Application of Poisson regression analysis for queueing system of the demand for medical and health service

Abstract

This paper suggests that log-linear analysis can be used to predict the expected number of patients in a queueing system. A log-linear Poisson regression model has been developed to analyse the time series of count data. In finding a Poisson regression model, parameters are estimated and goodness-of-fit is utilized to carefully extract the best model to fit the count data. The marginal effect is the basis function which can be used in the Poisson regression analysis. As a result, it allows us to arrive at better predictions of welfare health services and rehabilitation decision making. Health care utilization is a clinical marker of the well being of patients. One of the important end points of the demand for medical and health services in a queueing system is to identify factors associated with increased health care utilization; particularly those factors related to welfare health services. In this paper, we propose a Poisson model in which the number of patients in a queueing system is modeled by Poisson regression analysis. To this end, it is of great importance to assess the relationship between welfare health services and average waiting time in a queueing system. For this purpose, data were obtained from a survey conducted by the Samutpakran Hospital in Thailand for the year 2005. This is a difficult task for several reasons. First, even in the case of constant demand levels over the day, statistical fluctuations in individual patient waiting times and the variability in the time needed by a provider to service patients can create long delays even when overall average steady state capacity is greater than average demand. Second, the magnitude of delays is a log-linear function of the demand for medical and health services level, and are thus impossible to predict without the use of a queueing model (1). Herbert C. Heien, William A. Baumanm and Mezbahur Rahman have studied the categorical data analysis. In general, these models are termed Rate Models or Possion Regression Models. The Possion Regression Models can easily be connected to the standard Possion Models. Then, the Possion Models are directly related to the Exponential Models by making conversation of rate per unit interval with the waiting time until the first occurrence (2). To explore the relationship between the average waiting time and the number of welfare patient visits, one could consider a log-linear model. The average waiting time could be included in the model as a linear predictor. Log-linear models are among the most frequently used models for count data Possion regression analysis, but they offer only limited flexbility in accommodating the maginal effect of the independent varible (3).