Question

what issues could arise from the miscalculation of conditional probabilities in screening patients for disease?

Answer 1

I have given two examples choose any one of them or both according to your word limit or kindly comment for changes to the post.

The idea behind conditional probability is that knowledge about the occurrence or non-occurrence of an event may provide information that allows a better estimate of the probability of a different event. If there are any miscalculations of conditional probabilities in screening patients for disease this will result in the people who need to treated may be left untreated, and those who should not be treated may receive treatment.

Assume that a nurse working at a health care centre knows that approximately 15% of adults have a cholesterol level above the threshold of 240mg/dL. A man walks in (consider him a randomly selected man from the entire adult population), and the nurse thinks to herself: the probability that he has high cholesterol is 0.25. The nurse measures the blood pressure of the

patient and finds it elevated. She knows that there is an association between high cholesterol and high blood pressure. Given that the man has high blood pressure, she re-evaluates the situation and wonders if the probability that he has high cholesterol is greater than 0.25. This type of situation happens frequently. Under the absence of additional information, the probability of an event A given number. However, the occurrence of another event B might change the probability of A. This is what conditional probability is all about.

If she makes any mistake and gets the wrong probability, this will result in the people who need to treated may be left untreated, and those who should not be treated may receive treatment.

Another Example

The probability that a woman of age 35 has breast cancer is about 2%. If she has breast cancer, the probability that she tests positive on a screening mammogram is 92%. If she does not have breast cancer, the probability that the tests positive is 8 %. If the screening was not done properly then there is chances that someone who does not have a breast cancer may be treated.

The chance that a well-informed person calculates this probability correctly from the information given is not high. That wouldn't matter if it were purely a mathematical problem, but failing to understand the information given in this way is at the root of many medical and legal miscalculations. If the screening is not correctly done then there are chances that someone who has cancer is not treated at the proper time.