hybrid_Exponential {eventTrack}

Estimate survival function, as hybrid between Kaplan-Meier and Exponential tail

Description

This function estimates the values of the survival function as a hybrid of Kaplan-Meier for times smaller than the specified change point and an Exponential fit to the tail of the survival function. The Exponential tail fit is computed assuming a piecewise constant hazard with one change point.

Usage

hybrid_Exponential(t0, time = time, event = event, changepoint)

Arguments

t0

Value at which to compute value of survival function. Can be a vector.

time

Event times, censored or observed, in months.

event

Censoring indicator, 1 for event, 0 for censored.

changepoint

Pre-specified change point.

Value

A vector of the same dimension as t0 containing the values of the estimated survival function at t0.

Author(s)

Kaspar Rufibach (maintainer)
[e-mail]

References

Fang, L., Zheng, S. (2011). A hybrid approach to predicting events in clinical trials with time-to-event outcomes. Contemp. Clin. Trials, 32, 755–759.

Goodman, M.S., Li, Y., Tiwari, R.C. (2011). Detecting multiple change points in piecewise constant hazard functions. J. Appl. Stat, 38(11), 2523–2532.

Rufibach, K. (2016). Event projection: quantify uncertainty and manage expectations of broader teams. Slides for talk given in Basel Biometric Section Seminar on 28th April 2016. https://baselbiometrics.github.io/home/docs/talks/20160428/1_Rufibach.pdf.

Examples

# --------------------------------------------------
# simulate data 
# --------------------------------------------------
set.seed(2021)
n <- 600
time0 <- rexp(n, rate = log(2) / 20)
cens <- rexp(n, rate = log(2) / 50)
time <- pmin(time0, cens)
event <- as.numeric(time0 < cens)
accrual_after_ccod <- 1:(n - length(time)) / 30

# --------------------------------------------------
# compute hybrid estimate and predict timepoint
# --------------------------------------------------
plot(survfit(Surv(time, event) ~ 1), mark = "", xlim = c(0, 200), 
     ylim = c(0, 1), conf.int = FALSE, xaxs = "i", yaxs = "i",
     main = "estimated survival functions", xlab = "time", 
     ylab = "survival probability", col = grey(0.75), lwd = 5)

# how far out should we predict monthly number of events?
future.units <- 15
tab <- matrix(NA, ncol = 2, nrow = future.units)
tab[, 1] <- 1:nrow(tab)
ts <- seq(0, 100, by = 0.01)

# --------------------------------------------------
# starting from a piecewise Exponential hazard with 
# K = 5 change points, infer the last "significant"
# change point
# --------------------------------------------------
pe5 <- piecewiseExp_MLE(time = time, event = event, K = 5)
pe5.tab <- piecewiseExp_test_changepoint(peMLE = pe5, alpha = 0.05)
cp.select <- max(c(0, as.numeric(pe5.tab[, "established change point"])), na.rm = TRUE)

# the function predictEvents takes as an argument any survival function
# hybrid exponential with cp.select
St1 <- function(t0, time, event, cp){
     return(hybrid_Exponential(t0 = t0, time = time, event = event, 
     changepoint = cp))}

pe1 <- predictEvents(time = time, event = event, 
          St = function(t0){St1(t0, time = time, 
          event = event, cp.select)}, accrual_after_ccod, 
          future.units = future.units)
tab[, 2] <- pe1[, 2]
lines(ts, St1(ts, time, event, cp.select), col = 2, lwd = 2)

# --------------------------------------------------
# compute exact date when we see targeted number of events
# for hybrid Exponential model, through linear interpolation
# --------------------------------------------------
exactDatesFromMonths(predicted = tab, 450)