Semicontinuous Model Misspecification: Zero-Inflated Log-Normal and Zero-Inflated Gamma Distributions

• Activity Number: 655
• Type: Contributed
• Date/Time: Thursday, August 4, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Elizabeth Dastrup Mills*+ and Jeffrey D. Dawson
• Companies: University of Iowa and University of Iowa
• Keywords: mixture models ; zero-inflation ; regression

Abstract

Semicontinuous outcomes are random variables with a probability mass at a specific point value but which follow a continuous distribution elsewhere. Often the discrete point value is at zero, with the remaining values positive. For modeling such data, Duan et al (1983) proposed a two-part approach, with one part modeling the probability of zero vs. non-zero and the other part modeling the distribution of positive values. Moulton et al (2002) used this two-part model using logistic regression for the dichotomous response and log-normal regression for the positive values, while McLerran (2008) has proposed using gamma regression to model the positive response. For fully continuous data, Firth (1988) found that gamma models had greater efficiencies than log-normal models given reciprocal misspecification. In this study, we performed similar comparisons of gamma vs. log-normal performance in the presence of semicontinuous outcomes, examining Type I error rates, power, confidence interval coverage, and biasness based on simulations. We also illustrated both methods on real life data from our collaborations in the field of neurology.