How to calculate confidence interval for count data in R?

Question

As question, I have found something similar here, but how to do it in R?

Thanks.

Answer 1

You are looking for a confidence interval around the count from a Poisson process. If you put for example 42 into your linked example you get

You observed 42 objects in a certain volume or 42 events in a certain time period.

Exact Poisson confidence interval:

• The 90% confidence interval extends from 31.94 to 54.32
• The 95% confidence interval extends from 30.27 to 56.77
• The 99% confidence interval extends from 27.18 to 61.76

You can get this in R using poisson.test. For example

> poisson.test(42, conf.level = 0.9 )

        Exact Poisson test

data:  42 time base: 1 
number of events = 42, time base = 1, p-value < 2.2e-16
alternative hypothesis: true event rate is not equal to 1 
90 percent confidence interval:
 31.93813 54.32395 
sample estimates:
event rate 
        42  

and similarly the other values by changing conf.level. If you do not want all the background information, try something like

> poisson.test(42, conf.level = 0.95 )$conf.int
[1] 30.26991 56.77180
attr(,"conf.level")
[1] 0.95

Answer 2

If the number of event is too small, it would be better to use the exact method.

exactPoiCI <- function (X, conf.level=0.95) {
  alpha = 1 - conf.level
  upper <- 0.5 * qchisq((1-(alpha/2)), (2*X))
  lower <- 0.5 * qchisq(alpha/2, (2*X +2))
  return(c(lower, upper))
}
exactPoiCI(42)

Reference: Liddell FD. Simple exact analysis of the standardised mortality ratio. J Epidemiol Community Health. 1984;38:85-8.