title: Empirical constrained Bayes predictors accounting for non-detects among repeated measures.
abstract: When the prediction of subject-specific random effects is of interest, constrained Bayes predictors (CB) have been shown to reduce the shrinkage of the widely accepted Bayes predictor while still maintaining desirable properties, such as optimizing mean-square error subsequent to matching the first two moments of the random effects of interest. However, occupational exposure and other epidemiologic (e.g. HIV) studies often present a further challenge because data may fall below the measuring instrument's limit of detection. Although methodology exists in the literature to compute Bayes estimates in the presence of non-detects (Bayes(ND)), CB methodology has not been proposed in this setting. By combining methodologies for computing CBs and Bayes(ND), we introduce two novel CBs that accommodate an arbitrary number of observable and non-detectable measurements per subject. Based on application to real data sets (e.g. occupational exposure, HIV RNA) and simulation studies, these CB predictors are markedly superior to the Bayes predictor and to alternative predictors computed using ad hoc methods in terms of meeting the goal of matching the first two moments of the true random effects distribution.
authors.affiliation: Department of Biostatistics and Epidemiology, University of Pennsylvania School of Medicine, Philadelphia, PA 19104, USA. rhmoore@mail.med.upenn.edu
authors.forename: Reneé H
authors.initials: RH
authors.lastname: Moore
authors.forename: Robert H
authors.initials: RH
authors.lastname: Lyles
authors.forename: Amita K
authors.initials: AK
authors.lastname: Manatunga
mesh_terms: D001499:Bayes Theorem; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D018450:Disease Progression; D004391:Dust; D015340:Epidemiologic Research Design; D005260:Female; D015658:HIV Infections / Q000453:epidemiology; D006801:Humans; D016014:Linear Models; D008171:Lung Diseases / Q000453:epidemiology / Q000209:etiology; D016273:Occupational Exposure / Q000009:adverse effects / Q000706:statistics & numerical data; D011379:Prognosis; D012140:Respiratory Tract Diseases / Q000453:epidemiology / Q000209:etiology
chemical_list: D004391:Dust
references.citation: Stat Med. 2002 Aug 15;21(15):2199-214
references.pmid: 12210633
references.citation: J Mod Appl Stat Methods. 2009 May 1;8(1):81-94
references.pmid: 24415922
references.citation: Stat Med. 1999 Jan 15;18(1):35-52
references.pmid: 9990691
references.citation: Am J Epidemiol. 1997 Sep 15;146(6):459-69
references.pmid: 9290506
references.citation: Biometrics. 1987 Dec;43(4):929-39
references.pmid: 3509964
references.citation: Stat Med. 2007 Mar 15;26(6):1285-300
references.pmid: 16810716
references.citation: Biostatistics. 2000 Dec;1(4):355-68
references.pmid: 12933561
references.citation: Biometrics. 1999 Jun;55(2):625-9
references.pmid: 11318225
references.citation: Ann Occup Hyg. 1991 Feb;35(1):61-121
references.pmid: 2035954
references.citation: Stat Med. 2008 Jun 15;27(13):2497-508
references.pmid: 18167630
references.citation: Int Arch Occup Environ Health. 1993;65(1 Suppl):S29-35
references.pmid: 8406935