Handout17 - Lecture 17 1 Fitted probabilities from logistic...

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Lecture 17 1. Fitted probabilities from logistic regression 2. Hosmer-Lemeshow lack-of-±t test 3. Sensitivity, speci±city, false positive, false negative 4. Percent correctly predicted from logistic regression 5. ROC curve 1 Logistic regression example: hypertension in NHANES data National Center for Health Statistics posted a tutorial dataset, hypertension.xls , of 1019 NHANES observations for people over age 20. High blood pressure (hypertension) was either by blood pressure or by prescribed medication to treat hypertension. 37% of sample had hypertension. Proc Logistic descending data= NCHS ; class bmi_class; model hypertension = age male age*male bmi_class; bmi_class has 3 values: normal (18 BMI 25), overweight (25 < BMI 30), and obese (30 < BMI). 2
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The LOGISTIC Procedure Model Information Data Set WORK.A Response Variable hypertension hypertension Number of Response Levels 2 Model binary logit Optimization Technique Fisher’s scoring Number of Observations Read 1019 Number of Observations Used 952 Response Profile Ordered Total Value hypertension Frequency 11 3 1 9 2 0 633 Probability modeled is hypertension=1. NOTE: 67 observations were deleted due to missing values for the response or ex 3 Type 3 Analysis of Effects Wald Effect DF Chi-Square Pr > ChiSq age 1 120.9322 <.0001 male 1 13.3272 0.0003 bmi_class 2 28.9211 <.0001 age*male 1 13.4863 0.0002 Analysis of Maximum Likelihood Estimates Standard Wald Parameter DF Estimate Error Chi-Square Pr > ChiSq Intercept 1 -5.6453 0.4917 131.8290 <.0001 age 1 0.0914 0.00831 120.9322 <.0001 male 1 2.2425 0.6143 13.3272 0.0003 bmi_class 1 Obese 1 0.6313 0.1175 28.8729 <.0001 bmi_class 2 Overwt 1 -0.2912 0.1140 6.5283 0.0106 age*male 1 -0.0386 0.0105 13.4863 0.0002 Will we get any odds ratios? 4
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Odds Ratio Estimates Point 95% Wald Effect Estimate Confidence Limits bmi_class 1 Obese vs 3 Normal 2.642 1.745 3.998 bmi_class 2 Overwt vs 3 Normal 1.050 0.702 1.571 Why only these odds ratios? Interpretation: 5 Fitted probabilities from logistic regression Proc Logistic descending data= NCHS ; class bmi_class; model hypertension = age male age*male bmi_class/ output out =B predicted =phat lower =lowerCI upper =upperCI; Logistic regression is on the log scale (log-odds), so ftted probabilities ˆ p i are back-transFormed From log scale.
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Handout17 - Lecture 17 1 Fitted probabilities from logistic...

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