A mixed effects model for analyzing area under the curve of longitudinally measured biomarkers with missing data

Luoxi Shi, Dorothy K. Hatsukami, Joseph S. Koopmeiners, Chap T. Le, Neal L. Benowitz, Eric C. Donny, Xianghua Luo

Research output: Contribution to journalArticlepeer-review


A simple approach for analyzing longitudinally measured biomarkers is to calculate summary measures such as the area under the curve (AUC) for each individual and then compare the mean AUC between treatment groups using methods such as t test. This two-step approach is difficult to implement when there are missing data since the AUC cannot be directly calculated for individuals with missing measurements. Simple methods for dealing with missing data include the complete case analysis and imputation. A recent study showed that the estimated mean AUC difference between treatment groups based on the linear mixed model (LMM), rather than on individually calculated AUCs by simple imputation, has negligible bias under random missing assumptions and only small bias when missing is not at random. However, this model assumes the outcome to be normally distributed, which is often violated in biomarker data. In this paper, we propose to use a LMM on log-transformed biomarkers, based on which statistical inference for the ratio, rather than difference, of AUC between treatment groups is provided. The proposed method can not only handle the potential baseline imbalance in a randomized trail but also circumvent the estimation of the nuisance variance parameters in the log-normal model. The proposed model is applied to a recently completed large randomized trial studying the effect of nicotine reduction on biomarker exposure of smokers.

Original languageEnglish (US)
Pages (from-to)1249-1264
Number of pages16
JournalPharmaceutical statistics
Issue number6
Early online dateJun 20 2021
StatePublished - Nov 1 2021

Bibliographical note

Funding Information:
The authors would like to thank Dr Stephen S. Hecht's Laboratory in the University of Minnesota Masonic Cancer Center for analyzing the biomarkers used in this paper, Dr Kyle Rudser for serving on Ms Shi's MS thesis committee, and Dr Saonli Basu for the inspiring discussion with Ms Shi. This study was funded by National Institute on Drug Abuse and Food and Drug Administration grant U54DA031659. Mass spectrometry was carried out in the Analytical Biochemistry Shared Resource of the Masonic Cancer Center, supported in part by National Cancer Institute Cancer Center Support grant P30CA077598. REDCap (Research Electronic Data Capture) services were provided by grant UL1TR000114 from the National Center for Advancing Translational Sciences of the National Institutes of Health.

Publisher Copyright:
© 2021 John Wiley & Sons Ltd.


  • area under the curve
  • biomarker
  • longitudinal
  • missing data
  • mixed effects model

PubMed: MeSH publication types

  • Journal Article
  • Research Support, N.I.H., Extramural


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