Through a review of surveillance literature and interaction with surveillance practitioners we have decomposed the task of aberrancy detection into five main sub-tasks: (1) specify detection goal, (2) define data structure for analysis, (3) organize observed data, (4) forecast expected data, and (5) compare observation and expectation. The decomposition is shown in .
Task decomposition of aberrancy detection. Ellipses indicate tasks.
Specification of a detection goal elicits knowledge of the expected aberrancy, and selection of a data structure for analysis attempts to structure the data in a manner that will facilitate aberrancy detection. The elicited knowledge and defined data structure both inform the selection of appropriate methods to complete the subsequent three sub-tasks. In the remainder of this section, we describe each sub-task and begin to consider the knowledge used to select methods for sub-tasks.
1. Specify a Detection Goal
The detection goal defines the type of aberrancy one intends to identify and the relative importance of performance characteristics such as sensitivity. In some situations, it may be possible to describe the expected aberrancy in detail, whereas in other situations very little may be known about the aberrancy that one is attempting to detect. Either way, this information helps to select appropriate methods. For example, knowledge of the expected spatial pattern may allow one to select a method optimized to detect that type of pattern [Waller & Jacquez, 1995
], whereas limited knowledge of the expected aberrancy would suggest selection of a method with no specific alternate hypothesis [Wong et al., 2002
Our initial approach to describing the expected aberrancy identifies temporal, spatial and attribute aspects of the aberrancy. The temporal aspect includes the rate and magnitude of change, while the spatial aspect includes the extent and scale of clustering. The attribute aspect of the expected aberrancy refers to those attributes of the data, other than space and time, that may be associated with the aberrancy. For example, the expected aberrancy might be more apparent in a specific set of diagnostic categories, in an age group, or in an occupation.
Performance characteristics of aberrancy detection include sensitivity, timeliness, and predictive value [Frisen, 1992
]. Generally speaking, one performance characteristic is enhanced at the expense of another. Depending on the situation it may be possible to identify which performance characteristics are most important, or it may be desirable to weight all characteristics equally.
2. Define a Data Structure for Analysis
Data structure in this context means the stratification over attributes, the temporal resolution, and the spatial resolution of the data. The detection goal should inform the choice of data structure on the premise that knowledge of the expected aberrancy and desired performance characteristics can focus the aberrancy detection task towards specific aspects of the data.
If one is able to clearly define a detection goal, then this goal may strongly suggest a preferable data structure. For example, if the expected aberrancy is known to have a rapid onset, and timeliness of detection is an important performance characteristic, then it would be preferable to organize the data into high resolution temporal categories. Similarly, if the expected aberrancy is known to present as a spatial cluster, then it would be preferable to select a spatial resolution and zoning appropriate to the expected scale of clustering. Stratification over attributes refers to the categorization of data into groups based upon values of one or more variables. At a minimum, the detection goal should suggest stratification according to the main variable of interest (e.g., syndrome, diagnosis, or risk behaviour), but the detection goal may also suggest additional attributes for stratification. Choice of data structure must also take into count the frequency of events. At some combination of stratification and space-time resolution, events will become sparse. This may make it more difficult to detect aberrancy, and will influence the types of analytic methods that can be used.
In cases where the detection goal is not clearly defined, it may not be possible to clearly define a preferable data structure to limit the aberrancy detection task. As a result it may be necessary to use analytic methods that attempt to detect aberrancies over many attribute strata [Wong, Moore et al., 2002
] or multiple spatial and temporal resolutions [Kulldorff, 1997
3. Organize Observed Data
The observed data must be transformed into the structure defined for the analysis. This might be a trivial task that simply requires aggregating individual records into groups using look-up tables. For example, aggregating hospital visit records to syndrome and home address groups on the basis of ICD and ZIP codes. However, if the transformation from the raw data to the desired data structure is not so straightforward, this may require more complex methods. For example, classification of hospital visit records to syndromes using free-text chief complaint or electronic medical record data requires the use of methods more advanced than aggregation. Similarly, classification of home street address to ZIP requires more than a simple look-up function.
If the transformation from raw data to the structure required for analysis is straightforward, then the methods used to accomplish the transformation will likely have little effect on the overall aberrancy detection task. However, if approaches such as classification or georeferencing are required to transform the data, then the choice of methods may influence the overall aberrancy detection by introducing random or systematic error into the data.
4. Forecast Expected Data
Most approaches to aberrancy detection require a measure of expectation to which an observed value can be compared. The expected measure is usually derived from historical data, and often consists of a point estimate and possibly also a measure of variation around the point estimate. For example, time-series methods use moving average and autoregressive models to provide one-step-ahead forecasts and variance estimates. Other forecast methods for aspatial data include calculation of an arithmetic average (and variance) from historical values, and multiplication of a region-wide rate by a local measure of risk such as population.
Forecast methods for spatial data usually rely on one of two approaches. The first approach is to divide the region into tracts, and then use aspatial forecast methods for each tract [Raubertas, 1989
]. The second approach is to compute a single statistic of spatial or space-time clustering for the entire region, and then derive a forecast for that statistic [Rogerson, 1997
Selection of a forecasting method should be influenced by the detection goal, the characteristics of the observed data, and the method that will be used to compare observation and expectation. As an example of the influence of data characteristics on method selection, time-series methods are most appropriately used with data that satisfy a number of conditions (e.g., stationary, Gaussian distribution), and time-series methods are difficult to apply if there are missing values. In terms of the detection goal, it may be important to note that time-series methods incorporate immediately previous observations into the forecast and therefore the forecast value can quickly adjust to changes in the observed value. This adjustment of the expected value may affect detection characteristics.
5. Compare Observation and Expectation
Once observed and expected measures are in hand, there are many possible approaches to identifying aberrancy. The simplest approach, exemplified by the control chart, detects aberrancy if the observed measure exceeds the expected point estimate by some multiple of the variance of the point estimate. A similar approach is also used to compare observed values to expected values obtained through time-series forecasting methods, with the main difference being that the threshold is generally constant over time for a control chart, but varies over time in the time-series approach.
Another approach is to maintain a state variable of aberrancy, which is updated after each comparison of observation to expectation. The state variable accumulates deviation from expectation over time, and following each update, the variable is compared to a decision threshold, which is determined on the basis of desired performance characteristics as defined by the detection goal. A number of methods use this approach including the cumulative sum [Page, 1954
], cumulative score [Wolter, 1987
], and the sets method [Chen, 1978
Methods used for spatial data are tightly linked to the approach used to forecast expected values. If a single expected measure of spatial or space-time clustering is calculated for the entire region, then this measure can be compared to the observed measure using a control chart or aberrancy state variable [Rogerson, 1997
]. If expected measures are calculated for each tract within a region, then two approaches are possible. The first approach is to apply a separate control chart or aberrancy state method within each tract, and then make an aberrancy decision after correcting for the multiple comparisons made by looking at the tracts separately [Raubertas, 1989
]. The second approach is to use a method that identifies focussed clustering of deviation from expectation over space and/or time among the tracts. An aberrancy decision is then made if detected clusters are unlikely to have occurred by chance [Kulldorff, 1997
The selection and configuration of a method to compare observation to expectation should be based upon the detection goal and the characteristics of the data. For example, the expected aberrancy may be known to exhibit focussed spatial clustering at a known scale but at unknown location. This detection goal suggests that the data should be structured at an appropriate scale, and a spatial method optimized for detection of focussed clustering should be selected. The frequency of the observed events may provide further direction in selection among candidate methods.