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Blowfly strike in sheep flocks as an example of the use of a time–space scan statistic to control confounding
Preventive Veterinary Medicine 49 (2001) 61±69
Blowfly strike in sheep flocks as an example of the use of a time±space scan statistic to control confounding Michael P. Ward* Queensland Department of Primary Industries, Animal Research Institute, Locked Mail Bag 4, Moorooka, Qld 4105, Australia Received 23 May 2000; accepted 30 November 2000
Abstract The use of a time±space scan statistic Ð defined by a cylindrical window with a circular geographic base and height corresponding to time Ð was investigated as a method of detecting clustering in veterinary epidemiology whilst controlling confounding. The example data set consisted of farmer-recorded occurrence of body strike and breech strike between August 1998 and May 1999 in 26 sheep flocks located in two local government areas of southeastern Queensland, Australia. This information was derived from a questionnaire survey mailed to farmers. Potentially confounding factors included in the investigation were flock size (median, >median), flock structure (proportion of lambs, wethers, ewes and rams), pesticide application for flystrike control (yes, no) and rainfall (median, >median). The total sheep population within selected flocks was 92,660; 1012 (1.09%) and 518 (0.56%) cases of body strike and breech strike were reported in 16 and 10 flocks, respectively. Clustering analyses of body strike and breech strike were undertaken separately, because different predisposing factors are associated with these diseases. Significant clustering of body strike (28.768S, 151.828E) during March 1999 and breech strike (28.738S, 151.168E) between February and May 1999 was detected. Adjusting for flock structure, flock size, pesticide use and rainfall did not alter the most likely cluster of body strike identified Ð although the relative risk changed (>10%) after adjusting for flock structure. Adjustment for flock structure and rainfall resulted in different clusters of breech strike being identified. # 2001 Elsevier Science B.V. All rights reserved. Keywords: Time±space clustering; Scan statistic; Blowfly; Sheep-parasitological diseases; Australia *
Present address: Department of Veterinary Pathobiology, School of Veterinary Medicine, Purdue University, 1243 Veterinary Pathology Building, West Lafayette, IN 47907-1243, USA. Tel.: 1-765-494-5796; fax: 1-765-494-9830. E-mail address: [email protected] (M.P. Ward). 0167-5877/01/$ ± see front matter # 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 5 8 7 7 ( 0 1 ) 0 0 1 7 9 - 9
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1. Introduction A one-dimensional scan statistic has been used to study disease clusters in time and a two-dimensional scan statistic has been proposed for spatial disease clusters (Naus, 1965; Kulldorff, 1997). Kulldorff et al. (1998a) proposed extending the use of the scan statistic (defined by a cylindrical window with a circular geographic base and height corresponding to time) for time±space clustering. Statistical tests previously used in time±space clustering investigations in veterinary epidemiology include Knox's test, Mantel's test, Barton's method and the nearest-neighbour test (Ward and Carpenter, 2000a). These are global methods that test for clustering throughout the study area and period, without the ability to identify specific clusters. The scan statistic for time±space clustering is a cluster-detection test Ð able both to identify and to test the significance of specific clusters. This statistic has several potential advantages, including the ability to control for confounding by a method of indirect standardisation, application for analysing clustering in heterogenous populations and adjustment for multiple testing. In this paper, use of the scan statistic for time±space clustering in veterinary epidemiology is illustrated by analysis of a data set describing both breech and body blowfly strikes in 26 sheep flocks in southeastern Queensland. Flocks were selected from a sampling frame maintained by the Queensland Department of Primary Industries and included in a postal survey (Ward, 2001). Blowfly strike is a major economic disease in Australian sheep flocks (McLeod, 1995). Blowfly strike in Australia is caused predominantly (>80±90% of cases) by the blowfly Lucilia cuprina. Breech (affecting the area around the breech of sheep) and body (including head and foot) strikes are the most important types of blowfly strike recognised. Risk factors for breech strike include diarrhoea and urine soiling, and weaner sheep and ewes are therefore more susceptible. Management procedures (e.g. mulesing, crutching, tail docking, intestinal-parasites control) are used to reduce susceptibility. Body strike is influenced by climatic factors and by fleece characteristics and body conformation (Watts et al., 1979; Wardhaugh and Morton, 1990; Wardhaugh et al., 1994). The occurrence of blowfly strike is known to be clustered (Ward and Armstrong, 2000). However, it is important to identify clustering that may exist after adjusting for the effect of known risk factors. The scan statistic might potentially be useful in this situation. The aim of this study was to investigate the use of the scan statistic to detect and identify clustering whilst concurrently controlling for potential confounding factors. 2. Materials and methods 2.1. Data set A postal questionnaire survey of commercial sheep farmers Ð located within two adjacent local government areas of southeastern Queensland, Australia, and who grazed >500 sheep in 1998 Ð was undertaken in 1999 (Ward and Carpenter, 2000b; Ward, 2001). Approximately, 482,000 sheep are grazed within this study area. Ninety-three farmers identified from the sampling frame were sent the questionnaire in June, and
