Abstract: The generalized Poisson regression model has been used to model dispersed count data. It is a good competitor to the negative binomial regression model when the count data is over-dispersed. Zero-inflated Poisson and zero-inflated negative binomial regression models have been proposed for the situations where the data generating process results into too many zeros. In this paper, we propose a zero-inflated generalized Poisson (ZIGP) regression model to model domestic violence data with too many zeros. Estimation of the model parameters using the method of maximum likelihood is provided. A score test is presented to test whether the number of zeros is too large for the generalized Poisson model to adequately fit the domestic violence data
Abstract: A prospective, multi-institutional and randomized surgical trial involving 724 early stage melanoma patients was conducted to determine whether excision margins for intermediate-thickness melanomas (1.0 to 4.0 mm) could be safely reduced from the standard 4-cm radius. Patients with 1- to 4-mm-thick melanomas on the trunk or proximal extremities were randomly assigned to receive either a 2- or 4-cm surgical margin with or without immediate node dissection (i.e. immediate vs. later -within 6 months). The median follow-up time was 6 years. Recurrence rates did not correlate with surgical margins, even among stratified thickness groups. The hospital stay was shortened from 7.0 days for patients receiving 4-cm surgical margins to 5.2 days for those receiving 2-cm margins (p = 0.0001). This reduction was largely due to reduced need for skin grafting in the 2cm group. The overall conclusion was that the narrower margins significantly reduced the need for skin grafting and shortened the hospital stay. Due to the adequacy of subject follow up, recently a statistical focus was on what prognostics factors usually called covariates actually determined recurrence. As was anticipated, the thickness of the lesion (p = 0.0091) and whether or not the lesion was ulcerated (p = 0.0079), were determined to be significantly associated with recurrence events using the logistic regression model. This type of fixed effect analysis is rather a routine. The authors have determined that a Bayesian consideration of the results would afford a more coherent interpretation of the effect of the model assuming a random effect of the covariates of thickness and ulceration. Thus, using a Markov Chain Monte Carlo method of parameter estimation with non informative priors, one is able to obtain the posterior estimates and credible regions of estimates of these effects as well as their interaction on recurrence outcome. Graphical displays of convergence history and posterior densities affirm the stability of the results. We demonstrate how the model performs under relevant clinical conditions. The conditions are all tested using a Bayesian statistical approach allowing for the robust testing of the model parameters under various recursive partitioning conditions of the covariates and hyper parameters which we introduce into the model. The convergence of the parameters to stable values are seen in trace plots which follow the convergence patterns This allows for precise estimation for determining clinical conditions under which the response pattern will change.