The rate of myocardial infarction (MI) in 50-59 year old, disease-free women is

Question

The rate of myocardial infarction (MI) in 50-59 year old, disease-free women is approximately 2 per 1000 per year. Suppose that 3 MI's are reported over a 5-year period among 1000 postmenopausal women initially disease-free who have been taking postmenopausal hormones (a) The number of MIs reported among 1000 postmenopausal women, initially disease-free, over a 5-year period would follow what sort of distribution and parameters? (b) What is the probability of observing such an outcome as the one above among women who had not been taking postmenopausal hormones? (c) What probability of the same event is obtained when using an appropriate approximation?

Explanation / Answer

Here probability of having myocardial infarction (MI) in 50-59 year old, disease-free women p = 2/1000

Number of women surveyed n = 1000

it looks like binomial distriubtion with parameter n = 1000 and p = 2/1000 = 0.002

(b) probability of observing such an outcome as the one above among women who had not been taking postmenopausal hormones

Pr(X = 3 ; 1000 ; 0.002) = 1000C3 (0.002)3 (0.998)997 = 0.1806

(c) Now, if we take approximate approximation to poisson distribution becaus here n is very large and p is very small.

so, for Poisson distribution

Pr(X = 3) = POISSON (X = 3 ; 2) = e-2 23/3! = 0.1804

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