Sample size considerations for clinical research studies in nuclear cardiology

Abstract

Sample size calculation is an important element of research design that investigators need to consider in the planning stage of the study. Funding agencies and research review panels request a power analysis, for example, to determine the minimum number of subjects needed for an experiment to be informative. Calculating the right sample size is crucial to gaining accurate information and ensures that research resources are used efficiently and ethically. The simple question “How many subjects do I need?” does not always have a simple answer. Before calculating the sample size requirements, a researcher must address several aspects, such as purpose of the research (descriptive or comparative), type of samples (one or more groups), and data being collected (continuous or categorical). In this article, we describe some of the most frequent methods for calculating the sample size with examples from nuclear cardiology research, including for t tests, analysis of variance (ANOVA), non-parametric tests, correlation, Chi-squared tests, and survival analysis. For the ease of implementation, several examples are also illustrated via user-friendly free statistical software.

Appendix: G*Power Software

Case Study for Two-Sample Independent t Test (Two-Tailed)

For the two-sided, two-sample independent t test, select the appropriate test under the Test Family dropdown (see Fig. 2). The statistical test used will be selected from the dropdown as “Means: Difference between two independent means (two groups).” For all the analyses in this Appendix, we will select “A priori: Compute required sample size—given α, power, and effect size” since we are calculating sample size. Ensure that “Two” is selected for Tails. From here, the first step we would like to calculate is the effect size d. We can do this by clicking the “Determine” button to open the extended window. Where n1 = n2, input the means and standard deviations for each group and click “Calculate and transfer to main window” (Note: The means for groups 1 and 2 were adjusted so their difference is 1, as that is the clinically meaningful difference being assessed). We then include our standard type I error and power of 0.05 and 0.80, respectively, and leave the Allocation Ratio as 1 (we are assuming equal allocation). From here, clicking “Calculate” will yield the approximate sample size, similar to that which we calculated manually.

Figure 2

G*Power illustration of two-sample independent t test (two-sided)

Case Study for Two-Sample Independent t Test (One-Tailed)

For the two-sample independent t test using one tail, select the appropriate test under the Test Family dropdown (Fig. 3). The statistical test used will be selected from the dropdown as “Means: Difference between two independent means (two groups).” Ensure that “One” is selected for Tails. From here, the first step we would like to calculate is the effect size d. We can do this by clicking the “Determine” button to open the extended window. Where n1 = n2, input the means and standard deviations for each group and click “Calculate and transfer to main window” (Note: The means for groups 1 and 2 were adjusted so their difference is 1, as that is the clinically meaningful difference being assessed). We then include our standard type I error and power of 0.05 and 0.80, respectively, and leave the Allocation Ratio as 1 (we are assuming equal allocation). From here, clicking “Calculate” will yield the approximate sample size, similar to that which we calculated manually.

Figure 3

G*Power illustration of two-sample independent t test (one-sided)

Wilcoxon Rank-Sum Test (Non-parametric Version of Two-Sample Independent t Test)

For the Wilcoxon Rank-Sum Test, select the appropriate test under the Test Family dropdown (see Fig. 4). In this case, we are using the t tests still. The statistical test used will be selected from the dropdown as “Means: Wilcoxon-Mann-Whitney test (two groups).” Ensure that “Two” is selected for Tails. From here, the first step we would like to calculate is the effect size d. We can do this by clicking the “Determine” button to open the extended window. Where n1 = n2, input the means and standard deviations for each group and click “Calculate and transfer to main window.” We then include our standard type I error and power of 0.05 and 0.80, respectively, and leave the Allocation Ratio as 1 (we are assuming equal allocation). From here, clicking “Calculate” will yield the approximate sample size using Wilcoxon simulations.

Figure 4

G*Power illustration of Wilcoxon Rank-Sum test

Case Study for Two-Sample Proportions

For two-sample proportions, select the appropriate test under the Test Family dropdown. In this case, we are using the z test (see Fig. 5). The statistical test used will be selected from the dropdown as “Proportions: Difference between two independent proportions.” From here, we input our two proportions under Proportion p2 and Proportion p1. We then include our typical type I error and power of 0.05 and 0.80, respectively. The allocation ratio we are looking at is 1, as we would like for our groups to have equal sizes. From here, clicking “Calculate” will yield the approximate sample size, similar to that which we calculated manually.

Figure 5

G*Power illustration of two independent sample proportions z test

Fisher’s Exact Test

For two-sample proportions where the proportions are assumed to be different between exercise and vasodilator stress, select the appropriate test under the Test Family dropdown (see Fig. 6). In this case, we are using the exact test. The statistical test used will be selected from the dropdown as “Proportions: Inequality, two independent groups (Fisher’s exact test).” From here, we input our two proportions under Proportion p1 and Proportion p2. We then include our typical type I error and power of 0.05 and 0.80, respectively. The allocation ratio we are looking at is 1, as we would like for our groups to have equal sizes. From here, clicking “Calculate” will yield the approximate sample size.

Figure 6

G*Power illustration of Fisher’s exact test for two independent sample proportions