I have a study that shows 100 deaths occurred in a cohort of high-risk people. Given mortality rates in the general population, you would only expect 70 deaths to occur. The standardised mortality ratio is 100/70 = 1.4 and I have 30 excess deaths.
I calculated the confidence interval around the ratio using an exact poisson method (in R):
poisson.test(100, 70) # SMR = 1.43 (95% CI 1.16-1.74); p = 0.0006 # Similar to 1.43 +/- 1.96 * sqrt(100) / 70
Do you know if/how I can calculate a confidence interval around 30 excess deaths? One idea I had was to calculate the rate difference (my study has about 12000 person-years) using the same poisson method and then multiply by person years:
poisson.test(30, 12000)$conf.int * 12000 # 30 excess deaths (95% CI 20-43) # I then realised that this is the same as poisson.test(30, 1)
Is that correct?