Creates an epidist_meta_model object from individual level data, published
summary estimates, or a mix of the two.
This enables fitting a single delay distribution to all of the evidence
available using epidist().
Details
The meta model is experimental. Its interface may still change in future releases.
Individual level rows use the same likelihood as the marginal model (see
as_epidist_marginal_model()), imported from the
primarycensored package.
Summary rows are instead forward modelled. Given the delay distribution, the
model works out what the study's own estimation procedure would have
converged to, and fits the reported value to that. Published estimates that
did not adjust for right truncation, or that treated interval censored data
as continuous, can therefore still contribute unbiased information.
That holds only where the metadata describing what each study did is
correct. It is usually the analyst's judgement rather than something the
study reported, so state it explicitly and vary it in a sensitivity
analysis.
vignette("model") gives the forward model, the sampling likelihoods
and the accuracy of the approximations, and vignette("meta") works
through a simulated and a real example.
At least one of data and estimates must be supplied. Study level
heterogeneity is specified through the brms formula in epidist(), for
example mu ~ 1 + (1 | study), rather than through this function.
Individual level rows are labelled "individual" in the study column so
that they form their own level of any such term.
What this means in practice
Summaries that one study computed from the same delays are correlated, so
they are fitted jointly. Two are grouped when they agree on every column of
as_epidist_estimates_data() other than the summary itself, and a summary
supplied with its own se is fitted alone. A study that reported integer
date differences (cens_adjusted 0 or 3) is the exception: its mean and
standard deviation form one group and its quantiles another. One
observation is therefore a group rather than a single reported value, so
log_lik() and loo::loo() report per group, and loo only compares
fits to the same studies and the same mix of individual and summary rows.
Summary rows are evaluated in R for each posterior draw, so both are slow
for a fit with many draws and summary rows. Pass ndraws to use fewer
draws, as epidist_gen_meta_log_lik() explains. See vignette("faq").
epidist_meta_leave_one_out() asks the study level question instead,
refitting with each study held out.
The sampling standard errors are plug in quantities that depend on the
parameters, so allow for genuine differences between studies with a term
such as mu ~ 1 + (1 | study) rather than relying on them alone. Supply a
reported se in as_epidist_estimates_data() for quantiles read off a
fitted distribution rather than the empirical data. Where a study reported
integer date differences, keep its mean and standard deviation and drop its
quantiles. as_epidist_estimates_data() warns for the studies the
approximations serve least well, and documents the two settings, max_delay
and options(epidist.meta_n_quad = ), that trade accuracy against speed.
Advanced: an estimated growth rate
A summary row tilts its primary event, and weights the follow up of an
accrual design, by the growth_rate of its study. Where that rate is
NA in as_epidist_estimates_data(), or was given there with a
growth_rate_sd, the study estimates it as the pgrowth distributional
parameter instead. That is the parameter primary = "expgrowth"
estimates from individual level rows, so the two can share it. The model
adds pgrowth ~ 0 + study unless a pgrowth formula is given, and
epidist_model_prior() sets the priors from the reported rates.
Summaries carry little information about the rate on their own, so share
the coefficient with rows that do inform it, for example pgrowth ~ 1
with a line list from the same outbreak. vignette("model") gives the
details.
See also
as_epidist_estimates_data() for preparing the summary estimates,
and for the checks and the settings the approximations here depend on.
Other meta_model:
as_epidist_meta_model.NULL(),
as_epidist_meta_model.epidist_aggregate_data(),
as_epidist_meta_model.epidist_estimates_data(),
as_epidist_meta_model.epidist_linelist_data(),
assert_epidist.epidist_meta_model(),
epidist_family_model.epidist_meta_model(),
epidist_formula_model.epidist_meta_model(),
epidist_meta_leave_one_out(),
epidist_model_prior.epidist_meta_model(),
epidist_newdata.epidist_meta_model(),
epidist_transform_data_model.epidist_meta_model(),
is_epidist_meta_model(),
new_epidist_meta_model()