Description
The addicts data set is from a study by Caplehorn et al. (“Methadone Dosage
and Retention of Patients in Maintenance Treatment,” Med. J. Aust., 1991). These
data comprise the times in days spent by heroin addicts from entry to departure
from one of two methadone clinics.
There are two further covariates, namely, prison
record and methadone dose, believed to affect the survival times.
The data set and R input code are on the website. The variables are as follows:
• id: Subject ID
• clinic: Clinic (1 or 2)
• status: Survival status (0 = censored, 1 = departed from clinic)
• time: Survival time in days
• prison: Prison record (0 = none, 1 = any)
• methadone: Methadone dose (mg/day)
1. Plot the Kaplan-Meier survival curves for the two clinics.
2. Test for whether the two survival curves could have come from the same process using survdiff.
3. Plot the cumulative hazards from the Nelson-Aalen estimator.
4. A common comparison plot for proportional hazards is the complimentary
log-log survival plot which plots ln(− ln[Sˆ(x)]) = ln Hˆ (t) against ln(t). If the
hazards are proportional, then so are the cumulative hazards, and after taking
logs, the curves should be parallel. If the lines are straight, then the Weibull
model may be appropriate. Make this plot for the two clinics using the NelsonAalen estimator and comment on the results. You will use the “cloglog” option
in the plot command.
5. Construct a Cox model using only the clinic variable. Is the “survival” different at the two clinics? What is the estimated hazard (risk) ratio, a test for
significance, and a 95% confidence interval?
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6. Pick one test for the null hypothesis that the clinics do not differ. Why would
you depend on this test more than the others?
7. Consider adding the prison and methodone variables. Which of these covariates seems to improve the model?
8. Plot the two survival curves from your chosen Cox model and add the two KM
survival curves. What do you think?
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