Simulate daily counts with no outbreak

Simulates daily counts from a Poisson or negative binomial model with a trend, a seasonal pattern and a day-of-week pattern, after Noufaily et al. (2019). Use it to make a series with a known truth.

Usage

simulate_baseline_data(
  start_date,
  end_date,
  seasonal_pattern_n,
  weekly_pattern_n,
  alpha,
  beta,
  gamma_1,
  gamma_2,
  gamma_3,
  gamma_4,
  phi,
  shift_1
)

Arguments

start_date, end_date

The first and last day, as a Date or a "YYYY-MM-DD" string.

seasonal_pattern_n

The number of seasonal harmonics: 0 for none, 1 for an annual pattern, 2 to add a half-year harmonic.

weekly_pattern_n

The number of weekly harmonics.

alpha

The log of the baseline count.

beta

The trend on the log scale, per day.

gamma_1, gamma_2

The cosine and sine coefficients of the seasonal term.

gamma_3, gamma_4

The cosine and sine coefficients of the weekly term.

phi

The dispersion. 1 gives a Poisson count, and above 1 a negative binomial with variance phi * mu. Below 1 gives NA counts and a warning.

shift_1

A shift in days, added to t, that moves the peaks.

Value

A csfmt_rts_data_v1 with one row per day. Its columns include date, time (t), wday (1 is Sunday), mu, the mean, and n, the count.

Details

On day t, from 1, the log of the mean is alpha + beta * (t + shift_1) plus a seasonal term and a weekly term. With u = 2 * pi * (t + shift_1) / p, each term sums a * cos(l * u) + b * sin(l * u) over l = 1, ..., n:

• seasonal: p = 364, n = seasonal_pattern_n, a = gamma_1, b = gamma_2,

• weekly: p = 7, n = weekly_pattern_n, a = gamma_3, b = gamma_4.

With both n at 0, the log of the mean is alpha + beta * t. With seasonal_pattern_n > 0, weekly_pattern_n = 0 still adds a weekly term, because 1:0 in R is c(1, 0).

References

Noufaily A, Enki DG, Farrington P, Garthwaite P, Andrews N, Charlett A. An improved algorithm for outbreak detection in multiple surveillance systems. Statistics in Medicine. 2013.

See also

vignette("csalert", package = "csalert"), which simulates a series with a known outbreak.

Other data simulation functions: add_holiday_effect(), simulate_seasonal_outbreak_data(), simulate_spike_outbreak_data()

Examples

library(data.table)
set.seed(4)
baseline <- simulate_baseline_data(
  start_date = as.Date("2018-01-01"),
  end_date = as.Date("2019-12-31"),
  seasonal_pattern_n = 1,
  weekly_pattern_n = 1,
  alpha = 3,
  beta = 0,
  gamma_1 = 0.8,
  gamma_2 = 0.6,
  gamma_3 = 0.8,
  gamma_4 = 0.4,
  phi = 4,
  shift_1 = 29
)
print(baseline[, .(date, wday, mu, n)])
#>            date  wday        mu     n
#>          <Date> <num>     <num> <int>
#>   1: 2018-01-01     2  66.95830    64
#>   2: 2018-01-02     3  31.40319    32
#>   3: 2018-01-03     4  22.23175    19
#>   4: 2018-01-04     5  30.85457    37
#>   5: 2018-01-05     6  65.65786    72
#>  ---                                 
#> 726: 2019-12-27     6  64.73862    68
#> 727: 2019-12-28     7 119.96484   109
#> 728: 2019-12-29     1 121.67202   139
#> 729: 2019-12-30     2  66.95830    60
#> 730: 2019-12-31     3  31.40319    41