Methods for improving regression analysis for skewed continuous or counted responses

Abstract

Standard inference procedures for regression analysis make assumptions that are rarely satisfied in practice. Adjustments must be made to insure the validity of statistical inference. These adjustments, known for many years, are used routinely by some health researchers but not by others. We review some of these methods and give an example of their use in a health services study for a continuous and a count outcome. For the continuous outcome, we describe re-transformation using the smear factor, accounting for missing cases via multiple imputation and attrition weights and improving results with bootstrap methods. For the count outcome, we describe zero inflated Poisson and negative binomial models and the two-part model to account for overabundance of zero values. Recent advances in computing and software development have produced user-friendly computer programs that enable the data analyst to improve prediction and inference based on regression analysis.