Asymptotic properties of the two one-sided t-tests – new insights and the Schuirmann-constant

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Christian Palmes ◽  
Tobias Bluhmki ◽  
Benedikt Funke ◽  
Erich Bluhmki
Keyword(s):  
Sample Size ◽  
A Priori ◽  
Asymptotic Properties ◽  
Sample Size Calculation ◽  
R Package ◽  
Mean Difference ◽  
Complex Data ◽  
Statistical Equivalence ◽  
Sample Size Calculations ◽  
A Priori Distribution

Abstract 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.

scholarly journals Sample size calculation for phylogenetic case linkage

2021 ◽  
Vol 17 (7) ◽  
pp. e1009182
Author(s):  
Shirlee Wohl ◽  
John R. Giles ◽  
Justin Lessler
Keyword(s):  
Sample Size ◽  
Sensitivity And Specificity ◽  
Sample Size Calculation ◽  
R Package ◽  
Pathogen Transmission ◽  
Phylogenetic Study ◽  
Population Coverage ◽  
Statistical Framework ◽  
Phylogenetic Studies ◽  
Sample Size Calculations

Sample size calculations are an essential component of the design and evaluation of scientific studies. However, there is a lack of clear guidance for determining the sample size needed for phylogenetic studies, which are becoming an essential part of studying pathogen transmission. We introduce a statistical framework for determining the number of true infector-infectee transmission pairs identified by a phylogenetic study, given the size and population coverage of that study. We then show how characteristics of the criteria used to determine linkage and aspects of the study design can influence our ability to correctly identify transmission links, in sometimes counterintuitive ways. We test the overall approach using outbreak simulations and provide guidance for calculating the sensitivity and specificity of the linkage criteria, the key inputs to our approach. The framework is freely available as the R package phylosamp, and is broadly applicable to designing and evaluating a wide array of pathogen phylogenetic studies.

scholarly journals Sample Size Calculation for Phylogenetic Case Linkage

2020 ◽  
Author(s):  
Shirlee Wohl ◽  
John R Giles ◽  
Justin Lessler
Keyword(s):  
Sample Size ◽  
Sensitivity And Specificity ◽  
Sample Size Calculation ◽  
R Package ◽  
Pathogen Transmission ◽  
Phylogenetic Study ◽  
Population Coverage ◽  
Statistical Framework ◽  
Phylogenetic Studies ◽  
Sample Size Calculations

Sample size calculations are an essential component of the design and evaluation of scientific studies. However, there is a lack of clear guidance for determining the sample size needed for phylogenetic studies, which are becoming an essential part of studying pathogen transmission. We introduce a statistical framework for determining the number of true infector-infectee transmission pairs identified by a phylogenetic study, given the size and population coverage of that study. We then show how characteristics of the criteria used to determine linkage and aspects of the study design can influence our ability to correctly identify transmission links, in sometimes counterintuitive ways. We test the overall approach using outbreak simulations and provide guidance for calculating the sensitivity and specificity of the linkage criteria, the key inputs to our approach. The framework is freely available as the R package phylosamp, and is broadly applicable to designing and evaluating a wide array of pathogen phylogenetic studies.

scholarly journals Causality in Statistical Power: Isomorphic Properties of Measurement, Research Design, Effect Size, and Sample Size

Scientifica ◽  
2016 ◽  
Vol 2016 ◽  
pp. 1-5 ◽  
Author(s):  
R. Eric Heidel
Keyword(s):  
Sample Size ◽  
Cognitive Dissonance ◽  
Research Design ◽  
Effect Size ◽  
Statistical Power ◽  
Research Study ◽  
A Priori ◽  
Sample Size Calculation ◽  
Design Effect

Statistical power is the ability to detect a significant effect, given that the effect actually exists in a population. Like most statistical concepts, statistical power tends to induce cognitive dissonance in hepatology researchers. However, planning for statistical power by ana priorisample size calculation is of paramount importance when designing a research study. There are five specific empirical components that make up ana priorisample size calculation: the scale of measurement of the outcome, the research design, the magnitude of the effect size, the variance of the effect size, and the sample size. A framework grounded in the phenomenon of isomorphism, or interdependencies amongst different constructs with similar forms, will be presented to understand the isomorphic effects of decisions made on each of the five aforementioned components of statistical power.

scholarly journals Reporting of statistical sample size calculations in publications of trials on age-related macular degeneration, glaucoma and cataract

PLoS ONE ◽  
2021 ◽  
Vol 16 (6) ◽  
pp. e0252640
Author(s):  
Sabrina Tulka ◽  
Stephanie Knippschild ◽  
Sina Funck ◽  
Isabelle Goetjes ◽  
Yasmin Uluk ◽  
...  
Keyword(s):  
Sample Size ◽  
Primary Outcome ◽  
Outcome Measure ◽  
Sample Size Calculation ◽  
Primary Outcome Measure ◽  
Age Related Macular Degeneration ◽  
Age Related ◽  
Number Of Patients ◽  
Sample Size Calculations ◽  
Statistical Sample

