Interpolate Survival Curves — interp • survdistr

Interpolates survival curves (vector or matrix) at new time points using internal C++ interpolation functions. Output can be survival, cumulative distribution, density, hazard or cumulative hazard functions.

Usage

interp(
  x,
  times = NULL,
  eval_times = NULL,
  method = "const_surv",
  output = "surv",
  add_times = TRUE,
  check = TRUE,
  eps = 1e-12,
  trim_dups = FALSE
)

Arguments

x: (numeric() | matrix())
Survival vector or matrix (rows = observations, columns = time points).
times: (numeric() | NULL)
Anchor time points. If NULL, extracted from names/colnames.
eval_times: (numeric() | NULL)
New time points at which to interpolate. Values need to be unique, increasing non-negative numbers. If NULL, the anchor times are used.
method: (character(1))
Interpolation method; one of "const_surv" (default), "const_dens" (alias: "linear_surv") and "const_haz" (alias: "exp_surv").
output: (character(1))
Output type: "surv", "cdf", "cumhaz", "density" or "hazard".
add_times: (logical(1))
If TRUE, attach eval_times as names/colnames.
check: (logical(1))
If TRUE, run input matrix validation checks using assert_prob(); set to FALSE to skip checks (NOT recommended for external use).
eps: (numeric(1))
Small positive value used to replace extremely low survival probabilities when computing cumulative hazard, preventing numerical instability in \(-\log S(t)\) calculations.
trim_dups: (logical(1))
If TRUE, removes adjacent duplicate values from the input using trim_duplicates(). This eliminates flat segments in survival curves and improves interpolation efficiency. Default is FALSE.

Value

A numeric vector or matrix of interpolated values.

Details

Input must always be survival probabilities. We currently provide three interpolation options:

"const_surv": left-continuous constant interpolation of S(t) (default).
"const_dens"/"linear_surv": linear interpolation of S(t) (equivalent to piecewise constant interpolation of the density function).
"const_haz"/"exp_surv": exponential interpolation of S(t) (equivalent to piecewise constant interpolation of the hazard function).

We will provide tables with the interpolation formulas for each method in an upcoming arXiv preprint and link it here.

For constant hazard interpolation ("const_haz"), any right-anchor S(t) values equal to 0 are internally floored at min(1e-12, S_left) within each interval. This keeps hazards/densities finite without allowing a local increase in S(t).

Examples

x = matrix(c(1, 0.8, 0.6,
             1, 0.7, 0.4), nrow = 2, byrow = TRUE)
times = c(0, 8, 13)
eval_times = c(5, 10, 14)

# constant S(t) interpolation
interp(x, times, eval_times)
#>      5  10  14
#> [1,] 1 0.8 0.6
#> [2,] 1 0.7 0.4

# linear S(t) interpolation
interp(x, times, eval_times, method = "linear_surv")
#>           5   10   14
#> [1,] 0.8750 0.72 0.56
#> [2,] 0.8125 0.58 0.34

# exponential S(t) interpolation (same as `method = "const_haz"`)
interp(x, times, eval_times, method = "exp_surv")
#>              5        10        14
#> [1,] 0.8698237 0.7130410 0.5664525
#> [2,] 0.8001774 0.5596066 0.3576452

# Cumulative distribution with linear S(t) interpolation
interp(x, times, eval_times, method = "linear_surv", output = "cdf")
#>           5   10   14
#> [1,] 0.1250 0.28 0.44
#> [2,] 0.1875 0.42 0.66

# H(t) with linear S(t) interpolation
interp(x, times, eval_times, method = "linear_surv", output = "cumhaz")
#>              5        10        14
#> [1,] 0.1335314 0.3285041 0.5798185
#> [2,] 0.2076394 0.5447272 1.0788097

# f(t) with constant hazard interpolation
interp(x, times, eval_times, method = "const_haz", output = "density")
#>               5         10         14
#> [1,] 0.02426194 0.04102582 0.03259165
#> [2,] 0.03567540 0.06263294 0.04002878

# h(t) with constant hazard interpolation
interp(x, times, eval_times, method = "const_haz", output = "hazard")
#>               5         10         14
#> [1,] 0.02789294 0.05753641 0.05753641
#> [2,] 0.04458437 0.11192316 0.11192316