Estimate the corrected case fatality risk — .estimate

Estimates the maximum likelihood estimate and 95% confidence interval of a corrected severity, using the total cases and total cases with known outcomes, where the latter replaces the total number of deaths in the standard (naive) severity definition. We use a binomial likelihood, approximated by a Poisson likelihood for large samples.

Usage

.estimate_severity(
  total_cases,
  total_deaths,
  total_outcomes,
  poisson_threshold,
  p_mid = total_deaths/round(total_outcomes)
)

Arguments

total_cases: The total number of cases observed over the period of an outbreak of interest. The total number of cases must be greater than or equal to the total number of deaths.
total_deaths: The total number of deaths observed over the period of an outbreak of interest. The total number of deaths must be less than or equal to the total number of cases.
total_outcomes: The total number of outcomes expected to be observed over the period of an outbreak of interest. See estimate_outcomes().
poisson_threshold: The case count above which to use Poisson approximation. Set to 100 by default. Must be > 0.
p_mid: The initial severity estimate, which is used to determine the likelihood approximation used when total_cases > poisson_threshold. Defaults to total_deaths / round(total_outcomes).

Value

A <data.frame> with one row and three columns for the maximum likelihood estimate and 95% confidence interval of the corrected severity estimates, named "severity_estimate", "severity_low", and "severity_high".

Details

Special cases

When any two of total_cases, total_deaths, or total_outcomes are 0, the estimate and confidence intervals cannot be calculated and the output <data.frame> contains only NAs.
When total_outcomes <= total_deaths, estimate and confidence intervals cannot be reliably calculated and are returned as NA.