Background Transparent and complete publications of randomised controlled trials (RCT) ought to comply with the guidelines of the CONSORT Statement, which stipulates sample size calculation as an important aspect of trial planning. The objective of this study was to analyse and compare the reporting of statistical sample size calculations in RCT papers on the treatment of age-related macular degeneration (AMD), glaucoma and cataract published in 2018. Material and methods This study comprises a total of 113 RCT papers (RCT-P) published in 2018 (AMD: 14, glaucoma: 28, cataract: 71), in English or German, and identified through an internet-based literature search in PubMed and EMBASE. The primary outcome measure of the study was the number of trials providing a complete description of the underlying sample case calculation on the basis of the variables required (significance level, expected outcomes, power, and resulting sample size). Results Of the RCTs reviewed, 64% (AMD), 61% (glaucoma) and 31% (cataract) provided a justification of the number of patients included. A complete description of the described studies’ sample size calculation including all the necessary values (primary outcome measure of this study) was described by 21% of the AMD, 29% of the cataract and 18% of the glaucoma RCT publications (in total: 24 of 113 (21%) at a confidence interval of 95%: [13%; 29%]). Conclusion All three treatment areas analysed lacked reporting quality regarding the justification of the number of patients included in a clinical trial based on a sample size calculation required for ethical reasons. More than half of all RCT publications reviewed did not provide all of the required information on statistical sample size calculation, and thus lacked transparency and completeness. It is therefore urgently required to involve methodologists in a study’s planning and publishing processes to ensure that methodology descriptions are transparent and of high quality.

scholarly journals Adaptive sample size determination for the development of clinical prediction models

2020 ◽  
Author(s):  
Evangelia Christodoulou ◽  
Maarten van Smeden ◽  
Michael Edlinger ◽  
Dirk Timmerman ◽  
Maria Wanitschek ◽  
...  
Keyword(s):  
Ovarian Cancer ◽  
Sample Size ◽  
Prediction Models ◽  
A Priori ◽  
Sample Size Calculation ◽  
Model Performance ◽  
Sample Size Determination ◽  
Sample Sizes ◽  
Cancer Data ◽  
C Statistic

Abstract Background: We suggest an adaptive sample size calculation method for developing clinical prediction models, in which model performance is monitored sequentially as new data comes in. Methods: We illustrate the approach using data for the diagnosis of ovarian cancer (n=5914, 33% event fraction) and obstructive coronary artery disease (CAD; n=4888, 44% event fraction). We used logistic regression to develop a prediction model consisting only of a-priori selected predictors and assumed linear relations for continuous predictors. We mimicked prospective patient recruitment by developing the model on 100 randomly selected patients, and we used bootstrapping to internally validate the model. We sequentially added 50 random new patients until we reached a sample size of 3000, and re-estimated model performance at each step. We examined the required sample size for satisfying the following stopping rule: obtaining a calibration slope ≥0.9 and optimism in the c-statistic (ΔAUC) <=0.02 at two consecutive sample sizes. This procedure was repeated 500 times. We also investigated the impact of alternative modeling strategies: modeling nonlinear relations for continuous predictors, and applying Firth’s bias correction.Results: Better discrimination was achieved in the ovarian cancer data (c-statistic 0.9 with 7 predictors) than in the CAD data (c-statistic 0.7 with 11 predictors). Adequate calibration and limited optimism in discrimination was achieved after a median of 450 patients (interquartile range 450-500) for the ovarian cancer data (22 events per parameter (EPP), 20-24), and 750 patients (700-800) for the CAD data (30 EPP, 28-33). A stricter criterion, requiring ΔAUC <=0.01, was met with a median of 500 (23 EPP) and 1350 (54 EPP) patients, respectively. These sample sizes were much higher than the well-known 10 EPP rule of thumb and slightly higher than a recently published fixed sample size calculation method by Riley et al. Higher sample sizes were required when nonlinear relationships were modeled, and lower sample sizes when Firth’s correction was used. Conclusions: Adaptive sample size determination can be a useful supplement to a priori sample size calculations, because it allows to further tailor the sample size to the specific prediction modeling context in a dynamic fashion.

