R: 'EpiInvert' estimates the reproduction number Rt and a...

EpiInvert {EpiInvert}

R Documentation

`EpiInvert` estimates the reproduction number Rt and a restored incidence curve from the original daily incidence curve and the serial interval distribution. EpiInvert also corrects the festive and weekly biases present in the registered daily incidence.

Description

EpiInvert estimates the reproduction number Rt and a restored incidence curve from the original daily incidence curve and the serial interval distribution. EpiInvert also corrects the festive and weekly biases present in the registered daily incidence.

Usage

EpiInvert(
  incid,
  last_incidence_date,
  festive_days = rep("1000-01-01", 2),
  config = EpiInvert::select_params()
)

Arguments

`incid`	The original daily incidence curve (a numeric vector).
`last_incidence_date`	The date of the last value of the incidence curve in the format YYYY-MM-DD. EpiInvert does not allow missing values. On days when a country does not report data, a zero must be registered as the value associated with the incidence of that day.
`festive_days`	The festive or anomalous dates in the format YYYY-MM-DD (a character vector). In these dates we "a priori" expect that the incidence value is perturbed.
`config`	An object of class `estimate_R_config`, as returned by function `select_params`. The element of config are : si_distr: a numeric vector with the distribution of the serial interval (the default value is an empty vector). If this vector is empty, the serial interval is estimated using a parametric shifted log-normal. shift_si_distr: shift of the above user provided serial interval. This shift can be negative, which means that secondary cases can show symptoms before the primary cases (the default value is 0). max_time_interval: Maximum number of days used by EpiInvert (the default value is 150, which means that EpiInvert uses the last 150 days. The computational cost strongly depends on this value). mean_si: mean of the parametric shifted log-normal to approximate the serial interval (in the case the above si_distr vector is empty), (the default value is 12.267893). sd_si: standard deviation of the parametric shifted log-normal to approximate the serial interval (in the case the above si_distr vector is empty), (the default value is 5.667547). shift_si=: shift of the parametric shifted log-normal to approximate the serial interval (in the case the above si_distr vector is empty), (the default value is -5). Rt_regularization_weight: regularization weight for Rt in the variational model used by EpiInvert (the default value is 5). seasonality_regularization_weight: regularization weight for the weekly bias correction factors in the variational model used by EpiInvert (the default value is 5). incidence_weekly_aggregated: a boolean value which determines if we use weekly aggregated incidence. In such case every week a single data is stored with the accumulated incidence in the last 7 days (the default value is FALSE). NweeksToKeepIncidenceSum: number of weeks to keep the value of the incidence accumulation. The default is 2.

Details

EpiInvert estimates the reproduction number Rt and a restored incidence curve by inverting the renewal equation :

{i(t) = \sum_k i(t-k)R(t-k)\Phi(k)}

using a variational formulation. The theoretical foundations of the method can be found in references [1] and [2].

Value

an object of class estimate_EpiInvert, given by a list with components:

i_original: the original daily incidence curve. In the case of weekly aggregated incidence, we initialize the original curve assigning each day of the week 1/7 of the weekly aggregated value.
i_festive: the incidence after correction of the festive days bias.
i_bias_free: the incidence after correction of the festive and weekly biases.
i_restored: the restored incidence obtained using the renewal equation.
Rt: the reproduction number Rt obtained by inverting the renewal equation.
Rt_CI95: 95% confidence interval radius for the value of Rt taking into account the variation of Rt when more days are added to the estimation.
seasonality: the weekly bias correction factors.
dates: a vector of dates corresponding to the incidence curve.
festive: boolean associated to each incidence value to check if it has been considered as a festive or anomalous day.
epsilon: normalized error curve obtained as (i_bias_free-i_restored)/i_restored^a.
power_a: the power, a, which appears in the above expression of the normalized error.
si_distr: values of the distribution of the serial interval used in the EpiInvert estimation.
shift_si_distr: shift of the above distribution of the serial interval si_distr.

Author(s)

Luis Alvarez lalvarez@ulpgc.es

References

[1] Alvarez, L.; Colom, M.; Morel, J.D.; Morel, J.M. Computing the daily reproduction number of COVID-19 by inverting the renewal equation using a variational technique. Proc. Natl. Acad. Sci. USA, 2021.

[2] Alvarez, Luis, Jean-David Morel, and Jean-Michel Morel. "Modeling COVID-19 Incidence by the Renewal Equation after Removal of Administrative Bias and Noise" Biology 11, no. 4: 540. 2022.

[3] Ritchie, H. et al. Coronavirus Pandemic (COVID-19), OurWorldInData.org. Available online: https://ourworldindata.org/coronavirus-source-data (accessed on 5 May 2022).

Examples

## load data on COVID-19 daily incidence up to 2022-05-05 for France, 
## and Germany (taken from the official government data) and for UK and 
## the USA taken from reference [3]
data(incidence)

## EpiInvert execution for USA with no festive days specification
## using the incidence 70 days in the past
res <- EpiInvert(incidence$USA,
"2022-05-05",
"1000-01-01",
select_params(list(max_time_interval = 70))
)

## Plot of the results
EpiInvert_plot(res)

## load data of festive days for France, Germany, UK and the USA
data(festives)

## EpiInvert execution for France with festive days specification using
## 70 days in the past 
res <- EpiInvert(incidence$FRA,"2022-05-05",festives$FRA,
                 select_params(list(max_time_interval = 70)))

## Plot of the incidence between "2022-04-01" and "2022-05-01"
EpiInvert_plot(res,"incid","2022-04-01","2022-05-01")

## load data of a serial interval
data("si_distr_data")

## EpiInvert execution for Germany using the uploaded serial interval shifted
## -2 days, using the incidence 70 days in the past
res <- EpiInvert(incidence$DEU,"2022-05-05",festives$DEU,
       EpiInvert::select_params(list(si_distr = si_distr_data,
       shift_si_distr=-2,max_time_interval = 70)))
       
## Plot of the serial interval used (including the shift)
EpiInvert_plot(res,"SI")     
       
## EpiInvert execution for UK changing the default values of the parametric
## serial interval (using a shifted log-normal) using 70 days in the past
res <- EpiInvert(incidence$UK,"2022-05-05",festives$UK,
       EpiInvert::select_params(list(mean_si = 11,sd_si=6,shift_si=-1,max_time_interval = 70))
       )
       
## Plot of the reproduction number Rt including an empiric 95\% confidence 
## interval of the variation of Rt. To calculate Rt on each day t, EpiInvert 
## uses the past days (t'<=t) and the future days (t'>t) when available. 
## Therefore, the EpiInvert estimate of Rt varies when there are more days 
## available. This confidence interval reflects the expected variation of Rt 
## as a function of the number of days after t available.
EpiInvert_plot(res,"R")

[Package EpiInvert version 0.3.1 Index]

EpiInvert estimates the reproduction number Rt and a restored incidence curve from the original daily incidence curve and the serial interval distribution. EpiInvert also corrects the festive and weekly biases present in the registered daily incidence.