Challenges in disease mapping: predicting cancer incidence and analyzing models’ smoothing

Disease mapping aims to study geographic patterns and temporal trends of incidence and mortality of different diseases, essentially non-transmissible, such as cancer. Spatio-temporal models for areal data play a crucial role in describing the cancer impact in different populations, helping governments, policy makers, health professionals, and researchers to formulate cost-effective prevention, diagnosis and treatment strategies. However, the analysis of cancer data presents several challenges. On one hand, the lack of cancer incidence registries in certain geographical áreas makes the spatial or temporal analysis of cancer incidence patterns difficult. On the other hand, some cancer types, such as rare cancers, remain understudied due to the limited availability of comprehensive data. This thesis is dedicated to enhancing and developing methodologies to address the challenges associated with both cancer incidence data and the study of rare cancers. It aims to achieve the following primary objectives. The first objective is to focus on challenges associated with cancer data collection and to review the statistical methods used in the literature to deal with these challenges. Chapter 1 provides a general introduction on cancer data to understand the relevance of the problem. This thesis’s second objective is to develop new models that can predict cancer incidence rates in geographic areas lacking cancer registries. This will subsequently allow for national-level cancer incidence estimates. In Chapter 2, we leverage multivariate spatial models commonly employed in the disease mapping literature to predict cancer incidence. The third objective aims to extend the collection of multivariate spatio-temporal models by incorporating adaptable shared interaction terms. This will facilitate a more comprehensive analysis of both incidence and mortality for rare cancer cases. In Chapter 3, a detailed description of the proposed models is provided. These models allow the modulation of spatio-temporal interactions between incidence and mortality, allowing for changes in their relationship over time. The fourth objective is to assess the effectiveness of the models developed in Chapter 3 for short-term forecasting of cancer incidence rates, while handling missing data within the time series given the lack of cancer registries in certain geographical areas. In Chapter 4, a validation study is conducted to assess the predictive ability of the models for both forecasting and predicting missing data, using lung cancer mortality data from England’s administrative healthcare districts for a period covering 2001 to 2019. The fifth objective is to provide a comprehensive overview of the smoothness induced by the spatial univariate models. Implicit in these models is some degree of smoothing, wherein, for any particular unit, empirical risk or incidence estimates are adjusted towards a suitable mean or incorporate neighbour-based smoothing. Hence, while model explanation may be the primary objective, it is crucial to scrutinize the smoothing effect of the models. Further, a particular smoother has parameters and there has been no study regarding how varying these parameters affects the induced smoothing. Chapter 5 investigates, both theoretically and empirically, the extent of smoothing achieved by a given model. The sixth objective is transversal to all chapters. We have a strong commitment with reproducibility, and the code developed in this thesis is publicly available at the GitHub of our research group (https://github.com/spatialstatisticsupna). The thesis ends with the main conclusions and future research lines.