A priori power considerations in orthodontic research: a 3 year meta-epidemiologic study

2019 ◽  
Vol 42 (4) ◽  
pp. 454-459
Author(s):  
Sophia Gratsia ◽  
Despina Koletsi ◽  
Padhraig S Fleming ◽  
Nikolaos Pandis
Keyword(s):  
Sample Size ◽  
Study Design ◽  
Strong Predictor ◽  
Statistical Significance ◽  
A Priori ◽  
Epidemiologic Study ◽  
Observational Research ◽  
Power Calculations ◽  
Sample Size Calculations

Summary Aim To assess the prevalence of a priori power calculations in orthodontic literature and to identify potential associations with a number of study characteristics, including journal, year of publication and statistical significance of the outcome. Materials and methods The electronic archives of four leading orthodontic journals with the highest impact factor (American Journal of Orthodontics and Dentofacial Orthopedics, AJODO; European Journal of Orthodontics, EJO; Angle Orthodontist, ANGLE; Orthodontics and Craniofacial Research, OCR) were assessed over a 3 year period until December 2018. The proportion of articles reporting a priori power calculations were recorded, and the association with journal, year of publication, study design, continent of authorship, number of centres and researchers, statistical significance of results and reporting of confidence intervals (CIs) was assessed. Univariable and multivariable regression were used to identify significant predictors. Results Overall, 654 eligible articles were retrieved, with the majority published in the AJODO (n = 246, 37.6%), followed by ANGLE (n = 222, 33.9%) and EJO (n = 139, 21.3%). A total of 233 studies (35.6%) presented power considerations a priori along with sample size calculations. Study design was a very strong predictor with interventional design presenting 3.02 times higher odds for a priori power assumptions compared to observational research [odds ratio (OR): 3.02; 95% CIs: 2.06, 4.42; P &lt; 0.001]. Conclusions Presentation of a priori power considerations for sample size calculations was not universal in contemporary orthodontic literature, while specific study designs such as observational or animal and in vitro studies were less likely to report such considerations.

Optimal Sampling for Identifying a Cluster: An Application in Sorting

1993 ◽  
Vol 7 (3) ◽  
pp. 387-407
Author(s):  
Shmuel Gal ◽  
Dafna Sheinwald
Keyword(s):  
Sample Size ◽  
Sequential Sampling ◽  
A Priori ◽  
Optimal Sampling ◽  
Truncation Point ◽  
Fixed Sample Size ◽  
Fixed Sample ◽  
A Priori Distribution ◽  
Sampling Procedures ◽  
The Cost

We consider the following problem. For a given population of m items, we have to make a decision whether or not the population includes a relatively large cluster of identical items. This decision affects the effectiveness of a subsequent computational process, depending on the actual existence of the cluster and its size. To make a good decision, we use a statistical sample which should indicate the existence of a cluster and find a representative thereof. This paper describes the optimal sampling technique to be used in such a case, given the cost of the sampling and the potential gain in speed of the subsequent process. The optimal fixed sample size is specified, as well as the optimal sequential sampling, along with characterizing the dependence of the cost function on the truncation point.For the case that the a priori distribution of the cluster proportion is known, we present formulae by which the optimal sampling procedures can be easily calculated. For the common situation in which the a priori distribution is not known, we present, in the case of a fixed sample size, a tight upper bound for the sample size, which is independent of the a priori distribution, and for the case of the sequential sampling, we present an approximately optimal truncation point, which is also independent of the a priori distribution.The situation described arose in connection with choosing the best sorting method, an application that will be described in full detail. The most interesting practical result is that for our application truncating the sequential procedure at 35 observations, out of a population of 25,000–30,000 items, guarantees that in our sorting application we are always within 2.1% of the optimal cost independently of the a priori distribution.

scholarly journals Do Fallers and Nonfallers Equally Benefit from Balance Specific Exercise Program? A Pilot Study

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Darja Rugelj ◽  
Marija Tomšič ◽  
France Sevšek
Keyword(s):  
Sample Size ◽  
Postural Sway ◽  
Center Of Pressure ◽  
A Priori ◽  
Sample Size Calculation ◽  
Exercise Program ◽  
Vertical Direction ◽  
Vertical Axis ◽  
Specific Program ◽  
Significant Difference

The purpose of the study was to determine the sample size that would allow broad generalizability of the results. To investigate the differences in the responsiveness of fallers and nonfallers to a multicomponent functional balance specific program, 23 participating subjects (70.1 ± 6.6 years) were divided into nonfallers group (13) and fallers group (10). The components of the balance specific program were (1) changing of the center of gravity (CoG) in the vertical direction, (2) shifting of the CoG to the border of stability, (3) rotation of the head and body about the vertical axis, (4) standing and walking on soft surface, and (5) walking over obstacles or on a narrow path. At the end of eight months of the training program, there was no significant difference between the two groups regarding postural sway. The total center of pressure path length was used as the principal outcome measure for the sample size calculation. Based on these results the a priori sample size calculation yielded the estimate of 110 subjects required to be enrolled in order to get 20 subjects in fallers and 30 subjects in nonfallers group for the 80% power to detect the results as significant.

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