Abstract:
In Sri Lanka, dengue has become an increasing health concern in the recent past. The spread
of Dengue is influenced by the living surroundings. Therefore the dengue data are related to
the climate and also correlated within districts as the weather is similar within a district. The
survival time of a patient and the incidences of the disease (count) are frequently encountered
phenomenon in medical studies that can be related to each other. Therefore, it is important to
give attention to Dengue survival time and Dengue count simultaneously, because these can
provide interesting and improved results, rather than modelling survival time and count data
separately, while considering the multilevel structure of a district cluster effect. The objective
of this study is to perform a joint modeling of survival time and count. A semi-parametric
method for modelling the survival data is preferred as it is often difficult to determine the
survival distribution, and there is also censoring of the observations. Hence, a frailty piecewise
constant proportional hazard semi-parametric model with approximated baseline hazard was
preferred to model the survival response. As log of counts are normally distributed, the normal
model is preferred as the count sub model. The literature does not contain joint modelling of
survival time and the count using the above mentioned sub models, and therefore this is an
added novelty of this study. For this study, data recordings on dengue patients all over Sri
Lanka from 2006 to 2008 have been used. As explanatory variables, there were the climate
variables rainfall, temperature, and humidity with their first and second lag values, as well as
Year, Quarter, Outcome, Age, Sex, Classification and Expected Exposed. Districts are
considered as clusters. The performance of the proposed joint models is compared with
univariate fixed effect models that can be fitted separately for the two responses. According to
the model fit statistics which are -2 log likelihood, AIC, AICC and BIC values, the performance
of the joint model was superior to the separate univariate models.
