Estimate the peak date of an incidence curve using bootstrap

Source: R/estimate_peak.R

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.

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

Arguments

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.

Value

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

Details

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

See also

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

Author

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

Examples


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")

})}
#> > i <- incidence(fluH7N9_china_2013$date_of_onset)
#> 10 missing observations were removed.
#> > i
#> <incidence object>
#> [126 cases from days 2013-02-19 to 2013-07-27]
#> 
#> $counts: matrix with 159 rows and 1 columns
#> $n: 126 cases in total
#> $dates: 159 dates marking the left-side of bins
#> $interval: 1 day
#> $timespan: 159 days
#> $cumulative: FALSE
#> 
#> > plot(i)

#> > x <- bootstrap(i)
#> > x
#> <incidence object>
#> [126 cases from days 2013-02-27 to 2013-05-21]
#> 
#> $counts: matrix with 84 rows and 1 columns
#> $n: 126 cases in total
#> $dates: 84 dates marking the left-side of bins
#> $interval: 1 day
#> $timespan: 84 days
#> $cumulative: FALSE
#> 
#> > plot(x)

#> > peak_data <- estimate_peak(i)
#> > peak_data
#> $observed
#> [1] "2013-04-03"
#> 
#> $estimated
#> [1] "2013-04-06"
#> 
#> $ci
#>         2.5%        97.5% 
#> "2013-03-29" "2013-04-17" 
#> 
#> $peaks
#>   [1] "2013-04-03" "2013-04-08" "2013-04-14" "2013-04-08" "2013-04-08"
#>   [6] "2013-04-14" "2013-04-01" "2013-04-11" "2013-04-03" "2013-04-10"
#>  [11] "2013-04-06" "2013-03-29" "2013-04-03" "2013-04-12" "2013-04-06"
#>  [16] "2013-04-17" "2013-04-12" "2013-04-01" "2013-04-08" "2013-04-11"
#>  [21] "2013-04-01" "2013-04-06" "2013-04-10" "2013-04-11" "2013-04-06"
#>  [26] "2013-04-06" "2013-04-06" "2013-04-11" "2013-04-06" "2013-04-03"
#>  [31] "2013-04-01" "2013-04-17" "2013-03-29" "2013-04-06" "2013-04-06"
#>  [36] "2013-04-03" "2013-04-06" "2013-04-15" "2013-04-06" "2013-04-10"
#>  [41] "2013-04-14" "2013-04-10" "2013-04-17" "2013-04-11" "2013-04-03"
#>  [46] "2013-04-06" "2013-04-03" "2013-04-06" "2013-04-06" "2013-04-10"
#>  [51] "2013-04-03" "2013-04-03" "2013-04-08" "2013-04-08" "2013-04-11"
#>  [56] "2013-04-03" "2013-04-06" "2013-04-08" "2013-04-01" "2013-04-11"
#>  [61] "2013-03-29" "2013-04-10" "2013-04-12" "2013-04-04" "2013-04-03"
#>  [66] "2013-03-29" "2013-04-03" "2013-04-10" "2013-04-10" "2013-04-12"
#>  [71] "2013-04-06" "2013-03-29" "2013-04-14" "2013-03-29" "2013-04-03"
#>  [76] "2013-04-13" "2013-03-29" "2013-04-01" "2013-04-01" "2013-04-13"
#>  [81] "2013-04-03" "2013-04-03" "2013-04-06" "2013-04-03" "2013-04-14"
#>  [86] "2013-04-13" "2013-04-10" "2013-04-03" "2013-04-12" "2013-04-03"
#>  [91] "2013-04-11" "2013-04-01" "2013-04-11" "2013-04-10" "2013-04-01"
#>  [96] "2013-04-01" "2013-04-03" "2013-04-06" "2013-04-17" "2013-04-06"
#> 
#> > summary(peak_data$peaks)
#>         Min.      1st Qu.       Median         Mean      3rd Qu.         Max. 
#> "2013-03-29" "2013-04-03" "2013-04-06" "2013-04-06" "2013-04-11" "2013-04-17" 
#> > plot(i) + geom_vline(xintercept = peak_data$ci, col = "red", lty = 2)

#> > df <- data.frame(peak = peak_data$peaks)
#> > plot(i) + geom_density(data = df, aes(x = peak, y = 10 * ..scaled..), 
#> +     alpha = 0.2, fill = "red", color = "red")
#> Warning: The dot-dot notation (`..scaled..`) was deprecated in ggplot2 3.4.0.
#> ℹ Please use `after_stat(scaled)` instead.
#> ℹ The deprecated feature was likely used in the incidence package.
#>   Please report the issue at <https://github.com/reconhub/incidence/issues>.