Modelling spatially correlated survival data for individuals with multiple cancers

Abstract

Epidemiologists and biostatisticians investigating spatial variation in diseases are often interested in estimating spatial effects in survival data, where patients are monitored until their time to failure (for example, death, relapse). Spatial variation in survival patterns often reveals underlying lurking factors, which, in turn, assist public health professionals in their decision-making process to identify regions requiring attention. The Surveillance Epidemiology and End Results (SEER) database of the National Cancer Institute provides a fairly sophisticated platform for exploring novel approaches in modelling cancer survival, particularly with models accounting for spatial clustering and variation. Modelling survival data for patients with multiple cancers poses unique challenges in itself and in capturing the spatial associations of the different cancers. This paper develops the Bayesian hierarchical survival models for capturing spatial patterns within the framework of proportional hazard. Spatial variation is introduced in the form of county-cancer level frailties. The baseline hazard function is modelled semiparametrically using mixtures of beta distributions. We illustrate with data from the SEER database, perform model checking and comparison among competing models, and discuss implementation issues.

Figure 1

Distribution of cancer-specific frailties (Y-axis) under the different models. Y-axis range is from −4.0 to −1.0. Positive frailties indicate higher relative risks while negative values indicate the opposite

Figure 2

Distribution of average patient-specific frailties (Y-axes) from different counties (X-axes) in Iowa under Model I and Model III. Y-axes reference lines at Y = 0. Positive frailties indicate higher relative risks while negative values indicate the opposite

Figure 3

Distribution of spatial frailties (Y-axes) for colon and rectal cancers from different counties (X-axes) in Iowa under the different models. Y-axes range is from −1.0 to 1.0 with reference lines at Y = 0. Positive frailties indicate higher relative risks while negative values indicate the opposite. The plots for the other models show very similar patterns

Figure 4

Spatial frailties for colon and rectal cancers in Iowa under the different models. Color change from white to black indicates an increase from negative to positive spatial frailties. Cutoff values are one standard deviation units from the mean of each cancer type in each model. Locations of urban areas are also indicated to potentially account for clustering

Figure 5

Boxplots of the $CP{O}_{ij}^A-log\mathit{CP}{O}_{ij}^B$ for each model pair. Positive values indicate support for model A over model B while negative values indicate the opposite. A value equal to 0 indicates equivalence of the two models. The wider range of values in comparisons involving Model IV indicate the other models perform considerably better