Spatial modeling of repeated events

The analysis of disease incidence (or mortality) over space has broadly been used recently due to growing demand for reliable disease mapping. Spatial modeling of disease incidence is used to model spatial variations in the disease pattern and separate variability from random noise, a factor that typically overshadows crude disease incidence map. Map of areal disease incidence is a practical tool to determine spatial pattern of disease incidence for resource allocation. Borrowing strength from neighboring geographic sub-areas usually provides a reliable estimate of the underlying disease risk. Mixed models are commonly used to analyze spatial data which frequently occur in practice such as in health sciences and life studies. It is customary to incorporate spatial random effects into the model to account for the spatial variation of the data. In particular, mixed Poisson models are used to analyze the spatial count data. On the other hand, in some studies of health system services, using the Poisson regression may not be appropriate as events are not typically rare. It is then usual to consider a mixed binomial model for spatially correlated binary data. Global auto-normal conditional autoregressive (CAR)-based models are the most popular spatial smoothing approach, which are comparably convenient to accommodate spatial random effects. In this dissertation, the Leroux CAR (LCAR) model is used to capture the spatial random effects. We also consider quasi likelihood (QL) approach to account for the full spatial covariance structure of the data, which only demands the mean of the responses and the relationship between the mean and the variance rather than the exact specifications of the distribution. In many cases, the QL approach maintains a full or an approximately full efficiency. It is often assumed that the observations in each area, conditional on spatial random effects, are independent to each other. However, this may not be a valid assumption in practice. For instance, multiple asthma visits by a child to physicians/ hospitals (within a year) are not clearly independent observations. To overcome this problem, in Chapter 2, we develop spatial models with repeated events for count responses. In particular, a spatial compound Poisson model (SCPM) is introduced to account for the repeated events as well as the spatial variation of the count data in the case of rare events. The QL approach is used to estimate the model parameters including fixed and variance components. Performance of the proposed approach is evaluated through simulation studies of both regular and irregular neighborhood structures and also by a real dataset of children asthma visits to hospitals in the province of Manitoba, Canada. In Chapter 3, we develop spatial models with repeated events for binary responses and call it spatial probit Poisson model (SPPM) to account for the repeated events as well as the spatial variation of the binary responses. The QL approach is used to estimate the model parameters including fixed and variance components. Performance of the proposed approach is examined through simulation studies and also by a real dataset of children asthma visits to physicians in the province of Manitoba, Canada. {We propose spatial models considering repeated events} and conclude the dissertation with saying that if we ignore repeated events in spatially correlated count or binary data (which are widely used in health research), we may lead to wrong conclusions and misguide public and policy-makers for possible interventions/preventions and resource allocations for areas which are most needed.

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