11 Logistic Regression - Interpreting Parameters

11 Logistic Regression - Interpreting PARAMETERS11 Logistic Regression - Interpreting ParametersLet us expand on the material in the last section, trying to make sure we understand the logisticregression model and can interpretStataoutput. Consider first the case of a single binary predictor,wherex={1 if exposed to factor0 if not,andy={1 if develops disease0 does can be summarized in a simple 2 X 2 contingency table asExposureDisease101 (+)ab0 ( )cdwhere OR=adbc(why?) and we interpret OR >1 as indicating a risk factor, and OR <1 asindicating a protective the Logistic model:p(x) is the probability of disease for a given value of x, andlogit(p(x)) = log(p(x)1 p(x))= + for x = 0 (unexposed), logit(p(x)) = logit(p(0)) = + (0) = x = 1 (exposed),logit(p(x)) = logit(p(1)) = + (1) = + Also,odds of disease among unexposed:p(0)/(1 p(0))exposed:p(1)/(1 p(1))NowOR=odds of disease among exposedodds of disease among unexposed=p(1)/(1 p(1))}}

11 LOGISTIC REGRESSION - INTERPRETING PARAMETERS To interpret fl2, fix the value of x1: For x2 = k (any given value k) log odds of disease = fi +fl1x1 +fl2k odds of disease = efi+fl1x1+fl2k For x2 = k +1 log odds of disease = fi +fl1x1 +fl2(k +1) = fi +fl1x1 +fl2k +fl2 odds of disease = efi+fl1x1+fl2k+fl2 Thus the odds ratio (going from x2 = k to x2 = k +1 is OR

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