Collectively, the results of this analysis suggest three major findings: (i) existence of spatial variation in risk, (ii) existence of apparent local spread, and (iii) possible existence of other mechanisms of spread.
Spatial variation in PCVAD risk between the eastern and western part of the study area existed (as suggested by the GAM) and there was a general east-to-west trend in PCVAD spread (as suggested by Cox's proportional hazard model). Similar findings of directionality were observed in other studies that investigated outbreaks at the national or regional level. Woodbine et al , investigating outbreaks in Great Britain, reported that PCVAD outbreaks were first observed in the south of England, progressing toward the west and north. In Denmark, Vigre et al  reported the existence of two large spatial clusters of positive herds during an initial 2-y period of disease occurrence, and although geographical variability in the occurrence of disease existed, directionality was not apparent from the results, nor was it discussed. In the early phases of the outbreak, geographical variation was, as expected, found in other study regions [17, 18]. The observed directionality was contrary to the dominant winds in Ontario, but it was in close concordance with one of the "principal routes" of the Atlantic bird flyway http://www.birdnature.com/upperatlantic.html through the study area. In previous studies of PCVAD emergence, it was suggested that southern black-backed seagulls were possible mechanical vectors of indirect spread of a causative agent . Data collected in this study did not allow investigation of birds as mechanical or biological vectors. Moreover, the directional spread pattern might also be linked with other direct or indirect mechanisms. Finally, it cannot be completely excluded that farmers in eastern Ontario have different social contacts or sources of information than producers in the western part of the province, and would consequently have a different sensitivity or threshold to declare herds PCVAD-positive. Although only a few herds were sampled from this region, these herds did not appear to be outliers in either regression model. In addition, existence of differences in terms of social contacts cannot explain the apparent difference in spatial risk between herds located in zone 2 and zone 1, where the identical spatial trend was observed. Although the PCVAD risk surface, generated by GAM, suggested the existence of this directionality, we caution the reader that the actual numerical risk estimates are not directly interpretable as estimates of prevalence or of incidence risk in an area, particularly in the unadjusted GAM, because of the initial sampling and subsequent inclusion criteria (which might influence the estimate of the intercept and therefore the entire risk surface).
The lack of evidence of purely spatial clustering (ie, tendency of disease-positive farms to occur near other disease-positive farms - spatial autocorrelation), was not in agreement with detection of a significant purely spatial cluster, for two possible reasons. First, in theory, clusters of disease-positive cases could occur even in the absence of interaction (spread) between farms. A typical example would be environmental factors impacting herds independently. Thus, clusters could be detected even if spatial autocorrelation does not exist. Second, the methods used to identify the existence of spatial clusters might have higher sensitivity than those used to identify spatial clustering, at least as we used these methods in the study. We used the latter set of methods over the entire study area, in contrast to the use of similar methods (difference in K-functions) in specific regions to investigate other swine diseases . The rationale for our approach was that we had no predefined local area of interest prior to analysis, and we used methods intended to accommodate the heterogeneous distribution of the study population.
Apparent local spread (neighborhood spread) existed, as suggested by the existence of clustering and clusters on a small spatial and temporal scale. During the 2001 foot-and-mouth (FMD) epidemic in the UK the term "local spread" was used in a field when a new FMD case was identified within a 3 km of a previous FMD case, and contact with a more distant source of FMD could not be determined . This description of local spread was more in line with the field investigation of outbreaks on a case-by-case basis, whereas our approach to investigating local spread was comparable to the analytical approach taken by Picado et al . Similar findings for PCVAD clustering were reported in Denmark  and subsequently in Great Britain , although the scale of spatio-temporal clustering in the latter study seemed to be larger than in this study. High pig-farm density in the neighborhood was identified as a risk factor in other studies as well . A pattern of local spread could be the consequence of a combination of different mechanisms, including direct, indirect, and airborne transmission of an agent identified as a necessary cause (PCV2) or a component cause (eg. PRRSv). These mechanisms could not be easily discriminated using the data at hand. While the possibilities of direct and indirect transmission are discussed in previous reports, data concerning airborne spread are scant. Recently, Verreault et al  reported detection of PCV2 genome copies in the air of confined finisher barns in concentrations of up to 107 copies/m3. The significance of this finding is yet to be elucidated. Although none of the secondary likely spatio-temporal clusters were statistically significant, they exhibited some common characteristics. They were observed in zones 1 and 2, where the majority of pig herds in the study population were located, involved a small number of herds, and were short in duration and limited in geographical extent. The latter two observations were in agreement with the results of the spatio-temporal K-function. However, given the number of herds in this study, statistical evidence to support existence of apparent local spread was relatively weak. This could be a consequence of non-differential misclassification due to the non-specific case definition; alternatively, local spread may have been only one component of disease transmission, or perhaps that apparent local spread was confounded by clustering of farms under the same ownerships in the same geographical area. Thus, the results of this study suggest that farms in the vicinity of those experiencing PCVAD outbreaks were at increased risk of experiencing outbreaks for months. Recommendations based on these findings were modified once other factors were taken into account. The results and methodological approaches taken are reported in an accompanying article .
