DelayedSurvFit: Survival functions with single-crossing constraints

In nchenderson/DelayedSurvFit: Constrained Survival Estimation with Delayed Treatment

Survival functions with single-crossing constraints

Description

This computes nonparametric estimates of the survival curves in two treatment arms under the constraint that the two survival curves can cross at most one time.

Usage

DelayedSurvFit(times, events, trt, gamma.fixed=NULL, theta.fixed=NULL, 
               weights=NULL, max.times=100, inner.iter=50, final.iter=1000, 
               verbose=TRUE)

Arguments

times	vector of follow-up times
events	vector of event indicators: 1 for observed events, 0 for censored observations
trt	vector of treatment arm assignment: 1 for active treatment arm, 0 for control arm
gamma.fixed	optional fixed value of the superior long-term survival parameter: gamma.fixed = 1 means the active treatment arm has better long-term survival while gamma.fixed = -1 means the control arm has better long-term survival. This is estimated if not provided by the user.
theta.fixed	optional fixed value of theta. This is estimated if not provided by the user.
weights	optional vector of individual-level weights. This should be a vector with the same length as times.
max.times	The maximum number of bins to use for discretization of the follow-up times.
inner.iter	The number of iterations used to find the crossing time parameters.
final.iter	Given estimated crossing time parameter estimates, number of iterations used to find survival probabilities.
verbose	If TRUE, progress of the algorithm is printed to the screen.

Value

an object of class surv.delay

This is a list withthe following components

times	Vector of length m which has the unique, sorted follow-times after discretization.
surv0	Vector of length m which contains estimated control arm survival probabilities at each of the time points in the vector times
surv1	Vector of length m which contains estimated active treatment arm survival probabilities at each of the time points in the vector times
haz0	Vector of length m which contains estimated control arm hazards at each of the time points in the vector times
haz1	Vector of length m which contains estimated active treatment arm hazards at each of the time points in the vector times
nevents0	Vector of length m which contains estimated control arm survival probabilities at each of the time points in the vector times
nrisk0	Vector of the number at risk in control arm
nevents1	Vector of number of events in active treatment arm
nrisk1	Vector of the number at risk in active treatment arm
theta	Estimated value of the survival curve crossing time
gamma	Estimated value of which arm has superior long-term survival
discretized.times	Vector of discretized follow-up times used in the computation
negloglik.val	Value of the negative log-likelihood at convergence

Author(s)

Nicholas Henderson

Examples

set.seed(5172)

### Generate simulated survival data
n <- 400
cens.time <- 8
X1 <- rweibull(n, shape=2.3, scale=7)
X2 <- rweibull(n, shape=.8, scale=10)
Y1 <- pmin(X1, cens.time)
Y2 <- pmin(X2, cens.time)
e1 <- as.numeric(X1 < cens.time)
e2 <- as.numeric(X2 < cens.time)

times <- c(Y1, Y2)  ## follow-up times
events <- c(e1, e2) ## event indicators
trt <- rep(c(0,1), each=n)  ## treatment arm assignment

## Run the single-crossing constrained estimation procedure with a fixed 
## value of gamma = -1 and theta = 5.8
dsf.obj <- DelayedSurvFit(times, events, trt, gamma.fixed=-1, 
                          theta.fixed=5.8, max.times=100) 

km0 <- cumprod(1 - dsf.obj$nevents0/dsf.obj$nrisk0)
km1 <- cumprod(1 - dsf.obj$nevents1/dsf.obj$nrisk1)

## Plot the single-crossing constrained estimate with the KM estimate:
plot(dsf.obj, xlab="time", ylab="survival probability")
lines(dsf.obj$times, km0, type="s", lty=2)
lines(dsf.obj$times, km1, type="s", lty=2, col="red")

## Not run: 
## Try running DelayedSurvFit on the NivoIpili without fixing
## theta and gamma in advance

data(NivoIpili)
dsf.nivo <- DelayedSurvFit(times=NivoIpili$times, events=NivoIpili$evnt, 
                           trt=NivoIpili$trt) 
plot(dsf.nivo, xlab="Time", ylab="Survival", ylim=c(0, 1), las=1)

## End(Not run)

nchenderson/DelayedSurvFit documentation built on Aug. 18, 2024, 11:49 a.m.