a. The only possible, mutually exclusive outcomes of the surgery are death, reli

Question

a. The only possible, mutually exclusive outcomes of the surgery are death, relief of symptoms, (angina, dyspnea), or continuation of symptoms. The probability of death is 0.02 and the relief of symptoms is 0.80. What is the probability that the patient will continue to have symptoms?

b. Two known complications of heart surgery are stroke and heart attack, with probability of 0.02 and 0.05, respectively. The patient asks what chances he has of having both the complications. Assume that the complications are conditionally independent, and calculate your answer.

c. The patient wants to know the probability that he will have the stroke given that has a heart attack as a complication of surgery. Assume that 1 in 500 patients has both complications, that the probability of heart attack is 0.05 and that the events are independent. Calculate your answer.

Appendix: Derivation e the expected value of each of Bayes' Theorem terms of life expectancy. concerned that a patient with a Bayes' theorem is derived as follows. We denote at has a bacterial infection that the conditional probability of disease, D, given a quire antibiotic therapy (as test result, R, p[DIR]. The prior (pretest) proba o a viral infection, for which bility of D is plDl. The definition of conditional ent is available). Your treat probability is: hold is 0.4, and based on the on you estimate the probabil infection as 0.8. A test p[DIR] (3.1) p[R] le (TPR 0.75, TNR 0.85) ates the presence or absence The probability of a test result (plR) is the l infection. Should you per- sum of its probability in diseased patients and its est? Explain your reasoning. probability in nondiseased patients: d your analysis change if the tremely costly or involved t risk to the patient? he three kinds of bias that Substituting into Equation 3.1, we obtain: e measurement of test per- Explain what each one is p[R,D] (3.2) would adjust the p[DIR] to compensate for Again, from the definition of conditional a computer system ease probability, rforming a complex deci- earch the medical litera- p[RID] p[R,D] and plRI-D] for patients p[D] you are treating, what is question to con- These expressions can be rearranged hould you adjust proba- (3.3) t of the answer to this ink clinicians sometimes if the results will not agement of the patient? Substituting Eqs. 3.3 and 3.4 into Eq. 3.2, we e reasons that you iden- obtain Bayes' theorem: re they valid in only cer Explain your answers. 1998 issue of Medical p DIR) g for articles that dis differences in three patients

Explanation / Answer

here as these are mutually exclusive events,hence sum of their probability should be 1

therefore  probability that the patient will continue to have symptoms =1-0.02-0.8=0.18

b)as events are independent, chances he has of having both the complications. =0.02*0.05=0.001

c)let probability of heart attack=P(H)=0.05 and that stroke=P(S)

given P(SnH)=1/500=0.002

hence P(S|H)=P(SnH)/P(H) =0.002/0.05=0.04

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