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reminder letters were sent to non-responders in July. As part of the survey, information was requested on flock size and structure (number of lambs, wethers, ewes and rams) at the most recent shearing, and on the number and type of flystrike cases, total rainfall recorded and use of pesticides for flystrike control during the period August 1998 to May 1999. The location of flocks was identified visually from local government area maps by longitude and latitude coordinates of the approximate property centre. The average size of properties included in the survey was 3135 ha (95% CI, 1890±4380), so that approximate property centres were considered to represent the location of sheep flocks adequately. The survey return percentage was 68% (63 questionnaires). Of those questionnaires returned, two were duplicates (different owner-address, same flock), five respondents were not grazing sheep during the study period and two properties had been sold. 2.2. Data analysis A subset of farmers responding to the questionnaire survey was selected for analysis. These were the 32 farmers who had not used fly traps during the study period to control flystrike. Of the flocks selected, flock structure was unavailable for three flocks, rainfall was unavailable for five flocks, and pesticide use was unavailable for one flock. To allow valid comparisons between unadjusted and adjusted time±space analyses, only flocks (26) for which information on all potential confounding variables was available were included. The spatial distribution of these flocks was described by the nearest-neighbour index (R) (Clark and Evans, 1954; Ward and Carpenter, 2000b). An index < 1 indicates clustering Ð whereas an index > 1 indicates that the points are overdispersed. Clustering of body strike and breech strike was analysed using the scan statistic (Kulldorff et al., 1998a). Separate analyses were used for body strike and breech strike because different predisposing factors are associated with these diseases. The scan statistic allows the number of cases of disease expected within the scanning window (as it is moved across each centroid) to be distributed as either Poisson (rate data) or Bernoulli (case±control data). Using a Poisson model, the number of cases of disease within each study area (e.g. flock, postal code, local government area) is assumed to be proportional to the area's population size (or animal-years at-risk). Using a Bernoulli model, controls may be drawn randomly from the population of interest, or may be the total population (minus cases). When case:control is low (<10%), the Poisson model approximates the Bernoulli model and can be used to analyse binary data (and is computationally faster). The Poisson model allows control of any number of confounders (covariates) that can be categorised, by indirect standardisation to adjust the number of cases expected (Kulldorff et al., 1998a). Kulldorff et al. (1998b) provide an example of age as a confounder. If the incidence of a disease-of-interest varies with age, and if the distribution of ages varies at different locations (or in time intervals) of the population-of-interest, then spatial (or temporal) clustering of the disease may be simply due to age. Using knowledge of the distribution of the potential confounder, only those clusters above and beyond those expected due to the confounder will be identified. The expected number of cases under the null hypothesis is calculated based on the potential confounders, using indirect standardisation. Indirect standardisation uses class-specific proportions in each subpopulation to adjust Ð based on class-specific risks of disease in the population Ð
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the expected risk of disease in the subpopulation. For example, in the current study, the risk of body strike in lambs, wethers, ewes and rams was 2.7, 1.0, 0.3 and 0.7%, respectively (Ward, 2001). If a 1000-sheep flock included in the study had a flock structure of 40% lambs, 30% wethers, 29% ewes and 1% rams, the expected number of body strike cases in this flock Ð adjusted for flock structure Ð would be 0:027 400 0:01 300 0:003 2900 0:007 10 15. The expected risk of body strike occurrence Ð adjusted for flock structure Ð is 1.5%. This risk then would be used to assess whether excess body strike has occurred in time and space (replacing the crude estimate of body strike for this flock). The ratio of observed to expected disease risks is the standardised mortality (morbidity) ratio, SMR (Kahn and Sempos, 1989). If more than one potential confounder is specified, adjustment can be made for each factor as well as for the interaction between confounding factors. In addition, the size of each unit in the population can be replaced by an estimate adjusted for a confounder measured on a continuous scale (e.g. by the use of linear regression). For the scan statistic, either selection of controls or information on the size of the population within each study unit is used to account for heterogeneity of the population at-risk. The distribution of occurrence of body strike Ð or of breech strike Ð was assumed to be Poisson and the observed number of cases defined the distribution. The population at-risk used in analyses was that reported by flock owners at their most recent shearing. This measure was assumed to represent the flocks included in the study adequately. The data set was scanned for clusters with either low or high risks of flystrike (equivalent to a two-sided test). The scanning window consisted of a temporal dimension (`cylinder height') and a spatial dimension (`cylinder base'). The data set was scanned for clusters in spatial and temporal dimensions ranging from 0 to 50% of the total population at-risk (up to 50% of the study area Ð approximately 3150 km2 Ð and 50% of the study period Ð 5 months). A cluster of size larger than 50% would indicate a flock with exceptionally low occurrence of flystrike outside the scanning window, rather than a flock of exceptionally high flystrike occurrence within the window (Kulldorff et al., 1998b). Clusters were identified by the scanning window associated with the maximumlikelihood function, and a likelihood-ratio test statistic was calculated. The distribution of the likelihood ratio and its corresponding P-value was obtained by Monte Carlo simulation Ð randomly generating 999 replications of the data set under the null hypothesis. For hypothesis testing, the test statistic was calculated for each random replication Ð as well as for the flystrike data set Ð and if the latter was in the most extreme 5% of all test statistics calculated, then the hypothesis test was significant at P 0:05. Thus, the problem of performing multiple tests using many scanning windows was addressed and type-I error was restricted to 0.05. The number of replications chosen was considered to provide moderate statistical power whilst minimising computing time (Kulldorff et al., 1998b). All crude analyses were re-analysed adjusting for flock size, flock structure, rainfall and pesticide use for flystrike during the period August 1998 to May 1999, separately. Categorisation of flock size and rainfall was based on median flock size and median rainfall for flocks included in the study. Median flocks size was calculated from the flock size of all flocks included in the study at the most recent shearing. Rainfall (mm) was recorded by farmers during a 10-month period (August 1998 to May 1999, inclusive) as
