The Weibull model for estimating smooth survival curves

Survival Analysis in R

Heidi Seibold

Statistician at LMU Munich

Why use a Weibull model?

Weibull model:

wb <- survreg(Surv(time, event) ~ 1, data)

Weibull model:

wb <- survreg(Surv(time, event) ~ 1, data)

Kaplan-Meier estimate:

km <- survfit(Surv(time, event) ~ 1, data)

wb <- survreg(Surv(time, cens) ~ 1, data = GBSG2)

90 Percent of patients survive beyond time point:

predict(wb, type = "quantile", p = 1 - 0.9, newdata = data.frame(1))

       1 
384.9947

p = 1 - 0.9 because the distribution function is 1 - the survival function.

wb <- survreg(Surv(time, cens) ~ 1, data = GBSG2)

Survival curve:

surv <- seq(.99, .01, by = -.01)

t <- predict(wb, type = "quantile", p = 1 - surv, newdata = data.frame(1))
head(data.frame(time = t, surv = surv))

       time surv
 1  60.6560 0.99
 2 105.0392 0.98
 3 145.0723 0.97
 4 182.6430 0.96
 5 218.5715 0.95
 6 253.3125 0.94

Survival Analysis in R