Statistical primer: sample size and power calculations—why, when and how? (Source).

Abstract: When designing a clinical study, a fundamental aspect is the sample size. In this article, we describe the rationale for sample size calculations, when it should be calculated and describe the components necessary to calculate it. For simple studies, standard formulae can be used; however, for more advanced studies, it is generally necessary to use specialized statistical software programs and consult a biostatistician. Sample size calculations for non-randomized studies are also discussed and two clinical examples are used for illustration.

Reporting of sample size calculation in randomised controlled trials: review (Source).

Objectives: To assess quality of reporting of sample size calculation, ascertain accuracy of calculations, and determine the relevance of assumptions made when calculating sample size in randomised controlled trials.

Data sources: We searched MEDLINE for all primary reports of two arm parallel group randomised controlled trials of superiority with a single primary outcome published in six high impact factor general medical journals between 1 January 2005 and 31 December 2006. All extra material related to design of trials (other articles, online material, online trial registration) was systematically assessed. Data extracted by use of a standardised form included parameters required for sample size calculation and corresponding data reported in results sections of articles. We checked completeness of reporting of the sample size calculation, systematically replicated the sample size calculation to assess its accuracy, then quantified discrepancies between a priori hypothesised parameters necessary for calculation and a posteriori estimates.

Results: Of the 215 selected articles, 10 (5%) did not report any sample size calculation and 92 (43%) did not report all the required parameters. The difference between the sample size reported in the article and the replicated sample size calculation was greater than 10% in 47 (30%) of the 157 reports that gave enough data to recalculate the sample size. The difference between the assumptions for the control group and the observed data was greater than 30% in 31% (n=45) of articles and greater than 50% in 17% (n=24). Only 73 trials (34%) reported all data required to calculate the sample size, had an accurate calculation, and used accurate assumptions for the control group.

Conclusions: Sample size calculation is still inadequately reported, often erroneous, and based on assumptions that are frequently inaccurate. Such a situation raises questions about how sample size is calculated in randomised controlled trials.

Power Considerations in Designing and Interpreting Adaptive Clinical Trials (Source).

Adaptive clinical trials allow researchers to make preplanned modifications based on accumulating data from an ongoing trial while preserving the trial's integrity and validity. These modifications may include early termination in cases of successes or lack of efficacy, refining the sample size, altering treatments or doses, or focusing recruitment efforts on individuals most likely to benefit. In this issue of NEJM Evidence, Geisler et al.1 report results from the Apixaban for Treatment of Embolic Stroke of Undetermined Source (ATTICUS) trial, a multicenter randomized trial of apixaban compared with aspirin in patients with cardioembolism risk factors.

Methods for Sample Size Determination in Cluster Randomized Trials (Source).

Background: The use of cluster randomized trials (CRTs) is increasing, along with the variety in their design and analysis. The simplest approach for their sample size calculation is to calculate the sample size assuming individual randomization and inflate this by a design effect to account for randomization by cluster. The assumptions of a simple design effect may not always be met; alternative or more complicated approaches are required.

Methods: We summarise a wide range of sample size methods available for cluster randomized trials. For those familiar with sample size calculations for individually randomized trials but with less experience in the clustered case, this manuscript provides formulae for a wide range of scenarios with associated explanation and recommendations. For those with more experience, comprehensive summaries are provided that allow quick identification of methods for a given design, outcome and analysis method.

Results: We present first those methods applicable to the simplest two-arm, parallel group, completely randomized design followed by methods that incorporate deviations from this design such as: variability in cluster sizes; attrition; non-compliance; or the inclusion of baseline covariates or repeated measures. The paper concludes with methods for alternative designs.

Conclusions: There is a large amount of methodology available for sample size calculations in CRTs. This paper gives the most comprehensive description of published methodology for sample size calculation and provides an important resource for those designing these trials.

Reporting and methodological quality of sample size calculations in cluster randomized trials could be improved: a review (Source)

Objectives: To assess the quality of reporting and accuracy of a priori estimates used in sample size calculations for cluster randomized trials (CRTs).

Study design and setting: We reviewed 300 CRTs published between 2000 and 2008. The prevalence of reporting sample size elements from the 2004 CONSORT recommendations was evaluated and a priori estimates compared with those observed in the trial.

Results: Of the 300 trials, 166 (55%) reported a sample size calculation. Only 36 of 166 (22%) reported all recommended descriptive elements. Elements specific to CRTs were the worst reported: a measure of within-cluster correlation was specified in only 58 of 166 (35%). Only 18 of 166 articles (11%) reported both a priori and observed within-cluster correlation values. Except in two cases, observed within-cluster correlation values were either close to or less than a priori values.

Conclusion: Even with the CONSORT extension for cluster randomization, the reporting of sample size elements specific to these trials remains below that necessary for transparent reporting. Journal editors and peer reviewers should implement stricter requirements for authors to follow CONSORT recommendations. Authors should report observed and a priori within-cluster correlation values to enable comparisons between these over a wider range of trials.