Open elong0527 opened 2 years ago
There's no way of doing this using flexsurvspline
, I think, as that fits a cubic spline basis. At the moment you'd have to use flexsurvreg
and construct a custom piecewise exponential distribution with a fixed number of pieces. Easiest way would be via the hazard function and cumulative hazard functions.
Here's a quick example, which isn't tested much. Ideally there should be something built in to construct the functions automatically given the vector of knots.
hpwexp <- Vectorize(function(t, rate0, rate1, rate2){
rate <- c(rate0, rate1, rate2)
knots <- sort(knots)
rate[findInterval(t, knots) + 1]
})
Hpwexp <- Vectorize(function(t, rate0, rate1, rate2){
k0 <- c(0,knots)
rate <- c(rate0, rate1, rate2)
int <- findInterval(t, k0)
dk <- diff(k0)
cumrate <- c(0, cumsum(dk*rate[-length(rate)])) # cumulative rate up to each knot
cumrate[int] + rate[int]*(t - k0[int]) # add on the remainder for each t
})
knots <- c(2,6)
nk <- length(knots)
custom_pwexp <-
list(name = "pwexp",
pars = paste0("rate", 0:nk),
location = "rate0",
transforms = rep(list(log), nk+1),
inv.transforms = rep(list(exp), nk+1),
inits = function(t,aux) {lam <- sr.exp.inits(t,aux); rep(lam, nk+1)})
pwexpfs <- flexsurvreg(Surv(recyrs, censrec) ~ 1, data=bc, dist=custom_pwexp)
plot(pwexpfs, ci=FALSE)
plot(pwexpfs, type="hazard", ci=FALSE, ylim=c(0,0.5))
Thanks for the clarification.
I will cross check the function with the pch package.
Agree, it would be nice to add a built in function to handle piecewise exponential model that become popular in the study design literatures.
I think the code should be modified to set the location to a "dummy" variable so that covariates can be introduced (as per Chris's example).
The optimization doesn't really work as it takes quite a while and doesn't give finite confidence intervals. Are there additional distribution or density functions that should be provided to facilitate convergence?
hpwexp <- Vectorize(function(t, dummy, rate0, rate1, rate2){
rate <- c(rate0, rate1, rate2)
knots <- sort(knots)
dummy*(rate[findInterval(t, knots) + 1])
})
Hpwexp <- Vectorize(function(t,dummy, rate0, rate1, rate2){
k0 <- c(0,knots)
rate <- c(rate0, rate1, rate2)
int <- findInterval(t, k0)
dk <- diff(k0)
cumrate <- c(0, cumsum(dk*rate[-length(rate)])) # cumulative rate up to each knot
dummy*(cumrate[int] + rate[int]*(t - k0[int])) # add on the remainder for each t
})
knots <- c(0.45,1.869)
nk <- length(knots)
custom_pwexp <-
list(name = "pwexp",
pars = c("dummy", paste0("rate", 0:nk)),
location = "dummy",
transforms = rep(list(log), nk+2), #Add one more for dummy param
inv.transforms = rep(list(exp), nk+2), #Add one more for dummy param
inits = function(t,aux) {lam <- 0.2; c(1,rep(lam, nk+1))})
pwexpfs <- flexsurvreg(Surv(recyrs, censrec) ~ as.factor(group), data=bc, dist=custom_pwexp)
plot(pwexpfs)
For putting covariates in, I'd consider parameterising as (bhaz, hr2, hr3, ...)
where bhaz
is the hazard in period 1, and hr2
, hr3
are the hazard ratios between period 2, 3 etc. and period 1. bhaz
is the location parameter and putting covariates on that gives a proportional hazards model. This may or may not facilitate convergence - if the CIs can't be determined that's often just because the model isn't identifiable given the data.
Could anyone provide some hint if I can fit a piecewise exponential model using
flexsurv
?I feel I can do it using
flexsurvspline
, but not sure how to define the parameters for a piecewise linear model whenscale=hazard