Spatial data analysis: applications to population health

In recent years, studies in demographic forecasting have grown significantly. One of the goals of demography is to statistically analyse and predict mortality and fertility rates without relying on subjective opinions of experts. Therefore, to identify the characteristics of the mortality dynamics of a population, many models were developed since the intro- duction of the famous model proposed by Lee and Carter (1992). Many research available in the literature tend to focus on the time series perspective of forecasting mortality rates. Lack of studies from the spatial framework sparked our interest in investigating the mor- tality rates from the spatial framework. The extension of the Lee-Carter (1992) model by incorporating the idea of functional data analysis (FDA) inspired the first part of this thesis where the FDA concept was applied to the spatial demographic analysis framework. We investigate the existence of spatial autocorrelation in mortality data of neighbouring countries. A functional spatial principal component method is proposed to reveal spatial patterns by directly considering spatial information. A functional Moran’s I statistic is introduced. This statistic aids in determining the spatial autocorrelation in functional data through the implementation of the spatio-functional PCA. This functional Moran’s I statistic is the first of its kind in the functional data framework.

The second part of this thesis investigates the impact of the VigilanS system (program to prevent suicide reattempts in France) on suicide recidivism where the data from this system (patient’s age, sex, address, history of suicide attempts, hospital stay etc.) are mapped on the map of the Nord-Pas-de-Calais region while constructing spatial predic- tion models. The risks of suicide attempts are mapped with the help of spatial probit models. We propose a partially linear probit model for spatially dependent data. This model has not been investigated in the literature from a theoretical point of view and this part fills that gap by addressing a spatial autoregressive error (SAE) model where the spatial dependence structure is integrated in a disturbance term of the studied model. A semi-parametric estimation method is obtained by combining the generalized method of moments approach and the weighted likelihood method. We examined the use of this spatial probit regression model as well as other existing models in the literature to study the suicide relapses of patients involved in the VigilanS system.