PROC POWER Calculation

[kmardinian]

Hi, I have a power calculation question.

If I have an initial study that has 6 subjects and a follow-up study with 60 subjects.

Can I find the probability of any of the 60 subjects experiencing an Adverse event, if  >=33% of the 6 subjects develops an Adverse event. I was going to try to use PROC prower for this, but was unsure where to start.

Thank you!

[SteveDenham]

There is probably a way to do this in PROC POWER, but this is one case where I think a simple calculation can give the answer.  It is a matter of using the binomial formula [ NtakeM * pprob^M * (1-pprob)^(N - M) ].  So if you want the probability of at least one out of the 60, you calculate this as = (1 - prob(M=0)).  Using your prior estimate of pprob=0.333, I get prob(M=0) = 60take0 * (0.333)^0 * (1 - 0.333)^60 = 1 * 1 * 0.667^60 = 2.72e-11, which gives the probability of at least one adverse event as 1 - 2.72e-11 = 0.99999999997280278361063568173433.  The probability of exactly one adverse event is 60take1 * (0.333) * (1 - 0.333)^59 = 60 * 0.333 * 4.08e-11 = 8.1591649168092954797017275793104e-10.

SteveDenham

[kmardinian]

Thank you, that makes sense! But is 0.333 really the probability of the event occurring? I thought it was just the proportion of subjects that experienced the event.

[SteveDenham]

0.333 is the point estimate of the probability (2 out of 6).  The 95% exact confidence bounds are 0.0433 and 0.7772, so the true probability is likely to be in that interval in 95% of the calculations of the point estimate.

You could plug these bounds into the formulas I had earlier, and get estimates for the 50% fiducial limits (point limits) for the 2.5 %ile point and 97.5%ile point.

What i really think you might want is: Given a sample size of 60, what is the number of adverse events you would have to observe to be 95% confident that the true value was 0.333 with 80% power.  Now that, or something like that, is something you can plug into PROC POWER, using the onesamplefreq option.

SteveDenham

[kmardinian]

Hi Steve,

Thank you, that is a better idea. (Given a sample size of 60, what is the number of adverse events you would have to observe to be 95% confident that the true value was 0.333 with 80% power.)

How would you set that up in proc power?