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CUSUM surveillance of counts

Source: R/trn.R
cusrv.Rd

Watches a series of counts for a rise above what is expected: the cumulative sum \(s_t = \max(0, s_{t-1} + z_t - k)\) of the standardised excess \(z_t\) raises an alarm where \(s_t \ge h\). The expected counts are given (expd), or are the mean of the counts before start, the first period watched. z is (y - m) / sqrt(m) ("std"), Rossi's transform (y - 3 m + 2 sqrt(y m)) / (2 sqrt(m)) ("rossi"), Anscombe's 1.5 (y^(2/3) - m^(2/3)) / m^(1/6) ("anscombe") or the count itself ("none", for k and h on the count scale). With reset the sum starts again from 0 after an alarm.

Usage

cusrv(
  y,
  expd = NULL,
  start = NULL,
  k = 1.04,
  h = 2.26,
  trans = "std",
  reset = FALSE
)

Arguments

y

The counts: numbers from 0.

expd

NULL, or the expected count of each period: positive numbers.

start

Without expd, the first period watched: one whole number from 2.

k

The reference value subtracted each period: one number.

h

The decision limit: one positive number.

trans

The standardisation: "std", "rossi", "anscombe" or "none".

reset

TRUE to start again after each alarm.

Value

A data frame, one row per period watched: i, its position; y; expd; z; the sum s; and alarm.

References

Page, E. S. (1954). Continuous inspection schemes. Biometrika, 41(1-2), 100-115. doi:10.1093/biomet/41.1-2.100

Rossi, G., Lampugnani, L. and Marchi, M. (1999). An approximate CUSUM procedure for surveillance of health events. Statistics in Medicine, 18(16), 2111-2122. doi:10.1002/(SICI)1097-0258(19990830)18:16<2111::AID-SIM171>3.0.CO;2-Q

Examples

y <- c(10, 12, 9, 11, 10, 13, 19, 22, 25, 12)
cusrv(y, start = 6)
#>    i  y expd         z        s alarm
#> 1  6 13 10.4 0.8062258 0.000000 FALSE
#> 2  7 19 10.4 2.6667468 1.626747 FALSE
#> 3  8 22 10.4 3.5970073 4.183754  TRUE
#> 4  9 25 10.4 4.5272678 7.671022  TRUE
#> 5 10 12 10.4 0.4961389 7.127161  TRUE
cusrv(y, expd = rep(11, 10), trans = "rossi", reset = TRUE)
#>     i  y expd          z        s alarm
#> 1   1 10   11 -0.3051028 0.000000 FALSE
#> 2   2 12   11  0.2982325 0.000000 FALSE
#> 3   3  9   11 -0.6181361 0.000000 FALSE
#> 4   4 11   11  0.0000000 0.000000 FALSE
#> 5   5 10   11 -0.3051028 0.000000 FALSE
#> 6   6 13   11  0.5904378 0.000000 FALSE
#> 7   7 19   11  2.2483195 1.208320 FALSE
#> 8   8 22   11  3.0321034 3.200423  TRUE
#> 9   9 25   11  3.7939546 2.753955  TRUE
#> 10 10 12   11  0.2982325 0.000000 FALSE