estimate_peak: Estimate the peak date of an incidence curve using bootstrap
In incidence: Compute, Handle, Plot and Model Incidence of Dated Events

Description Usage Arguments Details Value Author(s) See Also Examples

This function can be used to estimate the peak of an epidemic curve stored as incidence, using bootstrap. See bootstrap for more information on the resampling.

1	estimate_peak(x, n = 100, alpha = 0.05)

`x`	An `incidence` object.
`n`	The number of bootstrap datasets to be generated; defaults to 100.
`alpha`	The type 1 error chosen for the confidence interval; defaults to 0.05.

Input dates are resampled with replacement to form bootstrapped datasets; the peak is reported for each, resulting in a distribution of peak times. When there are ties for peak incidence, only the first date is reported.

Note that the bootstrapping approach used for estimating the peak time makes the following assumptions:

the total number of event is known (no uncertainty on total incidence)
dates with no events (zero incidence) will never be in bootstrapped datasets
the reporting is assumed to be constant over time, i.e. every case is equally likely to be reported

A list containing the following items:

observed: the peak incidence of the original dataset
estimated: the mean peak time of the bootstrap datasets
ci: the confidence interval based on bootstrap datasets
peaks: the peak times of the bootstrap datasets

Thibaut Jombart thibautjombart@gmail.com, with inputs on caveats from Michael Höhle.

bootstrap for the bootstrapping underlying this approach and find_peak to find the peak in a single incidence object.

if (require(outbreaks) && require(ggplot2)) { withAutoprint({
  i <- incidence(fluH7N9_china_2013$date_of_onset)
  i
  plot(i)

  ## one simple bootstrap
  x <- bootstrap(i)
  x
  plot(x)

  ## find 95% CI for peak time using bootstrap
  peak_data <- estimate_peak(i)
  peak_data
  summary(peak_data$peaks)

  ## show confidence interval
  plot(i) + geom_vline(xintercept = peak_data$ci, col = "red", lty = 2)

  ## show the distribution of bootstrapped peaks
  df <- data.frame(peak = peak_data$peaks)
  plot(i) + geom_density(data = df,
                         aes(x = peak, y = 10 * ..scaled..),
                         alpha = .2, fill = "red", color = "red")

})}