Page 205 - Special Topic Session (STS) - Volume 4

STS580 Ross Sparks et. al

An approach to monitoring multivariate time

between events
Ross Sparks, Aditya Joshi, Cecile Paris, Sarvnaz Karimi
Data61, CSIRO Sydney, Australia

Abstract
This paper focuses on monitor plans aimed at the early detection of the
increase in the frequency of events. The literature recommends either
monitoring the Time Between Events (TBE) if events are rare or counting the
number of events per unit non-overlapping time intervals if events are not
rare. However, recently, work has suggested that monitoring counts in
preference to TBE is not recommended even when counts are moderately
high. Monitoring TBE is the real-time option for outbreak detection, because
outbreak information is accumulated whenever an event occurs. This is
preferred to waiting for the end of a period to count events. If the TBE reduces
significantly, then the incidence of these events increases significantly. This
paper explores multivariate TBE options (e.g., the time between flu events at
all the hospitals in a state of Australia). This will be compared with the
approach to monitoring counts. We consider the case when TBEs are Weibull
distributed in situations where daily counts are moderately low. The paper will
discuss and compare the approaches based on TBEs and counts.

Keywords
monitoring; multivariate; counts; time between events; statistical process
control

1. Introduction
Dealing with multivariate time between events is challenging because
events do not necessarily occur simultaneously in time for the population of
interest. The application considered in the paper is symptoms that people in
social media expressed that they are suffering from in terms of poor health
outcomes. These symptoms are taken as diarrhoea, vomiting, headache and
generally feeling unwell. Such symptoms are generally easy to self-diagnose.
The only time these occur simultaneously is when the same person expresses
that they are suffering from all of these, and in the dataset we considered, this
never occurred. The fact that people seldom expressed that they were
suffering from a combination of symptoms increases the challenge in dealing
with these in a multivariate way. This was the case in our application.
The option of imputing a censored estimated value for those events that
did not occur during the timing of one of these events was considered, but
this option would make finding an outbreak difficult when the imputed values
are based on the in-control distribution. One option was to impute these
based on the out-of-control model, but we don’t know the nature of this

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