Compute the Restricted Mean Survival Time (Trapezoidal Rule)

Calculates the area under a survival curve up to the last observed time point using the composite trapezoidal rule. The result equals the restricted mean survival time (RMST) when the input curve has been evaluated on a sufficiently fine grid.

Usage

rmst(time, surv)

Arguments

time

Numeric vector of time points (strictly increasing, same units as the survival data).

surv

Numeric vector of survival probabilities evaluated at each element of time. Must be the same length as time.

Value

A single numeric value: the area under the curve (RMST) in the same units as time.

Details

The trapezoidal approximation is: $$\text{RMST} \approx \sum_{i=1}^{n-1} (t_{i+1} - t_i) \cdot \frac{S(t_i) + S(t_{i+1})}{2}.$$ For uniform grids this simplifies to: $$\Delta t \cdot \Bigl[\tfrac{1}{2}S(t_0) + S(t_1) + \cdots + S(t_{n-2}) + \tfrac{1}{2}S(t_{n-1})\Bigr].$$

See also

run_tumour_analysis

Examples

# RMST from a synthetic exponential curve
t <- seq(0, 10, by = 0.1)
s <- exp(-0.1 * t)
rmst(t, s)   # close to 1/0.1 = 10 as horizon -> infinity
#> [1] 6.321258