rTFT fits discrete-time survival models to the times at which individual organisms fail under thermal exposure (e.g., loss of equilibrium, knockdown or death), using Bayesian inference in Stan through brms. The hazard is the product of a failure rate that depends on temperature, following Kingsolver and Umbanhowar (2018), and a baseline that may depend on the time under exposure.
Thermal tolerance is usually reported as a summary of an assay, such as the critical thermal maximum (CTmax) of a ramping trial or the time to failure at a constant temperature. These summaries depend on how the assay was run (e.g., the ramp rate or the temperatures chosen). In rTFT, a model is fitted to the failure times themselves (available in both types of assays), and the usual summaries are derived from the fitted model, each with its posterior uncertainty.
With the package, one can:
- fit failure times that are known-time, interval-censored or both, from static assays, ramping assays or both, with any of several functions for the failure rate and for the baseline;
- let the failure rate depend on covariates (e.g., body mass), on group-level effects (e.g., trials) and on other stressors (e.g., dissolved oxygen);
- check the fit of a model against the data;
- compare models by cross-validation that leaves out whole individuals or trials;
- derive static and dynamic critical thermal maxima, thermal death time curves and thermal tolerance landscapes, from one model or averaged over several;
- predict survival along a record of temperature (e.g., a stream during a heat wave), and of any co-stressors recorded with it, also from one model or averaged over several.
Installation
rTFT can be installed in either of two ways, both of which give the latest release.
From GitHub, where the package is built, vignettes included, on the computer it is installed on. With dependencies = TRUE the packages that build the vignettes (quarto, knitr and plotly) are installed too; the Quarto command line tool is also needed, and without it build_vignettes = TRUE is left out and the vignettes are read on the website.
# install.packages("remotes")
remotes::install_github("eogmartins/rTFT@*release", dependencies = TRUE, build_vignettes = TRUE)From R-universe, where the package is already built, vignettes included, so that neither remotes nor Quarto is needed.
install.packages("rTFT", repos = c("https://eogmartins.r-universe.dev", "https://cloud.r-project.org"))Fitting a model requires a working installation of Stan, through either cmdstanr or rstan (see the installation notes of brms). cmdstanr is recommended and was used to fit the models of the vignettes; it is not on CRAN and is installed with install.packages("cmdstanr", repos = c("https://stan-dev.r-universe.dev", getOption("repos"))) followed by cmdstanr::install_cmdstan(). It is asked for with backend = "cmdstanr" in fit_hazard(), as in the example below; without it, leave that argument out and brms uses rstan.
Example
Three simulated datasets are included with the package: a static assay (static_assay), a ramping assay run at two levels of dissolved oxygen (ramp_assay) and a record of stream temperature (stream_record). They were simulated from a known model, so that what a model estimates can be compared with the values used in the simulation.
The example below uses static_assay, which contains the times to loss of equilibrium of 120 juvenile salmonids held at 23, 25 or 27°C and checked every hour for five days. It shows the four steps of an analysis, which the vignette Getting started with rTFT describes in detail.
library(rTFT)
# 1. The table of intervals at risk, built from the temperature of each group of
# fish through time and the times of the checks.
path <- data.frame(path_id = rep(c("T23", "T25", "T27"), each = 2),
time = rep(c(0, 7200), times = 3),
temp = rep(c(23, 25, 27), each = 2))
checks <- expand.grid(path_id = c("T23", "T25", "T27"), time = seq(0, 7200, by = 60))
long <- build_hazard_data(static_assay, path, observation = "interval",
covariates = c("mass", "trial"), checks = checks)
# 2. An exponential failure rate with a Weibull baseline, with the failure rate
# depending on body mass and varying among trials.
fit <- fit_hazard(long, m_form = "exp", baseline = "weibull",
dpar_formulas = list(loga = ~ 1 + I(mass - 15) + (1 | trial)),
chains = 4, cores = 4, backend = "cmdstanr")
# 3. The static critical thermal maximum for an exposure of 60 min and the thermal
# death time curves of a 15 g fish.
tol <- derive_tdt_ttl(fit, newdata = data.frame(mass = 15), t_ref = 60)
tol$sctmax
plot_tdt(tol, time_unit = "min")
# 4. Survival along 30 days of hourly stream temperature.
pred <- predict_survival(fit, stream_record, newdata = data.frame(mass = 15))
plot_survival(pred, temperature = TRUE)Vignettes
Four vignettes describe the package, and are best read in this order. They can be read, with the help pages, on the website of the package.
-
Getting started with rTFT (
vignette("getting-started", package = "rTFT")): the model, a static assay, the checks of a fitted model, the derived quantities and a prediction of survival along a record of stream temperature. -
Ramping assays (
vignette("ramping-assays", package = "rTFT")): how a ramp is given to the package, the dynamic critical thermal maximum, and what the choice of ramp rates allows a model to estimate. -
Comparing and averaging models (
vignette("comparing-and-averaging-models", package = "rTFT")): cross-validation by individual or trial, model weights and averaged predictions. -
Temperature and a co-stressor (
vignette("temperature-and-a-co-stressor", package = "rTFT")): dissolved oxygen as a second stressor, with and without an interaction with temperature.
Getting help
Problems and bugs (an error, a result that looks wrong, a help page that does not match what a function does) should be reported on the issues page, https://github.com/eogmartins/rTFT/issues, with the code that shows the problem and the output of sessionInfo().
For questions about using the package (e.g., which model or design suits a study, how to read a result) and suggestions for new features, please use the discussions page, https://github.com/eogmartins/rTFT/discussions.
Citation
If you use the package, please cite it as:
Martins, E. G. (2026). rTFT: hazard models for thermal failure time data. R package version 0.1.1. https://doi.org/10.5281/zenodo.23319254
The same reference is given by citation("rTFT"). The DOI stands for every version of the package and leads to the most recent one; each version is archived with a DOI of its own on the same page.
Use of generative AI
The code, tests and documentation of this package were drafted with the assistance of Claude (Anthropic), used through Claude Code (models Opus 4.8–5.5 and Fable 5.1). The author specified the models, their parameterisation and the quantities derived from them, reviewed each function and its tests before they entered the package, and takes responsibility for its content.