A clinical trial of gamma globulin in the treatment of children with Kawasaki syndrome randomized approximately half of the patients to receive gamma globulin. The standard treatment is an aspirin regimen; however, about one quarter of these patients developed coronary abnormalities even, under the standard treatment. The outcome of interest was the development of coronary abnormalities (CA) over a 7-week follow-up period. The following 2 x 2 table summarizes the results. a) Calculate the odds of developing coronary abnormalities for those who took gamma globulin. Calculate the odds of developing coronary abnormalities for those who took aspirin. (b) Calculate the sample OR for developing coronary abnormalities comparing those on gamma globulin compared to those on aspirin. (c) Investigators constructed the following logistic model: whereLogit(i) = log [i / (1 - i) ] = = – 1.0076 – 1.4030 GGDoes it make sense to interpret the intercept in this model? If so, interpret it. Interpret the coefficient for the GG variable. (d) Exponentiate the estimated parameter values from the model in (c). How do they correspond with the values that you computed in parts (a) and (b) (e) Use the logistic model in (c) to determine the sample probability of developing coronary abnormalities for those who took gamma globulins. Compare this to the same probability obtained directly from the 2 x 2 table. (f) code for fitting the logistic model given in part (c).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.6: Exponential And Logarithmic Equations

Problem 6E

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A clinical trial of gamma globulin in the treatment of children with Kawasaki syndrome randomized approximately half of the patients to receive gamma globulin. The standard treatment is an aspirin regimen; however, about one quarter of these patients developed coronary abnormalities even, under the standard treatment. The outcome of interest was the development of coronary abnormalities (CA) over a 7-week follow-up period. The following 2 x 2 table summarizes the results. a) Calculate the odds of developing coronary abnormalities for those who took gamma globulin. Calculate the odds of developing coronary abnormalities for those who took aspirin. (b) Calculate the sample OR for developing coronary abnormalities comparing those on gamma globulin compared to those on aspirin. (c) Investigators constructed the following logistic model: where Logit(i) = log [i / (1 - i) ] = = – 1.0076 – 1.4030 GG Does it make sense to interpret the intercept in this model? If so, interpret it. Interpret the coefficient for the GG variable. (d) Exponentiate the estimated parameter values from the model in (c). How do they correspond with the values that you computed in parts (a) and (b) (e) Use the logistic model in (c) to determine the sample probability of developing coronary abnormalities for those who took gamma globulins. Compare this to the same probability obtained directly from the 2 x 2 table. (f) code for fitting the logistic model given in part (c).

Gamma Globulin (GG = 1)
Aspirin (GG = 0)
Coronary
Abnorm.
(CA = 1)
7
23
30
No Coronary
Abnorm.
(CA = 0)
78
63
141
85
86
171

л₁ = P(CA₁ = 1| GG₁ = x₁) where
CA=
=
[lif coronary abnorm.
Oif no coronary abnorm.
GG₁
=
Logit() = log [₁ / (1¹ - ;)]
1.4030 GG
[lif gamma globulin
Oif aspirin
= =
- 1.0076 -

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