algo.cusum {surveillance}R Documentation

CUSUM method

Description

Approximate one-side CUSUM method for a Poisson variate based on the cumulative sum of the deviation between a reference value k and the (standardized) observed values. An alarm is raised if the cumulative sum equals or exceeds a prespecified decision boundary h.

Usage


  algo.cusum(disProgObj, control = list(range = range, k = 1.04, h = 2.26, 
             m = NULL, trans = "standard", alpha = NULL))

Arguments

disProgObj object of class disProg (including the observed and the state chain).
control control object:
range
determines the desired time points which should be evaluated
k
is the reference value
h
the decision boundary
m
expected number of cases – if NULL then estimated from the data
trans
one of the following transformations (warning: anscombe and negbin transformations are experimental)
rossi
compute standardized variables z3 as proposed by Rossi
standard
compute standardized variables z1 (based on asympotic normality)
anscombe
anscombe residuals – experimental
anscombe2nd
anscombe residuals as in Pierce and Schafer (1986) based on 2nd order approximation of E(X) – experimental
pearsonNegBin
compute Pearson residuals for NegBin – experimental
anscombeNegBin
anscombe residuals for NegBin – experimental
none
no transformation
alpha
normal-bracket50bracket-normal
parameter of the negative binomial distribution, s.t. the variance is parameter of the negative binomial distribution, s.t. the variance is eqn

Details

The implementation is still experimental

Value

survRes algo.cusum gives a list of class survRes which includes the vector of alarm values for every timepoint in range and the vector of cumulative sums for every timepoint in range for the system specified by k and h, the range and the input object of class disProg.

Author(s)

Source

References

G. Rossi, L. Lampugnani and M. Marchi (1999), An approximate CUSUM procedure for surveillance of health events, Statistics in Medicine, 18, 2111–2122

D. A. Pierce and D. W. Schafer (1986), Residuals in Generalized Linear Models, Journal of the American Statistical Association, 81, 977–986

See Also

Examples


    # Xi ~ Po(5), i=1,...,500
    disProgObj <- create.disProg(week=1:500, observed= rpois(500,lambda=5),
                                    state=rep(0,500))
    # there should be no alarms as mean doesn't change
    res <- algo.cusum(disProgObj, control = list(range = 100:500,trans="anscombe"))
    plot(res)
        
    # simulated data 
    disProgObj <- sim.pointSource(p = 1, r = 1, length = 250,
                              A = 0, alpha = log(5), beta = 0, phi = 10,
                              frequency = 10, state = NULL, K = 0)                           
    plot(disProgObj)
    
    # Test week 200 to 250 for outbreaks
    surv <- algo.cusum(disProgObj, control = list(range = 200:250))
    plot(surv)

[Package surveillance version 0.9-2 Index]