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part of routine property book-keeping, and provided via questionnaire surveys. Flock size and rainfall were therefore used as binary variables for adjusting clustering analyses. Pesticide application was also used as a binary variable Ð if any pesticide applications were applied to sheep during the study period, the flock was categorised as `yes' for pesticide application. Flock structure was described by the number of lambs, wethers, ewes and rams present in each flock at the most recent shearing. The criterion for assessing confounding was junadjusted relative risk ÿ adjusted relative riskj=unadjusted relative risk 10%, relative risk being the number of cases of flystrike in the identified cluster compared to the number expected assuming that cases are distributed as Poisson. All calculations were performed using SaTScan software version 2.1, a shareware program (http:// dcp.nci.nih.gov/BB/SaTScan.html; Kulldorff et al., 1998b). 3. Results The total sheep population within the flocks included in the study was 92,660. The overall flock structure was 13% lambs, 63% wethers, 23% ewes and <1% rams. The total number of new cases of body strike and breech strike reported were 1012 (1.09% of sheep in the study population) and 518 (0.56% of sheep in the study population), respectively. The median flock size was 2500 sheep (range, 700±18,600 sheep). From August 1998 to May 1999, the median rainfall recorded on properties was 641 mm (range, 375±788 mm). Pesticides were applied in 19 (73%) of the selected flocks at some time during the study period for flystrike control. Body strike and breech strike were reported to occur in 16 and 10 flocks, respectively. Mean flock-specific, sheep-level cumulative incidence of body strike and breech strike was 1.6 and 0.4%, respectively, during the 9-month study period. In three flocks, an incidence of body strike >5% was reported (332 cases and 5867 sheep at-risk, 160 cases and 3060 sheep at-risk, and 70 cases and 900 sheep at-risk, respectively). The maximum incidence of breech strike reported was 2.5%. Most cases of body strike and breech strike (Table 1) occurred in early autumn (March 1999), although a secondary peak of cases of body strike occurred during spring (September±November 1998). The distribution of flocks (Fig. 1) was overdispersed (R 1:27; z 2:67, P < 0:01). Significant P < 0:01 clustering of body strike and breech strike in time and space in the selected flocks was detected. The most likely (largest log-likelihood statistic) cluster of body strike was located at 28.768S, 151.828E during March 1999, where 332 cases were observed in one flock and seven cases were expected (Table 2). The most likely cluster of breech strike was located at 28.738S, 151.168E between February and May 1999, where 375 cases were observed in five flocks and 61 cases were expected (Table 3). Adjusting for flock structure, flock size, pesticide use and rainfall did not alter the most likely cluster of body strike identified Ð the same flock was included in the cluster (332 cases of body strike) and the period of clustering was unaltered (March 1999). However, adjustment for flock structure and rainfall substantially altered (35 and 14%, respectively) the estimated relative risk of body strike in this cluster (Table 2). Adjusting for flock size and pesticide use did not alter the most likely cluster of breech strike identified (five flocks centred at 28.738S, 151.168E with 375 cases of breech strike occurring between
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Table 1 Temporal distribution of cases of blowfly strike in 26 southeastern Queensland sheep flocks selected for the study of time±space clustering, 1998±1999 Month
Body strike Number
August September October November December January February March April May Total
4 52 147 102 14 139 18 515 9 12 1012
Breech strike % 0.4 5.1 14.5 10.1 1.4 13.7 1.8 50.9 0.9 1.2 100
Number 0 12 20 0 4 16 85 237 42 102 518
% ± 2.3 3.9 ± 0.8 3.1 16.4 45.8 8.1 19.7 100
February and March 1999). However, adjustment for flock structure resulted in the location of the identified cluster changing to 28.638S, 151.318E Ð a distance of approximately 18 km (Fig. 1) Ð as a result of the addition of three flocks being included in the cluster. The estimated relative risk associated with this cluster (6.1) decreased to 4.2 after adjusting for flock structure. Adjusting for rainfall resulted in the estimated
Fig. 1. Crude (left) and flock structure adjusted clustering of breech strike in 26 sheep flocks in southeastern Queensland (most likely cluster (*)).
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Table 2 Most likely cluster of body strike identified in 26 southeastern Queensland sheep flocks from a crude analysis and analyses adjusting for potential confounders. In all analyses, the most likely cluster of strike occurred during March 1999 and consisted of one flock Ð located at 28.768S, 151.828E Ð in which 332 cases of body strike were reported (degrees of freedom 25) Confounder
Expected No. of cases
Relative riska
log-likelihood ratio
No confounder Flock size Flock structure Pesticide use Rainfall
7 6 10 7 8
51 55 33 46 44
1038 1062 899 1002 987
a
Ratio of the number of cases observed in the identified cluster and the number of cases expected in the cluster, assuming that cases of body strike are Poisson distributed. Table 3 Most likely clusters of breech strike identified in 26 southeastern Queensland sheep flocks from a crude analysis and analyses adjusting for potential confounders. In all analyses, clustering was detected between February and May 1999 (degrees of freedom 25) Confounder
No. of flocks
Cluster location
No confounder Flock size Flock structure Pesticide use Rainfall
5 5 8 5 8
28.738S, 28.738S, 28.638S, 28.738S, 28.638S,
151.168E 151.168E 151.318E 151.168E 151.318E
Observed No. of cases
Expected No. of cases
Relative riska
log-likelihood ratio
375 375 415 375 405
61 62 98 65 87
6.1 6.1 4.2 5.8 4.7
513 511 452 491 472
a Ratio of the number of cases observed in the identified cluster and the number of cases expected in the cluster, assuming that cases of breech strike are Poisson distributed.
