Calibrate a Weibull survival curve to target points

Finds the formula and shape whose simstudy Weibull curve, S(t) = exp(-exp(formula) * t^(1 / shape)) with scale fixed at 1, passes as closely as possible through the supplied points. The fit is a least-squares fit of log(time) on log(-log(survival)), run with L-BFGS-B, and the returned formula and shape can be handed straight to define_survival() or survival_curve().

Usage

calibrate_survival(time, survival)

Arguments

time

Increasing positive times. A finite numeric vector of at least two strictly increasing values, the same length as survival.

survival

Survival probabilities at those times. A finite numeric vector strictly inside (0, 1) and strictly decreasing.

Value

A one-row base data.frame with the calibrated numeric formula and shape, the optim() convergence code (always 0, since a non-converged fit raises an error), and rmse, the root mean squared residual on the log-time scale.

Examples

calibrate_survival(time = c(50, 100, 150), survival = c(0.9, 0.7, 0.4))
#>     formula    shape convergence       rmse
#> 1 -9.950622 0.510809           0 0.03467959