Sample size for equivalence studies

Equivalence studies

Equivalence trials are defined as trials that test whether a drug has the same (or similar) efficacy as an active agent or standard therapy. In practice, this is done by defining an “equivalence margin”, or limits, within which the treatment effect must lie to be considered equivalent.

Calculations in R

Can be performed in 2 packages: TrialSize and SampleSize4ClinicalTrials.

Comparing means for parallel design (unpaired)

Example 1

It is anticipated that patients will have the same mean diastolic BP of 96 mmHg on both the new drug and the active comparator. It is also anticipated that the SD (ơ) of the diastolic BP is approximately 8 mmHg. The decision is made by clinical to accept equivalence if the difference found between the treatments is less than 5 mmHg. How many patients are required for an 80% power and an overall significance level of 5%?

# TrialSize:
TwoSampleMean.Equivalence(0.05,0.2,8,1,5,0)

[1] 43.8469

# SampleSize4ClinicalTrials:
ssc_meancomp(design = 4L, ratio = 1, alpha = 0.05, power = 0.8, sd = 8, theta = 0, delta = 5)

  Treatment Control
1        44      44

Example 2

A client is interested in conducting a clinical trial to compare two cholesterol lowering agents for treatment of hypercholesterolemic patients through a parallel design. The primary efficacy parameter is a low-density lipidprotein cholesterol (LDL-C). For establishing equivalence, suppose the true mean difference is 0.01 (1%) and the equivalence limit is 0.05 (5%). Assuming SD = 0.1 (10%), how many patients are required for an 80% power and an overall significance level of 5%?

# TrialSize:
TwoSampleMean.Equivalence(0.05,0.2,0.1,1,0.05,0.01)

[1] 107.0481

# SampleSize4ClinicalTrials:
ssc_meancomp(design = 4L, ratio = 1, alpha = 0.05, power = 0.8, sd = 0.1, theta = 0.01, delta = 0.05)

  Treatment Control
1       108     108

Comparing means for crossover design (paired)

Example

Let’s consider a standard standard two-sequence, two period crossover design for trials to establish therapeutic equivalence between a test drug and a standard therapy. The sponsor is interested in heaving an 80% power for stablishing equivalence. Based on the results from previous trials, it is estimated that the variance (of the difference) is 0.2 (20%). Suppose that the true mean difference is -0.1 (-10%) and the equivalence limit is 0.25 (25%). What is the required sample size, assuming significance level of 5%?

# TrialSize:
TwoSampleCrossOver.Equivalence(0.05,0.2,0.2,0.25,-0.1)

[1] 7.612309

References

Majority of the examples are taken from: Chow SC, Liu JP (1998). Design and analysis of clinical trials. Concepts and methodologies. Wiley, New York. and Machin, D., Campbell, M. J., Fayers, P., & Pinol, A. (Eds.) (1997). Sample Size Tables for Clinical Studies. (2nd ed.) Blackwell Science.