I'm trying to calculate the 95% confidence interval of a standardized mortality ratio, from this article: https://www.sciencedirect.com/science/article/pii/S0167527314018658#bb0020
The observed number of deaths are: 53 and the expected are 48.62, which gives a ratio of: 1.09. I have calculated the confidence using this example: https://ibis.health.state.nm.us/resource/SMR_ISR.html but I am not sure it is correct. I have done the following:
SMR = O/E, where SMR is the Standardized Mortality Rate, O is the observed deaths and E is the expected deaths.
CI = 1.96*sqrt(O)/E, where CI is the Confidence Interval. This gives us:
1.96*sqrt(53)/48.62 = 0.29.
Are these calculations correct, or have I forgotten some basic assumptions?
Any help would be much appreciated!