple continuous and discrete components are often employed as primary outcome measures in clinical trials. These may be in the form of co‐primary endpoints, which conclude effectiveness overall if an effect occurs in all of the components, or multiple primary endpoints, which require an effect in at least one of the components. Alternatively, they may be combined to form composite endpoints, which reduce the outcomes to a one‐dimensional endpoint. There are many advantages to joint modeling the individual outcomes, however in order to do this in practice we require techniques for sample size estimation. In this article we show how the latent variable model can be used to estimate the joint endpoints and propose hypotheses, power calculations and sample size estimation methods for each. We illustrate the techniques using a numerical example based on a four‐dimensional endpoint and find that the sample size required for the co‐primary endpoint is larger than that required for the individual endpoint with the smallest effect size. Conversely, the sample size required in the multiple primary case is similar to that needed for the outcome with the largest effect size. We show that the empirical power is achieved for each endpoint and that the FWER can be sufficiently controlled using a Bonferroni correction if the correlations between endpoints are less than 0.5. Otherwise, less conservative adjustments may be needed. We further illustrate empirically the efficiency gains that may be achieved in the composite endpoint setting. [ABSTRACT FROM AUTHOR]

Formulating Bayes's theorem in terms of odds leads to HT ht . Sepsis may be seen as systemic inflammatory response due to infection. Keywords: likelihood ratio; predictive values; receiver operator curve; sample size estimation; sensitivity; software R; specificity EN likelihood ratio predictive values receiver operator curve sample size estimation sensitivity software R specificity 801 807 7 05/12/22 20220501 NES 220501 Motivating example Worldwide, sepsis and its sequelae still remain a frequent cause of acute illness and death in patients with community and nosocomial acquired infections [[1]]. [Extracted from the article]

The two one-sided t-tests (TOST) method is the most popular statistical equivalence test with many areas of application, i.e., in the pharmaceutical industry. Proper sample size calculation is needed in order to show equivalence with a certain power. Here, the crucial problem of choosing a suitable mean-difference in TOST sample size calculations is addressed. As an alternative concept, it is assumed that the mean-difference follows an a-priori distribution. Special interest is given to the uniform and some centered triangle a-priori distributions. Using a newly developed asymptotical theory a helpful analogy principle is found: every a-priori distribution corresponds to a point mean-difference, which we call its Schuirmann-constant. This constant does not depend on the standard deviation and aims to support the investigator in finding a well-considered mean-difference for proper sample size calculations in complex data situations. In addition to the proposed concept, we demonstrate that well-known sample size approximation formulas in the literature are in fact biased and state their unbiased corrections as well. Moreover, an R package is provided for a right away application of our newly developed concepts. [ABSTRACT FROM AUTHOR]

Abstract Automated cell type identification is a key computational challenge in single‐cell RNA‐sequencing (scRNA‐seq) data. To capitalise on the large collection of well‐annotated scRNA‐seq datasets, we developed scClassify, a multiscale classification framework based on ensemble learning and cell type hierarchies constructed from single or multiple annotated datasets as references. scClassify enables the estimation of sample size required for accurate classification of cell types in a cell type hierarchy and allows joint classification of cells when multiple references are available. We show that scClassify consistently performs better than other supervised cell type classification methods across 114 pairs of reference and testing data, representing a diverse combination of sizes, technologies and levels of complexity, and further demonstrate the unique components of scClassify through simulations and compendia of experimental datasets. Finally, we demonstrate the scalability of scClassify on large single‐cell atlases and highlight a novel application of identifying subpopulations of cells from the Tabula Muris data that were unidentified in the original publication. Together, scClassify represents state‐of‐the‐art methodology in automated cell type identification from scRNA‐seq data.