relative risk associated with the most likely cluster changing by 23% to 4.7 with the addition of two flocks to the cluster. 4. Discussion Statistical tests are necessary to investigate time±space clustering of disease objectively (Ward and Carpenter, 2000a). The distribution of flocks included in this study was overdispersed R 1:27. The scan statistic can accommodate uneven population densities, because analysis is conditioned on the total number of cases observed. If only the nearest-neighbour index was used in the present study, it might have been concluded that cases of body strike or of breech strike were overdispersed. Therefore, a test that accounts for population heterogeneity should be used in time±space clustering analyses. Flock structure appeared to be the most important confounding factor of the clustering of flystrike in time and space. Clustering was not as strong after accounting for the structure of flocks included in the study. For example, the most likely cluster of body
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strike consisted of a population of 2139 (36%) lambs and 1995 (34%) ewes, compared to 13 and 23%, respectively, in the overall population. The most likely cluster of breech strike (five flocks) consisted of 5131 (19%) lambs and 9612 (35%) ewes. Predisposing factors for body strike include genetics (body conformation, fleece characteristics), climate (rainfall, humidity) and pasture type grazed (long grass). Young sheep tend to be more susceptible to body strike Ð perhaps due to certain fleece characteristics such as staple form (Hayman, 1953). Therefore, flock structure should be taken into account when investigating the clustering of flystrike. Another advantage of the scan statistic is the ability to calculate statistical significance using a Monte Carlo approach (Kulldorff et al., 1998b). This enables type-I error to be specified Ð regardless of the number of tests being performed Ð so that the hypothesis test is unbiased and the resulting significance level is neither conservative nor liberal. Finally, the scan statistic for time±space clustering is flexible. Information on either individuals or aggregated data can be used, depending on the population of interest. For example, clustering of flystrike could be investigated with this procedure at the flock-, postal code-, local government area- or wool district-level. The size of the scanning window can be varied by the investigator (if a priori reasons exist, e.g. knowledge of incubation periods, so that the maximum window size is reduced from 50% of the study area and period). Scanning can focus on clusters with either unusually high or unusually low rates of disease (both situations constituting clustering Ð although most investigations generally focus on the former, `outbreak' situation). Clustering also can be investigated if information is available only on cases of disease and controls (rather than on the population at-risk). Few examples of investigating the interaction of time and space in disease clustering exist in the veterinary literature (Ward and Carpenter, 2000a). Reasons may include inappropriate study design, difficulty in visualising and explaining the concept of time± space interaction, the implicit assumption of homogeneity of the population of interest in some techniques, lack of accessibility to suitable analytical software, and publication bias due to insufficient power of available analytical methods. Development of monitoring and surveillance and geographical information systems in veterinary epidemiology are likely to increase the need for time±space analyses. The clustering of flystrike in sheep flocks has been investigated by Ward and Armstrong (2000). These investigations focused on larger geographical (state of Queensland) and temporal (1995±1997) scales and more flocks (57) than the present study. Using Knox's method, flystrike that occurred in flocks located within 150 km of each other and within a 3-month period was significantly clustered. It was suggested that factors common to a district are responsible for clustering of flystrike in Queensland. The present study Ð undertaken on a subpopulation of Queensland sheep flocks Ð confirms that clustering of flystrike is localised, and supports the view that control of flystrike needs to focus within districts. Results highlight the need to consider potentially confounding factors when investigating the clustering of disease in time and space and formulating diseasecausation hypotheses. In the present example, failure to consider the structure of selected flocks when investigating blowfly strike would have resulted in spurious clustering being identified. The scan statistic for time±space clustering of disease appears to have
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application in veterinary epidemiology Ð it can be used as both a global test for clustering and a cluster identification test in heterogenous populations whilst controlling confounding, it overcomes the problem of multiple testing, model specification is flexible and software is freely available. References Clark, P.J., Evans, F.C., 1954. Distance to nearest neighbor as a measure of spatial relationships in populations. Ecology 35, 445±453. Hayman, R.H., 1953. Studies in fleece-rot of sheep. Aust. J. Agric. Res. 4, 430±468. Kahn, H.A., Sempos, C.T., 1989. Statistical Methods in Epidemiology. Oxford University Press, New York, 1989, pp. 95±105. Kulldorff, M., 1997. A spatial scan statistic. Commun. Statist.: Theory Meth. 26, 1481±1496. Kulldorff, M., Athas, W.F., Feuer, E.J., Miller, B.A., Key, C.R., 1998a. Evaluating cluster alarms: a space±time scan statistic and brain cancer in Los Alamos. Am. J. Public Health 88, 1377±1380. Kulldorff, M., Rand, K., Gherman, G., Williams, G., DeFrancesco, D., 1998b. SaTScan Version 2.1: Software for the Spatial and Space±Time Scan Statistics. National Cancer Institute, Bethesda, MD. McLeod, R.S., 1995. Costs of major parasites to the Australian livestock industries. Int. J. Parasitol. 25, 1363± 1367. Naus, J., 1965. The distribution of the size of maximum cluster of points on the line. J. Am. Statist. Assoc. 60, 532±538. Ward, M.P., 2001. A postal survey of blowfly strike occurrence in two Queensland shires. Aust. Vet. J., in press. Ward, M.P., Armstrong, R.T.F., 2000. Time±space clustering of reported blowfly strike in Queensland sheep flocks. Prev. Vet. Med. 43, 195±202. Ward, M.P., Carpenter, T.E., 2000a. Techniques for analysis of disease clustering in space and in time in veterinary epidemiology. Prev. Vet. Med. 45, 257±284. Ward, M.P., Carpenter, T.E., 2000b. Analysis of time±space clustering in veterinary epidemiology. Prev. Vet. Med. 43, 225±237. Wardhaugh, K.G., Morton, R., 1990. The incidence of flystrike in sheep in relation to weather conditions, sheep husbandry, and the abundance of the Australian sheep blowfly, Lucilia cuprina (Wiedemann) (Diptera: Calliphoridae). Aust. J. Agric. Res. 41, 1155±1167. Wardhaugh, K.G., Bedo, D., Vogt, W.G., 1994. Management model for the control of flystrike on sheep. In: Proceedings of the Australian Sheep Veterinarian Society Meeting, Canberra, pp. 70±73. Watts, J.E., Murray, M.D., Graham, N.P.H., 1979. The blowfly strike problem of sheep in New South Wales. Aust. Vet. J. 55, 325±334.
