Bayesian Inference for Skew-Normal Mixture Models With Left-Censoring

Abstract

Assays to measure concentration of antibody after vaccination are often subject to left-censoring due to a lower detection limit (LDL), leading to a high proportion of observations below the detection limit. Not accounting for such left-censoring appropriately can lead to biased parameter estimates. To properly adjust for left-censoring and a high proportion of observations at LDL, this article proposes a mixture model combining a point mass below LDL and a Tobit model with skew-elliptical error distribution. We show that skew-elliptical distributions, where the skew-normal and skew-t are special cases, have great flexibility for simultaneously handling left-censoring, skewness, and heaviness in the tails of a distribution of a response variable with left-censored data. A Bayesian procedure is used to estimate model parameters. Two real data sets from a study of the measles vaccine and an HIV/AIDS study are used to illustrate the proposed models.

Key Words:

• Bayesian inference
• Censoring
• Mixed-effects models
• Skew-normal distribution
• Tobit model

ACKNOWLEDGMENTS

The author gratefully acknowledges the editor and two anonymous referees for their insightful comments and constructive suggestions that led to a marked improvement of the article. This research was partially supported by NIMH grant R01MH040859-22.

Notes

Note. RSS =residual sum of squares, EPD =expected predictive deviance.