Transplant survival times of 434 kidney recipients, where the two kidneys of a donor may have been transplanted into two different recipients (Collett, 2023, Example 10.4).
Format
A data frame with 434 rows and 7 variables:
- patient
Patient number (1-434).
- donor
Donor number (1-270). Recipients of kidneys from the same donor share this value.
- time
Transplant survival time in days; the earlier of graft failure and death with a functioning graft.
- status
Event indicator: 1 = transplant failure, 0 = right-censored.
- age
Age of the recipient in years.
- diabetes
Diabetes status: 0 = absent, 1 = present.
- cit
Cold ischaemic time, in hours, between retrieval of the kidney and transplantation.
Source
Collett, D. (2023) Modelling Survival Data in Medical Research, 4th ed. Chapman & Hall/CRC, Example 10.4 (Table 10.5). Data from the UK Transplant Registry.
Details
The transplants used organs from deceased donors following circulatory death. Of the 270 donors, 106 gave one kidney and 164 gave both, so many recipients are clustered within donors and their survival times are likely to be correlated; there are 71 failures. The example fits Weibull models with and without a shared frailty effect for the donor (Example 10.4).
See kidney_centres for transplant survival in eight centres, a centre-level analogue of the same problem.
Aliases
The data set is available under the alias d10.4; 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 10.4: shared gamma frailty for kidneys from the same donor
survival::coxph(
survival::Surv(time, status) ~ age + cit + diabetes +
frailty(donor, distribution = "gamma"),
data = kidney
)
#> Call:
#> survival::coxph(formula = survival::Surv(time, status) ~ age +
#> cit + diabetes + frailty(donor, distribution = "gamma"),
#> data = kidney)
#>
#> coef se(coef) se2 Chisq DF p
#> age 0.0189 0.0103 0.0101 3.3896 1.0 0.066
#> cit 0.0238 0.0215 0.0211 1.2197 1.0 0.269
#> diabetes -0.2386 0.4440 0.4374 0.2888 1.0 0.591
#> frailty(donor, distributi 11.9769 11.4 0.399
#>
#> Iterations: 4 outer, 18 Newton-Raphson
#> Variance of random effect= 0.169 I-likelihood = -415.8
#> Degrees of freedom for terms= 1.0 1.0 1.0 11.4
#> Likelihood ratio test=27.3 on 14.3 df, p=0.02
#> n= 434, number of events= 71
# Modern tools --------------------------------------------------------
if (requireNamespace("coxme", quietly = TRUE)) {
coxme::coxme(
survival::Surv(time, status) ~ age + cit + diabetes + (1 | donor),
data = kidney
)
}
#> Cox mixed-effects model fit by maximum likelihood
#> Data: kidney
#> events, n = 71, 434
#> Iterations= 18 93
#> NULL Integrated Fitted
#> Log-likelihood -418.4392 -415.7184 -397.1621
#>
#> Chisq df p AIC BIC
#> Integrated loglik 5.44 4.00 0.2449100 -2.56 -11.61
#> Penalized loglik 42.55 21.02 0.0036057 0.52 -47.03
#>
#> Model: survival::Surv(time, status) ~ age + cit + diabetes + (1 | donor)
#> Fixed coefficients
#> coef exp(coef) se(coef) z p
#> age 0.01875744 1.0189345 0.01037614 1.81 0.071
#> cit 0.02356823 1.0238482 0.02177577 1.08 0.280
#> diabetes -0.25440249 0.7753797 0.44946736 -0.57 0.570
#>
#> Random effects
#> Group Variable Std Dev Variance
#> donor Intercept 0.5283623 0.2791667