1. 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

2. 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

3. 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 β 1 is the coefficient assigned through regression X 1 is the unit of the exposure variable But for logistic regression the model is: ln ( Y’ ) =A + β 1 X 1 + β 2 X 2 + β 3 X 3 1-Y’

4. 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

5. 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

6. 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?

7. 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

8. For next week Read articles Read text Chapter 9 Start modelling your own data using the appropriate multivariable technique