Cellular heterogeneity underlies cancer evolution and metastasis. Advances in single-cell technologies such as single-cell RNA sequencing and mass cytometry have enabled interrogation of cell type-specific expression profiles and abundance across heterogeneous cancer samples obtained from clinical trials and preclinical studies. However, challenges remain in determining sample sizes needed for ascertaining changes in cell type abundances in a controlled study. To address this statistical challenge, we have developed a new approach, named Sensei, to determine the number of samples and the number of cells that are required to ascertain such changes between two groups of samples in single-cell studies. Sensei expands the t-test and models the cell abundances using a beta-binomial distribution. We evaluate the mathematical accuracy of Sensei and provide practical guidelines on over 20 cell types in over 30 cancer types based on knowledge acquired from the cancer cell atlas (TCGA) and prior single-cell studies. We provide a web application to enable user-friendly study design via https://kchen-lab.github.io/sensei/table_beta.html. [ABSTRACT FROM AUTHOR]

In cluster randomized trials (CRTs) groups rather than individuals are randomized to different interventions. Individuals' responses within clusters are commonly more similar than those across clusters. This dependency introduces complexity when calculating the number of clusters required to reach a specified statistical power for nominal significance levels and effect sizes. Current CRTs' sample size estimation approaches rely on asymptotic-based formulae or Monte Carlo methods. We propose a new Monte Carlo procedure which is based on the potential outcomes framework. By explicitly defining the causal estimand, the data generating, the sampling, and the treatment assignment mechanisms, this procedure allows for sample size calculations in a broad range of study designs including sample size calculations in finite and infinite populations. It can also address financial and administrative considerations by allowing for unequal allocation of clusters. The R package CRTsampleSearch implements the method and we provide examples for using this package. [ABSTRACT FROM AUTHOR]

Abstract Background Patient-reported outcome measures (PROMs) are now frequently used in randomised controlled trials (RCTs) as primary endpoints. RCTs are longitudinal, and many have a baseline (PRE) assessment of the outcome and one or more post-randomisation assessments of outcome (POST). With such pre-test post-test RCT designs there are several ways of estimating the sample size and analysing the outcome data: analysis of post-randomisation treatment means (POST); analysis of mean changes from pre- to post-randomisation (CHANGE); analysis of covariance (ANCOVA). Sample size estimation using the CHANGE and ANCOVA methods requires specification of the correlation between the baseline and follow-up measurements. Other parameters in the sample size estimation method being unchanged, an assumed correlation of 0.70 (between baseline and follow-up outcomes) means that we can halve the required sample size at the study design stage if we used an ANCOVA method compared to a comparison of POST treatment means method. So what correlation (between baseline and follow-up outcomes) should be assumed and used in the sample size calculation? The aim of this paper is to estimate the correlations between baseline and follow-up PROMs in RCTs. Methods The Pearson correlation coefficients between the baseline and repeated PROM assessments from 20 RCTs (with 7173 participants at baseline) were calculated and summarised. Results The 20 reviewed RCTs had sample sizes, at baseline, ranging from 49 to 2659 participants. The time points for the post-randomisation follow-up assessments ranged from 7 days to 24 months; 464 correlations, between baseline and follow-up, were estimated; the mean correlation was 0.50 (median 0.51; standard deviation 0.15; range − 0.13 to 0.91). Conclusions There is a general consistency in the correlations between the repeated PROMs, with the majority being in the range of 0.4 to 0.6. The implications are that we can reduce the sample size in an RCT by 25% if we use an ANCOVA model, with a correlation of 0.50, for the design and analysis. There is a decline in correlation amongst more distant pairs of time points.

Abstract Background Log-linear and multinomial modeling offer a flexible framework for genetic association analyses of offspring (child), parent-of-origin and maternal effects, based on genotype data from a variety of child-parent configurations. Although the calculation of statistical power or sample size is an important first step in the planning of any scientific study, there is currently a lack of software for genetic power calculations in family-based study designs. Here, we address this shortcoming through new implementations of power calculations in the R package Haplin, which is a flexible and robust software for genetic epidemiological analyses. Power calculations in Haplin can be performed analytically using the asymptotic variance-covariance structure of the parameter estimator, or else by a straightforward simulation approach. Haplin performs power calculations for child, parent-of-origin and maternal effects, as well as for gene-environment interactions. The power can be calculated for both single SNPs and haplotypes, either autosomal or X-linked. Moreover, Haplin enables power calculations for different child-parent configurations, including (but not limited to) case-parent triads, case-mother dyads, and case-parent triads in combination with unrelated control-parent triads. Results We compared the asymptotic power approximations to the power of analysis attained with Haplin. For external validation, the results were further compared to the power of analysis attained by the EMIM software using data simulations from Haplin. Consistency observed between Haplin and EMIM across various genetic scenarios confirms the computational accuracy of the inference methods used in both programs. The results also demonstrate that power calculations in Haplin are applicable to genetic association studies using either log-linear or multinomial modeling approaches. Conclusions Haplin provides a robust and reliable framework for power calculations in genetic association analyses for a wide range of genetic effects and etiologic scenarios, based on genotype data from a variety of child-parent configurations.

