R0 (version 1.1-2)

est.R0.ML: Estimate the reproduction number by maximum likelihood

Description

Estimate the reproduction number by maximum likelihood

Usage

est.R0.ML(epid, GT, t = NULL, begin = NULL, end = NULL, date.first.obs = NULL, 
    time.step = 1, range = c(0.01, 50), impute.values = FALSE, 
    checked = FALSE, ...)

Arguments

epid

the epidemic curve

GT

generation time distribution

t

Vector of dates at which incidence was calculated

begin

At what time estimation begins

end

Time at which to end computation

date.first.obs

Optional date of first observation, if t not specified

time.step

Optional. If date of first observation is specified, number of day between each incidence observation

range

Range in which the maximum must be looked for

impute.values

Boolean value. If TRUE, will impute unobserved cases at the beginning of the epidemic to correct for censored data

checked

Internal flag used to check whether integrity checks were ran or not.

...

parameters passed to inner functions

Value

• A list with components:
• R
  The estimate of the reproduction ratio.
• conf.int
  The 95% confidence interval for the R estimate.
• epid
  the epidemic curve
• epid.orig
  Original epidemic data.
• GT
  generation time distribution
• begin
  At what time estimation begins
• begin.nb
  The number of the first day used in the fit.
• end
  Time at which to end computation
• end.nb
  The number of the las day used for the fit.
• pred
  Prediction on the period used for the fit.
• Rsquared
  Correlation coefficient between predicted curve (by fit.epid) and observed epidemic curve.
• call
  Call used for the function.
• method
  Method used for fitting.
• method.code
  Internal code used to designate method.

Details

For internal use. Called by est.R0. The principle of the methods described by White & all is to compute the expected number of cases in the future, and optimise to get R using a Poisson distribution.

References

White, L.F., J. Wallinga, L. Finelli, C. Reed, S. Riley, M. Lipsitch, and M. Pagano. "Estimation of the Reproductive Number and the Serial Interval in Early Phase of the 2009 Influenza A/H1N1 Pandemic in the USA." Influenza and Other Respiratory Viruses 3, no. 6 (2009): 267-276.

Examples

#Loading package
library(R0)

## Data is taken from paper by Nishiura for key transmission parameters of an institutional
## outbreak during the 1918 influenza pandemic in Germany)

data(Germany.1918)
mGT<-generation.time("gamma", c(2.45, 1.38))
est.R0.ML(Germany.1918, mGT, begin=1, end=27, range=c(0.01,50))
# Reproduction number estimate using  Maximum Likelihood  method.
# R :  1.307222[ 1.236913 , 1.380156 ]

res=est.R0.ML(Germany.1918, mGT, begin=1, end=27, range=c(0.01,50))
plot(res)

## no change in R with varying range 
## (dates here are the same index as before. Just to illustrate different use)
est.R0.ML(Germany.1918, mGT, begin="1918-09-29", end="1918-10-25", range=c(0.01,100))
# Reproduction number estimate using  Maximum Likelihood  method.
# R :  1.307249[ 1.236913 , 1.380185 ]