Blowfly strike in sheep flocks as an example of the use of a time±space scan statistic to control confounding Michael P. Ward* Queensland Department of Primary Industries, Animal Research Institute, Locked Mail Bag 4, Moorooka, Qld 4105, Australia Received 23 May 2000; accepted 30 November 2000
Abstract The use of a time±space scan statistic Ð defined by a cylindrical window with a circular geographic base and height corresponding to time Ð was investigated as a method of detecting clustering in veterinary epidemiology whilst controlling confounding. The example data set consisted of farmer-recorded occurrence of body strike and breech strike between August 1998 and May 1999 in 26 sheep flocks located in two local government areas of southeastern Queensland, Australia. This information was derived from a questionnaire survey mailed to farmers. Potentially confounding factors included in the investigation were flock size (median, >median), flock structure (proportion of lambs, wethers, ewes and rams), pesticide application for flystrike control (yes, no) and rainfall (median, >median). The total sheep population within selected flocks was 92,660; 1012 (1.09%) and 518 (0.56%) cases of body strike and breech strike were reported in 16 and 10 flocks, respectively. Clustering analyses of body strike and breech strike were undertaken separately, because different predisposing factors are associated with these diseases. Significant clustering of body strike (28.768S, 151.828E) during March 1999 and breech strike (28.738S, 151.168E) between February and May 1999 was detected. Adjusting for flock structure, flock size, pesticide use and rainfall did not alter the most likely cluster of body strike identified Ð although the relative risk changed (>10%) after adjusting for flock structure. Adjustment for flock structure and rainfall resulted in different clusters of breech strike being identified. # 2001 Elsevier Science B.V. All rights reserved. Keywords: Time±space clustering; Scan statistic; Blowfly; Sheep-parasitological diseases; Australia *
Present address: Department of Veterinary Pathobiology, School of Veterinary Medicine, Purdue University, 1243 Veterinary Pathology Building, West Lafayette, IN 47907-1243, USA. Tel.: 1-765-494-5796; fax: 1-765-494-9830. E-mail address: [email protected] (M.P. Ward). 0167-5877/01/$ ± see front matter # 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 5 8 7 7 ( 0 1 ) 0 0 1 7 9 - 9
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1. Introduction A one-dimensional scan statistic has been used to study disease clusters in time and a two-dimensional scan statistic has been proposed for spatial disease clusters (Naus, 1965; Kulldorff, 1997). Kulldorff et al. (1998a) proposed extending the use of the scan statistic (defined by a cylindrical window with a circular geographic base and height corresponding to time) for time±space clustering. Statistical tests previously used in time±space clustering investigations in veterinary epidemiology include Knox's test, Mantel's test, Barton's method and the nearest-neighbour test (Ward and Carpenter, 2000a). These are global methods that test for clustering throughout the study area and period, without the ability to identify specific clusters. The scan statistic for time±space clustering is a cluster-detection test Ð able both to identify and to test the significance of specific clusters. This statistic has several potential advantages, including the ability to control for confounding by a method of indirect standardisation, application for analysing clustering in heterogenous populations and adjustment for multiple testing. In this paper, use of the scan statistic for time±space clustering in veterinary epidemiology is illustrated by analysis of a data set describing both breech and body blowfly strikes in 26 sheep flocks in southeastern Queensland. Flocks were selected from a sampling frame maintained by the Queensland Department of Primary Industries and included in a postal survey (Ward, 2001). Blowfly strike is a major economic disease in Australian sheep flocks (McLeod, 1995). Blowfly strike in Australia is caused predominantly (>80±90% of cases) by the blowfly Lucilia cuprina. Breech (affecting the area around the breech of sheep) and body (including head and foot) strikes are the most important types of blowfly strike recognised. Risk factors for breech strike include diarrhoea and urine soiling, and weaner sheep and ewes are therefore more susceptible. Management procedures (e.g. mulesing, crutching, tail docking, intestinal-parasites control) are used to reduce susceptibility. Body strike is influenced by climatic factors and by fleece characteristics and body conformation (Watts et al., 1979; Wardhaugh and Morton, 1990; Wardhaugh et al., 1994). The occurrence of blowfly strike is known to be clustered (Ward and Armstrong, 2000). However, it is important to identify clustering that may exist after adjusting for the effect of known risk factors. The scan statistic might potentially be useful in this situation. The aim of this study was to investigate the use of the scan statistic to detect and identify clustering whilst concurrently controlling for potential confounding factors. 2. Materials and methods 2.1. Data set A postal questionnaire survey of commercial sheep farmers Ð located within two adjacent local government areas of southeastern Queensland, Australia, and who grazed >500 sheep in 1998 Ð was undertaken in 1999 (Ward and Carpenter, 2000b; Ward, 2001). Approximately, 482,000 sheep are grazed within this study area. Ninety-three farmers identified from the sampling frame were sent the questionnaire in June, and
