cfr_static {cfr} | R Documentation |
Estimate a static disease severity measure
Description
Calculates the severity of a disease, while optionally correcting for reporting delays using an epidemiological delay distribution of the time between symptom onset and death (onset-to-death).
Other delay distributions may be passed to calculate different disease severity measures such as the hospitalisation fatality risk.
Usage
cfr_static(data, delay_density = NULL, poisson_threshold = 100)
Arguments
data |
A Note that the Note also that the total number of cases must be greater than the total number of reported deaths. |
delay_density |
An optional argument that controls whether delay
correction is applied in the severity estimation.
May be |
poisson_threshold |
The case count above which to use Poisson approximation. Set to 100 by default. Must be > 0. |
Value
A <data.frame>
with the maximum likelihood estimate and 95%
confidence interval of the severity estimates, named "severity_mean",
"severity_low", and "severity_high".
Details: Adjusting for delays between two time series
The method used in cfr_static()
follows Nishiura et al.
(2009).
The function calculates a quantity u_t
for each day within the input
data, which represents the proportion of cases estimated to have
a known outcome on day t
.
Following Nishiura et al., u_t
is calculated as:
u_t = \dfrac{\sum_{i = 0}^t
\sum_{j = 0}^\infty c_i f_{j - i}}{\sum_{i = 0} c_i}
where f_t
is the value of the probability mass function at time t
and c_t
, d_t
are the number of new cases and new deaths at time
t
, (respectively).
We then use u_t
at the end of the outbreak in the following likelihood
function to estimate the severity of the disease in question.
{\sf L}({\theta \mid y}) = \log{\dbinom{u_tC}{D}} + D \log{\theta} +
(u_tC - D)\log{(1.0 - \theta)}
C
and D
are the cumulative number of cases and deaths
(respectively) up until time t
.
\theta
is the parameter we wish to estimate, the severity of the
disease. We estimate \theta
using simple maximum-likelihood methods,
allowing the functions within this package to be quick and easy tools to use.
The precise severity measure — CFR, IFR, HFR, etc — that \theta
represents depends upon the input data given by the user.
The epidemiological delay-distribution density function passed to
delay_density
is used to evaluate the probability mass function
parameterised by time; i.e. f(t)
which
gives the probability that a case has a known outcome (usually death) at time
t
, parameterised with disease-specific parameters before it is supplied
here.
References
Nishiura, H., Klinkenberg, D., Roberts, M., & Heesterbeek, J. A. P. (2009). Early Epidemiological Assessment of the Virulence of Emerging Infectious Diseases: A Case Study of an Influenza Pandemic. PLOS ONE, 4(8), e6852. doi:10.1371/journal.pone.0006852
Examples
# load package data
data("ebola1976")
# estimate severity without correcting for delays
cfr_static(ebola1976)
# estimate severity for each day while correcting for delays
# obtain onset-to-death delay distribution parameters from Barry et al. 2018
# The Lancet. <https://doi.org/10.1016/S0140-6736(18)31387-4>
cfr_static(
ebola1976,
delay_density = function(x) dgamma(x, shape = 2.40, scale = 3.33)
)