Survival times from registration for a lung transplant for 196 UK patients (Collett, 2023, Example 10.3).
Format
A data frame with 196 rows and 7 variables:
- patient
Patient identifier.
- time
Survival time in days from registration for a transplant.
- status
Event indicator: 1 = death, 0 = right-censored.
- age
Age at registration in years.
- gender
Gender: 1 = male, 2 = female.
- bmi
Body mass index at registration.
- disease
Primary disease: 1 = COPD, 2 = fibrosis, 3 = suppurative disease, 4 = other.
Source
Collett, D. (2023) Modelling Survival Data in Medical Research, 4th ed. Chapman & Hall/CRC, Example 10.3 (Table 10.2). Data from the UK Transplant Registry.
Details
The patients were registered in 2004 and survival is measured from registration to death regardless of any intervening transplantation; 123 of the 196 patients died. Times are censored at removal from the list, at the last known follow-up date, or at 30 April 2012 for patients still alive. The disease codings above follow the values in the distributed file (they can be checked against Table 10.2 of the book).
The example compares a Weibull model with and without an individual lognormal frailty term (Example 10.3). See kidney for a shared frailty example and liver_wait for a similar waiting-list cohort.
Aliases
The data set is available under the alias d10.3; dX.Y is the alias for
the data set used in Example X.Y of Collett (2023). See
dataset_by_exercise for the complete index.
Examples
# Collett (2023), Chapter 17 style -----------------------------------
# Example 10.3: an individual gamma frailty for each patient
survival::coxph(
survival::Surv(time, status) ~ age + bmi + factor(gender) + factor(disease) +
frailty(patient, distribution = "gamma"),
data = lung_transplant
)
#> Warning: Inner loop failed to coverge for iterations 4
#> Call:
#> survival::coxph(formula = survival::Surv(time, status) ~ age +
#> bmi + factor(gender) + factor(disease) + frailty(patient,
#> distribution = "gamma"), data = lung_transplant)
#>
#> coef se(coef) se2 Chisq DF p
#> age 0.00551 0.01836 0.01204 0.09011 1 0.76
#> bmi -0.02402 0.04322 0.02806 0.30878 1 0.58
#> factor(gender)2 -0.31294 0.35962 0.23660 0.75727 1 0.38
#> factor(disease)2 2.15032 0.46108 0.34148 21.74957 1 3.1e-06
#> factor(disease)3 0.90018 0.61095 0.40528 2.17092 1 0.14
#> factor(disease)4 0.81206 0.58413 0.37877 1.93264 1 0.16
#> frailty(patient, distribu 253.13694 122 3.7e-11
#>
#> Iterations: 6 outer, 69 Newton-Raphson
#> Variance of random effect= 2.23 I-likelihood = -576.5
#> Degrees of freedom for terms= 0.4 0.4 0.4 1.4 122.3
#> Likelihood ratio test=311 on 125 df, p=<2e-16
#> n= 196, number of events= 123
# Modern tools --------------------------------------------------------
if (requireNamespace("coxme", quietly = TRUE)) {
coxme::coxme(
survival::Surv(time, status) ~ age + bmi + factor(gender) +
factor(disease) + (1 | patient),
data = lung_transplant
)
}
#> Cox mixed-effects model fit by maximum likelihood
#> Data: lung_transplant
#> events, n = 123, 196
#> Iterations= 5 30
#> NULL Integrated Fitted
#> Log-likelihood -587.5631 -578.6475 -528.0029
#>
#> Chisq df p AIC BIC
#> Integrated loglik 17.83 7.00 1.2755e-02 3.83 -15.85
#> Penalized loglik 119.12 50.57 1.8520e-07 17.99 -124.21
#>
#> Model: survival::Surv(time, status) ~ age + bmi + factor(gender) + factor(disease) + (1 | patient)
#> Fixed coefficients
#> coef exp(coef) se(coef) z p
#> age 0.01214971 1.0122238 0.01316725 0.92 3.6e-01
#> bmi -0.02556212 0.9747618 0.02850448 -0.90 3.7e-01
#> factor(gender)2 -0.11458167 0.8917391 0.23272674 -0.49 6.2e-01
#> factor(disease)2 1.24061666 3.4577451 0.31033264 4.00 6.4e-05
#> factor(disease)3 0.68395999 1.9817098 0.42619997 1.60 1.1e-01
#> factor(disease)4 0.48490335 1.6240180 0.37262565 1.30 1.9e-01
#>
#> Random effects
#> Group Variable Std Dev Variance
#> patient Intercept 0.7337883 0.5384453