1. Lecture 10

2. Examples of count data –Number of panic attacks occurring during 6-month intervals after receiving treatment –Number of infant deaths per month before and after introduction of a prenatal care program The Poisson distribution has been the most commonly used to model count data: Marginal Poisson Regression Model and GEE

3. Epileptic seizures Clinical Trial of 59 epileptics For each patient, the number of epileptic seizures was recorded during a baseline period of 8 weeks Patients were randomized to treatment with the anti-epileptic drug progabide or placebo # of seizures was then recorded in four consecutive 2-week intervals Question: Does progabide reduce the rate of epileptic seizures?

4. Poisson Regression Model

5. In the progabide example: exp(β) represents the ratio of average seizure rates, measured as the number of seizures per 2-week period, for the treated compared to the controls: If β<0, then the treatment is effective relative to the placebo in controlling the seizure rate

6. Overdispersed Data Var(Y ij ) > E[Y ij ] is called the “overdispersion parameter”

7. Irregular times Suppose that the interval times t ij, during which the events are observed, are not the same for all subjects. The problem can be solved by decomposing the marginal mean E[Y ij ] as:

8. Epileptic Seizures Clinical Trial of 59 epileptics –31 patients received an anti-epileptic drug progabide –28 received placebo Patients from the 2 groups are comparable in terms of age and 8-week baseline seizure counts

9. => High-degree of extra-Poisson variation

11. Cross-product ratio: => Some indication of treatment effect

12. Poisson Regression Model and GEE Method X i2 allows different baseline seizure counts for the treated and the control groups

13. Parameter Interpretation exp(β 1 ): ratio of the average seizure rate after treatment to the average rate before treatment, for the placebo group β 3 : (parameter of interest) represents the difference in the log of the post-to-pre treatment ratio between the progabide and the placebo groups. –β 3 < 0 corresponds to a greater reduction in the seizure counts for the progabide group

14. Results If patient 207 is included, then …suggests very little difference between treatment and placebo groups in the change of seizure counts before and after randomization If patient 207 is excluded, then …suggests modest evidence that progabide is favored over the placebo

15. Results (cont’d) We have completely ignored correlation within subjects…