Statistics is widely used in healthcare both in hospitals and in research. In research, statistical methods, such as binomial distribution, is used to test the probability of side effects of certain drugs.
In healthcare settings, binomial distribution can also be used to track the probability of adverse events associated with treatment. In particular, in our hospital binomial distribution can be used track the probability of hospital acquired infections (HAIs) as a result of treatment. According to Centers for Disease Control and Prevention (CDC, 2022), HAIs are infections resulting from complications of healthcare linked with high morbidity and mortality (CDC, 2022). Approximately 1 in 31 accepted hospital patients gets infected with HAI, which implies that the probability of having HAI for every individual patient in the US is 3.23%.
I work in a hospital that has high standards of HAI prevention, and proud of all low HAI rates. Assume that the hospital claims to have HAI rate of 1 in 40, which corresponds to 2.5% chance for every individual patient to get infected with an HAI. In order to test this assumption, a sample of 500 patients was randomly selected from the database and 13 patients were diagnosed with an HAI after receiving treatment. The situation can be modelled using the following probability statement:
The results demonstrate that the hospital would expect 487 or fewer patients having HAIs in 500 trials when the success rate should be 0.975 about 48.2% of the time. The results demonstrate that even though 13 in 500 (2.6%) is very close to the desired 2.5%, the probability of the statement that only 1 in 40 patients has HAI in the hospital will be true in less than 50% of the cases.
References
Centers for Disease Control and Prevention. (2022). Health Topics – Healthcare-associated Infections (HAI). Web.