Marginal and conditional approaches to multivariate variables subject to limit of detection

L. Nie, H. Chu, Y. Cheng, C. Spurney, K. Nagaraju, J. Chen

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


A marginal approach and a variance-component mixed effect model approach (here called a conditional approach) are commonly used to analyze variables that are subject to limit of detection. We examine the theoretical relationship and investigate the numerical performance of these two approaches. We make some recommendations based on our results. The marginal approach is recommended for bivariate normal variables, and the variance-component mixed effect model is preferable for other multivariate analysis in most circumstances. Two approaches are illustrated through one case study from a preclinical experiment.

Original languageEnglish (US)
Pages (from-to)1151-1161
Number of pages11
JournalJournal of Biopharmaceutical Statistics
Issue number6
StatePublished - Nov 2009

Bibliographical note

Funding Information:
We thank the editor and two referees for their very insightful and constructive comments, which have greatly improved the quality of the article. Dr. Chu was supported in part by the Lineberger Cancer Center Core Grant CA16086 from the U.S. National Cancer Institute and P30-AI-50410 from the U.S. National Institutes of Health.


  • Limit of detection
  • Marginal approach
  • Maximum likelihood estimate
  • Variance-component mixed effect model


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