Dr. Urma Zoolander, an environmental health scientist, is interested in the role of air quality as a risk factor for childhood asthma. She has participated in a study that followed 1000 children from birth to age 10, recording whether or not they developed asthma during that period (Y = 1 for yes and Y = 0 for no). The study also collected information on potential risk factors and protective effects from the child's first year of life including X₁, an indicator for whether the child's family lived in an urban setting (Yes = 1, No = 0), X₂, the average annual pollution level in thousands of particles per cm3 for the county in which the child lived, X₃, an index of socio-economic status for the child's family (higher is better),X₄, the number of months for which the child was breast-fed, X₅, an indicator for whether there was a family history of asthma (1 = Yes, 0 = No), and X₆, gender (1 = Female, 0 = Male). The data are given in the accompanying file

Give a brief interpretation of the odds ratio estimate for the family history variable and the corresponding confidence interval. Show how you would compute the odds ratio and its CI from the table of estimated regression coefficients and vice versa.

 

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Parameter Estimates ses 95% Wald Confidence Interval Std. Parameter Error B (Intercept) -0.047 1.6558 -3.292 3.198 [urban=1] -0.077 0.3021 -0.669 0.515 [urban=0] 0a pollution 0.077 0.0200 0.037 [famhist=1] 1.180 0.2230 0.743 [famhist=0] 0a [gender-1] -1.095 0.2179 [gender=0] 0a -0.082 0.0346 0.006 0.0103 -0.015 1b 0.116 1.617 Lower Upper Square df Sig. Exp(B) 0.001 1 0.977 0.954 0.065 1 0.798 0.926 1 0.000 1.080 0.000 3.255 1 0.000 0.335 1 1 0.018 0.921 1 0.579 1.006 -1.522 -0.668 Hypothesis Test -0.150 -0.014 0.026 Wald Chi- 14.664 27.996 25.245 5.597 0.308 breastfed (Scale) Dependent Variable: asthma Model: (Intercept), urban, pollution, famhist, gender, ses, breastfed a. Set to zero because this parameter is redundant. b. Fixed at the displayed value. . 1 1 . 1 95% Wald Confidence Interval for Exp(B) Lower Upper 0.037 24.490 0.512 1.673 1.038 2.102 0.218 0.861 0.986 1.123 5.039 0.513 0.986 1.026 Parameter Estimates ses 95% Wald Confidence Interval Std. Parameter Error B (Intercept) -0.047 1.6558 -3.292 3.198 [urban=1] -0.077 0.3021 -0.669 0.515 [urban=0] 0a pollution 0.077 0.0200 0.037 [famhist=1] 1.180 0.2230 0.743 [famhist=0] 0a [gender-1] -1.095 0.2179 [gender=0] 0a -0.082 0.0346 0.006 0.0103 -0.015 1b 0.116 1.617 Lower Upper Square df Sig. Exp(B) 0.001 1 0.977 0.954 0.065 1 0.798 0.926 1 0.000 1.080 0.000 3.255 1 0.000 0.335 1 1 0.018 0.921 1 0.579 1.006 -1.522 -0.668 Hypothesis Test -0.150 -0.014 0.026 Wald Chi- 14.664 27.996 25.245 5.597 0.308 breastfed (Scale) Dependent Variable: asthma Model: (Intercept), urban, pollution, famhist, gender, ses, breastfed a. Set to zero because this parameter is redundant. b. Fixed at the displayed value. . 1 1 . 1 95% Wald Confidence Interval for Exp(B) Lower Upper 0.037 24.490 0.512 1.673 1.038 2.102 0.218 0.861 0.986 1.123 5.039 0.513 0.986 1.026

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An odds ratio OR is a measure of association between an exposure and an outcome The OR represents the odds that an outcome will occur given a particular exposure compared to the odds of the outcome oc... View the full answer