algo.cusum.Rd
Approximate one-side CUSUM method for a Poisson variate based on the cumulative sum of the deviation between a reference value k and the transformed observed values. An alarm is raised if the cumulative sum equals or exceeds a prespecified decision boundary h. The function can handle time varying expectations.
algo.cusum(disProgObj, control = list(range = range, k = 1.04, h = 2.26,
m = NULL, trans = "standard", alpha = NULL))
object of class disProg (including the observed and the state chain)
control object:
range
determines the desired time points which should be evaluated
k
is the reference value
h
the decision boundary
m
how to determine the expected number of cases -- the following arguments are possible
numeric
a vector of values having the
same length as range
. If a single numeric
value is specified then this value is replicated
length(range)
times.
NULL
A single value is estimated by
taking the mean of all observations previous to
the first range
value.
"glm"
A GLM of the form $$\log(m_t)
= \alpha + \beta t + \sum_{s=1}^S (\gamma_s
\sin(\omega_s t) + \delta_s \cos(\omega_s t)),$$
where \(\omega_s = \frac{2\pi}{52}s\) are the
Fourier frequencies is fitted. Then this model is
used to predict the range
values.
trans
one of the following transformations (warning: Anscombe and NegBin transformations are experimental)
rossi
standardized variables z3 as proposed by Rossi
standard
standardized variables z1 (based on asymptotic normality) - This is the default.
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
parameter of the negative binomial distribution, s.t. the variance is \(m+\alpha *m^2\)
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"
.
The upperbound
entry shows for each time instance the number of diseased individuals
it would have taken the cusum to signal. Once the CUSUM signals no resetting is applied, i.e.
signals occurs until the CUSUM statistic again returns below the threshold.
In case control$m="glm"
was used, the returned
control$m.glm
entry contains the fitted "glm"
object.
This implementation is experimental, but will not be developed further.
M. Paul and M. Höhle
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
# 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)