Sample Size, Precision and Power Calculations: A Unified Approach

2011 ◽  
Vol 02 (05) ◽  
Author(s):  
James A Hanley ◽  
Erica EM Moodie
Keyword(s):  
Sample Size ◽  
Unified Approach ◽  
Power Calculations

A unified approach to power and sample size determination for log-rank tests under proportional and nonproportional hazards

2021 ◽  
pp. 096228022098857
Author(s):  
Yongqiang Tang
Keyword(s):  
Sample Size ◽  
Proportional Hazards ◽  
Sample Size Calculation ◽  
Unified Approach ◽  
Rank Tests ◽  
Trial Duration ◽  
Nonproportional Hazards ◽  
Equivalence Trials ◽  
Superiority Trials ◽  
Log Rank Tests

Log-rank tests have been widely used to compare two survival curves in biomedical research. We describe a unified approach to power and sample size calculation for the unweighted and weighted log-rank tests in superiority, noninferiority and equivalence trials. It is suitable for both time-driven and event-driven trials. A numerical algorithm is suggested. It allows flexible specification of the patient accrual distribution, baseline hazards, and proportional or nonproportional hazards patterns, and enables efficient sample size calculation when there are a range of choices for the patient accrual pattern and trial duration. A confidence interval method is proposed for the trial duration of an event-driven trial. We point out potential issues with several popular sample size formulae. Under proportional hazards, the power of a survival trial is commonly believed to be determined by the number of observed events. The belief is roughly valid for noninferiority and equivalence trials with similar survival and censoring distributions between two groups, and for superiority trials with balanced group sizes. In unbalanced superiority trials, the power depends also on other factors such as data maturity. Surprisingly, the log-rank test usually yields slightly higher power than the Wald test from the Cox model under proportional hazards in simulations. We consider various nonproportional hazards patterns induced by delayed effects, cure fractions, and/or treatment switching. Explicit power formulae are derived for the combination test that takes the maximum of two or more weighted log-rank tests to handle uncertain nonproportional hazards patterns. Numerical examples are presented for illustration.

scholarly journals Considerations of sample size and power calculations given a range of analytical scenarios

2021 ◽  
Author(s):  
Alice Carter ◽  
Kate Tilling ◽  
Marcus Robert Munafo
Keyword(s):  
Sample Size ◽  
Statistical Power ◽  
Poor Quality ◽  
Research Quality ◽  
Design Stage ◽  
Design Consideration ◽  
Power Calculations ◽  
Critical Design ◽  
Study Planning ◽  
Research Questions

The sample size of a study is a key design and planning consideration. However, sample size and power calculations are often either poorly reported or not reported at all, which suggests they may not form a routine part of study planning. Inadequate understanding of sample size and statistical power can result in poor quality studies. Journals increasingly require a justification of sample size, for example through the use of reporting checklists. However, for meaningful improvements in research quality to be made, researchers need to consider sample size and power at the design stage of a study, rather than at the publication stage. Here we briefly illustrate sample size and statistical power in the context of different research questions and how they should be viewed as a critical design consideration.

scholarly journals Understanding between-cluster variation in prevalence and limits for how much variation is plausible

2020 ◽  
pp. 096228022095183
Author(s):  
Mark D Chatfield ◽  
Daniel M Farewell
Keyword(s):  
Standard Deviation ◽  
Sample Size ◽  
Correlation Coefficient ◽  
Coefficient Of Variation ◽  
Binary Data ◽  
True Cluster ◽  
Power Calculations ◽  
Log Odds ◽  
Cluster Variation ◽  
Cluster Correlation

In clinical trials and observational studies of clustered binary data, understanding between-cluster variation is essential: in sample size and power calculations of cluster randomised trials, for example, the intra-cluster correlation coefficient is often specified. However, quantifications of between-cluster variation can be unintuitive, and an intra-cluster correlation coefficient as low as 0.04 may correspond to surprisingly large between-cluster differences. We suggest that understanding is improved through visualising the implied distribution of true cluster prevalences – possibly by assuming they follow a beta distribution – or by calculating their standard deviation, which is more readily interpretable than the intra-cluster correlation coefficient. Even so, the bounded nature of binary data complicates the interpretation of variances as primary measures of uncertainty, and entropy offers an attractive alternative. Appealing to maximum entropy theory, we propose the following rule of thumb: that plausible intra-cluster correlation coefficients and standard deviations of true cluster prevalences are both bounded above by the overall prevalence, its complement, and one third. We also provide corresponding bounds for the coefficient of variation, and for a different standard deviation and intra-cluster correlation defined on the log odds scale. Using previously published data, we observe the quantities defined on the log odds scale to be more transportable between studies with different outcomes with different prevalences than the intra-cluster correlation and coefficient of variation. The latter increase and decrease, respectively, as prevalence increases from 0% to 50%, and the same is true for our bounds. Our work will help clinical trialists better understand between-cluster variation and avoid specifying implausibly high values for the intra-cluster correlation in sample size and power calculations.

Sign in / Sign up

Export Citation Format

Share Document