# Given the lack of use of these models in emergency medical resear

Given the lack of use of these models in emergency medical research we will describe each method below. Before proceeding to any multiple regression modeling, descriptive statistics were generated to characterize the sample under investigation. For continuously distributed variables we presented means and standard deviations; whereas, for categorical variables we presented counts and percentages. Inhibitors,research,lifescience,medical Regression Models for Count Outcomes Perhaps the most parsimonious and widely implemented method for modeling count data in the public health sciences is Poisson

regression. The Poisson regression model assumes that the number of events (yi) experienced by patient i follows a Poisson distribution: P(Yi=yi|xi)=e-μiμiyiyi! where μi represents the conditional mean response of a given patient, which is assumed to depend on a set of observed

data (xi) and an estimated vector of coefficients (β). Mathematically, this relationship takes Inhibitors,research,lifescience,medical the following form: E(yi|xi)=μi=exiβ Taking the natural logarithm of the conditional mean allows for the response under consideration to vary linearly as a function of observed predictor variables multiplied by the effect of their corresponding regression coefficients. Various numerical maximization methods exist for selleck inhibitor iteratively estimating the values of the coefficient vector, β, and the associated -covariance matrix. variance Estimates are typically found by finding Inhibitors,research,lifescience,medical the parameter estimates that maximize the following log-likelihood Inhibitors,research,lifescience,medical function: LLPoisson= ∑i=1n[-μi+yiln(μi)-ln(yi!)] Since the natural logarithm of the likelihood function for the Poisson regression model is globally concave, a unique maximum can be found if it exists . A restrictive assumption attached to the Poisson regression model is that the conditional variance is assumed to be equal to the conditional mean. As a result, the Poisson regression model is not always an ideal model for count data, especially in instances where a large mass of observations exists on the corner of the empirical distribution. This typically arises Inhibitors,research,lifescience,medical in the form of observed zeroes in

a data set that are in excess of what would be predicted by the Poisson distribution. In severe instances, fitting a Poisson model to data with excess zeroes can result in model misspecification, inefficient parameters estimates and incorrect inferences. A less parsimonious, but more flexible extension to the Poisson regression model is the negative binomial regression model. The negative binomial ALOX15 regression model does not assume that the conditional variance of the response is equal to the conditional mean. A simple extension to the specification of the Poisson conditional mean leads to a negative binomial regression model, which is illustrated below: E(yi|xi)=μi=exiβ+εi=exiβeεi=exiβδi Above, the conditional mean for the Poisson model has been adjusted by adding an individual specific random term, εi, that is assumed to be uncorrelated with the observation vector, xi.