Purpose: To investigate and to provide guidance for sample size selection based on the current practice in MR technical development studies in which healthy volunteers are examined. Methods: All original articles published in Magnetic Resonance in Medicine between 2017 and 2019 were investigated and categorized according to technique, anatomical region, and magnetic field strength. The number of examined healthy volunteers (ie, the sample size) was collected and evaluated, whereas the number of patients was not considered. Papers solely measuring patients, animals, phantoms, specimens, or studies using existing data, for example, from an open databank, or consisting only of theoretical work or simulations were excluded. Results: The median sample size of the 882 included studies was 6. There were some peaks in the sample size distribution (eg, 1, 5, and 10). In 49.9%, 82.1%, and 95.6% of the studies, the sample size was smaller or equal to 5, 10, and 20, respectively. Conclusion: We observed a large variance in sample sizes reflecting the variety of studies published in Magnetic Resonance in Medicine. Therefore, it can be concluded that it is current practice to balance the need for statistical power with the demand to minimize experiments involving healthy humans, often by choosing small sample sizes between 1 and 10. Naturally, this observation does not release an investigator from ensuring that sufficient data are acquired to reach statistical conclusions. [ABSTRACT FROM AUTHOR]

Introduction: Evidence that can be used to improve clinical practice patterns and processes is frequently generated through standard, parallel-arms cluster randomized trial (CRT) designs that test interventions implemented at the center-level. Although the primary endpoint of these trials is often a center-level outcome, patient-level factors may vary between centers and, consequently, may influence the center-level outcome. Furthermore, there may be important factors that predict the variation in the center-level outcome and this knowledge can help contextualize the trial results and inform practice patterns. Methods: Our symbolic two-step method that applies symbolic data analysis to account for patient-level factors when estimating and testing a center-level effect on both the average center-level outcome and its variation was developed for such settings. Herein, we sought to extend the method to prospectively size a CRT so that the application of our method in data analysis is consistent with the design. Results: Our formulaic approach to sample size planning incorporated predictive factors of the within-center variation and accounted for patient-level characteristics. The sample size approximation performed well in many different pragmatic settings. Conclusions: Our symbolic two-step method provides an alternate approach in the design and analysis of CRTs evaluating novel improvement processes within care delivery research.

The Multiple Comparison Procedure – Modelling (MCP-Mod) method was qaulified by regulatory agencies (e.g., EMA in 2014 and FDA in 2016) as an efficient statistical method for Phase 2 dose-finding studies when there is uncertainty about dose-response relationship. As this is a relatively new approach, there is limited literature providing practical guidance on its application. In this paper, we evaluated the performance of the MCP-Mod method for clinical trials with a binary primary endpoint, focusing on (1) the impact of sample size, data variability and treatment effect size on the performance of the MCP-Mod, (2) the impact of candidate model mis-specification, and (3) optimal sample allocation under a fixed sample size. The evaluation was performed via simulations under different scenarios.

Cluster randomized trials (CRTs) refer to experiments with randomization carried out at the cluster or the group level. While numerous statistical methods have been developed for the design and analysis of CRTs, most of the existing methods focused on testing the overall treatment effect across the population characteristics, with few discussions on the differential treatment effect among subpopulations. In addition, the sample size and power requirements for detecting differential treatment effect in CRTs remain unclear, but are helpful for studies planned with such an objective. In this article, we develop a new sample size formula for detecting treatment effect heterogeneity in two‐level CRTs for continuous outcomes, continuous or binary covariates measured at cluster or individual level. We also investigate the roles of two intraclass correlation coefficients (ICCs): the adjusted ICC for the outcome of interest and the marginal ICC for the covariate of interest. We further derive a closed‐form design effect formula to facilitate the application of the proposed method, and provide extensions to accommodate multiple covariates. Extensive simulations are carried out to validate the proposed formula in finite samples. We find that the empirical power agrees well with the prediction across a range of parameter constellations, when data are analyzed by a linear mixed effects model with a treatment‐by‐covariate interaction. Finally, we use data from the HF‐ACTION study to illustrate the proposed sample size procedure for detecting heterogeneous treatment effects. [ABSTRACT FROM AUTHOR]

