We illustrated the application of spatial regression models to examine the association between county-level racial/ethnic composition and reported cases of 2 STDs (chlamydia and gonorrhea), using Texas data for the year 2000. Our results imply that a unit change in percent black is associated with 1.6% (1.1% for Hispanic) and 3.3% (0.5% for Hispanic) change (on average) in chlamydia and gonorrhea rates respectively, compared with percent white. Thus while the average percent change in chlamydia rate associated with a unit change in percent black was slightly higher than the average percent change associated with a unit change in percent Hispanic (1.6% vs. 1.1%), the average percent change in gonorrhea rate associated with a unit change in percent black was substantially higher (3.3% vs. 0.5%)—over 6 times higher. Additionally, for percent black, the magnitude of the association is about 2 times higher for gonorrhea than for chlamydia (3.3% vs. 1.6%). In contrast, the magnitude of the association for percent Hispanic was about 2 times higher for chlamydia than for gonorrhea. The results confirmed the relatively higher association between percent black and STDs found in studies that accounted for spatial autocorrelation.12,13,37,38 However, none of them included percent Hispanic in their regression analyses so we cannot make any comparisons concerning the relative magnitude of association.
The control variables used in the analysis had the expected signs except the socio-economic variables. Their signs seemed counter-intuitive because higher rates of STDs are expected to be negatively associated with socio-economic status.10,52,53 However, at the county level, median household income was relatively high in the urban counties, which also tended to have higher STD rates. This may explain the positive association between STDs and median household income. On the other hand, percent owner-occupied had a negative association because urban counties with relatively higher STD rates had lower proportion of single-family homes, on average.
Although the spatial models (SAM and SEM) were superior (using standard criteria) it is important to point out that we did not find any substantial difference in the coefficients. Koumans et al13 did not provide information on alternative model comparisons with the spatial variable. Greenberg et al12 found substantial difference in the coefficients between the OLS and spatial model results using county-level gonorrhea data for 2002 in the United States. Delcher and Stover37 did not highlight the differences between the models they used. Semaan et al38 studied state-level association between social capital and STDs (gonorrhea and syphilis). Semaan et al38 also found no difference between OLS and spatial regression results when they controlled for population-level variables. Consequently, they suggested that the bulk of the spatial effect may have been captured by the racial composition variable, which may also explain our results. Thus spatial regression models may not always result in substantial changes in the coefficients of interest. However, they are superior methods and have become an indispensable part of regression analyses when, in theory, location plays an important part of the issue being studied, which is undeniably true for STDs.
We note limitations in the STD incidence data we used. The data were assembled from reported cases of infection which are dependent upon medical providers testing for primarily asymptomatic infections and providers or laboratory reporting positive results. Additionally, different localities may focus screening efforts on specific subpopulations thereby limiting the ability to generalize or extrapolate to the general population in any particular geographic unit. For instance, differences or similarities in how counties adhere to annual chlamydia screening for women in certain age groups recommended by individuals and national organizations54–58 may affect the county-level geographic distribution of the reported cases of chlamydia in this study. However, the extent to which it affects the results is difficult to assess. Also, the measure of percent Hispanic as reported by the 2000 census introduces some overlap in our measure of racial/ethnic composition as the Hispanic ethnic category includes other races.
Consensus on appropriate methods for adjusting rates to reduce variance instability and to make comparing rates from different locations more reliable has not been reached.59 Temporal smoothing is one method but may not be the best for STDs. However, for the purpose of identifying differences in STDs for counties in this study, it was a fairly robust measure because it provided an average over a 3-year period. More work is needed in this area to develop validated methods to reduce the “small-number problem” with incidence rates.
By focusing on only the counties within Texas, our analysis ignored spatial effects from counties that are contiguous to border counties but located in neighboring states. This omission may have affected our estimates, but it is difficult to determine the extent of the effect. This potential limitation, together with the problem of spatial heterogeneity illustrates the need for more studies to develop methods that use data from a relatively wider geographic area (such as all counties in the United States), while controlling for spatial autocorrelation and heterogeneity. Such methods would be useful to help understand the overall extent of the association between county-level racial/ethnic composition and STD rates.
This study has shown that, for the state of Texas, the exact specification of the spatial relationship (Queen or Rook) was important in measuring the extent of the spatial autocorrelation in STD rates. The difference was primarily because most counties in Texas were represented by “well-arranged” regular rectangular polygons. The difference may not exist with irregularly shaped or positioned polygons. Additionally, the exact reason for this difference may be understood from a contextual framework of local activities generating the signals from the existing data. In view of this, depending on the overall configuration of the polygons representing the spatial units of analyses, it is important to explore which specification gives the best results, because the exact type of spatial relationship used may be a source of statistically significant difference in the results obtained.32,36 The few studies that accounted for spatial autocorrelation in STD studies did not explore different spatial relationships and spatial regression models. Our study and previous studies have used larger geographic units (counties and states). Thus, further research is needed in this area, using smaller geographic units such as census blocks or cities, including more investigation into higher-order contiguity measures (i.e., spatial dependence that goes beyond the adjacent neighbors and accounts for the effects of the “neighbors of neighbors”).
Numerous previous studies have documented higher rates of reported STDs among certain minority racial/ethnic groups. Using county-level data on reported cases of chlamydia and gonorrhea for the state of Texas, we found that these disparities persisted at the county level even when controlling for STD rates in neighboring counties, although the association between county-level STD rates and racial/ethnic composition was dependent on the STD in question. In spite of the fact that there were no substantial differences in the magnitude of the estimated parameters, our illustrative analyses showed that the spatial regression models used were superior to the ordinary regression models and should be carefully explored in future studies.
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APPENDIX A. SPATIAL VARIABLES CREATED USING QUEEN AND ROOK CRITERIA
Carson county’s Queen contiguous (or first-order) neighbors are all eight counties that are contiguous to it - Moore, Hutchinson, Roberts, Potter, Gray, Randall, Armstrong, and Donley counties (see the zoomed insert in Fig. 1). Carson county’s Rook contiguous neighbors are Hutchinson, Potter, Gray, and Armstrong counties.
A nine-by-nine binary contiguity matrix for Queen and Rook neighbors based on the clipped insert in Figure 1 is presented below, where contiguous counties are assigned 1, or 0 otherwise.
Queen contiguity matrix:
Rook contiguity matrix:
The corresponding row-standardized (rows sum to unity) matrix is postmultiplied by the nine-by-one vector of the temporally smoothed rates. In matrix multiplication, each corresponding element in the resulting matrix is obtained by summing up the product of each row element in the first matrix and the corresponding column element in the second matrix.
i.e., WQueen · R = r
As an example, Carson county’s spatial lag (rC) created using the standardized Queen contiguity matrix gives:
Which is the average smoothed rate of all its 8 contiguous neighbors - Moore, Hutchinson, Roberts, Potter, Gray, Randall, Armstrong, and Donley.
i.e., WRook · R = r
By the same procedure, the spatial lag created using the standardized Rook contiguity matrix for Carson county gives:
Which is the average smoothed rates of its 4 contiguous neighbors with a common side - Hutchinson, Potter, Gray, and Armstrong.