The epsilon 4-allele of the gene encoding apolipoprote in E (APOE) is strongly a

Question

The epsilon 4-allele of the gene encoding apolipoprote in E (APOE) is strongly associated with Alzheimer's disease. A study was conducted among 2188 patients who were evaluated at autopsy for Alzheimer's disease by previously established pathological criteria. Patients were also evaluated clinically (based on symptoms while they were alive) for the presence of Alzheimer's disease. Suppose the pathological diagnosis is considered the "gold standard" for Alzheimer's disease (D+). If both the epsilon 4-allele and clinical diagnosis are present it is considered a positive screening test result (T+). a) What is the specificity of the test? b) What is the probability for a false positive? c) Circa 3 percent of the population between 65 and 74 years of age has Alzheimer's disease. Given that a 74 year old patient has the epsilon 4 allele and has been clinically diagnosed as possibly having Alzheimer's, what is the probability he or she actually has AD?

Explanation / Answer

a)specificity =test result negative given negatively diagnosed =352/418=0.8421

b)probabilty of false positive =1-specificity =1-0.8421=0.1579

c)here probability of clinically diagonised =0.03*(1076/1770)+0.97*(0.1579)=0.1714

ehnce probability of actually have AD given  clinically diagonised =0.03*(1076/1770)/0.1714 =0.1064

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