Derive the temperature giving a target survival at a fixed exposure

derive_ctmax() inverts the fitted 4PL for temperature: it returns the assay temperature at which survival equals a target surv after exposure duration. By default surv is the relative midpoint threshold (low + up) / 2 and duration is tref, so derive_ctmax(fit) reproduces the fitted CTmax. Supplying an absolute surv gives the absolute- threshold critical temperature (the analogue of the bayesTLS extract_tdt() absolute mode), with the asymmetry correction qlogis((surv - low) / (up - low)) / k built in.

Usage

derive_ctmax(object, surv = NULL, duration = NULL, group = NULL)

Arguments

object

A profile_tls fit from fit_tls().

surv

Target survival probability in (low, up). NULL (default) uses the relative midpoint (low + up) / 2, reproducing CTmax at tref.

duration

Exposure duration(s) (native time unit; strictly positive). Defaults to the fit's tref.

group

Optional single group level (grouped fits only).

Value

A numeric vector of temperatures (degrees C), one per duration.

Details

Solving surv = low + (up - low) * plogis(-k (log10(duration) - mid)) with mid = log10(tref) - (temp - CTmax) / z for the temperature gives $$temp = CTmax - z\Big(\log_{10} duration - \log_{10} t_{ref} + \mathrm{qlogis}\!\big(\tfrac{surv - low}{up - low}\big) / k\Big).$$ The target surv must lie strictly between low and up. For a random-effects fit this is a population-level derived quantity; it does not add a group BLUP.

Examples

d <- simulate_tls(family = "binomial", CTmax = 36, z = 4, seed = 1)
fit <- fit_tls(d, y = survived, n = total, time = duration, temp = temp,
               family = "binomial", tref = 1)
derive_ctmax(fit)                                  # ~ CTmax (relative, at tref)
#> [1] 35.92586
derive_ctmax(fit, surv = 0.5, duration = c(1, 4))  # absolute 50% survival
#> [1] 35.92114 33.51409