**Resarch Reports**
# No 2007:1:

Effect of dependency in systems for multivariate surveillance

*Eva Andersson *()

**Abstract:** In many situations we need a system for detecting changes
early. Examples are early detection of disease outbreaks, of patients at
risk and of financial instability. In influenza outbreaks, for example, we
want to detect an increase in the number of cases. Important indicators
might be the number of cases of influenza-like illness and pharmacy sales
(e.g. aspirin). By continually monitoring these indicators, we can early
detect a change in the process of interest. The methodology of statistical
surveillance is used. Often, the conclusions about the process(es) of
interest is improved if the surveillance is based on several indicators.
Here three systems for multivariate surveillance are compared. One system,
called LRpar, is based on parallel likelihood ratio methods, since the
likelihood ratio has been shown to have several optimality properties. In
LRpar, the marginal density of each indicator is monitored and an alarm is
called as soon as one of the likelihood ratios exceeds its alarm limit. The
LRpar is compared to an optimal alarm system, called LRjoint, which is
derived from the full likelihood ratio for the joint density. The
performances of LRpar and LRjoint are compared to a system where the
Hotellings T2 is monitored. The evaluation is made using the delay of a
motivated alarm, as a function of the times of the changes. The effect of
dependency is investigated: both dependency between the monitored processes
and correlation between the time points when the changes occur. When the
first change occurs immediately, the three methods work rather similarly,
for independent processes and zero correlation between the change times.
But when all processes change later, the T2 has much longer delay than
LRjoint and LRpar. This holds both when the processes are independent and
when they have a positive covariance. When we assume a positive correlation
between the change times, the LRjoint yields a shorter delay than LRpar
when the changes actually do occur simultaneously, whereas the opposite is
true when the changes do actually occur at different time point.

**Keywords:** Multivariate; Surveillance; Dependency; Optimal; Covariance; Likelihood ratio; (follow links to similar papers)

**JEL-Codes:** C10; (follow links to similar papers)

30 pages, January 1, 2007

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