Survival times, in days, of 90 patients with locally advanced gastric cancer, randomised to chemotherapy alone or chemotherapy plus radiotherapy (Collett, 2023, Example 11.2).
Format
A data frame with 90 rows and 4 variables:
- patient
Patient number (1-90).
- time
Time from randomisation to death from gastric cancer, in days.
- status
Event indicator: 1 = death from gastric cancer, 0 = right-censored.
- treat
Treatment: 0 = chemotherapy alone, 1 = chemotherapy plus radiotherapy.
Source
Collett, D. (2023) Modelling Survival Data in Medical Research, 4th ed. Chapman & Hall/CRC, Example 11.2 (Table 11.2). Data from Stablein and Koutrouvelis (1985).
Details
The trial was carried out by the Gastrointestinal Tumor Study Group; the patients were followed for over eight years. There are 82 deaths. The estimated survivor functions cross, so the proportional hazards assumption is not tenable and the data are used to motivate non-proportional hazards: the log-cumulative hazard plot, the restricted mean survival time and time-dependent effects (Examples 11.2 and 11.3).
Aliases
The data set is available under the aliases d11.2, d11.3; 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 -----------------------------------
# Examples 11.2 and 11.3: evidence against proportional hazards
survival::cox.zph(survival::coxph(survival::Surv(time, status) ~ treat, data = gastric))
#> chisq df p
#> treat 13.2 1 0.00028
#> GLOBAL 13.2 1 0.00028
# A treatment effect that differs between time periods
gastric_cp <- survival::survSplit(
gastric,
cut = c(360, 720, 1080),
end = "time", event = "status", start = "tstart",
episode = "period"
)
survival::coxph(
survival::Surv(tstart, time, status) ~ treat + treat:strata(period),
data = gastric_cp
)
#> Call:
#> survival::coxph(formula = survival::Surv(tstart, time, status) ~
#> treat + treat:strata(period), data = gastric_cp)
#>
#> coef exp(coef) se(coef) z p
#> treat 0.8767 2.4029 0.3351 2.616 0.00890
#> treat:strata(period)period=2 -1.1294 0.3232 0.5348 -2.112 0.03472
#> treat:strata(period)period=3 -1.9772 0.1385 0.8695 -2.274 0.02297
#> treat:strata(period)period=4 -2.0589 0.1276 0.7861 -2.619 0.00882
#>
#> Likelihood ratio test=12.79 on 4 df, p=0.01234
#> n= 184, number of events= 82
# Modern tools --------------------------------------------------------
# The restricted mean survival time summarises the same non-proportional effect
rmst <- summary(
survival::survfit(survival::Surv(time, status) ~ treat, data = gastric),
rmean = 1000
)
rmst$table[, c("rmean", "se(rmean)")]
#> rmean se(rmean)
#> treat=0 557.7778 45.45431
#> treat=1 422.4444 51.83743