Other Considerations: When unequal samples sizes matter and when they don’t:
In some cases it may be useful to have unequal sample sizes. For example in epidemiological studies it may not be possible to get more cases but more controls are available. Suppose N subjects are required per group, but only N0 are available for one of the groups (where N0 < N). To get the same precision as with N in each group, take kN0subjects in the second group, where k = N / (2 N0 – N).
For example, suppose sample size calculations show that N =16 cases and controls are needed, but only 12 cases are available. Then k = 16 / (2x12 – 16) = 2 and kN0 = 2x12 = 24. That is, use 24 controls to go with the 12 cases.
Rearranging this formula gives N0 =[(k + 1)/2k] x N. With two cases per control, k=2, then
N0 = 0.75N. That is only 75% as many cases are needed.
Sample size estimation determines the number of complete cases which are needed for analysis. But some subjects who enroll in the study may drop out, others may be protocol failures and still others may have incomplete data, especially on the key outcome variables. To deal with this, decide on an “attrition rate” and inflate the sample size by this factor. For example, if you expect to lose about 20% of the sample, then the sample size should be increased by a factor of 1 / (1 - 0.2) or 1.25. That is, enroll 25% more subjects that the sample size calculation called for. This is a reasonable “attrition rate” for many studies – but might it need to be set as high as 33% if elderly or very ill patients are the subjects.
Sometimes subjects are sample by groups. For example, consider a design where 20 physician practices are randomly assigned to the treatment group and 20 to a control group. Then 500 charts are reviewed for each practice. Is the sample size 20 (i.e. 20 practices per group), or 1000 (i.e. the number of charts)? The answer is … “It depends”! It depends how similar the patients are within a practice and on what the unit of analysis is. Are you interested in comparing practices or patients? For example, each practice might be given a score which is the percentage of patients in the practice who had the characteristic being looked for in the chart review.
To show that two groups are “not different”, that is, they are equivalent, requires setting power higher (say .90 or .95) and the effect size smaller, small enough so as not to be clinically significant. With greater power and smaller effect sizes, equivalence studies therefore require larger sample sizes!