This work presents a statistically principled method for estimating the required number of instances in the experimental comparison of multiple algorithms on a given problem class of interest. This approach generalises earlier results by allowing researchers to design experiments based on the desired best, worst, mean or median-case statistical power to detect differences between algorithms larger than a certain threshold. Holm's step-down procedure is used to maintain the overall significance level controlled at desired levels, without resulting in overly conservative experiments. This paper also presents an approach for sampling each algorithm on each instance, based on optimal sample size ratios that minimise the total required number of runs subject to a desired accuracy in the estimation of paired differences. A case study investigating the effect of 21 variants of a custom-tailored Simulated Annealing for a class of scheduling problems is used to illustrate the application of the proposed methods for sample size calculations in the experimental comparison of algorithms. [ABSTRACT FROM AUTHOR]

In survival trials with fixed trial length, the patient accrual rate has a significant impact on the sample size estimation or equivalently, on the power of trials. A larger sample size is required for the staggered patient entry. During enrollment, the patient accrual rate changes with the recruitment publicity effect, disease incidence and many other factors and fluctuations of the accrual rate occur frequently. However, the existing accrual models are either over-simplified for the constant rate assumption or complicated in calculation for the subdivision of the accrual period. A more flexible accrual model is required to represent the fluctuant patient accrual rate for accurate sample size estimation. In this paper, inspired by the flexibility of the Gaussian mixture distribution in approximating continuous densities, we propose the truncated Gaussian mixture distribution accrual model to represent different variations of accrual rate by different parameter configurations. The sample size calculation formula and the parameter setting of the proposed accrual model are discussed further. [ABSTRACT FROM AUTHOR]

Automated cell type identification is a key computational challenge in single‐cell RNA‐sequencing (scRNA‐seq) data. To capitalise on the large collection of well‐annotated scRNA‐seq datasets, we developed scClassify, a multiscale classification framework based on ensemble learning and cell type hierarchies constructed from single or multiple annotated datasets as references. scClassify enables the estimation of sample size required for accurate classification of cell types in a cell type hierarchy and allows joint classification of cells when multiple references are available. We show that scClassify consistently performs better than other supervised cell type classification methods across 114 pairs of reference and testing data, representing a diverse combination of sizes, technologies and levels of complexity, and further demonstrate the unique components of scClassify through simulations and compendia of experimental datasets. Finally, we demonstrate the scalability of scClassify on large single‐cell atlases and highlight a novel application of identifying subpopulations of cells from the Tabula Muris data that were unidentified in the original publication. Together, scClassify represents state‐of‐the‐art methodology in automated cell type identification from scRNA‐seq data. Synopsis: scClassify is a multiscale classification framework based on ensemble learning and cell type hierarchies, enabling sample size estimation required for accurate cell type classification and joint classification of cells using multiple references. scClassify performs multiscale cell type classification based on cell type hierarchies constructed from single or multiple reference datasets.It implements a post‐hoc clustering procedure for discovering novel cell types from cells that are unassigned due to the absence of their types in the reference data.It enables the estimation of the number of cells required in a reference dataset to accurately discriminate a given cell type in a cell type hierarchy.Application to large atlas datasets such as Tabula Muris demonstrates its ability to refine cell types and identify cells from sub‐populations. [ABSTRACT FROM AUTHOR]

