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Transcript

Week 5: Logistic regression analysis Overview Questions from last week What is logistic regression analysis? The mathematical model Interpreting the β coefficient and odds ratios Maximum likelihood model fitting An example using SPSS (with our Ottawa hospital data) Discussion of the 2 articles Data analysis discussion What is logistic regression analysis? • Used to learn more about the relationship between several exposure variables and a dichotomous outcome variable • Logistic regression is an extension of the 2X2 table with several exposure variables instead of just one • No assumptions about the distribution of the variables The mathematical model • In linear regression Y’ (known as Y prime) is the predicted value on the outcome variable • A is the Y axis intercept • β1 is the coefficient assigned through regression • X1 is the unit of the exposure variable • But for logistic regression the model is: • ln • ( Y’ 1-Y’ ) =A + β1X1 + β2X2 + β3X3 Interpreting the coefficient • The regression equation in logistic regression tells us the (natural log of the) probability of being in one group divided by the probability of being in the other group • The exponentiated coefficient gives us the odds ratio • The significance of each coefficient is tested by dividing the coefficient by its standard error Maximum likelihood model fitting • Most logistic regression models use the maximum likelihood model to fit regression models • The log-likelihood is calculated based on predicted and actual outcomes • A goodness-of-fit chi-square is calculated (usually compares a constant-only model to the one you created) • Tries to find the best fit for the variables included A logistic regression example Background • Remember our Ottawa CHIRPP data • We want to compare the odds of going to a children’s hospital with going elsewhere • The outcome variable is pediatric hospital compared to other hospital • The exposure variables are: • Age group, disposition, others? Statistical analysis • Univariate statistics (histograms for continuous variables, frequency distributions for categorical variables) • Bivariate statistics (t-tests and chi square statistics) • Logistic regression analysis • Let’s try it in SPSS For next week • Read articles • Read text Chapter 9 • Start modelling your own data using the appropriate multivariable technique