Modeling dependent survival data through random effects with spatial correlation at the subject level

Dynamical phenomena such as infectious diseases are often investigated by following up subjects longitudinally, thus generating time to event data. The spatial aspect of such data is also of primordial importance, as many infectious diseases are transmitted from one subject to another. In this paper, a spatially correlated frailty model is introduced that accommodates for the correlation between subjects based on the distance between them. Estimates are obtained through a stochastic approximation version of the Expectation Maximization algorithm combined with a Monte-Carlo Markov Chain, for which convergence is proven. The novelty of this model is that spatial correlation is introduced for survival data at the subject level, each subject having its own frailty. This univariate spatially correlated frailty model is used to analyze spatially dependent malaria data, and its results are compared with other standard models.