Evaluating disease progression

Disease surveillance involves the assessment of temporal case occurrence data in a spa- tial context in an effort to alert decision makers to unusual patterns in space and time (Pfeiffer 2004). Space-time clustering occurs when excess numbers of cases of disease are observed within small geographical locations at limited periods of time, which cannot be explained in terms of general excesses at those locations or times.

To study the space-time pattern of raccoon rabies in the north of the USA, Tinline et al. (2002) used the Knox test (Knox 1964). While the size of the wildlife populations involved in these studies (i.e. reported dead raccoons) may have been sufficiently large for variations to not affect the outcome of the Knox test, this is often not the cases when studying many other diseases of wildlife. Short-term changes in the spatial distribution of the population of interest, as a result of animal dispersion, immigration, population explosions or control activities, has the potential to introduce errors in the outcome of the space-time Knox test (N¨orstrom et al. 2000). This is because the spatio-temporal dynamic of the disease of interest would be modified, showing a greater number of cases in areas where the population is large (or has increased). In this situation, the space-time Knox

test would therefore detect changes in the spatial distribution of the population of interest rather than the presence of epizootic activities.

Compared with the Knox test, Kulldorff’s space-time scan statistic (Kulldorff 2001, Kulldorff 2006) is less prone to errors due to variations in space and time of the pop- ulation of interest since it allows for changes in population size to be accounted for. The space-time scan statistic has similar properties to the spatial scan statistic. It iden- tifies the location and time frame of identified spatio-temporal clusters without being af- fected by non-stationary spatial processes (McKenzie 1999). Although it is not a global test it identifies the locations of the most-likely spatio-temporal clusters as well as sec- ondary areas and time frames of high (or low) incidence. After collating the data at township/range/section area (TRS) level, Miller et al. (2007) used the space-time scan statistic to determine whether there were ‘spatial’ clusters of TB cases in hunter-harvested white-tailed deer in north eastern Michigan from 1995 to 2002. Throughout the study pe- riod, four areas were identified as showing greater space-time activities, of which three were located within the boundaries of the core area of TB infection. Comparing TRS inside and outside these high risk areas in regards to environmental variables, these au- thors concluded that space-time clustering of tuberculosis was related to natural cover, access to water and, to a lesser extent, human contact. Although the authors attempted to correct their analyses for the subjective selection of maximum size for the scan statis- tic window, specifying the critical time distance was not considered. This time distance is an important feature to consider as it depends on the latent period of the disease un- der investigation. Long latent periods reduce the power of the analysis as some exposed individuals will have moved away between exposure and diagnosis (Kulldorff 2001).

When conducting surveillance for wildlife diseases, details of the population at risk may be unavailable or manifest significant non-random geographic patterns due to nat- ural variations in species distribution or due to variations in the intensity and quality of census data collection. Kulldorff et al. (2003) extended the space-time scan statistic into a prospective space-time permutation scan statistic which allows disease clusters to be detected on the basis of case numbers. This approach does not require details of a control group or the population at risk, but instead evaluates changes in the geographic distribution of recent events comparing them with a historical baseline. In a study eval- uating the effectiveness of the spatial scan statistic as a prospective WNV surveillance

tool, Mostashari et al. (2003) applied this method to a data set comprised of details of dead birds collected in New York from 2001. Despite the limitations of an approach which relies on public reporting (see Section 2.3.2 for more details), analysing this in- formation in real time provided useful information which allowed interventions to reduce mosquito breeding activity to be undertaken four weeks before West Nile Virus was con- firmed in vertebrate hosts. A similar approach was used to retrospectively identify areas where enzootic activity of raccoon rabies were increased (i.e. space-time clusters) in New York state in 1997 – 2003 (Recuenco et al. 2007). The space-time permutation approach showed that increased enzootic activities occurred between 1997 and 2000 and were con- centrated into several foci of rabies activities. Although no interventions were put in place following the identification of the different foci of rabies activities, the authors acknowl- edged that prioritising these areas for control may prove valuable. These authors also recommended applying permutation space-time scan statistics over cases occurring in the spring and early summer of a year, to detect areas that should be prioritised in the design of the control activities implemented in late summer and autumn.

