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?