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reminder letters were sent to non-responders in July. As part of the survey, information was requested on flock size and structure (number of lambs, wethers, ewes and rams) at the most recent shearing, and on the number and type of flystrike cases, total rainfall recorded and use of pesticides for flystrike control during the period August 1998 to May 1999. The location of flocks was identified visually from local government area maps by longitude and latitude coordinates of the approximate property centre. The average size of properties included in the survey was 3135 ha (95% CI, 1890±4380), so that approximate property centres were considered to represent the location of sheep flocks adequately. The survey return percentage was 68% (63 questionnaires). Of those questionnaires returned, two were duplicates (different owner-address, same flock), five respondents were not grazing sheep during the study period and two properties had been sold. 2.2. Data analysis A subset of farmers responding to the questionnaire survey was selected for analysis. These were the 32 farmers who had not used fly traps during the study period to control flystrike. Of the flocks selected, flock structure was unavailable for three flocks, rainfall was unavailable for five flocks, and pesticide use was unavailable for one flock. To allow valid comparisons between unadjusted and adjusted time±space analyses, only flocks (26) for which information on all potential confounding variables was available were included. The spatial distribution of these flocks was described by the nearest-neighbour index (R) (Clark and Evans, 1954; Ward and Carpenter, 2000b). An index < 1 indicates clustering Ð whereas an index > 1 indicates that the points are overdispersed. Clustering of body strike and breech strike was analysed using the scan statistic (Kulldorff et al., 1998a). Separate analyses were used for body strike and breech strike because different predisposing factors are associated with these diseases. The scan statistic allows the number of cases of disease expected within the scanning window (as it is moved across each centroid) to be distributed as either Poisson (rate data) or Bernoulli (case±control data). Using a Poisson model, the number of cases of disease within each study area (e.g. flock, postal code, local government area) is assumed to be proportional to the area's population size (or animal-years at-risk). Using a Bernoulli model, controls may be drawn randomly from the population of interest, or may be the total population (minus cases). When case:control is low (<10%), the Poisson model approximates the Bernoulli model and can be used to analyse binary data (and is computationally faster). The Poisson model allows control of any number of confounders (covariates) that can be categorised, by indirect standardisation to adjust the number of cases expected (Kulldorff et al., 1998a). Kulldorff et al. (1998b) provide an example of age as a confounder. If the incidence of a disease-of-interest varies with age, and if the distribution of ages varies at different locations (or in time intervals) of the population-of-interest, then spatial (or temporal) clustering of the disease may be simply due to age. Using knowledge of the distribution of the potential confounder, only those clusters above and beyond those expected due to the confounder will be identified. The expected number of cases under the null hypothesis is calculated based on the potential confounders, using indirect standardisation. Indirect standardisation uses class-specific proportions in each subpopulation to adjust Ð based on class-specific risks of disease in the population Ð
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the expected risk of disease in the subpopulation. For example, in the current study, the risk of body strike in lambs, wethers, ewes and rams was 2.7, 1.0, 0.3 and 0.7%, respectively (Ward, 2001). If a 1000-sheep flock included in the study had a flock structure of 40% lambs, 30% wethers, 29% ewes and 1% rams, the expected number of body strike cases in this flock Ð adjusted for flock structure Ð would be 0:027 400 0:01 300 0:003 2900 0:007 10 15. The expected risk of body strike occurrence Ð adjusted for flock structure Ð is 1.5%. This risk then would be used to assess whether excess body strike has occurred in time and space (replacing the crude estimate of body strike for this flock). The ratio of observed to expected disease risks is the standardised mortality (morbidity) ratio, SMR (Kahn and Sempos, 1989). If more than one potential confounder is specified, adjustment can be made for each factor as well as for the interaction between confounding factors. In addition, the size of each unit in the population can be replaced by an estimate adjusted for a confounder measured on a continuous scale (e.g. by the use of linear regression). For the scan statistic, either selection of controls or information on the size of the population within each study unit is used to account for heterogeneity of the population at-risk. The distribution of occurrence of body strike Ð or of breech strike Ð was assumed to be Poisson and the observed number of cases defined the distribution. The population at-risk used in analyses was that reported by flock owners at their most recent shearing. This measure was assumed to represent the flocks included in the study adequately. The data set was scanned for clusters with either low or high risks of flystrike (equivalent to a two-sided test). The scanning window consisted of a temporal dimension (`cylinder height') and a spatial dimension (`cylinder base'). The data set was scanned for clusters in spatial and temporal dimensions ranging from 0 to 50% of the total population at-risk (up to 50% of the study area Ð approximately 3150 km2 Ð and 50% of the study period Ð 5 months). A cluster of size larger than 50% would indicate a flock with exceptionally low occurrence of flystrike outside the scanning window, rather than a flock of exceptionally high flystrike occurrence within the window (Kulldorff et al., 1998b). Clusters were identified by the scanning window associated with the maximumlikelihood function, and a likelihood-ratio test statistic was calculated. The distribution of the likelihood ratio and its corresponding P-value was obtained by Monte Carlo simulation Ð randomly generating 999 replications of the data set under the null hypothesis. For hypothesis testing, the test statistic was calculated for each random replication Ð as well as for the flystrike data set Ð and if the latter was in the most extreme 5% of all test statistics calculated, then the hypothesis test was significant at P 0:05. Thus, the problem of performing multiple tests using many scanning windows was addressed and type-I error was restricted to 0.05. The number of replications chosen was considered to provide moderate statistical power whilst minimising computing time (Kulldorff et al., 1998b). All crude analyses were re-analysed adjusting for flock size, flock structure, rainfall and pesticide use for flystrike during the period August 1998 to May 1999, separately. Categorisation of flock size and rainfall was based on median flock size and median rainfall for flocks included in the study. Median flocks size was calculated from the flock size of all flocks included in the study at the most recent shearing. Rainfall (mm) was recorded by farmers during a 10-month period (August 1998 to May 1999, inclusive) as
