 ## Sample size calculations

What sample size to use is a question commonly asked of Datapharm. The answer requires a collaborative approach as it depends on many factors, both theoretical and practical. To ensure that your study is adequately powered to address the study objectives, it is crucial to have a sufficiently large sample. However, this should be weighed against saving both time and resources, and raising ethical concerns over potential unnecessary risk of harm towards subjects.

The factors to consider when determining sample size often include the:

• Study design. For example, a parallel or cross-over design, and the number of treatment groups or crossovers.
• Subject number per group.
• Outcome measure e.g. the difference in group means, a hazard ratio.
• Statistical analysis to be used, such as a t-test or a GLM.
• Expected outcome measure values, such as mean and standard deviation. These are one of the most important aspects. A literature search may be necessary to estimate these values.
• Desired significance (alpha) level, which is usually set at 5%.
• Whether the treatment outcome is to be two-sided or one-sided.
• Desired level of statistical power, such as 80%.
• If relevant, the expected correlation coefficient.
• Expected amount of missing data and/or number of subject dropouts. Although not inherently included in theoretical calculations, these can lower the actual sample size.

Once these factors are clarified in consultation and with guidance from our experienced statistical team, we do the calculations for you to determine the appropriate sample size for your study. One such formulation for comparing two means is:

n=22(Z/2+Z)2/2

Where n is the expected sample size per treatment group, is the expected standard deviation, Z/2 is derived from the desired alpha level (usually approximated as 1.96, assuming a two-sided alpha of 0.05), Z is derived from the desired power level (usually approximated as 0.84), and is the expected effect size (difference between means). This formulation assumes that both groups have an equal sample size. This would be appropriate for some inferential statistical analyses, such as a t-test, but not others, such as a mixed method.

The team at Datapharm includes many experienced professionals, including statisticians, who can discuss the study requirements with you and your team to calculate an appropriate and practical sample size for your study. If you have any studies that require a sample size calculation, please contact us today.