The company is doing a standard hypothesis test. In all hypothesis test there are two hypotheses; the null hypothesis and the alternative hypothesis. The null hypothesis states the status quo (ie no difference in survival rate between treatments) where the alternative states the opposite (ie a difference in survival rate between treatments). when the test is performed, the statistician tests the null hypothesis and either rejects or does not reject the null hypothesis in favour of the alternative hypothesis.
So a p-value is the probability of rejecting the null hypothesis when it is in fact true. In your case, a p-value of 0.02 indicates that there is a 2% chance that the statisticians conclusion (ie the rejection of the null hypothesis and thus the rejection of no difference between treatments) is wrong. The smaller the p-value the less chance the null hypothesis is correct.
Now I don't know what you mean by 'power', but to answer your question about 3 month OS and 6 months. The company will need to do two statistical tests if they want to know the difference in OS for either 3 months or 6 months. They can't conclude anything about the 3 month OS from the 6 months. Having said that, if the p-value for the 6 months is 0.03 for arguments sake, then the 3 month p-value will be smaller than 0.03. How much smaller will depend on the data.
Let me know if this makes sense or if you need any further information.
Vic
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