Sample Size Calculation Method Research Articles

Applying Exercise Capacity and Physical Activity as Single vs Composite Endpoints for Trials of Cardiac Rehabilitation Interventions: Rationale, Use-case, and a Blueprint Method for Sample Size Calculation

ObjectiveTo conceptualize a composite primary endpoint for parallel-group RCTs of exercise-based cardiac rehabilitation (CR) interventions and to explore its application and statistical efficiency. DesignWe conducted a statistical exploration of sample size requirements. We combined exercise capacity and physical activity for the composite endpoint (CE), both being directly related to reduced premature mortality in patients with cardiac diseases. Based on smallest detectable and minimal clinically important changes (change in exercise capacity of 15 W and change in physical activity of 10 min/day), the CE combines 2 dichotomous endpoints (achieved/not achieved). To examine statistical efficiency, we compared sample size requirements based on the CE to single endpoints using data from 2 completed CR trials. SettingCardiac rehabilitation phase III. ParticipantsPatients in cardiac rehabilitation. InterventionsNot applicable. Main Outcome Measure(s)Exercise capacity (Pmax assessed by incremental cycle ergometry) and physical activity (daily minutes of moderate to vigorous physical activity assessed by accelerometry). ResultsExpecting, for example, a 10% between-group difference and improvement in the clinical outcome, the CE would increase sample size by up to 21% or 61%, depending on the dataset. When expecting a 10% difference and designing an intervention with the aim of non-deterioration, the CE would allow to reduce the sample size by up to 55% or 70%. ConclusionsTrialists may consider the utility of the CE for future studies in exercise-based CR to reduce sample size requirements. However, perhaps surprisingly at first, the CE could also lead to an increased sample size needed, depending on the observed baseline proportions in the trial population and the aim of the intervention.

Analysis of the impact of indoor thermal comfort data characteristics on dataset quality

The impact of data characteristics on dataset quality is of significant guidance in the field of thermal comfort field surveys. In this paper, a Chinese thermal comfort database has been established, comprising quality-controlled on-site survey data. The database encompasses 41,977 sets of on-site survey data collected from 50 cities across 24 provinces, spanning a period of nearly 20 years from 2001 to 2021. It includes the five thermal zones in China and encompasses three seasons—summer, transitional, and winter—as well as four types of buildings: office buildings, residential buildings, student dormitories, and classrooms. The database exhibits an extensive data distribution, demonstrating a certain level of representativeness in terms of environmental temperature and survey locations. Based on this established database, the thermal sensation model was employed as the criterion for evaluating dataset quality. This study analyzed the impact of data characteristics on dataset qualityfrom three perspectives: sample size, data distribution, and data range. A sample size calculation method using interval estimation was adopted, determiningthat a minimum sample size of 350 is required for on-site thermal comfort surveys in office and residential buildings. A comparison revealed that compared to data with the normal distribution and uniform distribution, data with the positively skewed distribution exhibit lower neutral temperatures, while data with the negatively skewed distribution exhibit higher neutral temperatures. The thermal sensation model constructed based on data with uniform distribution demonstrates greater robustness. As the temperature range decreases, the neutral temperature increases in winter and decreases in summer, resulting in reduced accuracy of the constructed thermal sensation model.

Sample size calculation for comparing two ROC curves

AbstractBiomarkers are key components of personalized medicine. In this paper, we consider biomarkers taking continuous values that are associated with disease status, called case and control. The performance of such a biomarker is evaluated by the area under the curve (AUC) of its receiver operating characteristic curve. Oftentimes, two biomarkers are collected from each subject to test if one has a larger AUC than the other. We propose a simple non‐parametric statistical test for comparing the performance of two biomarkers. We also present a simple sample size calculation method for this test statistic. Our sample size formula requires specification of AUC values (or the standardized effect size of each biomarker between cases and controls together with the correlation coefficient between two biomarkers), prevalence of cases in the study population, type I error rate, and power. Through simulations, we show that the testing on two biomarkers controls type I error rate accurately and the proposed sample size closely maintains specified statistical power.

Sample size calculation in clinical trials with two co-primary endpoints including overdispersed count and continuous outcomes.

