Farrington flexible algorithm

Formula: a quasi-Poisson GLM with overdispersion fitted to the reference baseline – the same calendar window in each of the previous baseline_years years, plus/minus reference_window time units – and a 2/3-power upper threshold at the current point.

Usage

Farsig(
  counts,
  baseline_years = 5,
  reference_window = 3,
  period = 52,
  alpha = 0.005,
  reweight = TRUE,
  trend = TRUE
)

Arguments

counts

Full count series; the LAST element is the point tested.

baseline_years

Number of previous years b in the baseline.

reference_window

Half-width w around each anniversary.

period

Observations per year (52 for weekly data).

alpha

Two-sided level for the threshold.

reweight

Apply the Anscombe-residual re-weighting pass.

trend

Include the linear time trend.

Value

List with estimate, observed, expected, threshold, alarm, phi, phi_raw, trend_coef, score, nbaseline, n, method.

Details

With log mu_i = alpha + beta t_i, dispersion phi = max(1, sum w_i (y_i - mu_i)^2 / mu_i / (n - p)), prediction mu0 and its response-scale standard error se0, the threshold is (Farrington et al 1996 sec. 2.3)

  tau = phi + se0^2 / mu0
  se  = sqrt(4/9 mu0^(1/3) tau)
  U   = (mu0^(2/3) + z_{1-alpha/2} se)^(3/2)

and an alarm is raised when the current count exceeds U. When reweight is set the fit is repeated with Farrington weights from standardised Anscombe residuals a_i = 1.5 (y^(2/3) mu^(-1/6) - mu^(1/2)) / sqrt(phi (1 - h_i)), down-weighting past outbreaks by a_i^-2. Following Noufaily et al (2013) the trend term is retained whether or not it is significant.

References

Farrington, Andrews, Beale & Catchpole (1996), JRSS-A 159(3):547-563, doi:10.2307/2983331; Noufaily, Enki, Farrington, Garthwaite, Andrews & Charlett (2013), Statistics in Medicine 32(7):1206-1222, doi:10.1002/sim.5595.

Examples

set.seed(1)
Farsig(rpois(300, 10))
#> $estimate
#> [1] 0.09317964
#> 
#> $observed
#> [1] 10
#> 
#> $expected
#> [1] 8.982152
#> 
#> $threshold
#> [1] 19.90566
#> 
#> $alarm
#> [1] 0
#> 
#> $phi
#> [1] 1.085141
#> 
#> $phi_raw
#> [1] 1.085141
#> 
#> $trend_coef
#> [1] -7.524089e-06
#> 
#> $score
#> [1] 0.09317964
#> 
#> $nbaseline
#> [1] 35
#> 
#> $n
#> [1] 300
#> 
#> $method
#> [1] "Farrington flexible algorithm"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"