Recurrent peritonitis is a major complication of Continuous Ambulatory Peritoneal Dialysis (CAPD). As a therapy for patients with end stage renal disease, CAPD entails a continuous interaction between patient and various medical devices. The assumptions one makes regarding this interaction play an essential role when estimating the rate of recurrent peritonitis for a given patient population. Assuming that each patient has a constant rate of peritonitis, two models for evaluating the risk of recurrent peritonitis are considered. One model, the Poisson probability model, applies when the rate of peritonitis is the same from patient to patient. When this occurs, the frequency of peritoneal infections will be randomly distributed among patients (Corey, 1981). A second model, the negative binomial probability model, applies when the rate of peritonitis varies from one patient to another. In this event, the distribution of peritoneal infections will differ from patient to patient. The poisson model would be applicable when, for example, patients behave similarly with respect to their interactions with the medical devices and with potential risk factors. The negative binomial model, on the other hand, makes allowances for patient differences both in terms of their handling of routine exchanges and in their exposure to various risk factors. This paper provides methods for estimating the mean peritonitis rate under each model. In addition, “survival” curve estimates depicting the probability of remaining peritonitis free (i.e. “surviving”) over time are provided. It is shown, using data from a multi-center clinical trial, that the risk of peritonitis is best described in terms of survival curves rather than the mean peritonitis rate. For both models, the mean peritonitis rate was found to be 0.85 episodes per year. However, under the negative binomial model, the one-year survival rate, expressed as the percentage of patients remaining free of peritonitis, is 52% as compared with only 42% under the Poisson model. Moreover, the negative binomial model provided a significantly better fit to the observed frequency of peritonitis. These findings suggest that the negative binomial model provides a more realistic and accurate portrayal of the risk of peritonitis and that this risk is not nearly as high as would otherwise be indicated by a Poisson analysis.
Factors associated with mortality from tuberculosis in Iran: an application of a generalized estimating equation-based zero-inflated negative binomial model to national registry data