Revision-lag distributions

The distribution g_C of the revision lag: how long after a case is reported its result comes back. Pass one to revision_process() as revision_delay.

Usage

lognormal_revision(mu = numeric(0), sigma = numeric(0))

gamma_revision(shape = numeric(0), rate = numeric(0))

generalized_gamma_revision(mu = numeric(0), sigma = numeric(0), Q = numeric(0))

dirichlet_revision(alpha = numeric(0), bins = numeric(0))

Arguments

mu: Log-mean intercept (delay_mu).
sigma: Log-scale / SD parameter > 0.
shape, rate: Gamma delay parameters (the shape slot is the log-mean, the rate slot the delay SD; see the original parameterisation).
Q: GenGamma shape (delay_Q); Q = 0 recovers lognormal.
alpha: Dirichlet concentration (scalar broadcast to all bins).
bins: Dirichlet: number of explicit delay bins (geometric tail beyond).

Value

A delay_process_class object, for the revision_delay slot of revision_process().

Details

These are aliases of the corresponding delay_process constructors – a revision lag is an ordinary non-negative delay, only measured from the report rather than from the event – so the parameters, priors and behaviour are identical. The one difference is the support, and it depends on the mode: under retraction_only the lag lives on {1, 2, ...} (a retraction lands strictly after the report it withdraws, so a case retracted in the same period is dropped by nowcast() – it was never visible in any data vintage), while under confirmation_only and both it lives on {0, 1, ...}, since a test can come back the day it was ordered.

Which one to use

dirichlet_revision() is the safest default when the counts are large. The correction applied to a pending report of age j is rho(j) = p / (p + (1 - p) * (1 - G_C(j))), so at high counts a shape error in g_C biases the nowcast by more than its Monte-Carlo noise: on a COVID series of ~8000 cases/day a lognormal g_C fitted to a 1 + Poisson(2) lag left a ~0.9% bias and lost nominal coverage, while the Dirichlet recovered rho to four decimals. At low counts the parametric families are fine and estimate fewer parameters.

Examples

revision_process(lognormal_revision())
#> <diseasenowcasting::revision_process_class>
#>  @ revision_delay: <diseasenowcasting::lognormal_delay_class>
#>  .. @ name               : chr "LogNormal"
#>  .. @ num_id             : int 1
#>  .. @ num_delay_seasons  : int 1
#>  .. @ season_distribution: <diseasenowcasting::prior_class>
#>  .. .. @ name       : chr "StdNormal"
#>  .. .. @ num_id     : int 0
#>  .. .. @ stan_params: num(0) 
#>  .. @ mu                 : num(0) 
#>  .. @ sigma              : num(0) 
#>  @ p             : num(0) 
#>  @ stratified_p  : logi FALSE
#>  @ mode          : chr "auto"
#>  @ active        : logi TRUE
revision_process(dirichlet_revision(bins = 10))
#> <diseasenowcasting::revision_process_class>
#>  @ revision_delay: <diseasenowcasting::dirichlet_delay_class>
#>  .. @ name               : chr "Dirichlet"
#>  .. @ num_id             : int 4
#>  .. @ num_delay_seasons  : num 1
#>  .. @ season_distribution: <diseasenowcasting::prior_class>
#>  .. .. @ name       : chr "StdNormal"
#>  .. .. @ num_id     : int 0
#>  .. .. @ stan_params: num(0) 
#>  .. @ alpha              : num(0) 
#>  .. @ bins               : int 10
#>  @ p             : num(0) 
#>  @ stratified_p  : logi FALSE
#>  @ mode          : chr "auto"
#>  @ active        : logi TRUE

# Held-fixed revision lag, e.g. from an external study
revision_process(gamma_revision(shape = log(3), rate = 2))
#> <diseasenowcasting::revision_process_class>
#>  @ revision_delay: <diseasenowcasting::gamma_delay_class>
#>  .. @ name               : chr "Gamma"
#>  .. @ num_id             : int 2
#>  .. @ num_delay_seasons  : int 1
#>  .. @ season_distribution: <diseasenowcasting::prior_class>
#>  .. .. @ name       : chr "StdNormal"
#>  .. .. @ num_id     : int 0
#>  .. .. @ stan_params: num(0) 
#>  .. @ shape              : num 1.1
#>  .. @ rate               : num 2
#>  @ p             : num(0) 
#>  @ stratified_p  : logi FALSE
#>  @ mode          : chr "auto"
#>  @ active        : logi TRUE