Background: Log-linear and multinomial modeling offer a flexible framework for genetic association analyses of offspring (child), parent-of-origin and maternal effects, based on genotype data from a variety of child-parent configurations. Although the calculation of statistical power or sample size is an important first step in the planning of any scientific study, there is currently a lack of software for genetic power calculations in family-based study designs. Here, we address this shortcoming through new implementations of power calculations in the R package Haplin, which is a flexible and robust software for genetic epidemiological analyses. Power calculations in Haplin can be performed analytically using the asymptotic variance-covariance structure of the parameter estimator, or else by a straightforward simulation approach. Haplin performs power calculations for child, parent-of-origin and maternal effects, as well as for gene-environment interactions. The power can be calculated for both single SNPs and haplotypes, either autosomal or X-linked. Moreover, Haplin enables power calculations for different child-parent configurations, including (but not limited to) case-parent triads, case-mother dyads, and case-parent triads in combination with unrelated control-parent triads. Results: We compared the asymptotic power approximations to the power of analysis attained with Haplin. For external validation, the results were further compared to the power of analysis attained by the EMIM software using data simulations from Haplin. Consistency observed between Haplin and EMIM across various genetic scenarios confirms the computational accuracy of the inference methods used in both programs. The results also demonstrate that power calculations in Haplin are applicable to genetic association studies using either log-linear or multinomial modeling approaches. Conclusions: Haplin provides a robust and reliable framework for power calculations in genetic association analyses for a wide range of genetic effects and etiologic scenarios, based on genotype data from a variety of child-parent configurations. [ABSTRACT FROM AUTHOR]

Experimental comparisons of performance represent an important aspect of research on optimization algorithms. In this work we present a methodology for defining the required sample sizes for designing experiments with desired statistical properties for the comparison of two methods on a given problem class. The proposed approach allows the experimenter to define desired levels of accuracy for estimates of mean performance differences on individual problem instances, as well as the desired statistical power for comparing mean performances over a problem class of interest. The method calculates the required number of problem instances, and runs the algorithms on each test instance so that the accuracy of the estimated differences in performance is controlled at the predefined level. Two examples illustrate the application of the proposed method, and its ability to achieve the desired statistical properties with a methodologically sound definition of the relevant sample sizes. [ABSTRACT FROM AUTHOR]

Background: The estimation of an effect size is an important step in designing an adequately powered, feasible clinical trial intended to change clinical practice. During the planning phase of VA Cooperative Study #590, “Double-Blind Placebo-Controlled Study of Lithium for Preventing Repeated Suicidal Self-Directed Violence in Patients with Depression or Bipolar Disorder (Li+),” it was not clear what effect size would be considered large enough to influence prescribing behavior among practicing clinicians. Methods: We conducted an online survey of VA psychiatrists to assess their interest in the study question, their clinical experience with lithium, and their opinion about what suicide reduction rate would change their prescribing habits. The 9-item survey was hosted on SurveyMonkey© and VA psychiatrists were individually emailed an invitation to complete an anonymous online survey. Three email waves were sent over three weeks. Results: Overall, 862 of 2713 VA psychiatrists (response rate = 31.8%) responded to the anonymous survey. 74% of the respondents would refer a patient to the proposed trial, 9% would not, and 17% were unsure. Presented with suicide reduction rates in 10% increments ranging from 10 to 100%, 61% of respondents indicated that they would use lithium if suicide attempts were reduced by at least 40%; 83% would use lithium if it reduced attempts by at least 50%. Conclusions: Even with the limitations of response bias and the reliability of responses on future prescribing behavior, a survey of potential users of a clinical trial's results offers a convenient, empirical method for determining and justifying clinically relevant effect sizes.

The size of the sample significantly impacts the accuracy of research outcomes. While preliminary results have been achieved in acupuncture imaging research, sample size estimation is often subjective and arbitrary, leading to insufficient reliability of study results. This article reviews the current application of sample size estimation in acupuncture imaging research, and provides recommendations to address existing issues. It is suggested that future researches should include the sample sizes that meet statistical power based on the characteristics of functional magnetic resonance imaging (fMRI) protocols, with group sizes of 12 and 20-30 cases having become the "minimum requirement" for confirmatory studies and a common choice. Additionally, the adoption of adaptive design approaches, which dynamically adjust sample sizes based on accumulated data, can be considered. Furthermore, efforts should be made to establish an open platform for sharing acupuncture imaging data to enhance data accessibility, and consequently, improve the quality and overall impact of acupuncture imaging research.