Estimation and inference on correlations between biomarkers with repeated measures and left-censoring due to minimum detection levels

Xianhong Xie, Xiaonan (Nan) Xue, Stephen J. Gange, Howard Strickler, Mimi Kim, Andrea Kovacs, Robert D. Burk, Howard Minkoff, Joel M. Palefsky, Kathryn Anastos, Alexandra M. Levine

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Statistical approaches for estimating and drawing inference on the correlation between two biomarkers that are repeatedly assessed over time and subject to left-censoring because minimum detection levels are lacking. We propose a linear mixed-effects model and estimate the parameters with the Monte Carlo expectation maximization (MCEM) method. Inferences regarding the model parameters and the correlation between the biomarkers are performed by applying Louis's method and the delta method. Simulation studies were conducted to compare the proposed MCEM method with existing methods including the maximum likelihood estimation method, the multiple imputation method, and two widely used ad hoc approaches: replacing the censored values with the detection limit or with half of the detection limit. The results show that the performance of the MCEM with respect to relative bias and coverage probability for the 95% confidence interval is superior to the detection limit and half of the detection limit approaches and exceeds that of the multiple imputation method at medium to high levels of censoring, and the standard error estimates from the MCEM method are close to ideal. The maximum likelihood estimation method can estimate the parameters accurately; however, a nonpositive definite information matrix can occur so that the variances are not estimable. These five methods are illustrated with data from a longitudinal human immunodeficiency virus study to estimate and draw inference on the correlation between human immunodeficiency virus RNA levels measured in plasma and in cervical secretions at multiple time points.

Original languageEnglish (US)
Pages (from-to)2275-2289
Number of pages15
JournalStatistics in Medicine
Volume31
Issue number21
DOIs
StatePublished - Sep 20 2012

Fingerprint

Left Censoring
Repeated Measures
Biomarkers
Detection Limit
Expectation Maximization
Limit of Detection
Multiple Imputation
Maximum Likelihood Estimation
Virus
Estimate
Linear Mixed Effects Model
Delta Method
HIV
Information Matrix
Secretion
Coverage Probability
Censoring
Standard error
Confidence interval
Error Estimates

Keywords

  • Information matrix
  • Longitudinal data
  • Mixed-effects
  • Monte Carlo expectation maximization

ASJC Scopus subject areas

  • Epidemiology
  • Statistics and Probability

Cite this

Estimation and inference on correlations between biomarkers with repeated measures and left-censoring due to minimum detection levels. / Xie, Xianhong; Xue, Xiaonan (Nan); Gange, Stephen J.; Strickler, Howard; Kim, Mimi; Kovacs, Andrea; Burk, Robert D.; Minkoff, Howard; Palefsky, Joel M.; Anastos, Kathryn; Levine, Alexandra M.

In: Statistics in Medicine, Vol. 31, No. 21, 20.09.2012, p. 2275-2289.

Research output: Contribution to journalArticle

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