It is the primary focus of this aim to broaden the definition of the survivor, density and hazard function to include spatial labeling by explicit modeling of the spatial dependency. This involves the direct derivation of (s,t), S(s,t), and h(s,t and their related marginal and conditional functions. The application of these novel derivations with standard geographically-augmented survival distributions will be examined. Spatially dependent censoring is also a focus as a sub- aim. We plan to model this aspect and evaluate the role of this in direct spatial and contextual survival models. Predictors in survival modeling can be individual (age, gender, race etc) or contextual (e. g. census tract demographics). They can also vary spatially in their linkage to survival risk. We propose to examine the development of models where predictor selection has a spatial label and where some regions do include and other exclude predictors in models. We plan to implement the modeling approaches above via the use of the Bayesian paradigm and will likely use McMC based packages or, if appropriate, INLA. Evaluation will be simulation based and we will use R and associated linked software (MCMCpack, BRugs, R2WinBUGS, R2OpenBUGS) for this purpose.
This proposal focusses on the development and evaluation of novel methodology for the analysis of spatially referenced cancer survival. First we aim to broaden the definition of the survivor, density and hazard function to include spatial labeling by explicit modeling of the spatial dependency within these functions. As a sub-aim we also wish to explore models for spatially-dependent censoring. Second we aim to develop novel approaches to incorporation of predictor effects within different sub-regions of study areas. Finally, the simulation-based evaluation of the new methods and their computational implementation will be pursued.