2.4.11 The article \"Clinical and Radiographic Outcomes of Four Different Treatm

Question

2.4.11 The article "Clinical and Radiographic Outcomes of Four Different Treatment Strategies in Patients with Early Rheuma- toid Arthritis" [Arthritis & Rheunatism (2005, Vol. 52, pp. 3381-3390)] considered four treatment groups. The groups con- sisted of patients with different drug therapies (such as prednisone and infliximab): sequential monotherapy (group 1), step-up com- bination therapy (group 2), initial combination therapy (group 3), or initial combination therapy with infliximab (group 4). Radio- graphs of hands and feet were used to evaluate disease progres- sion. The number of patients without progression of joint damage was 76 of 1 14 patients (67%), 82 of 1 12 patients (73%), 104 of 120 patients (87%), and i 13 of 121 patients (93%) in groups I-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 y probabilities:

Explanation / Answer

from above:

a)

P(A U B)=P(A)+P(B)-P(A n B) =(114/467)+(375/467)-(76/467)= 0.8844

b)

P(A'U B') =1-P(A n B)=1-76/467=0.8373

second method: ((A'U B')=P(A')+P(B')-P(A' n B')=(467-114)/467+92/467-(30+16+8)/467=0.8373)

c)

P(A U B')=1-P(A' n B) =1-(82+104+113)/467=0.3597

second method: (P(A u B')=P(A)+P(B')-P(A n B')=114/467+92/467-38/467=0.3597)

group 1 group 2 group 3 group 4 total no progression 76 82 104 113 375 with progression 38 30 16 8 92 total 114 112 120 121 467

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