2-119. The article [“Clinical and Radiographic Outcomes of Four Different Treatm

Question

2-119. The article [“Clinical and Radiographic Outcomes of Four Different Treatment Strategies in Patients with Early Rheumatoid Arthritis,” Arthritis & Rheumatism (2005, Vol. 52, pp. 3381– 3390)] considered four treatment groups. The groups consisted of patients with different drug therapies (such as prednisone and infliximab): sequential monotherapy (group 1), step-up combination therapy (group 2), initial combination therapy (group 3), or initial combination therapy with infliximab (group 4). Radiographs of hands and feet were used to evaluate disease progression. The number of patients without progression of joint damage was 76 of 114 patients (67%), 82 of 112 patients (73%), 104 of 120 patients (87%), and 113 of 121 patients (93%) in groups 1–4,respectively. Suppose that a patient is selected randomly. Let A denote the event that the patient is in group 1, and let B denote the event that there is no progression. Determine the following probabilities:

(a) P(B | A)

(b) P(A | B)

(c) P(A | B')

(d) P(A'| B)

Explanation / Answer

P(A)=0.244

P(B)=0.8029

P(AB)=0.162(a)

P(AUB) = P(A) + P(B) - P(AB)= 114/467 + 375/467 – 76/467 = 0.884(b)

P(A'UB') = 1 - (AB) = 1 – 76/467 =0.838(c)

P(AUB') = P(A) + P(B') - P(AB') = 114/467 + (1 – 375/467) – (114 – 76)/467 = 0.359

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