Sample size needed and post hoc power study

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    Kay Smith

    I have a study where the same surgery is done (two different patient groups) by two different surgeons. 

    Research question: what is the rate of complications between the two surgeons

    Statistical questions:

    (1) How many patients are needed to detect a 50% difference in complication rates


    Current figures (“pilot”)

    Group A —> 15 patients —> 20% complications

    Group B —> 11 patients —-> 36% complications


    The surgery is not common so we literally don’t have access to alot of patients.  If the above patient cohort is all we could get – then is it possible to calculate a power on this study?


    I have used an online calculator but cannot interpret the meaning of the numbers it gives me.(screendump attached)


    Power and sample size are the most common queries I am asked.  I have done so much reading but still cannot get my head around it

    Any help appreciated


    Dave Collingridge

    Do you plan on counting the number of complications for each patient and comparing the counts with a t-test (ideal approach if multiple complications per patient are common). To power this test you need to know the expected mean number of complications in both groups and an estimate of standard deviation (can be the same for both groups). Also what power level are you aiming for?

    Kay Smith

    If a patient has for example, a infection, bruising and blood poisoning then this would be classed as a “complication” (the number of complications per patient isn’t relevant)  We have no idea what the complication rate will be and no previous studies to base this on so we are treating the rates I have quoted above  as the “expected” number of complications. 

    We are aiming for 80% but will accept 60%!

    Dave Collingridge

    You need to decide what test you will use and then run a power and sample size analysis for that test. Your options are a test of independent proportions or a binary logistic regression. The test of proportions will compare proportions without regard for controlling other variables (comorbidities etc.), while the logistic regression will allow you to control for other variables. Because your sample size is relatively small, a test of proportions may be best. If you have no idea what the complication rate will be, you might consider an exploratory pilot study which does not need to be powered. But if clinical experience enables you to select a complication rate, then you can go with that expectation.

    Anyway, I powered an independent test of proportions where prop1 = 20% and prop2 = 36%. With an alpha=.05 on a 2-tailed test and a sample size allocation ratio of 15/11 = 1.364, there would be a 80% chance of correctly rejecting the null hypothesis with 112 cases in group 1 and 153 cases in group 2 (total N = 265).

    I am not sure what you mean by a 50% difference in complication rates. Is that a 50% increase over the lower rate of 20% complications, or are you referring to an absolute difference as in 25% versus 75%?



    Kay Smith

    Thankyou david

     that has clarified a few things and makes sense – with my understanding of sample size and power.  I understand the concepts but can never carry it through to calculation.. Think I need to do a course,,,Your answer is great though – appreciated

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