As Lawson (2001) noted, we have to distinguish the notion of clustering and interac- tion when analysing spatial and temporal features of epidemiologic data. Although spatial clustering occurs when neighbouring events (points or areas) interact in time, it can also arise when no interaction occurs (Kulldorff & Hjalmars 1999). Although the scan statis- tic is an effective method to localise space-time clustering, it is not designed to provide insight into whether the process is due to a point source or due to contagion between in- dividuals. The space-timeK-function (Diggle et al. 1995) addresses this issue. Using the same principle as the spatialK-function, D0(s, t)quantifies the proportional increase in the number of cases due to space-time interaction when both purely spatial and temporal patterns are accounted for. The D0(s, t) function is analogous to the risk difference in epidemiology (French et al. 2005) and may be plotted as a function of distancesand time t. When a contagious pattern is present, there will be peaks on the surface ofD0(s, t). On the other hand, when no space-time interaction occurs, no peaks will be evident and the surface will remain centred near zero.

To the best of our knowledge, few studies of wildlife disease have been published using the space-time K-function, despite numerous examples of its use in human and veteri- nary epidemiology (Gerbier & Chadeouf 2000, Wilesmith et al. 2003, French et al. 2005,

Houben et al. 2005, Sanchez et al. 2005, Picado et al. 2007, Rushton et al. 2007). Using the space-timeK-function, French et al. (1999) showed evidence of space-time clustering of sheep scab in Great Britain, particularly within the first 12 kilometres and 5 months of a case. Rushton et al. (2007) investigated the epidemiology ofMycobacterium aviumand

M. malmoenseinfections in humans in northern England from 2000 to 2005. The results suggest that space-time interaction occurred in juvenile cases of M. avium, peaking at a time interval of 100 to 200 days and a residential separation distance of 2.5 kilometres. No space-time interaction was detected forM. malmoenseand adult cases of M. avium. These authors concluded that the clustering amongst juvenile cases provides evidence that juvenileM. aviumis contagious or that there are unmeasured environmental risks influ- encing disease occurrence. The latter explanation is somewhat unlikely as environmental risk factors would imply the presence of spatial risk which would be accounted for in the space-timeK-function analysis. A third hypothesis is that variations inM. aviumdiagno- sis and/or reporting may have occurred, potentially biasing inferences from the analysis. Fenton et al. (2004) investigated the effect of underreporting on the interpretation of a sec- ond order correlation that was detected using the space-time K-function. These authors conducted simulation-based studies to determine the conditions of under reporting under which Monte Carlo tests would provide a valid test of the null hypothesis. These authors showed that the space-time K-function provided sufficient power to detect the presence of spatio-temporal clustering when the level of under-reporting was random and up to a level of 20%. TheK-function was also found to be robust under conditions of position- dependent under-reporting but was affected if reporting variations were defined in space and time. These studies showed that the Monte Carlo test for space-time clustering is robust to most types of thinning, both random and non-random (e.g position-dependent), but the diagnostics used to describe the nature and scale of clustering may be biased by these processes.

Acknowledging that extra space-time interactions may occur when monitoring the pop- ulation at risk on the base of a discontinuous grid sampled at discrete times, Carslake et al. (2005) evaluated space-time interaction among bank voles Clethrionomys glareolusand wood mice Apodemus sylvaticus with cowpox. Two sets of analyses were conducted: the first involving animals infected with cowpox virus and the second involving the pop- ulation at risk. For both species, space-time interactions were present in cases and the

population at risk, but the estimates of D0(s, t) as a function of distance and time were significantly greater in cases than in the population at risk. These authors concluded that, as expected, cases of cowpox show positive space-time interaction with a distance corresponding to one home-range diameter and the infectious period of cowpox virus. Although the study of Carslake et al. (2005) provides a good example of the informa- tion that can be derived from the space-time K-function, the cost of collecting data for its implementation may limit its widespread use. Indeed, this approach requires detailed information regarding disease status, and the location and time of capture of individuals within a study site of large size over a relatively long period of time. In the study of wildlife diseases, few data sets meet these criteria with a small number of exceptions: the Castlepoint study of TB in possums in New Zealand (Pfeiffer 1994, Jackson 1995), the Woodchester Park, Gloucestershire study of TB in badgers (Delahay et al. 2000), and the data of rabies in Ethiopian wolves from the Bale Mountains, Ethiopia (Haydon et al. 2006).