Overcoming the Modifiable Areal Unit Problem and Residential Mobility Bias: Methodological Exploration and Prospective Application of the Dual-Track Joint Log-Gaussian Cox Process in Spatial Epidemiology

**[Preprint Status & Author's Note]** This manuscript represents the foundational methodological framework (Phase I) of an ongoing research initiative. It focuses on the theoretical construction, mathematical proofs, and analytical design of the proposed model. Empirical validation using full-scale spatial datasets is currently underway and will be appended in subsequent versions. AbstractAs global urbanization continues to accelerate, high-density urban built environments have been widely recognized as core structural determinants influencing the incidence and progression of chronic non-communicable diseases (NCDs) such as lung cancer. However, current epidemiological studies aimed at assessing the spatial association between micro-physical environments and population health face a series of profound methodological challenges and theoretical limitations. First, traditional areal aggregation models based on administrative boundaries or artificial grids are inevitably compromised by the scale and zoning effects of the Modifiable Areal Unit Problem (MAUP), which artificially fragments continuous physical exposure surfaces and leads to unstable statistical inferences. Second, due to the barriers in acquiring life-course longitudinal residential trajectory data, the vast majority of cross-sectional spatial epidemiological studies rely solely on the "current residence" at the time of diagnosis for environmental exposure assessment. This approach fails to account for the cross-spatiotemporal "exposure misclassification" and "residential mobility bias" induced by highly mobile populations. Finally, when introducing highly flexible latent spatial random fields to control for spatial autocorrelation, models are highly susceptible to the trap of "spatial confounding", resulting in the fixed effects of built environments facing the risks of overfitting, shrinkage to zero, and compromised causal explanatory power. To systematically address and overcome these three major methodological limitations, this study proposes a prospective point process analytical framework oriented towards continuous physical space joint inference. This study constructs the "Dual-Track Joint Log-Gaussian Cox Process (Joint LGCP)", which fundamentally eliminates the topological truncation and MAUP interference caused by areal data aggregation through infinite-dimensional integral calculus of inhomogeneous Poisson processes in a two-dimensional continuous observation domain. [cite_start]Addressing the absence of longitudinal exposure data, this study innovatively introduces the "space-time substitution" concept from ecology and geomorphology into spatial epidemiology. By utilizing China's unique Hukou system as a topological anchor for long-term residential trajectories, and quantifying the spatial separation between the cases' "current residence" and "Hukou registration place," the global sample is orthogonally decoupled into a dual-track layer: a "permanent resident" group representing long-term in situ exposure, and a "migrant" group carrying historical heterotopic exposure debts. This mechanism maximizes the quantification and filtration of the lagged bias of historical exposure under cross-sectional data constraints. Furthermore, by integrating Penalized Complexity Priors (PC Priors) and Restricted Spatial Regression (RSR) constraints into the underlying Bayesian inference, this framework mathematically circumvents the collinearity competition between Gaussian random fields and spatial fixed effects, ensuring the independent causal explanatory power of micro-urban built environment factors. The methodological reconstruction in spatial epidemiology presented in this study not only provides a more robust quantitative tool for clarifying the nonlinear spatial coupling mechanisms between complex built environments and chronic respiratory diseases, but also lays a solid scientific and theoretical foundation for promoting proactive, forward-deployed spatial defenses in future healthy city planning. Keywords: Spatial Epidemiology; Log-Gaussian Cox Process; Spatial Confounding; Modifiable Areal Unit Problem (MAUP); Residential Mobility Bias; [cite_start]Space-for-time Substitution