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

Sample Size Determination for Food Sampling

Industry and public health agencies sample and test food products for various purposes related to food safety and quality. Methods of sample selection and sample size determination are important in designing an optimal sampling plan. The appropriate sample size of a sampling plan depends on the objective. We examine the methods of sample size calculation for the following four objectives commonly associated with food sampling: (1) estimate prevalence (e.g., of contaminated products), (2) detect presence (e.g., of contaminated products), (3) estimate maximum prevalence, and (4) compare estimated prevalence with a specified value (e.g., a previous estimate or a threshold value). We illustrate these methods using examples and provide a web-based application (https://simple-sample.galaxytrakr.org/) written in R, using the shiny package, to help users with the application of each method.

Sample size calculation in clinical trial using R.

Since the era of evidence-based medicine, it has become a matter of course to use statistics to create objective evidence in clinical research. As an extension of this, it has become essential in clinical research to calculate the correct sample size to demonstrate a clinically significant difference before starting the study. Also, because sample size calculation methods vary from study design to study design, there is no formula for sample size calculation that applies to all designs. It is very important for us to understand this. In this review, each sample size calculation method suitable for various study designs was introduced using the R program (R Foundation for Statistical Computing). In order for clinical researchers to directly utilize it according to future research, we presented practice codes, output results, and interpretation of results for each situation.

A statistical framework for calculating prospective sample sizes and classifying efficacy results for faecal egg count reduction tests in ruminants, horses and swine

The faecal egg count reduction test (FECRT) is the primary diagnostic tool used for detecting anthelmintic resistance at the farm level. It is therefore extremely important that the experimental design of a FECRT and the susceptibility classification of the result use standardised and statistically rigorous methods. Several different approaches for improving the analysis of FECRT data have been proposed, but little work has been published on how to address the issue of prospective sample size calculations. Here, we provide a complete and detailed overview of the quantitative issues relevant to a FECRT starting from basic statistical principles. We then present a new approach for determining sample size requirements for the FECRT that is built on a solid statistical framework, and provide a rigorous anthelminthic drug efficacy classification system for use with FECRT in livestock. Our approach uses two separate statistical tests, a one-sided inferiority test for resistance and a one-sided non-inferiority test for susceptibility, and determines a classification of resistant, susceptible or inconclusive based on the combined result. Since this approach is based on two independent one-sided tests, we recommend that a 90 % CI be used in place of the historically used 95 % CI. This maintains the desired Type I error rate of 5 %, and simultaneously reduces the required sample size. We demonstrate the use of this framework to provide sample size calculations that are rooted in the well-understood concept of statistical power. Tailoring to specific host/parasite systems is possible using typical values for expected pre-treatment and post-treatment variability in egg counts as well as within-animal correlation in egg counts. We provide estimates for these parameters for ruminants, horses and swine based on a re-examination of datasets that were available to us from a combination of published data and other sources. An illustrative example is provided to demonstrate the use of the framework, and parameter estimates are presented to estimate the required sample size for a hypothetical FECRT using ivermectin in cattle. The sample size calculation method and classification framework presented here underpin the sample size recommendations provided in the upcoming FECRT WAAVP guidelines for detection of anthelmintic resistance in ruminants, horses, and swine, and have also been made freely available as open-source software via our website (https://www.fecrt.com).

Sample size variation in single-time post-dose assessment vs multi-time post-dose assessment

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.

Measuring educational neglect using the Q method: A model based on the burden of disseminated tungiasis.

