We adapted the model suggested by Abellan et al.  in the context of binomial variability to the Poisson case in order to analyze the space-time patterns of bladder cancer incidence in Utah for the period 1973-2004. Sparseness is quite common in disease mapping at small area level. Richardson et al.  showed that Bayesian hierarchical models for disease mapping are highly specific but may have low sensitivity in the presence of sparseness. We aggregated the number of cases over 4-year periods to partly remedy this. The distribution of Utah population is highly heterogeneous, with nearly 77% concentrated in 4 of the 29 Utah counties (Salt Lake, Utah, Davis and Weber). As the population in these areas was relatively high, we had more statistical power to detect not only spatial excess RRs, but also sizeable space-time interactions.
Some of the risk factors for bladder cancer are different for males and females as occupational exposure is more predominant amongst males. But in our analysis, including the females enabled us to strengthen the patterns observed for males only, pointing towards non-occupational risk factors.
Census tracts are small statistical subdivisions of a county. They usually have between 2,500 and 8,000 residents. Administrative boundaries may not be ideal for mapping health outcomes and for interpreting associations between environmental exposures and health effects. This is also related to the modifiable areal unit problem, which arises from over-imposing an arbitrary spatial aggregation on a continuous spatial process . Changes in spatial aggregation or arrangement of areas can affect the underlying values for those areas, so observations are usually only relevant for the scale of analysis and should not be imputed to individuals.
Our results indicated that 19.4% of census tracts had an excess RR, and most of them were located in Salt Lake County. Our model was also used to assess areas for which the excess RR was stable over time. We found that in 93 areas out of the 96 with high spatial RR, this excess was sustained over the 32 years considered. This suggests that risk factors were continually present in most areas in Utah. The performance of exceedance probabilities to detect areas with high or low risk may be dependent on the model used (i.e. whether spatially unstructured or spatially structured random effects are included, and the way the spatial structure is modelled too) and on the data as well (level of sparseness, weak or strong spatial autocorrelation, etc.). The model chosen here for the spatial random effects as well as the rules we applied to the pure spatial effects to classify areas have been thoroughly investigated in the last years. Lawson et al.  and Best et al.  carried out simulation studies to compare several models in the pure spatial context and showed that the CAR is one of the most robust models for spatial random effects in disease mapping. Recently, it has been argued that it performs poorly in the case of heavy spatial autocorrelation , but this is rarely the case with incidence or mortality data of chronic diseases. The exceedance probability rules, P(exp(s
) > 1|data) > 0.8, used here to classify the spatial risks have their limitations [25, 26] but their general usefulness as a measure of uncertainty has been proved in simulation studies .
We also explored which areas showed 'unusual' time trends compared with statewide trends. Using the decision rule based on marginal posterior probabilities with a threshold of 0.6, we found 13 census tracts classified as 'unusual'. Space-time departures were mainly detected for the period 1997-2000 when the highest level of risk was observed in the temporal trend. This unexpected time variation in the risk could correspond to a change in recording practices or to a real excess of cases and our results deserve further scrutiny. With a long latency disease like bladder cancer, we did not expect to find a large number of significant space-time interactions that can be interpreted epidemiologically. This was consistent with our findings. These areas were not geographically clustered, which suggests that chance rather than an environmentally driven process generated these unusual area-specific patterns.
The time trend of risk of bladder cancer incidence in Utah fluctuated over the 32 years analyzed. A steady decrease was observed between 1977 and 1992, followed by an abrupt increase until the period 1997-2000. Assuming that bladder cancer has a latency of 15-30 years, then the spike in 1997-2000 may be correlated with the urbanization and industrialization of Weber, Davis, Salt Lake and Utah counties (77% of the population). Prior to 1975, these counties were primarily rural and agricultural in nature with some industries around the small urban centers in the county. From 1975 through 1985, these counties underwent a substantial urbanization as the freeway I-15 was completed in 1974 and Utah actively recruited industry to establish in these counties. These counties had substantial growth (near 35% increase in population) period between 1970 and 1980 which is nearly double that of the decade before and after (both around 17-19%). During those years, the new population was brought into close proximity with the new industry, and consequently the occupational exposure of people working in industry may be more important. Subsequent to those years, improved regulatory controls and technologies have reduced the exposure even though the population remains close to the sources.
Staying at the aggregated level, we thus proposed a novel strategy of using areas with stable risk to carry out a 'geographical' case-control study of association between risk of bladder cancer and presence of TRI sites. To this end, we considered areas with high risk sustained over time as cases, and the remaining areas with stable 'neutral' risk as controls. We restricted the case-control study to areas with sustained risk because of the mismatch between the periods of exposure and health outcomes considered here. Data on TRI sites are only available from 1988, though toxic sites may have existed long before that. The results of the case-control study showed some evidence of positive association after adjusting for the fraction of the population belonging to the LDS Church. However, because of the important migration, the association of bladder cancer with the presence of TRI sites may be diluted .
Because the TRI data is collected for regulatory purposes and not for exposure assessment purpose, there is considerable criticism over its use to estimate exposure. The EPA frequently changes the reporting requirements in what agents are to be reported and at what threshold (magnitude of release) they are to be reported. In addition, there is no assurance that all the industries that should be reporting are reporting. In some cases what is reported is left to the interpretation of the industry. Releases are computed using a complex modeling system rather than actual monitoring. For those industries that are reporting, in order to minimize the regulatory impacts, they might underestimate their actual release when possible. There has also been a concern about a potential problem of miss-locating the TRI sites since coordinates of these sites are only stored with minimal decimal places. We used more precise information from the UDOH data for which aerial photographs are used to pinpoint each site to remedy this.