Posterior cumulative incidence and hazards of death and recovery

Turns a fit's outcome probability and delay distributions into the quantities a competing-risks analysis reports, for each covariate pattern in newdata. The cumulative incidence of death and of recovery by time t since onset are $$I_D(t) = p \, F_D(t), \qquad I_R(t) = (1 - p) \, F_R(t)$$ where p is prob and F_D and F_R are the distribution functions of the death and recovery delays, censored for the day of onset and truncated at each delay's max as in the likelihood.

Usage

posterior_cumulative_incidence(
  object,
  newdata = NULL,
  times = NULL,
  type = c("cumulative_incidence", "hazard", "subdistribution_hazard"),
  pwindow = 1
)

Arguments

object

A cfrnow_fit from fit_cfr().

newdata

A data frame with the covariates of the prob and delay formulas, one row per covariate pattern. Defaults to the distinct covariate patterns among the fitted cases, in the order they first appear in object$data (a single row for a fit without covariates).

times

Days since onset at which to evaluate. Defaults to every day from 0 to the longest follow-up in the fitted data.

type

"cumulative_incidence" (the default), "hazard" for the cause-specific hazard or "subdistribution_hazard".

pwindow

Width of the onset window, in days, that the delays are censored over. Defaults to a single day.

Value

A data frame with one row per posterior draw, row of newdata, time and outcome: .draw, row (the row of newdata), time, outcome ("death" or "recovery") and value. A hazard is NA at a time when every case has already resolved.

Details

The hazards are daily, matching the daily resolution of the data. The cause-specific hazard of death on day t is the probability of dying during [t, t + 1) among cases still unresolved at t, $$h_D(t) = \frac{I_D(t + 1) - I_D(t)}{1 - I_D(t) - I_R(t)},$$ and the subdistribution (Fine-Gray) hazard keeps cases that have recovered in the risk set, $$\tilde h_D(t) = \frac{I_D(t + 1) - I_D(t)}{1 - I_D(t)}.$$ Recovery works the same way. Hazard ratios between two covariate patterns are ratios of these draws. They vary with t, since the model does not assume proportional hazards; covariates act on prob and on the delays separately.

A fit without a recovery_delay returns death only. Its survivors never resolve in the model, so the cause-specific and subdistribution hazards coincide. Loss to follow-up only changes which outcomes get recorded and plays no part here.

See also

Other fit: fit_cfr(), posterior_prob_death(), pp_check_cfr(), summary.cfrnow_fit()

Examples

if (FALSE) { # \dontrun{
ll <- simulate_linelist(n = 500, cfr = 0.4, delay = LogNormal(2.4, 0.5))
ll$group <- sample(c("a", "b"), nrow(ll), replace = TRUE)
d <- prepare_cfr_data(ll,
  obs_time = max(ll$onset_date) - 5,
  covariates = "group"
)
fit <- fit_cfr(d,
  delay = LogNormal(Normal(2.4, 0.2), Normal(0.5, 0.15)),
  formula = brms::bf(mu ~ group, prob ~ group)
)
groups <- data.frame(group = c("a", "b"))

# cumulative incidence of death by day 7, 14 and 28 in each group
ci <- posterior_cumulative_incidence(fit, groups, times = c(7, 14, 28))
aggregate(value ~ row + time, ci, stats::median)

# cause-specific hazard ratio of death, group b vs a, over time
h <- posterior_cumulative_incidence(fit, groups,
  times = 0:28,
  type = "hazard"
)
a <- h[h$outcome == "death" & h$row == 1, ]
b <- h[h$outcome == "death" & h$row == 2, ]
a$hr <- b$value / a$value
aggregate(hr ~ time, a, stats::median)
} # }