Propagate uncertainty from several estimates when combining these estimates via a function.
This is done by using the parametric bootstrap to simulate values from the distribution of each estimate to build up an empirical distribution of the combined parameter.
Finally either the percentile method is used or the highest density interval is chosen to derive a confidence interval for the combined parameter with the desired coverage.
Gaussian copulas are used for when parameters are assumed to be dependent / correlated.
References: Davison and Hinkley (1997,ISBN:0-521-57471-4) for the parametric bootstrap and percentile method, Gelman et al. (2014,ISBN:978-1-4398-4095-5) for the highest density interval, Stockdale et al. (2020)<doi:10.1016/j.jhep.2020.04.008> for an example of combining conditional prevalences.

Daniel Gerlanc <dgerlanc@enplusadvisors.com> and Kris Kirby
<kkirby@williams.edu>
Functions for calculating bootstrap effect sizes

Bootstrap Confidence Intervals on Effect Sizes
c(
person(
"Daniel",
"Gerlanc",
role=c("aut", "cre"),
email="dan@gerlanc.com"),
person(
"Kris",
"Kirby",
role="aut",
email="kkirby@hush.com"))
Calculate robust measures of effect sizes using the bootstrap.
Daniel Gerlanc [aut, cre],
Kris Kirby [aut]

Daniel Gerlanc <dgerlanc@enplusadvisors.com> and Kris Kirby <kkirby@williams.edu>

c(person(given = "Marsel",
family = "Scheer",
role = c("aut", "cre"),
email = "scheer@freescience.de"),
person(given = "Gerhard",
family = "Dikta",
role = c("aut"),
email = "dikta@fh-aachen.de"))
Bootstrap based goodness-of-fit tests. It allows
to perform rigorous statistical tests to check if a chosen
model family is correct based on the marked empirical
process. The implemented algorithms are described in
(Dikta and Scheer (2021) <doi:10.1007/978-3-030-73480-0>)
and can be applied
to generalized linear models without any further implementation
effort. As far as certain linearity conditions are fulfilled
the resampling scheme are also applicable beyond generalized
linear models. This is reflected in the software architecture
which allows to reuse the resampling scheme by implementing
only certain interfaces for models that are not supported
natively by the package.
testthat, covr, roxygen2, pkgdown, devtools, tinytest,
mockery, knitr, rmarkdown, minpack.lm, MASS
Marsel Scheer [aut, cre],
Gerhard Dikta [aut]