In medicine patient-years is a popular concept. Example: $100$ patients are followed for $2$ years. In this case, there are $200$ patient-years in total. If there were $8$ myocardial infarctions in the group, the rate would be $8$ MIs per $200$ patient years or $8/200*100= 4$ MIs per $100$ patient-years or $8/200*1000= 40$ per $1,000$ patient years, and so on (see here).
See here for an example where confidence intervals are reported for patient years:
For MGUS patients we estimated a mortality rate of 52 [95% CI 48-56] per 1000 patient-years, whereas for MGRS patients the rate was 29 [14-58] per 1000 patient-years.
How can I get CI for patient-years like this?
Thanks to @EdM for the great answer. There are two problems:
- I get other results. The link in the answer suggests to use the Poisson distribution with
poisson.test. Doing so for the results above gives me for example:
poisson.test(52, conf.level = 0.95)$conf.int
38.84 to 68.19. But in the source above it is 52 [95% CI 48-56]
- The results differ depending on what time frame the rate refers to. For example, if we choose mortality rate per 10,000 patient years instead the CI's change. For mortality rate per 1,000 patient years the CI's overlap (52[38.84-68.19] and 29[19.42-41.65]). For the morality rate per 10,000 patient years the CI's don't overlap (520[476.26-566.68] and 290[257.58-325.37]).