shortfall in the available donor organs, donor kidneys are now being transplanted which would in the past have been discarded; the so-called Expanded Criteria Donor (ECD) kidneys. By definition, ECD kidneys are more likely to suffer graft failure (GF), the condition wherein the transplanted kidney stops functioning sufficiently. A random sample of U.S. transplant recipients was assembled, in order to study the effects on the mortality hazard of ECD (vs non-ECD) kidneys and graft failure (GF). Data are contained in the file “kidney-ECD-1.sas7bdat”, with fields: IDNUM: patient ID number ECD: equals 1 for an ECD kidney, and 0 for non-ECD time-to-GF: time until graft failure (missing, if GF did not occur) time-to-death: time until death (missing, if death not observed) time-to-censor: potential time until censoring (non-missing for all patients) 2
AGE: age at transplant (years) SEX DIABETES: indicator that diabetes was the cause of renal failure COMORBID: number of comorbid conditions (illnesses, not counting ESRD, existing at the time of transplant) For each of the following parts, submit you SAS code and output as an appendix. (a) Fit a model which contains only factors known at the time of transplant ( t = 0). List the factors that significantly predict death. (b) Interpret the ECD effect from the model from (a). 4. A randomized trial is carried out to compare the hazard for time until infection between treated ( Z i = 1) and control ( Z i = 0) patients. The following data are observed. i 1 2 3 4 5 6 7 X i 3 5 6 9 12 15 22 Δ i 0 1 1 0 1 0 1 Z i 1 0 1 0 1 0 1 (a) Write out the partial likelihood function, PL ( β ). Your final answer should not have a summation sign or any subscripts. (b) Derive the log partial likelihood function, ‘ ( β ). (c) Derive the score function U ( β ). (d) Based on these data, it is estimated through PL that λ ( t | Z i = 1) λ ( t | Z i = 0) = 1 . 405 Estimate Λ 0 (10). (e) Estimate S (10 | Z i = 1). 3
You've reached the end of your free preview.
Want to read all 3 pages?
- Fall '08
- zi, LAF