A paramount factor in the control of neglected tropical diseases from both medical and social aspects is education. New strategies must be constantly pursued to test and provide educational information related to diseases affecting vulnerable populations. We applied the Q method as a model to measure educational neglect based on the burden of disseminated tungiasis. Using a saturation method for sample size calculation, we recruited students and healthcare professionals to evaluate and classify 27 statements related to the prevention, control and treatment of tungiasis. After quantitative analysis, the Q method was applied based on the paired use of the centroid method and Varimax rotation, and 4 factors were extracted representing the main sets of viewpoints among the participants. We included 119 healthcare professionals with different academic degrees. Statements classified by specialists with a + agreement were also classified as a + agreement by most of the participants. However, we detected 5 important disagreements related to the topical treatment of tungiasis and control of the disease in the environment and animals. The Q method showed that almost no consensus was detected for four statements. The classification of each statement was not related to the participants' academic degree. There is significant educational neglect related to tungiasis prevention and treatment in healthcare sciences in Brazil. We conclude that the Q method may be an interesting strategy alone or associated with quantitative strategies for detecting educational limitations related to neglected diseases. In countries where neglected diseases are endemic, a detailed study evaluating the quality of education related to these diseases must be prioritized.

Reporting quality in preclinical animal experimental research in 2009 and 2018: A nationwide systematic investigation.

Lack of translation and irreproducibility challenge preclinical animal research. Insufficient reporting methodologies to safeguard study quality is part of the reason. This nationwide study investigates the reporting prevalence of these methodologies and scrutinizes the reported information's level of detail. Publications were from two time periods to convey any reporting progress and had at least one author affiliated to a Danish University. We retrieved all relevant animal experimental studies using a predefined research protocol and a systematic search. A random sampling of 250 studies from 2009 and 2018 led to 500 publications in total. Reporting of measures known to impact study results estimates were assessed. Part I discloses a simplified two-level scoring "yes/no" to identify the presence of reporting. Part II demonstrates an additional three-level scoring to analyze the reported information's level of detail. Overall reporting prevalence is low, although minor improvements are noted. Reporting of randomization increased from 24.0% in 2009 to 40.8% in 2018, blinded experiment conduct from 2.4% to 4.4%, blinded outcome assessment from 23.6% to 38.0%, and sample size calculation from 3.2% to 14.0%. Poor reporting of details is striking with reporting of the random allocation method to groups being only 1.2% in 2009 and 6.0% in 2018. Reporting of sample size calculation method was 2.4% in 2009 and 7.6% in 2018. Only conflict-of-interest statements reporting increased from 37.6% in 2009 to 90.4%. Measures safeguarding study quality are poorly reported in publications affiliated with Danish research institutions. Only a modest improvement was noted during the period 2009-2018, and the lack of details urgently prompts institutional strategies to accelerate this. We suggest thorough teaching in designing, conducting and reporting animal studies. Education in systematic review methodology should be implemented in this training and will increase motivation and behavior working towards quality improvements in science.

Sample size calculation for prevalence studies using Scalex and ScalaR calculators

BackgroundAlthough books and articles guiding the methods of sample size calculation for prevalence studies are available, we aim to guide, assist and report sample size calculation using the present calculators.ResultsWe present and discuss four parameters (namely level of confidence, precision, variability of the data, and anticipated loss) required for sample size calculation for prevalence studies. Choosing correct parameters with proper understanding, and reporting issues are mainly discussed. We demonstrate the use of a purposely-designed calculators that assist users to make proper informed-decision and prepare appropriate report.ConclusionTwo calculators can be used with free software (Spreadsheet and RStudio) that benefit researchers with limited resources. It will, hopefully, minimize the errors in parameter selection, calculation, and reporting. The calculators are available at: (https://sites.google.com/view/sr-ln/ssc).

Sample Size Calculation for Clinical Trials of Medical Decision Support Systems with Binary Outcome.

Currently, software products for use in medicine are actively developed. Among them, the dominant share belongs to clinical decision support systems (CDSS), which can be intelligent (based on mathematical models obtained by machine learning methods or other artificial intelligence technologies) or non-intelligent. For the state registration of CDSSs as software medical products, clinical trials are required, and the protocol of trial is developed jointly by the developer and an authorized medical organization. One of the mandatory components of the protocol is the calculation of the sample size. This article discusses the calculation of the sample size for the most common case, the binary outcome in diagnostic/screening and predictive systems. For diagnostic/screening models, cases of a non-comparative study, comparative study with testing of the superiority hypothesis, comparative study with testing of a hypothesis of non-inferiority in cross-sectional studies are considered. For predictive models, cases of randomized controlled trials of the complex intervention "prediction + prediction-dependent patient management" with testing of the hypothesis of superiority and non-inferiority are considered. It is emphasized that representativeness of the sample and other design components are no less important in clinical trials than sample size. They are even more important since systematic biases in clinical trials are primary, and even the most sophisticated statistical analysis cannot compensate for design defects. The reduction of clinical trials to external validation of models (i.e. evaluation of accuracy metrics on external data) seems completely unreasonable. It is recommended to perform clinical trials with the design adequate to the tasks, so that further clinical and economic analysis and comprehensive assessment of medical technologies are possible. The sample size calculation methods described in the article can potentially be applied to a wider range of medical devices.

