# Sample Size for Case-Control Study

We wanted to perform a case-control study and used the calculation below. Using alpha = 0.05, beta = 0.20, p1-p2 = 0.003, and a ratio of controls to cases of 1000:1, we came up with a sample size of 2608 cases.

When we pulled the data, we only had 2240 cases. We gave the customer a report with the raw numbers but said we couldn't perform the statistical analysis due to not meeting the required sample size for cases.

The customer takes the raw numbers and calculates a Risk Ratio as follows:

27 cases of HIV in the ME (exposure) group of 3869.

2,213 cases of HIV in the no ME group of 2,587,299

RR 8.2 (95%CI 5.59 to 11.92), P < 0.0001

Is it statistically kosher to make this RR calculation given that we didn't meet our sample size for the case-control study?

## 2 Answers

Typically, sample size determinations are done to ensure a reasonable probability of rejection given the null hypothesis is false in a certain way (with an effect of a certain size).

It is prudent to try to plan a study with large enough sample that it will likely meet its objectives.

However, after you have data---even if not as much as you had projected---if you get a significant result, then that result stands on its own. Maybe the effect is larger than expected, the sample variance is lower than expected, or whatever. Just check assumptions to make sure the 'significant' result was produced by a valid test procedure.

A sample size that's a little low doesn't invalidate the findings of the study.

Yes, it is "kosher" (that is, Okay) to do this.

Power analysis should be done before you start a project in order to know how many subjects you will need to have a reasonable chance of finding statistical significance if your theory or hypothesis is correct.

Doing analysis with a smaller sample size is not invalid, it's just that a nonsignificant result is highly possible, even if the effect is what you thought it was. In this case, the proportions were 0.00697 and 0.000855. You hypothesized a difference of 0.003, but it was actually much larger. (Also, they did a ratio rather than a difference).