Abstract:
In many epidemiological studies time to event data are grouped into strata (or clusters), such as, geographic region, districts, villages and so on. Consequently, cluster specific effects on survival times may cause an extra variation. Under such circumstance, it is substantive importance to draw inference on the nature and magnitude of these effects albeit the primary focus being on survival times. In model based analysis the aforesaid effect (called frailty) are usually accommodated by the use of frailty survival models. The objective of this thesis is to model the time to first malaria infection due to p. falcuiprum in children living near to the Gilgel Gibe dam using Cox proportional hazards and shared gamma frailty models with an attempt to compare these two modelling approaches. We apply the two modelling approaches to the analysis of malaria dataset. The dataset comprise time to first malaria infection of 2040 under 10 children observed during the period from July 2008 to June 2010. This study revealed that, Cox PH model estimates the risk of malaria infection for children residing in proximity to the dam is significantly lower than children’s living in distant from the dam. However, when we take the clustering of children within locality into account (using frailty model) there was no statistical significant difference in hazard of contracting malaria between the two groups, namely at risk and control. The likelihood ratio test of the heterogeneity parameter (theta) in all the fitted frailty models, however, showed that theta is significantly different from zero (P<0.000), indicating that there is a clear clustering of study subjects (children) with in their localities. In the future, it is better to see also the result by including a frailty term at least in a pairwise manner and also spatial distance of households, in the modelling of time-to-malaria.