Sample size calculation for randomized selection trials with a time-to-event endpoint and a margin of practical equivalence.

Selection trials are used to compare potentially active experimental treatments without a control arm. While sample size calculation methods exist for binary endpoints, no such methods are available for time‐to‐event endpoints, even though these are ubiquitous in clinical trials. Recent selection trials have begun using progression‐free survival as their primary endpoint, but have dichotomized it at a specific time point for sample size calculation and analysis. This changes the clinical question and may reduce power to detect a difference between the arms. In this article, we develop the theory for sample size calculation in selection trials where the time‐to‐event endpoint is assumed to follow an exponential or Weilbull distribution. We provide a free web application for sample size calculation, as well as an R package, that researchers can use in the design of their studies.

Sample size determination with a pilot study.

We analyse standard confidence intervals for the mean of a finite population, with a view to sample size determination. We first consider a standard method for sample size determination based on the assumption of knowledge of the population variance parameter. We then consider the more realistic case where the population variance is treated as an unknown, and we derive a new method of sample size determination that accounts for the uncertainty in this parameter. We develop a sample size calculation method based on a preliminary sample of data which allows us to increase the accuracy of our inference by some specified amount with a specified level of confidence. We compare this method to the standard method.

Influential methods reports for group-randomized trials and related designs

This article identifies the most influential methods reports for group-randomized trials and related designs published through 2020. Many interventions are delivered to participants in real or virtual groups or in groups defined by a shared interventionist so that there is an expectation for positive correlation among observations taken on participants in the same group. These interventions are typically evaluated using a group- or cluster-randomized trial, an individually randomized group treatment trial, or a stepped wedge group- or cluster-randomized trial. These trials face methodological issues beyond those encountered in the more familiar individually randomized controlled trial. PubMed was searched to identify candidate methods reports; that search was supplemented by reports known to the author. Candidate reports were reviewed by the author to include only those focused on the designs of interest. Citation counts and the relative citation ratio, a new bibliometric tool developed at the National Institutes of Health, were used to identify influential reports. The relative citation ratio measures influence at the article level by comparing the citation rate of the reference article to the citation rates of the articles cited by other articles that also cite the reference article. In total, 1043 reports were identified that were published through 2020. However, 55 were deemed to be the most influential based on their relative citation ratio or their citation count using criteria specific to each of the three designs, with 32 group-randomized trial reports, 7 individually randomized group treatment trial reports, and 16 stepped wedge group-randomized trial reports. Many of the influential reports were early publications that drew attention to the issues that distinguish these designs from the more familiar individually randomized controlled trial. Others were textbooks that covered a wide range of issues for these designs. Others were "first reports" on analytic methods appropriate for a specific type of data (e.g. binary data, ordinal data), for features commonly encountered in these studies (e.g. unequal cluster size, attrition), or for important variations in study design (e.g. repeated measures, cohort versus cross-section). Many presented methods for sample size calculations. Others described how these designs could be applied to a new area (e.g. dissemination and implementation research). Among the reports with the highest relative citation ratios were the CONSORT statements for each design. Collectively, the influential reports address topics of great interest to investigators who might consider using one of these designs and need guidance on selecting the most appropriate design for their research question and on the best methods for design, analysis, and sample size.

