5 of 30 procedures resulted in death within 30 days. If the national proportion for death in these cases is .05, then is there evidence to suggest that your hospital’s proportion of deaths is more extreme than the national proportion? Model both as a binomial and a Poisson, and provide your R code solutions.
N=30 P=0.05 Number of deaths=5 P(X=5|N=30, P=0.05)
dbinom(5,30,0.05)## [1] 0.01235302Meaning that the probability of experiencing 5 deaths in 30 patients is 1.24%
Lambda=5 t=(30/100) t value was established as per the number of events in this sample, compared to the percentage of deaths that can be established as 100 given that Lambda was 5. P(Y=5|Lamba=5, t=30/100)
dpois(5,5*(30/100))## [1] 0.01411996Meaning that the probability of experiencing 5 deaths in 30 patients is of 1.41%