Convert an object to an epidist_meta_model object

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().

Usage

as_epidist_meta_model(data = NULL, estimates = NULL, ...)

Arguments

data

An epidist_linelist_data or epidist_aggregate_data object of individual level observations, an epidist_estimates_data object of published summary estimates, or NULL.

estimates

An epidist_estimates_data object of published summary estimates, or NULL.

...

Additional arguments passed to methods.

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 and the sampling likelihoods, 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. 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. See vignette("faq").

Three consequences of the sampling likelihoods change what you should do.

• The standard errors are plug in quantities that depend on the parameters, so studies no single distribution can explain may be accommodated by inflating the implied standard deviation rather than by moving the location, and sampling can become multimodal. Allow for genuine differences with a term such as mu ~ 1 + (1 | study) rather than relying on the sampling error alone.

• Quantiles read off a fitted distribution rather than the empirical data have smaller sampling error than assumed here. Supply a reported se in as_epidist_estimates_data() for those rows, which also takes them out of the joint quantile likelihood.

• The normal approximations degrade at small study sample sizes, and summaries of different kinds from one study, such as a mean and a median, are treated as independent. A study that published draws of its parameters avoids the second, because as_epidist_multivariate() turns them into a covariance over the summaries that is fitted jointly.

Two approximations are worth knowing about before fitting quantiles.

• A study that took integer date differences reports quantiles of a discrete distribution. The model interpolates its grid distribution function through the mid points of the cells, but the reported value is itself rounded to that grid, and what is left does not shrink with the study sample size. It stays under 4% on the mean and 9% on the standard deviation once the reported quantiles sit twenty five or more cells above the smallest delay the study counted, and reaches tens of percent on both when they sit within ten. Refitting the median and interquartile range of a lognormal delay of mean 5.9 days, on daily windows with an observation time of 12 days, recovers a delay mean 27% high and a standard deviation 69% high. The same study's mean and standard deviation recover the truth, so prefer those where a study reports them, and check that swindow is the resolution it worked at. as_epidist_estimates_data() warns for studies in this range.

• The accrual weight applied to a study that stopped collecting at a calendar date treats the last primary window as complete, so it is exact on the grid only when relative_obs_time is a multiple of pwindow, and it averages over the primary window for a study that adjusted the secondary interval only. With a weekly primary window, a collection window of 28 days and a delay of mean 4.6 days the latter puts the implied mean 0.8% high at a growth rate of 0.05 and 2.6% high at 0.2. vignette("model") gives the measurements.

Two settings trade accuracy against speed: max_delay in as_epidist_estimates_data(), which sets the grid a study that adjusted for right truncation is summarised on and needs raising for a long tailed delay, and options(epidist.meta_n_quad = ), the smallest number of quadrature intervals used where a study is summarised by quadrature instead. Each study is given as many intervals as it needs to resolve the spread it reported, up to a cap of 2000 that the option lifts when set above it, and the number is held in the n_quad column of the model data.

See also

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_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()