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Lecture 10

Lecture 10. Marginal Poisson Regression Model and GEE. 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

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Lecture 10

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  1. Lecture 10

  2. Marginal Poisson Regression Model and GEE • 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:

  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. Poisson Regression Model 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 DataVar(Yij) > E[Yij] is called the “overdispersion parameter”

  7. Irregular times • Suppose that the interval times tij, during which the events are observed, are not the same for all subjects. The problem can be solved by decomposing the marginal mean E[Yij] 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

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

  11. Poisson Regression Model and GEE Method Xi2 allows different baseline seizure counts for the treated and the control groups

  12. Parameter Interpretation • exp(β1): ratio of the average seizure rate after treatment to the average rate before treatment, for the placebo group • β3: (parameter of interest) represents the difference in the log of the post-to-pre treatment ratio between the progabide and the placebo groups. • β3 < 0 corresponds to a greater reduction in the seizure counts for the progabide group

  13. 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

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

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