Bayesian Updating: Increasing Sample Size During the Course of A Study

2021 ◽  
Author(s):  
Mirjam Moerbeek
Keyword(s):  
Sample Size ◽  
Simulation Study ◽  
Error Rate ◽  
Effect Size ◽  
Bayes Factor ◽  
A Priori ◽  
Sample Size Calculation ◽  
Bayesian Updating ◽  
A Priori Estimate ◽  
Priori Estimate

Abstract Background: A priori sample size calculation requires an a priori estimate of the size of the effect. An incorrect estimate may result in a sample size that is too low to detect effects or that is unnecessarily high. An alternative to a priori sample size calculation is Bayesian updating, a procedure that allows increasing sample size during the course of a study until sufficient support for a hypothesis is achieved. This procedure does not require and a priori estimate of the effect size. This paper introduces Bayesian updating to researchers in the biomedical field and presents a simulation study that gives insight in sample sizes that may be expected for two-group comparisons. Methods: Bayesian updating uses the Bayes factor, which quantifies the degree of support for a hypothesis versus another one given the data. It can be re-calculated each time new subjects are added, without the need to correct for multiple interim analyses. A simulation study was conducted to study what sample size may be expected and how large the error rate is, that is, how often the Bayes factor shows most support for the hypothesis that was not used to generate the data. Results: The results of the simulation study are presented in a Shiny app and summarized in this paper. Lower sample size is expected when the effect size is larger and the required degree of support is lower. However, larger error rates may be observed when a low degree of support is required and/or when the sample size at the start of the study is small. Furthermore, it may occur sufficient support for neither hypothesis is achieved when the sample size is bounded by a maximum. Conclusions: Bayesian updating is a useful alternative to a priori sample size calculation, especially so in studies where additional subjects can be recruited easily and data become available in a limited amount of time. The results of the simulation study show how large a sample size can be expected and how large the error rate is.

scholarly journals Bayesian updating: increasing sample size during the course of a study

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Mirjam Moerbeek
Keyword(s):  
Sample Size ◽  
Simulation Study ◽  
Error Rate ◽  
Effect Size ◽  
Bayes Factor ◽  
A Priori ◽  
Sample Size Calculation ◽  
Bayesian Updating ◽  
A Priori Estimate ◽  
Priori Estimate

Abstract Background A priori sample size calculation requires an a priori estimate of the size of the effect. An incorrect estimate may result in a sample size that is too low to detect effects or that is unnecessarily high. An alternative to a priori sample size calculation is Bayesian updating, a procedure that allows increasing sample size during the course of a study until sufficient support for a hypothesis is achieved. This procedure does not require and a priori estimate of the effect size. This paper introduces Bayesian updating to researchers in the biomedical field and presents a simulation study that gives insight in sample sizes that may be expected for two-group comparisons. Methods Bayesian updating uses the Bayes factor, which quantifies the degree of support for a hypothesis versus another one given the data. It can be re-calculated each time new subjects are added, without the need to correct for multiple interim analyses. A simulation study was conducted to study what sample size may be expected and how large the error rate is, that is, how often the Bayes factor shows most support for the hypothesis that was not used to generate the data. Results The results of the simulation study are presented in a Shiny app and summarized in this paper. Lower sample size is expected when the effect size is larger and the required degree of support is lower. However, larger error rates may be observed when a low degree of support is required and/or when the sample size at the start of the study is small. Furthermore, it may occur sufficient support for neither hypothesis is achieved when the sample size is bounded by a maximum. Conclusions Bayesian updating is a useful alternative to a priori sample size calculation, especially so in studies where additional subjects can be recruited easily and data become available in a limited amount of time. The results of the simulation study show how large a sample size can be expected and how large the error rate is.

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 A Multi-faceted Mess: A Review of Statistical Power Analysis in Psychology Journal Articles

2019 ◽  
Author(s):  
Rob Cribbie ◽  
Nataly Beribisky ◽  
Udi Alter
Keyword(s):  
Sample Size ◽  
Effect Size ◽  
Power Analysis ◽  
Statistical Power ◽  
Type I Error ◽  
A Priori ◽  
Type I ◽  
Specific Level ◽  
Maximum Sample Size ◽  
Power Analyses

Many bodies recommend that a sample planning procedure, such as traditional NHST a priori power analysis, is conducted during the planning stages of a study. Power analysis allows the researcher to estimate how many participants are required in order to detect a minimally meaningful effect size at a specific level of power and Type I error rate. However, there are several drawbacks to the procedure that render it “a mess.” Specifically, the identification of the minimally meaningful effect size is often difficult but unavoidable for conducting the procedure properly, the procedure is not precision oriented, and does not guide the researcher to collect as many participants as feasibly possible. In this study, we explore how these three theoretical issues are reflected in applied psychological research in order to better understand whether these issues are concerns in practice. To investigate how power analysis is currently used, this study reviewed the reporting of 443 power analyses in high impact psychology journals in 2016 and 2017. It was found that researchers rarely use the minimally meaningful effect size as a rationale for the chosen effect in a power analysis. Further, precision-based approaches and collecting the maximum sample size feasible are almost never used in tandem with power analyses. In light of these findings, we offer that researchers should focus on tools beyond traditional power analysis when sample planning, such as collecting the maximum sample size feasible.

scholarly journals A PRIORI ESTIMATE FOR AN EQUATION WITH FRACTIONAL DERIVATIVES WITH DIFFERENT ORIGINS

2019 ◽  
pp. 41-47
Author(s):  
Л.М. Энеева
Keyword(s):  
Fractional Derivatives ◽  
Model Equation ◽  
A Priori ◽  
A Priori Estimate ◽  
Equation Of Motion ◽  
Point Boundary ◽  
Priori Estimate ◽  
Fractal Media ◽  
Different Origins ◽  
Variable Potential

В работе исследуется обыкновенное дифференциальное уравнение дробного порядка, содержащее композицию дробных производных с различными началами, с переменным потенциалом. Рассматриваемое уравнение выступает модельным уравнением движения во фрактальной среде. Для исследуемого уравнения доказана априорная оценка решения смешанной двухточечной краевой задачи. We consider an ordinary differential equation of fractional order with the composition of leftand right-sided fractional derivatives, and with variable potential. The considered equation is a model equation of motion in fractal media. We prove an a priori estimate for solutions of a mixed two-point boundary value problem for the equation under study.

scholarly journals A Discrete Analog of the Lyapunov Function for Hyperbolic Systems

2018 ◽  
Vol 64 (4) ◽  
pp. 591-602
Author(s):  
R D Aloev ◽  
M U Khudayberganov
Keyword(s):  
Lyapunov Function ◽  
Hyperbolic Systems ◽  
A Priori ◽  
A Priori Estimate ◽  
Discrete Analog ◽  
Priori Estimate ◽  
Constant Coefficients ◽  
The Difference ◽  
Dissipative Boundary ◽  
Linear Hyperbolic System

We study the difference splitting scheme for the numerical calculation of stable solutions of a two-dimensional linear hyperbolic system with dissipative boundary conditions in the case of constant coefficients with lower terms. A discrete analog of the Lyapunov function is constructed and an a priori estimate is obtained for it. The obtained a priori estimate allows us to assert the exponential stability of the numerical solution.

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