# Question about sample size calculation for a single arm long term follow-up study

I'm looking at a long term follow-up project and in the sample size consideration section it is described as such:

The total person-years of follow-up is approximately 9045 for the 1500 enrolled patients. This number of person-years of follow-up will provide 91% likelihood of seeing at least one event of interest, if the true rate per 15 years of exposure is at least 1:250.

I don't understand how the 91% likelihood is calculated. Can someone please explain?

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• A follow-up question: it was mentioned "91% likelihood of seeing at least one event of interest", is "likelihood" or "probability" the appropriate term to use here?

• In this context, I believe they are using the them interchangeably. In statistics, there is a technical difference in what we mean when we say likelihood versus probability, but in standard English usage they can be used interchangeably. So saying "the likelihood this coin lands on heads is 50%" and "the probability the coin lands on heads is 50%" has the same meaning. That seems to be the case here.

• I agree that "probability" should be used here as it refers to the chance something will happen while "likelihood" is bound to the parameters of statistical model being examined. Thank you.