The incidence rate ratio (and 95% confidence interval) of rotavirus gastroenteritis for the vaccine group compared to the placebo group is $0.67 (0.55, 0.82)$.
I want to know approximately how many cases of rotavirus gastroenteritis would be prevented over a 60 week period after giving 10,000 infants the vaccine, as opposed to not giving these 10,000 infants the vaccine?
Why is my answer 3,300 wrong?
3,300 is wrong because you've simply multiplied the N of 10,000 by 1-IRR of to obtain 3,300. This would only be correct if everybody in the placebo arm was expected had Rota GE at least once by 60 weeks. You can see from the Kaplan-Meier curve that that figure is closer to ~0.06 i.e. 94% of placebo patients are Rota GE-free. It is precisely that number (the intercept) you need to predict the number of cases prevented. If the incidence rate was in fact 0.06, then the formula would be N * 0.06 - N * IRR * 0.06 which is closer to 200.
Note you didn't share the intercept, and the information presented isn't adequate to answer the question.
Ratio of Incidence Rates$\;=\frac{Incidence\;Rate_1}{Incidence\;Rate_2}$ can be interpreted as impact at the "individual level" (Personal health)
Difference in Incidence Rates$\;=Incidence\;Rate_1−Incidence\;Rate_2$ can be interpreted as impact on a fixed number of persons (Public health)
The question above concerns the aspect of public health and thus the difference in incidence rates should be calculated.
I want to know approximately how many cases of rotavirus gastroenteritis would be prevented over a 60 week period after giving 10,000 infants the vaccine, as opposed to not giving these 10,000 infants the vaccine?
Difference in Incidence Rates$\;=Incidence\;Rate_1−Incidence\;Rate_2 = 0.07-0.02 =0.05\;$ (5%) (approximately, using the graph)
As such, approximately 500 cases of rotavirus gastroenteritis would be prevented over a 60 week period after giving 10,000 infants the vaccine, as opposed to not giving these 10,000 infants the vaccine.
