Fit the real-time mixture-cure CFR model

Estimates a real-time case fatality ratio from line-list data. Each case is fatal with probability cfr and, when fatal, dies at an onset-to-death delay; cases still alive at the cut-off are right-censored, correcting the downward bias of the naive deaths / cases ratio. The delay and the CFR prior are given as distspec distributions.

Usage

fit_cfr(
  data,
  delay = LogNormal(meanlog = Normal(2, 1), sdlog = Normal(0.5, 0.3)),
  cfr_prior = Beta(1, 1),
  recovery_delay = NULL,
  formula = mu ~ 1,
  ...
)

Arguments

data: Output of prepare_cfr_data(), or an epidist_cure_model / data frame with y, outcome, pwindow, swindow.
delay: Onset-to-death delay as a distspec distribution (distspec::LogNormal() or distspec::Gamma()) whose native parameters are fixed numbers or Normal() priors.
cfr_prior: CFR prior as a distspec::Beta(). Defaults to Beta(1, 1).
recovery_delay: Optional onset-to-recovery delay (same form as delay) for the two-outcome fit; may use a different family from delay.
formula: A brms formula for the delay location mu and, optionally, the CFR (cfr ~ ...). Defaults to mu ~ 1. The cfr_prior normally lands on the CFR intercept; when the CFR formula drops the intercept (e.g. cfr ~ 0 + group, one logit-CFR per group) it is placed on those coefficients instead. It then applies to every cfr coefficient, so an intercept-free formula should carry only factor terms.
...: Passed to epidist::epidist() and on to brms::brm() (e.g. chains, iter, backend, seed).

Value

A brmsfit with class cfrnow_fit; summarise with cmdstanr::summary().

Details

The delay's native parameters may each be a fixed number (held fixed; fixing the whole delay gives the Ghani/Nishiura estimator) or a Normal() prior (co-estimated). The family (LogNormal() or Gamma()) sets the delay distribution. cfr_prior is a Beta(); it matters because the CFR is weakly identified early on (Beta(1, 1) is uniform, Beta(1, 9) favours a low CFR, Beta(6.6, 13.4) suits a high-fatality pathogen).

The model is fitted through epidist::epidist(), so covariates (or a smooth time effect) can be put on the CFR or the delay through formula, e.g. formula = brms::bf(mu ~ 1, cfr ~ age). When the line list carries recovery dates, pass a recovery_delay to fit the two-outcome model that also times recoveries.

Examples

if (FALSE) { # \dontrun{
ll <- simulate_linelist(n = 500, cfr = 0.4, delay = LogNormal(2.4, 0.5))
d <- prepare_cfr_data(ll, obs_time = max(ll$onset_date) - 5)
otd <- LogNormal(meanlog = Normal(2.41, 0.2), sdlog = Normal(0.51, 0.15))

# co-estimated delay
fit <- fit_cfr(d, delay = otd, cfr_prior = Beta(1, 1), backend = "cmdstanr")
summary(fit)

# fixed delay (Ghani/Nishiura), a gamma family, and a CFR covariate
fit_cfr(d, delay = LogNormal(meanlog = 2.41, sdlog = 0.51))
fit_cfr(d, delay = Gamma(shape = Normal(3.3, 1), rate = Normal(0.26, 0.08)))
fit_cfr(d, delay = otd, formula = brms::bf(mu ~ 1, cfr ~ group))
} # }