At least two inconsistencies in the results suggest the existence of patterns of spread other than apparent local spread. Firstly, while the existence of a spatial trend in the study region was confirmed in various analyses, the most likely spatio-temporal clusters occurred almost haphazardly in x direction and time (Figure 11). This suggests that disease did not spread as a sequence of geographically connected outbreaks in the east-west direction. Secondly, the expected time to outbreak in herds located in zone 3 was equivalent to that in zone 1, while herds located in zone 3 had the largest residuals and were influential points in the GAMs. It is possible that herds in this area were more isolated from the major centers of swine production than herds in the other three areas. This "isolation" could be with respect to direct or indirect potential sources of infection. The infectious agent could have also spread via other transmission pathways, primarily through movements within swine production companies and their suppliers. Bigras-Poulin et al  showed that patterns of swine movement in Denmark had the topology of a scale-free network. Theoretically, much lower transmission probabilities on scale-free networks are sufficient to spread or maintain "infection" on these networks than under the assumption of a homogeneous mixing . Recently, Firth et al , using PCV2 sequence data, reported several significant diffusion pathways for this agent between different continents and between different countries. The pathways identified were similar to the trade patterns of swine. Despite the limitations inherent to such data (ie, reporting time of sequence data) and study design (ecological study), the conclusions suggest that live-animal movements contributed to disease spread. Woodbine et al  identified purchase of breeding stock as a risk factor for herd outbreaks in the early phase of the PCVAD epidemics in Great Britain. In this respect, it is possible that Ontario herds in zone 4 (>700 km east) interacted more with herds in the neighboring province (Quebec) than with other Ontario herds. In contrast, herds in zone 3 (600 to <700 km east) were likely sufficiently distant in both geographical and road distances from centers of intensive production in the highly swine-dense areas of Ontario and Quebec to decrease the frequency of direct contacts (through animals) and indirect contacts (through fomites) with herds from these centers. This is consistent with the findings of Madec et al , who argued that contact between pigs is the main route of transmission for PCVAD. In agreement with direct contact as a major contributor to PCVAD spread, ownerships as proxy measurements for network memberships were investigated in the accompanying article . However, regardless of whether spread through networks occurred or not, it should be stressed that detailed investigation of production-disease epidemics in intensive production systems that prevail today in industrialized countries is challenging if appropriate movement and contact information is not readily available. Despite these limitations, results gained through this exploratory analysis support the spread of the infectious agent in accordance with other studies [14, 15].
Generalized additive models were useful with respect to investigating different aspects of PCVAD. Some advantages of the trend surface produced by the GAM were that it could be easily adjusted for risk factors, and residuals and influential values could be examined. In addition, deviance residuals could be produced from the model using binomial (aggregated) data to construct an empirical variogram. This approach has the advantage of evaluating second-order effects (clustering) after accounting for the first-order effects (geographical trends). However, this aggregation of herd-level (Bernoulli) data to areal (binomial) data (in our case using a 2 × 2-km grid) introduced two limitations. First, herd-level covariates could not be used in a model unless they were aggregated to the same level as the outcome. Second, as in any logistic regression model, a reasonable number of observations in each covariate pattern is needed to achieve desirable properties of residuals . For the aggregation used in this study, this could be attained only if the density of sampled points in a grid was high or the area of the grid used to collapse the data was large. Finally, the GAM further offered the opportunity to investigate the location and significance of local clusters. This approach was based on previously published methodology . In this study, both approaches identified spatial clusters in the same region, although the location and the extent of the two high risk areas only partially agreed. We opted to use the GAM approach to identify spatial trend and risk factors in a purely spatial model, as opposed to the logistic regression based on fully Bayesian linear mixed model with spatially structured residuals (for example, see Peng et al ). Although performance of the two approaches was not compared, one of the advantages of the GAM approach over a generalized linear model (Bayesian or otherwise) is that the GAM allows for fitting a very flexible trend surface for spatial point data.
