Discussion Question

Let’s assume that a hospital’s neurosurgical team performed N procedures for in-brain bleeding last year. x of these procedures resulted in death within 30 days. If the national proportion for death in these cases is pi, then is there evidence to suggest that your hospital’s proportion of deaths is more extreme than the national proportion?

N  <- 100    # sample size
x  <- 10     # sample deaths within 30 days
pi <- 0.08   # national proportion of death

Poisson

lambda <- (N * pi)

1 - ppois( q          = 10,
           lambda     = 8, 
           lower.tail = TRUE
           )
## [1] 0.1841142

Binomial

?dbinom
dbinom(x   = 10, 
       size = 100, 
       prob = 0.08
       )
## [1] 0.102355

Answer

There is higher probability for deaths to occur within the 30 days in the hospital than the national average. There is discrepancy between the answers given by the poisson and binomial methods.