  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.
