We have a study involving 10,000 patients, 5,000 of them treated with drug A and 5,000 with drug B. We want to know if drug A is more effective than B. The median time to event (death) after treatment with drug A is 1,000 days and for drug B it is 2,000 days. Suppose we wish to subsample 100 patients receiving either treatment (200 total) from this larger sample to test the same hypothesis.
There are two proposed subsampling strategies:
- We are given data (time to event) for 100 patients who received drug A and 100 patients who received drug B.
- We are given data for 100 patients who died between 800-1200 days after treatment (some of them received A, some B, we pick randomly) and data for 100 patients who died between 1800-2200 days after treatment.
For the two cases above, which are the appropriate analytical tools to consider? Which has more power?