Computes survival function, density function, -2*log-likelihood based on input dataset and intervals for piecewise constant failure rates. Initial version assumes observations are right censored or events only.
Arguments
- Srv
input survival object (see
Surv); note that only 0 = censored, 1 = event forSurv- intervals
Vector containing positive values indicating interval lengths where the exponential rates are assumed. Note that a final infinite interval is added if any events occur after the final interval specified.
Value
A matrix with rows containing interval length, estimated rate, -2*log-likelihood for each interval.
Examples
# use default arguments for delayed effect example dataset (Ex1delayedEffect)
library(survival)
# example 1
rateall <- pwexpfit()
rateall
#> intervals ttot event rate m2ll
#> 1 3 937.1785 97 0.10350216 634.0236
#> 2 3 605.3572 71 0.11728612 446.3257
#> 3 3 346.8482 30 0.08649317 206.8614
#> 4 Inf 254.1148 20 0.07870458 141.6822
# example 2
# Estimate by treatment effect
rate1 <- with(subset(Ex1delayedEffect, trt == 1), pwexpfit(Surv(month, evntd)))
rate0 <- with(subset(Ex1delayedEffect, trt == 0), pwexpfit(Surv(month, evntd)))
rate1
#> intervals ttot event rate m2ll
#> 1 3 620.4375 64 0.10315302 418.75734
#> 2 3 415.8482 36 0.08657005 248.16970
#> 3 3 256.2053 19 0.07415927 136.85853
#> 4 Inf 205.4186 13 0.06328542 97.76261
rate0
#> intervals ttot event rate m2ll
#> 1 3 316.74106 33 0.1041861 215.26408
#> 2 3 189.50899 35 0.1846878 188.23619
#> 3 3 90.64288 11 0.1213554 68.39871
#> 4 Inf 48.69624 7 0.1437483 41.15568
rate1$rate/rate0$rate
#> [1] 0.9900847 0.4687372 0.6110917 0.4402517
# chi-square test for (any) treatment effect (8 - 4 parameters = 4 df)
pchisq(sum(rateall$m2ll) - sum(rate1$m2ll + rate0$m2ll),
df = 4,
lower.tail = FALSE)
#> [1] 0.006424744
# compare with logrank
survdiff(formula = Surv(month, evntd) ~ trt, data = Ex1delayedEffect)
#> Call:
#> survdiff(formula = Surv(month, evntd) ~ trt, data = Ex1delayedEffect)
#>
#> N Observed Expected (O-E)^2/E (O-E)^2/V
#> trt=0 121 86 67.7 4.97 7.35
#> trt=1 240 132 150.3 2.24 7.35
#>
#> Chisq= 7.3 on 1 degrees of freedom, p= 0.007
# example 3
# simple model with 3 rates same for each for 3 months,
# different for each treatment after months
rate1a <- with(subset(Ex1delayedEffect, trt == 1), pwexpfit(Surv(month, evntd), 3))
rate0a <- with(subset(Ex1delayedEffect, trt == 0), pwexpfit(Surv(month, evntd), 3))
rate1a$rate/rate0a$rate
#> [1] 0.9900847 0.4808339
m2ll0 <- rateall$m2ll[1] + rate1a$m2ll[2] + rate0a$m2ll[2]
m2ll1 <- sum(rate0$m2ll) + sum(rate1$m2ll)
# as a measure of strength, chi-square examines improvement in likelihood
pchisq(m2ll0-m2ll1, df = 5, lower.tail=FALSE)
#> [1] 0.741822