algo.hmm.Rd
This function implements on-line HMM detection of outbreaks based on
the retrospective procedure described in Le Strat and Carret (1999).
Using the function msm
(from package msm) a specified HMM
is estimated, the decoding problem, i.e. the most probable state
configuration, is found by the Viterbi algorithm and the most
probable state of the last observation is recorded. On-line
detection is performed by sequentially repeating this procedure.
Warning: This function can be very slow - a more efficient implementation would be nice!
algo.hmm(disProgObj, control = list(range=range, Mtilde=-1,
noStates=2, trend=TRUE, noHarmonics=1,
covEffectEqual=FALSE, saveHMMs = FALSE, extraMSMargs=list()))
object of class disProg (including the observed and the state chain)
control object:
range
determines the desired time points which should be evaluated. Note that opposite to other surveillance methods an initial parameter estimation occurs in the HMM. Note that range should be high enough to allow for enough reference values for estimating the HMM
Mtilde
number of observations back in time
to use for fitting the HMM (including
the current observation). Reasonable values are a multiple of
disProgObj$freq
, the default is
Mtilde=-1
, which means to use all possible
values - for long series this might take very long time!
noStates
number of hidden states in the HMM
-- the typical choice is 2. The initial rates are set
such that the noStates
'th state is the one
having the highest rate. In other words: this state is considered
the outbreak state.
trend
Boolean stating whether a linear time trend exists, i.e. if TRUE
(default) then \(\beta_j \neq 0\)
noHarmonics
number of harmonic waves to include in the linear predictor. Default is 1.
covEffectEqual
see details
saveHMMs
Boolean, if TRUE
then the result of the fitted HMMs is saved. With this option the function can also be used to analyse data retrospectively. Default option is FALSE
extraMSMArgs
A named list with additional arguments to send to the msm
HMM fitting function. Note that the msm
arguments formula
, data
, qmatrix
, hmodel
, hcovariates
and hconstraint
are automatically filled by algo.hmm
, thus these should NOT be modified.
algo.hmm
gives a list of class survRes
which includes the
vector of alarm values for every timepoint in range
. No
upperbound
can be specified and is put equal to zero.
The resulting object contains a slot control$hmm
, which
contains the msm
object with the fitted HMM.
For each time point t the reference values values are extracted. If the number of requested values is larger than the number of possible values the latter is used. Now the following happens on these reference values:
A noState
-State Hidden Markov Model (HMM) is used based on
the Poisson distribution with linear predictor on the log-link
scale. I.e. $$Y_t | X_t = j \sim Po(\mu_t^j),$$ where $$\log(\mu_t^j) = \alpha_j + \beta_j\cdot
t + \sum_{i=1}^{nH} \gamma_j^i \cos(2i\pi/freq\cdot (t-1)) +
\delta_j^i \sin(2i\pi/freq\cdot (t-1))$$
and \(nH=\)noHarmonics
and \(freq=12,52\) depending on the
sampling frequency of the surveillance data. In the above \(t-1\) is
used, because the first week is always saved as t=1
, i.e. we
want to ensure that the first observation corresponds to cos(0) and
sin(0).
If covEffectEqual
then all covariate effects parameters are
equal for the states, i.e. \(\beta_j=\beta, \gamma_j^i=\gamma^i,
\delta_j^i=\delta^i\) for all \(j=1,...,noState\).
In case more complicated HMM models are to be fitted it is possible to
modify the msm
code used in this function. Using
e.g. AIC
one can select between different models (see the
msm package for further details).
Using the Viterbi algorithms the most probable state configuration
is obtained for the reference values and if the most probable
configuration for the last reference value (i.e. time t) equals
control$noOfStates
then an alarm is given.
Note: The HMM is re-fitted from scratch every time, sequential updating schemes of the HMM would increase speed considerably! A major advantage of the approach is that outbreaks in the reference values are handled automatically.
M. Höhle
Y. Le Strat and F. Carrat, Monitoring Epidemiologic Surveillance Data using Hidden Markov Models (1999), Statistics in Medicine, 18, 3463--3478
I.L. MacDonald and W. Zucchini, Hidden Markov and Other Models for Discrete-valued Time Series, (1997), Chapman & Hall, Monographs on Statistics and applied Probability 70
#Simulate outbreak data from HMM
set.seed(123)
counts <- sim.pointSource(p = 0.98, r = 0.8, length = 3*52,
A = 1, alpha = 1, beta = 0, phi = 0,
frequency = 1, state = NULL, K = 1.5)
if (FALSE) {
#Do surveillance using a two state HMM without trend component and
#the effect of the harmonics being the same in both states. A sliding
#window of two years is used to fit the HMM
surv <- algo.hmm(counts, control=list(range=(2*52):length(counts$observed),
Mtilde=2*52,noStates=2,trend=FALSE,
covEffectsEqual=TRUE,extraMSMargs=list()))
plot(surv,legend=list(x="topright"))
}
if (require("msm")) {
#Retrospective use of the function, i.e. monitor only the last time point
#but use option saveHMMs to store the output of the HMM fitting
surv <- algo.hmm(counts,control=list(range=length(counts$observed),Mtilde=-1,noStates=2,
trend=FALSE,covEffectsEqual=TRUE, saveHMMs=TRUE))
#Compute most probable state using the viterbi algorithm - 1 is "normal", 2 is "outbreak".
viterbi.msm(surv$control$hmm[[1]])$fitted
#How often correct?
tab <- cbind(truth=counts$state + 1 ,
hmm=viterbi.msm(surv$control$hmm[[1]])$fitted)
table(tab[,1],tab[,2])
}