Fitting correlation adjusted generalized linear models to clustered dengue data measured over time

Abstract

In this paper the authors address the issue of fitting generalized linear models (GLM’s) in the presence of correlated observations, particularly when the data is clustered. In the usual GLM the responses obtained on each unit are considered independent. In this case the commonly used approach for the estimation of parameters is the method of maximum likelihood. However if correlation is present and is not taken into account then the standard errors of the parameter estimates will not be valid. One method of solution to this issue is estimation using Generalized Estimating Equations (GEE). In this paper the procedure involved in fitting GLM’s with GEE method of estimation is discussed in detail and is illustrated using a set of data of dengue incidence in Sri Lanka in the years 2004 and 2005. The primary objective of this paper is to illustrate how generalized linear models can be fitted, in the presence of correlated data, by using generalized estimating equations. The secondary objective is to determine the factors effecting dengue incidence. This study showed that the dengue incidence can be adequately modeled using a GLM with negative binomial response. Patients within districts are believed to be more similar than patients in different districts and therefore a cluster effect is assumed within district. Also responses were believed to be correlated over time. This correlation structure is accommodated by using a autoregressive procedure of order one within the GEE framework. Rainfall and temperature in the current month and previous months up to a lag of two months were shown to effect incidence of dengue. In addition to these climatic variables dengue incidence also shows a changing pattern over time.