i.e. if the incidence rate of an event in the control group is 150 per patient-year and I would like to calculate the sample size per group needed to detect a 30% decrease in the incidence rate in the intervention group, with alpha = 0.05, beta = 0.80
Or do I need to use statistical software to do this? I've found a few different formulas but not sure if they are correct (and using them I am getting ridiculously small sample sizes needed so wanted to double check). Thanks
Selina,
Since the change you expect is 30%, then your sample size calculation could be based on repeated measures using .30 as the effect and calculating the effect size with the standard deviation. Below is an section taken from Columbia University epidemiology/statistics department (link, provided)
Percentage Change in Means
Clinical researchers may be more comfortable thinking in terms of percentage changes rather than differences in means and variability. For example, someone might be interested in a 20% difference between two groups in data with about 30% variability. Professor van Belle presents a neat approach to these kinds of numbers that uses the coefficient of variation (c.v.) 4 and translating percentage change into a ratio of means.
Variance on the log scale (see chapter 5 in van Belle) is approximately equal to coefficient of variation on the original scale, so Lehr’s formula can be translated into a version that uses c.v.
ngroup=16(c.v.)2(ln(μ0)−ln(μ1))2ngroup=16(c.v.)2(ln(μ0)−ln(μ1))2
We can then use the percentage change as the ratio of means, where
r.m.=μ0−μ1μ0=1−μ1μ0r.m.=μ0−μ1μ0=1−μ1μ0
to formulate a rule of thumb:
ngroup=16(c.v.)2(ln(r.m.))2ngroup=16(c.v.)2(ln(r.m.))2
In the example above, a 20% change translates to a ratio of means of 1−.20=.801−.20=.80. (A 5% change would result in a ratio of means of 1−.05=.951−.05=.95; a 35% change 1−.35=.651−.35=.65, and so on.) So, the sample size for a study seeking to demonstrate a 20% change in means with data that varies about 30% around the means would be
ngroup=16(.3)2(ln(.8))2=29ngroup=16(.3)2(ln(.8))2=29
http://www.columbia.edu/~cjd11/charles_dimaggio/DIRE/styled-4/code-12/
Thanks.... I assumed that since the events are "count" data it would be in a Poisson distribution so tried to apply Lehr's equation by taking the square root....(as on that same website you referenced) but got a very small n value....
Please let me know if the following reference/site is helpful to you:
Sample size calculation for meta-epidemiological studies.
Giraudeau B, Higgins JP, Tavernier E, Trinquart L.
Stat Med. 2016 Jan 30;35(2):239-50. doi: 10.1002/sim.6627. Epub 2015 Aug 19.
PMID:
26286683
Dennis
Dennis Mazur
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