A two-part model for reference curve estimation subject to a limit of detection.
Reference curves are commonly used to identify individuals with extreme values of clinically relevant variables or stages of progression which depend naturally on age or maturation. Estimation of reference curves can be complicated by a technical limit of detection (LOD) that censors the measurement from the left, as is the case in our study of reproductive hormone levels in boys around the time of the onset of puberty. We discuss issues with common approaches to the LOD problem in the context of our pubertal hormone study, and propose a two-part model that addresses these issues. One part of the proposed model specifies the probability of a measurement exceeding the LOD as a function of age. The other part of the model specifies the conditional distribution of a measurement given that it exceeds the LOD, again as a function of age. Information from the two parts can be combined to estimate the identifiable portion (i.e. above the LOD) of a reference curve and to calculate the relative standing of a given measurement above the LOD. Unlike some common approaches to LOD problems, the two-part model is free of untestable assumptions involving unobservable quantities, flexible for modeling the observable data, and easy to implement with existing software. The method is illustrated with hormone data from the Third National Health and Nutrition Examination Survey.
Division of Epidemiology, Statistics and Prevention Research, Eunice Kennedy Shriver National Institute of Child Health and Human Development, Bethesda, MD 20892-7510, USA. zhiwei.zhang@nih.gov
Z
Z
Zhang
O Y
OY
Addo
J H
JH
Himes
M L
ML
Hediger
P S
PS
Albert
A L
AL
Gollenberg
P A
PA
Lee
G M Buck
GM
Louis
D000367:Age Factors; D002648:Child; D003627:Data Interpretation, Statistical; D006801:Humans; D007265:Inhibins / Q000097:blood; D057230:Limit of Detection; D007986:Luteinizing Hormone / Q000097:blood; D008297:Male; D015233:Models, Statistical; D011627:Puberty / Q000502:physiology; D012016:Reference Values; D013739:Testosterone / Q000097:blood
C422364:inhibin B; D013739:Testosterone; D007265:Inhibins; D007986:Luteinizing Hormone
Stat Med. 1992 Jul;11(10):1305-19
1518992
Stat Med. 1993 May 30;12(10):917-24
8337548
Stat Med. 2000 Nov 15;19(21):2943-62
11042625
Methods Inf Med. 1995 Dec;34(5):523-8
8713769
Ann Hum Biol. 1988 Jan-Feb;15(1):17-22
3348588
Biometrics. 1999 Jun;55(2):645-51
11318228
Stat Med. 1991 May;10(5):675-90
2068420
Biometrics. 1999 Jun;55(2):625-9
11318225
Am J Hum Biol. 1989;1(2):165-173
28514008
Stat Med. 2007 Oct 15;26(23):4273-92
17330248
Stat Med. 2010 Feb 28;29(5):558-72
20013898
Stat Methods Med Res. 1999 Jun;8(2):93-112
10501648
Stat Med. 2004 Jun 15;23(11):1749-65
15160406
Vital Health Stat 11. 2002 May;(246):1-190
12043359
Biometrics. 2001 Sep;57(3):681-8
11550915
Stat Med. 2001 Apr 30;20(8):1259-77
11304741
Ann Hum Biol. 1990 Nov-Dec;17(6):475-81
2281939
Stat Med. 1990 May;9(5):539-48
2349405