Consider that T repeated count responses are collected from each of K independent individuals. Let yi = (yi1, ..., yit, ..., yiT) denote the T repeated count responses obtained from the i th individual, i = 1, 2, ..., K and xit = (xit1, ..., xitj, ..., xitp) be the p × 1 vector of covariates associated with response yit. Let β = (β 1, ..., βj , ..., βp) be the p × 1 vector of regression coefficients which we want to estimate and µi = (µi1, ..., µit, ..., µiT) be the T × 1 vector of mean of response yi , with µit = E(Yit); i = 1,2, ..., K and t = 1, 2, ..., T. Also let Let Σi be the T × T variance-covariance matrix of Yt i.e. Σi = Var (Yi) = ?itt with Var (Yit) = ?itt'. Furthermore, suppose that the marginal density of the response yit is of the exponential family form f(yit) = exp[yit it – α(?it)Ø + b(yit, Ø)] (2.1) (Liang and Zeger 1986, Sutradhar 2003), where -it = h(ηit) with ηit = x'it β; a(.), b(.) and h(.) of known functional forms and Ø is a possibly unknown scale parameter and β is the p × 1 vector of parameters of interest. In many important situations, for example, for binary and Poisson data, one may use Ø = 1. Consequently, for Poisson data, we use Ø = 1 in (2.1) and write the mean and the variance of yit as E(Yit) = α'(?it) and Var (Yit) = α''(?it) Under regression setup, the most common approach assumes that the count responses follow a Poisson distribution. Note, however, that for rare events, Poisson regression model is also used as a generalization of the binomial distribution (Cameron et al. 1998). Under the longitudinal count model, we assume that the response variable, number of visits, yit follows Poisson distribution with mean µit. Therefore, E(Yit) = µit = Var(Yit) = exp (X'it β) Furthermore, in the longitudinal setup, the components of the vector yi are repeated responses, which are likely to be correlated. Let C(ρ) be the T × T true correlation matrix of yi , which is unknown in practice. Here ρ is, say, a s×1 vector of correlation parameters that fully characterizes C(ρ). It is of primary interest to estimate β after taking the longitudinal correlation structure C(ρ) into account. Estimation of Parameters Sutradhar and Das (1999) showed that even though the Liang and Zeger (1986) approach in many situations yields consistent estimators for the regression parameters, these estimators are usually inefficient as compared to the regression estimators obtained by using the independence estimating equation approach. In this aspect, a recently developed methodology is the generalized quasi-likelihood (GQL) approach which was introduced by Sutradhar (2003). We have used follow-up data of registered patients collected by BIRDEM hospital where the patients visit at least two years but must visit at least one of last two years during the follow-up period of 1993 to 1996. In the follow-up period, we took 872 individuals (patients) with their various characteristics such as body mass index (BMI**), age, heredity, area of residence, education level, physical exercise etc. As the responses (number of visits of patients per year) are counts, it is appropriate to assume that the response variable marginally follows the Poisson distribution and the repeated counts recorded for four years will be longitudinally correlated. It is of scientific interest to take the longitudinal correlations into account. In the study, we treat all the covariates as categorical variables. The covariate age is used as a categorical variable with three categories- age < 40, age 40 - 60 and age > 60 years. Again, gender is also a categorical variable with two categories- male and female, education level is used as three categories- pre-secondary, secondary and higher, area of residence has two categories- rural and urban, physical exercise has two categories-exercised and non-exercised and heredity has also two categories- heredity and non-heredity. We have considered rural patients as a combination of rural and semi-urban patients in the study. We treat the covariate body mass index as two categories- under-weight and overweight.