Statistical methods for seamless phase II/III design

The seamless phase II/III design combining phases II and III into a single trial has been shown growing interest for improving the efficiency of drug development, becoming the most frequent adaptive design type. It typically consists of two stages, the trial objectives being often different in each stage. The primary objectives are to select optimal experimental treatment group(s) in the first stage and compare the efficacy between the selected treatment and control groups in the second stage. In the final analysis, appropriate statistical methods should be applied to avoid increasing the type I error rate and selection bias. This paper reviews several statistical methods that can be applied to adaptive seamless phase II/III designs. Especially, the most representative methods such as the group sequential design approach, combination test approach, and conditional error function approach, are organized in a unified framework and the characteristics of the methods are compared. As related topics, statistical methods for the case where endpoints are different between stages 1 and 2, and the method of sample size calculation will also be discussed. Examples of actual applications are also presented.

Estimation of multivariate treatment effects in contaminated clinical trials.

The paper addresses estimating and testing treatment effects with multivariate outcomes in clinical trials where imperfect diagnostic devices are used to assign subjects to treatment groups. The paper focuses on the pre-post design and proposes two novel methods for estimating and testing treatment effects. In addition, methods for sample size and power calculations are developed. The methods are compared with each other and with a traditional method in a simulation study. The new methods show significant advantages in terms of power, coverage probability, and required sample size. The application of the methods is illustrated with data from electroencephalogram (EEG) recordings of alcoholic and control subjects.

Power considerations for generalized estimating equations analyses of four-level cluster randomized trials.

In this article, we develop methods for sample size and power calculations in four-level intervention studies when intervention assignment is carried out at any level, with a particular focus on cluster randomized trials (CRTs). CRTs involving four levels are becoming popular in healthcare research, where the effects are measured, for example, from evaluations (level 1) within participants (level 2) in divisions (level 3) that are nested in clusters (level 4). In such multilevel CRTs, we consider three types of intraclass correlations between different evaluations to account for such clustering: that of the same participant, that of different participants from the same division, and that of different participants from different divisions in the same cluster. Assuming arbitrary link and variance functions, with the proposed correlation structure as the true correlation structure, closed-form sample size formulas for randomization carried out at any level (including individually randomized trials within a four-level clustered structure) are derived based on the generalized estimating equations approach using the model-based variance and using the sandwich variance with an independence working correlation matrix. We demonstrate that empirical power corresponds well with that predicted by the proposed method for as few as eight clusters, when data are analyzed using the matrix-adjusted estimating equations for the correlation parameters with a bias-corrected sandwich variance estimator, under both balanced and unbalanceddesigns.

On sample size calculation in testing treatment efficacy in clinical trials

Summary Sample size calculation is an integral part of any clinical trial design, and determining the optimal sample size for a study ensures adequate power to detect statistical significance. It is a critical step in designing a planned research protocol, since using too many participants in a study is expensive, exposing more subjects to the procedure. If a study is underpowered, it will be statistically inconclusive and may cause the whole protocol to fail. Amidst the attempt to maximize power and the underlying effort to minimize the budget, the optimization of both has become a significant issue in the determination of sample size for clinical trials in recent decades. Although it is hard to generalize a single method for sample size calculation, this study is an attempt to offer something that might be a basis for finding a permanent answer to the contradictions of sample size determination, by the use of simulation studies under simple random and cluster sampling schemes, with different sizes of power and type I error. The effective sample size is much higher when the design effect of the sampling method is smaller, particularly less than 1. Sample size increases for cluster sampling when the number of clusters increases.

Sample size calculation for clustered survival data under subunit randomization.

Each cluster consists of multiple subunits from which outcome data are collected. In a subunit randomization trial, subunits are randomized into different intervention arms. Observations from subunits within each cluster tend to be positively correlated due to the shared common frailties, so that the outcome data from a subunit randomization trial have dependency between arms as well as within each arm. For subunit randomization trials with a survival endpoint, few methods have been proposed for sample size calculation showing the clear relationship between the joint survival distribution between subunits and the sample size, especially when the number of subunits from each cluster is variable. In this paper, we propose a closed form sample size formula for weighted rank test to compare the marginal survival distributions between intervention arms under subunit randomization, possibly with variable number of subunits among clusters. We conduct extensive simulations to evaluate the performance of our formula under various design settings, and demonstrate our sample size calculation method with some real clinical trials.