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part of routine property book-keeping, and provided via questionnaire surveys. Flock size and rainfall were therefore used as binary variables for adjusting clustering analyses. Pesticide application was also used as a binary variable Ð if any pesticide applications were applied to sheep during the study period, the flock was categorised as `yes' for pesticide application. Flock structure was described by the number of lambs, wethers, ewes and rams present in each flock at the most recent shearing. The criterion for assessing confounding was junadjusted relative risk ÿ adjusted relative riskj=unadjusted relative risk 10%, relative risk being the number of cases of flystrike in the identified cluster compared to the number expected assuming that cases are distributed as Poisson. All calculations were performed using SaTScan software version 2.1, a shareware program (http:// dcp.nci.nih.gov/BB/SaTScan.html; Kulldorff et al., 1998b). 3. Results The total sheep population within the flocks included in the study was 92,660. The overall flock structure was 13% lambs, 63% wethers, 23% ewes and <1% rams. The total number of new cases of body strike and breech strike reported were 1012 (1.09% of sheep in the study population) and 518 (0.56% of sheep in the study population), respectively. The median flock size was 2500 sheep (range, 700±18,600 sheep). From August 1998 to May 1999, the median rainfall recorded on properties was 641 mm (range, 375±788 mm). Pesticides were applied in 19 (73%) of the selected flocks at some time during the study period for flystrike control. Body strike and breech strike were reported to occur in 16 and 10 flocks, respectively. Mean flock-specific, sheep-level cumulative incidence of body strike and breech strike was 1.6 and 0.4%, respectively, during the 9-month study period. In three flocks, an incidence of body strike >5% was reported (332 cases and 5867 sheep at-risk, 160 cases and 3060 sheep at-risk, and 70 cases and 900 sheep at-risk, respectively). The maximum incidence of breech strike reported was 2.5%. Most cases of body strike and breech strike (Table 1) occurred in early autumn (March 1999), although a secondary peak of cases of body strike occurred during spring (September±November 1998). The distribution of flocks (Fig. 1) was overdispersed (R 1:27; z 2:67, P < 0:01). Significant P < 0:01 clustering of body strike and breech strike in time and space in the selected flocks was detected. The most likely (largest log-likelihood statistic) cluster of body strike was located at 28.768S, 151.828E during March 1999, where 332 cases were observed in one flock and seven cases were expected (Table 2). The most likely cluster of breech strike was located at 28.738S, 151.168E between February and May 1999, where 375 cases were observed in five flocks and 61 cases were expected (Table 3). Adjusting for flock structure, flock size, pesticide use and rainfall did not alter the most likely cluster of body strike identified Ð the same flock was included in the cluster (332 cases of body strike) and the period of clustering was unaltered (March 1999). However, adjustment for flock structure and rainfall substantially altered (35 and 14%, respectively) the estimated relative risk of body strike in this cluster (Table 2). Adjusting for flock size and pesticide use did not alter the most likely cluster of breech strike identified (five flocks centred at 28.738S, 151.168E with 375 cases of breech strike occurring between
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Table 1 Temporal distribution of cases of blowfly strike in 26 southeastern Queensland sheep flocks selected for the study of time±space clustering, 1998±1999 Month
Body strike Number
August September October November December January February March April May Total
4 52 147 102 14 139 18 515 9 12 1012
Breech strike % 0.4 5.1 14.5 10.1 1.4 13.7 1.8 50.9 0.9 1.2 100
Number 0 12 20 0 4 16 85 237 42 102 518
% ± 2.3 3.9 ± 0.8 3.1 16.4 45.8 8.1 19.7 100
February and March 1999). However, adjustment for flock structure resulted in the location of the identified cluster changing to 28.638S, 151.318E Ð a distance of approximately 18 km (Fig. 1) Ð as a result of the addition of three flocks being included in the cluster. The estimated relative risk associated with this cluster (6.1) decreased to 4.2 after adjusting for flock structure. Adjusting for rainfall resulted in the estimated
Fig. 1. Crude (left) and flock structure adjusted clustering of breech strike in 26 sheep flocks in southeastern Queensland (most likely cluster (*)).
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Table 2 Most likely cluster of body strike identified in 26 southeastern Queensland sheep flocks from a crude analysis and analyses adjusting for potential confounders. In all analyses, the most likely cluster of strike occurred during March 1999 and consisted of one flock Ð located at 28.768S, 151.828E Ð in which 332 cases of body strike were reported (degrees of freedom 25) Confounder
Expected No. of cases
Relative riska
log-likelihood ratio
No confounder Flock size Flock structure Pesticide use Rainfall
7 6 10 7 8
51 55 33 46 44
1038 1062 899 1002 987
a
Ratio of the number of cases observed in the identified cluster and the number of cases expected in the cluster, assuming that cases of body strike are Poisson distributed. Table 3 Most likely clusters of breech strike identified in 26 southeastern Queensland sheep flocks from a crude analysis and analyses adjusting for potential confounders. In all analyses, clustering was detected between February and May 1999 (degrees of freedom 25) Confounder
No. of flocks
Cluster location
No confounder Flock size Flock structure Pesticide use Rainfall
5 5 8 5 8
28.738S, 28.738S, 28.638S, 28.738S, 28.638S,
151.168E 151.168E 151.318E 151.168E 151.318E
Observed No. of cases
Expected No. of cases
Relative riska
log-likelihood ratio
375 375 415 375 405
61 62 98 65 87
6.1 6.1 4.2 5.8 4.7
513 511 452 491 472
a Ratio of the number of cases observed in the identified cluster and the number of cases expected in the cluster, assuming that cases of breech strike are Poisson distributed.
