Derive the lethal / survival-threshold duration at a temperature

derive_lt() solves the fitted 4PL for the duration at which survival crosses a target probability p at a given temperature (an "LT" / lethal- time-style quantity, e.g. p = 0.5 gives the absolute 50% survival time). To obtain the curve's relative midpoint, use p = (low + up) / 2; that crossing has log10(duration) = mid exactly.

Usage

derive_lt(object, p = 0.5, temp, group = NULL)

Arguments

object: A profile_tls fit from fit_tls().
p: Absolute target survival probability in (low, up) (default 0.5).
temp: Numeric temperature(s) at which to solve.
group: Optional single group level (grouped fits only). Required when the fit is grouped.

Value

A numeric vector of durations (same length as temp) on the data's native time unit.

Details

Survival follows p = low + (up - low) * plogis(-k (log10(duration) - mid)), so the duration at which survival equals a target p solves $$\log_{10}(duration) = mid - \mathrm{qlogis}\!\left(\frac{p - low}{up - low}\right) / k.$$ The target must lie strictly between low and up for a finite crossing; otherwise the survival curve never reaches p and derive_lt() aborts with an explanatory message (confidence-language, never silent). 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)
# Absolute 50% survival duration at 36 C:
derive_lt(fit, p = 0.5, temp = 36)
#> [1] 0.9555978