This study has several important limitations. First, the study population represented a biased sample of the Ontario swine population at that time. One explicit inclusion criterion was that the referent veterinarian was to be a member of the Ontario Association of Swine Veterinarians (OASV), and information was shared through OASV's e-mail list. This group of veterinarians consults for most commercial swine herds in Ontario. Premises holding small numbers of pigs may be under-represented in the study population because these farmers may be less likely to ask for the services of a veterinarian. We believe that this increased the accuracy of diagnosis, because clinical signs suggestive of systemic PCVAD are easier to observe in large populations. Moreover, we believe that this study was not biased with respect to geographic location, because two diagnostic laboratories that perform PRRSv testing are located within a 30-km Euclidean distance, and some samples from the alternate diagnostic laboratory were eventually included in the study when PRRSv sequencing at no cost was offered as an incentive to participate in the study. Therefore, we believe most eligible herds were included in the study. We cannot provide complete statistics on this, since inclusion of a herd was the responsibility of not only the research team (e.g., whether an interview could be arranged), but also of the veterinarian (e.g., whether samples should be submitted, whether the premise and the case submission should be included in the study). It was anticipated that a comparatively high percentage of PRRSv-negative herds would be identified in eastern Ontario, as the density of swine herds in this region is much lower than in western or southern Ontario. We included the PRRSv status of a herd at the time of sampling in an attempt to adjust analytically for such stratification, when the risk surface was produced. Results of adjusted analysis suggested that the spatial trend was simpler and more suggestive of directionality than the expectations from the unadjusted analysis. A mapping approach using GAM was very useful in this respect.
Bias might also influence detection of clustering and clusters. We believe that the impact of this bias is small for the following reasons: (i) PCVAD-positive and negative herds were selected from the same target population using the same selection mechanism, and (ii) premises with multiple herds included over time were aggregated to only one, the most relevant herd. Since PRRSv-positive status is associated with higher odds of being a PCVAD-positive herd, potential spread of PRRSv or a specific PRRSv genotype might have positively contributed to measures of clustering for PCVAD.
The second important limitation of the study is a non-specific case definition that depended on the memories of the producers. The extent and influence of potential misclassification bias is difficult to ascertain. However, results of the several initial analyses that were based on more stringent criteria to define a case (e.g., was PCVAD verified by laboratory testing) confirmed the same conclusions with respect to temporal (Figure 6) and spatial trends (data not shown). Consequently, we decided to use the maximum amount of data available. In addition, herd-level diagnosis of PCVAD is difficult, as even identifying PCVAD in individual pigs does not necessarily equate to a clinical problem in the herd. Herd-level diagnosis of PCVAD is ultimately based on mortality rate in the growing pig, which, in the absence of regular electronic monitoring, has to rely on the operator's assessment. The reader should also be aware that under the "Circovirus Inoculation Program" , swine producers could qualify for compensation for diagnostic testing and vaccination for PCV2 performed between March 1, 2006, and December 31, 2008. This likely increased diagnostic testing and confidence in declaring PCVAD status of a herd. Finally, within a region, spatially referenced data about the spread of a disease such as PCVAD is difficult to obtain under current conditions.
Third, one could also argue that a large number of herds were excluded from our analysis. However, the purpose of this step was to eventually have only one, the most relevant, data point per premises - representing the first occurrence of a disease at that site.
Fourth, introduction and uptake of effective vaccines might have had an undue influence on our results. At least one commercial vaccine was introduced in Canada and the USA starting in late March and April of 2006 [32, 33] under conditional license. Due to limited supply, it was initially distributed to herds with documented outbreaks. At the time of vaccine introduction, the peak of the outbreak in this study population had already occurred in June of 2005 (Figure 6). Thus, the most likely impact of this intervention on the results of the study was to diminish any effects identified. This also illustrates a need to evaluate possible time-varying patterns of disease spread. Despite its limitations, we believe our investigation will provide additional information about this important disease, particularly under North American farming conditions.