Hospitalization and Mortality in a Panel of AIDS Patients

• Problem is panel data with endogenous attrition (death).
• Or, from another perspective, survival with an endogenous covariate (hospitalizations)
• Inpatient episodes are point events arising in a Poisson process of rate .
• Hazard for death is .
• Gamma with mean 1 and variance
• are N, the number of events: t the period he was observed: whether the observation terminated in death or right censoring.
• are values of v for the m patients.
• Parameters are
• Let T denote survival time.

• For someone who dies at t we observe T=t and N=n. Given this has probability

  

• For someone right censored at t we observe T>t and N=n. Given this has probability

  

• So is elementary.
• But is product of Gamma densities.
• So is elementary, even though is a mess.

• Refutable Implications:
  1. is Pascal.
  2. Regressions and are concave and proportional
  3. is concave --- decreasing hazard.
• This model is generalized bivariate survival: Cox and Oakes(1984), chapter 10.

Tony Lancaster

Last modified: 12 September 1995