relative risk associated with the most likely cluster changing by 23% to 4.7 with the addition of two flocks to the cluster. 4. Discussion Statistical tests are necessary to investigate time±space clustering of disease objectively (Ward and Carpenter, 2000a). The distribution of flocks included in this study was overdispersed R 1:27. The scan statistic can accommodate uneven population densities, because analysis is conditioned on the total number of cases observed. If only the nearest-neighbour index was used in the present study, it might have been concluded that cases of body strike or of breech strike were overdispersed. Therefore, a test that accounts for population heterogeneity should be used in time±space clustering analyses. Flock structure appeared to be the most important confounding factor of the clustering of flystrike in time and space. Clustering was not as strong after accounting for the structure of flocks included in the study. For example, the most likely cluster of body
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strike consisted of a population of 2139 (36%) lambs and 1995 (34%) ewes, compared to 13 and 23%, respectively, in the overall population. The most likely cluster of breech strike (five flocks) consisted of 5131 (19%) lambs and 9612 (35%) ewes. Predisposing factors for body strike include genetics (body conformation, fleece characteristics), climate (rainfall, humidity) and pasture type grazed (long grass). Young sheep tend to be more susceptible to body strike Ð perhaps due to certain fleece characteristics such as staple form (Hayman, 1953). Therefore, flock structure should be taken into account when investigating the clustering of flystrike. Another advantage of the scan statistic is the ability to calculate statistical significance using a Monte Carlo approach (Kulldorff et al., 1998b). This enables type-I error to be specified Ð regardless of the number of tests being performed Ð so that the hypothesis test is unbiased and the resulting significance level is neither conservative nor liberal. Finally, the scan statistic for time±space clustering is flexible. Information on either individuals or aggregated data can be used, depending on the population of interest. For example, clustering of flystrike could be investigated with this procedure at the flock-, postal code-, local government area- or wool district-level. The size of the scanning window can be varied by the investigator (if a priori reasons exist, e.g. knowledge of incubation periods, so that the maximum window size is reduced from 50% of the study area and period). Scanning can focus on clusters with either unusually high or unusually low rates of disease (both situations constituting clustering Ð although most investigations generally focus on the former, `outbreak' situation). Clustering also can be investigated if information is available only on cases of disease and controls (rather than on the population at-risk). Few examples of investigating the interaction of time and space in disease clustering exist in the veterinary literature (Ward and Carpenter, 2000a). Reasons may include inappropriate study design, difficulty in visualising and explaining the concept of time± space interaction, the implicit assumption of homogeneity of the population of interest in some techniques, lack of accessibility to suitable analytical software, and publication bias due to insufficient power of available analytical methods. Development of monitoring and surveillance and geographical information systems in veterinary epidemiology are likely to increase the need for time±space analyses. The clustering of flystrike in sheep flocks has been investigated by Ward and Armstrong (2000). These investigations focused on larger geographical (state of Queensland) and temporal (1995±1997) scales and more flocks (57) than the present study. Using Knox's method, flystrike that occurred in flocks located within 150 km of each other and within a 3-month period was significantly clustered. It was suggested that factors common to a district are responsible for clustering of flystrike in Queensland. The present study Ð undertaken on a subpopulation of Queensland sheep flocks Ð confirms that clustering of flystrike is localised, and supports the view that control of flystrike needs to focus within districts. Results highlight the need to consider potentially confounding factors when investigating the clustering of disease in time and space and formulating diseasecausation hypotheses. In the present example, failure to consider the structure of selected flocks when investigating blowfly strike would have resulted in spurious clustering being identified. The scan statistic for time±space clustering of disease appears to have
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application in veterinary epidemiology Ð it can be used as both a global test for clustering and a cluster identification test in heterogenous populations whilst controlling confounding, it overcomes the problem of multiple testing, model specification is flexible and software is freely available. References Clark, P.J., Evans, F.C., 1954. Distance to nearest neighbor as a measure of spatial relationships in populations. Ecology 35, 445±453. Hayman, R.H., 1953. Studies in fleece-rot of sheep. Aust. J. Agric. Res. 4, 430±468. Kahn, H.A., Sempos, C.T., 1989. Statistical Methods in Epidemiology. Oxford University Press, New York, 1989, pp. 95±105. Kulldorff, M., 1997. A spatial scan statistic. Commun. Statist.: Theory Meth. 26, 1481±1496. Kulldorff, M., Athas, W.F., Feuer, E.J., Miller, B.A., Key, C.R., 1998a. Evaluating cluster alarms: a space±time scan statistic and brain cancer in Los Alamos. Am. J. Public Health 88, 1377±1380. Kulldorff, M., Rand, K., Gherman, G., Williams, G., DeFrancesco, D., 1998b. SaTScan Version 2.1: Software for the Spatial and Space±Time Scan Statistics. National Cancer Institute, Bethesda, MD. McLeod, R.S., 1995. Costs of major parasites to the Australian livestock industries. Int. J. Parasitol. 25, 1363± 1367. Naus, J., 1965. The distribution of the size of maximum cluster of points on the line. J. Am. Statist. Assoc. 60, 532±538. Ward, M.P., 2001. A postal survey of blowfly strike occurrence in two Queensland shires. Aust. Vet. J., in press. Ward, M.P., Armstrong, R.T.F., 2000. Time±space clustering of reported blowfly strike in Queensland sheep flocks. Prev. Vet. Med. 43, 195±202. Ward, M.P., Carpenter, T.E., 2000a. Techniques for analysis of disease clustering in space and in time in veterinary epidemiology. Prev. Vet. Med. 45, 257±284. Ward, M.P., Carpenter, T.E., 2000b. Analysis of time±space clustering in veterinary epidemiology. Prev. Vet. Med. 43, 225±237. Wardhaugh, K.G., Morton, R., 1990. The incidence of flystrike in sheep in relation to weather conditions, sheep husbandry, and the abundance of the Australian sheep blowfly, Lucilia cuprina (Wiedemann) (Diptera: Calliphoridae). Aust. J. Agric. Res. 41, 1155±1167. Wardhaugh, K.G., Bedo, D., Vogt, W.G., 1994. Management model for the control of flystrike on sheep. In: Proceedings of the Australian Sheep Veterinarian Society Meeting, Canberra, pp. 70±73. Watts, J.E., Murray, M.D., Graham, N.P.H., 1979. The blowfly strike problem of sheep in New South Wales. Aust. Vet. J. 55, 325±334.