## Sample Size Calculation/power calcuation for retrospective study

Hi all,

I recently completed a study looking at hospital records over a 5 year period (fixed population of participants based on study period). We looked at 'blood transfusion' as a binary measure (didn't receive a transfusion = 0, did receive a transfusion = 1) between three groups identified in the population. The three groups were created (transformed) from a continuous variable and were labelled as low, medium, high.
In total 803 patients were included in analysis. 145 in low group, 404 in medium group and 254 in high group. Transfusion occurred in 338/803 patients, 30/145 (20.69%) low, 147/404 (36.39%) medium and 161/254 (63.39%) high group.

We found a statistically significant difference between low vs medium and medium vs high groups.

We are in writing stages and my question is: Do I need to include anywhere in the paper a justification of sample size or a power calculation?

Things about the study:
1. The population number was unknown prior to research beginning (we had no idea how many patients would be included in the 5 years of records)
2. The population breakdown was unknown prior to research beginning (% of subjects falling into each group)
3. We did not know being in the high group conferred an increased risk of being transfused relative to medium group, or that being in low group was protective for transfusion relative to medium group, we loosely hypothesized this would be the case, the study confirmed it.

Most of what I have read online and in the literature has stated post hoc power calculations should never be performed and if they are performed it is usually to prove that a negative study (ours however was statistically significant) was negative due to inadequate power.

A good piece titled The Abuse of Power: The Pervasive Fallacy of Power Calculations for Data Analysis, 2001 covers this, but I would also like to know people’s opinions on the question above. My supervisor is pushing for this and I hope to have a solid answer to give him as to why this is not necessary for this type of study.

Many thanks