Survival data for the 12 patients in the cirrhosis study, with the log(bilirubin) level as a time-dependent covariate, in counting process format (Collett, 2023, Example 8.4).
Format
A data frame with 54 rows and 7 variables:
- patient
Patient number (1-12).
- start
Start of the interval, in days.
- stop
End of the interval, in days.
- status
Event indicator for the interval: 1 = death at
stop, 0 = otherwise.- treat
Treatment: 0 = placebo, 1 = Liverol.
- age
Age of the patient in years.
- lbrt
Time-dependent log(bilirubin) value in effect during the interval, i.e. the most recent measurement after
startand up tostop.
Source
Collett, D. (2023) Modelling Survival Data in Medical Research, 4th ed. Chapman & Hall/CRC, Example 8.4 (Tables 8.4 and 8.5).
Details
Each row is a time interval during which all covariates are constant, so a
patient with many visits contributes several rows. Patient 1, for example,
has log(bilirubin) 3.2 for t <= 47, 3.8 for 47 < t <= 184, 4.9 for
184 < t <= 251 and 5.0 for 251 < t <= 281. The data are used to fit a Cox
model with a time-dependent covariate (start, stop and status form the
response).
The baseline values are in cirrhosis and the repeated measurements in cirrhosis_lbr.
Aliases
Used in Example 8.4, but the alias d8.4 is the baseline cirrhosis; this
counting-process form has no alias of its own. See dataset_by_exercise
for the complete index.
Examples
# Collett (2023), Chapter 17 style -----------------------------------
# Example 8.4: counting process form of the cirrhosis study
# (patient 5 and patient 8 have a zero-length interval, hence the filter)
cp <- subset(cirrhosis_cp, stop > start)
survival::coxph(survival::Surv(start, stop, status) ~ lbrt + age, data = cp)
#> Call:
#> survival::coxph(formula = survival::Surv(start, stop, status) ~
#> lbrt + age, data = cp)
#>
#> coef exp(coef) se(coef) z p
#> lbrt 3.49468 32.93982 2.02534 1.725 0.0844
#> age -0.06233 0.93957 0.06969 -0.894 0.3711
#>
#> Likelihood ratio test=13.98 on 2 df, p=0.0009227
#> n= 52, number of events= 8
# Without the time-dependent covariate, for comparison with the baseline data
survival::coxph(survival::Surv(start, stop, status) ~ treat + age, data = cp)
#> Call:
#> survival::coxph(formula = survival::Surv(start, stop, status) ~
#> treat + age, data = cp)
#>
#> coef exp(coef) se(coef) z p
#> treat -1.87146 0.15390 1.21605 -1.539 0.124
#> age -0.07635 0.92649 0.07702 -0.991 0.322
#>
#> Likelihood ratio test=5.79 on 2 df, p=0.05521
#> n= 52, number of events= 8