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. Test proportionality of hazards with cox.zph on the model with clinic, prison,
and methadone. Make the three plots vs. time of the Schoenfeld residuals for
clinic, prison, and methadone. Interpret the results
2. Plot the cumulative hazard of the Cox-Snell residuals and interpret the apparent goodness of fit.
3. Plot the martingale residuals (omitting methadone) vs. methodone. The
original paper using these data treated dose as a categorical variable with
categories < 60, 60–79, and 80+. Make a categorized methadone variable using
cut. Try fitting the model using categorized dose as a factor and compare to
dose in statistical significance of the variable using the LR test (maybe with
drop1) . Compare the two full models by AIC. Does it make an important
difference to replace the quantitative variable by a 3-category factor? Note
that you cannot compare the two models directly by a LR test since they are
not nested.
4. Plot the martingale residuals vs. the linear predictor, the deviance residuals
vs. the linear predictor, and the three dfbeta values by observation order.
Identify possibly interesting observations and try to interpret the results. Since
the clinic hazards are clearly not proportional, this is not the final answer, but
it will do for the moment.
