Frailty modelling for clustered recurrent incidence of diarrhoea

Recurrent incidence of infant diarrhoea is studied, using daily data collected in Salvador, Brazil, from 754 children over 455 days. Aalen's additive intensity model is taken as the basis of the modelling strategy and a frailty extension is proposed. The idea is to estimate the frailty dynamically as time proceeds and information accrues. This provides an alternative to the inclusion of dynamic covariates based on individual event patterns. Simulation results indicate good performance of the estimation methods. In our first analysis, there is no account taken in the natural clustering of the children into 21 different districts of the city. The model is therefore extended to incorporate the possibility of spatial or spatio-temporal clustering effects, possibly caused by unobserved environmental factors or infectivity. Significant frailty and significant clustering are both identified in the data.