See email exchange below:
On May 19, 2015, at 11:12 PM, Polevoi, Steve <Steve.Polevoi@ucsf.edu> wrote:
Can you explain how to use McCulloch's variance Excel calculators? I have time tomorrow morning to talk if you are free..
On May 20, 2015, at 7:56 AM, "McCulloch, Charles" <Charles.McCulloch@ucsf.edu> wrote:
The basic idea is just like the example in class for the cluster randomized trial:
First figure out how to do the power calculation for a before/after design assuming independence (e.g., a t-test). Then use the Excel calculator to see if you need to inflate the sample size or modify the detectable effect size.
For example, suppose you are collecting monthly data on readmission rates in a difficult population and you are going to do a study with 5 months of data before an intervention to reduce those rates and for 5 months afterward. You know from historical data that the monthly readmission rate has a mean of 0.2 with a SD of 0.05. Plugging into a calculator such as PSPower ( http://biostat.mc.vanderbilt.edu/wiki/Main/PowerSampleSize with t-test/SD=0.05/n=5/m=1) gives a detectable effect size of 0.1 with power .8. But suppose we think the autocorrelation of monthly admission rates is 0.3. Then the n=5 calculator (plugging in 0.3 in cell A5) gives a variance ratio of 1.49, which would mean the SD increases by sqrt(1.49) or 1.22. So we would need to modify the SD that went into the calculation and use 1.22*0.05 = 0.061 instead, giving a detectable effect size of 0.12 instead of 0.10.
CEM