Visualizing and testing the impact of place on late-stage breast cancer incidence: a non-parametric geostatistical approach

Abstract

This paper describes the combination of three-way contingency tables and geostatistics to visualize the non-linear impact of two putative covariates on individual-level health outcomes and test the significance of this impact, accounting for the pattern of spatial correlation and correcting for multiple testing. The methodology is used to explore the influence of distance to mammography clinics and census-tract poverty level on the rate of late-stage breast cancer diagnosis in three Michigan counties. Incidence rates are significantly lower than the area-wide mean (18.04%) mainly in affluent neighbourhoods [0-5% poverty], while higher incidences are mainly controlled by distance to clinics. The new simulation-based multiple testing correction is very flexible and less conservative than the traditional false discovery rate approach that results in a majority of tests becoming non-significant. Classes with significantly higher frequency of late-stage diagnosis often translate into geographic clusters that are not detected by the spatial scan statistic.

Fig. 1

Maps of late-stage breast cancer incidence rate (A) and number of cancer cases (B) in three Michigan counties, by census tract (CT), 1985-2002. Maps of percentage of habitants living below the federally defined poverty line in 1990: original census tract data (C) and results of disaggregation using ATP kriging (D). Location of mammography clinics in 2006 (E), and map of population-based distance to the closest clinic (F). Note the contrasted economic statistics for the Twin Cities of Benton Harbor and St Joseph, denoted by letters B and J in Fig. 1C.

Fig. 2

Late-stage breast cancer incidence rates computed for 169 classes of poverty level × distance to mammography clinics (A), and their row and column averages (B,C). Rates based on less than 10 cases are considered missing and displayed in white in the frequency table.

Fig. 3

Experimental indicator semivariograms with the model fitted (solid line) computed for different options: omnidirectional for short distances (A) and directional for long distances (B).

Fig. 4

Location of patient residences and the simulated stage at diagnosis (x = early stage, ● = late stage). Frequency tables and marginal frequency plots are generated for each of the three simulated maps and compared to results obtained from actual data in Figure 2 in order to compute the p-values of the tests of hypothesis.

Fig. 5

Impact of multiple testing correction on the significance of joint and marginal frequencies computed in Figure 2: No correction (1^st column), False discovery rate (FDR) correction (2^nd column), and simulation-based procedure (3^rd column). In all graphs, blue (red) pixels and segments represent incidence rates that are significantly lower (higher) than the incidence rate expected under the assumption of no impact of covariates on late-stage diagnosis (α=0.05).

Fig. 6

Map of the probability of occurrence of significantly higher frequency of late-stage diagnosis (B) obtained using kriging and the semivariogram model inferred from indicator data (A). Ellipses represent the primary (solid) and secondary (dashed) clusters of high relative risks of late-stage diagnosis detected using the spatial scan statistic.