Effect of Dependency in Systems for Multivariate Surveillance

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.

Methodological challenges to multivariate syndromic surveillance: a case study using Swiss animal health data

“…in dairy cows) is best conceived as a chain of events through time: we may first observe an increase in the number of animals presenting fever, followed a few weeks later by an increase in the number of abortions reported, and even later an increase in the number of carcasses condemned at slaughter. The optimal surveillance method may depend on both the dependency between the monitored processes and the correlation between the time points when the changes occur [82]. For example, parallel surveillance works well when the changes occur far apart but a dimension reduction approach [83] is optimal when the changes occur very close in time to one another.…”

Hotelling's T 2 Method in Multivariate On-Line Surveillance: On the Delay of an Alarm

“…A simulation study reveal the following, regarding the CED(t 1 ,t 2 ) of the T2 method (the complete study is presented in (Andersson 2007)). Below, CED curves for ρ={0, 0.5} are presented.…”

Author's Response

“…The relation between the change points is important, as described by Andersson (2008). It makes a great difference whether the parameters change simultaneously or not.…”