A Multivariate Random Frailty Effects Model for Multiple Spatially Dependent Survival Data

The inclusion of geographically-based information in many epidemiological studies has led to the development of statistical and estimation methods that account for spatially dependent risks of health outcomes across geographical areas. Many of these developments have been concerned with spatial modelling of aggregated count data, for example incidence rates of cancer at the small–area level. In this chapter, we consider individual time­to­event data, where the individual subjects are hierarchically nested in natural or administrative areas. The individual failure time data are modelled using proportional hazards models, which are modified to include both spatially uncorrelated and correlated area frailty random effects; the latter accounting for local spatial dependence in the data. This model is expanded to accommodate multiple failure events, where the set of within and between failure-event spatial frailty random effects are assumed to have a multivariate normal distribution. We illustrate the proposed methodology with an analysis of timing of first childbirth and timing of first marriage across health districts in South Africa for women aged between 15 and 49 years. For each failure event, the spatial dependence is modelled using a multiple membership multiple classification (MMMC) model. A multivariate version of the MMMC model is then used to obtain estimates of covariance parameters between various failure-event spatial random effects.