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Introduction to Logistic Regression

Introduction to Logistic Regression. Coronary Heart Disease (CHD) Baseline: CAT, ECG Age: potential confounder or modifier. Definitions. p = probability of CHD C = catecholamine level (0=low, 1=high) E = ECG (0=normal,1=abnormal) A = age (in years) p/(1-p) = odds of CHD

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Introduction to Logistic Regression

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  1. Introduction to Logistic Regression Coronary Heart Disease (CHD) Baseline: CAT, ECG Age: potential confounder or modifier

  2. Definitions • p = probability of CHD • C = catecholamine level (0=low, 1=high) • E = ECG (0=normal,1=abnormal) • A = age (in years) • p/(1-p) = odds of CHD • logit(p) = log(p/(1-p))

  3. Logistic Model • The log of the odds of CHD as a linear combination C, E and A • Graphical Interpretation: 4 lines – log(odds) versus age; for each of the 4 C/E groups • No interactions

  4. Estimates: • logit chd cat ecg age • Logit estimates Number of obs = 609 • LR chi2(3) = 19.54 • Prob > chi2 = 0.0002 • Log likelihood = -209.51066 Pseudo R2 = 0.0445 • ------------------------------------------------------------------------------ • chd | Coef. Std. Err. z P>|z| [95% Conf. Interval] • -------------+---------------------------------------------------------------- • cat | .6516069 .3192993 2.04 0.041 .0257917 1.277422 • ecg | .3422883 .2909117 1.18 0.239 -.2278881 .9124647 • age | .0289636 .0145909 1.99 0.047 .0003659 .0575613 • _cons | -3.911011 .8003698 -4.89 0.000 -5.479707 -2.342315 • ------------------------------------------------------------------------------ • So the estimates are: • This model assumes that the rate of change of the log of the odds of CHD per year of age does not depend on CAT or ECG and is estimated to be 0.0289 • There is another assumption here. See the graphs.

  5. CAT effect & ECG effect • This model assumes that the effect of CAT on the log of the odds of CHD does not depend on ECG or age. It is estimated by: 0.6516 • This model assumes that the effect of ECG on the log of the odds of CHD does not depend on CAT or age. It is estimated by 0.3422 • …sound familiar? • Study the graphs to see this clearly • The dependent variable has changed. Instead of studying changes in expected values, we study changes in logarithms of odds.

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