This paper examines and applies methods for modelling of longitudinal binary data subject to both intermittent missingness and dropout. The paper is based around the analysis of data from a study into the health impact of a sanitation programme carried out in Salvador, Brazil. Our objective is to investigate risk factors associated with incidence and prevalence of diarrhoea in children aged up to 3 years old. In total 926 children were followed up at home twice a week from October 2000 to January 2002, from which daily occurrence of diarrhoea was recorded for each child being followed up. A challenging factor in analysing these data is the presence of between subject heterogeneity not explained by known risk factors, combined with significant loss of observed data through either intermittent missingness (average of 78 days per child) or dropout (21% of children). We discuss modelling strategies and show the advantages of taking an event history approach with an additive discrete time regression model.