PMID- 37871480
OWN - NLM
STAT- MEDLINE
DCOM- 20231114
LR  - 20231129
IS  - 1872-7565 (Electronic)
IS  - 0169-2607 (Linking)
VI  - 242
DP  - 2023 Dec
TI  - Critical appraisal of two Box-Cox formulae for their utility in determining 
      reference intervals by realistic simulation and extensive real-world data 
      analyses.
PG  - 107820
LID - S0169-2607(23)00486-8 [pii]
LID - 10.1016/j.cmpb.2023.107820 [doi]
AB  - BACKGROUND: The reference interval (RI) is defined as the central 95 % range of 
      reference values (RVs) from healthy individuals. The ideal method for determining 
      RIs is to transform RV distribution into Gaussian and estimate its 95 % range 
      parametrically. One-parameter Box-Cox formula (1pBC) is widely used for 
      correcting skewness (Sk) or kurtosis (Kt) in data distribution. However, 1pBC is 
      not popular for computing RIs due to its unreliability in Gaussian 
      transformation. While its two-parameter version (2pBC) is not used due to a 
      challenge in fitting power (lambda) and shift (alpha) parameters simultaneously. In this 
      study, technical issues in fitting both formulae are assessed, and an alternative 
      algorithm for successful use of 2pBC is proposed. METHODS: For fitting 1pBC, 
      optimal lambda was determined by stepwise linear search. For 2pBC, optimal [lambda, alpha] 
      combination was pursued in two ways: by grid search of lambda and alpha (2pBCgrid) or by 
      using the grid search but keeping alpha-range close to the reference distribution 
      (2pBCopt). Their accuracy and precision in determining RIs were compared by 
      generating power-normal distributions simulating RVs of 23 major chemistry 
      analytes. Additionally, their practical utilities were compared by analyzing 776 
      real-world datasets comprising test results of 25 analytes that were obtained 
      from the global multicenter RV study of IFCC. For comparison, the performance of 
      nonparametric method was evaluated in both settings. RESULTS: For analytes with 
      not-much-skewed distributions, unbiased estimation of RIs was accomplished by all 
      methods. Nevertheless, when reference distributions are located far from zero, lambda 
      estimated by1pBC and 2pBCgrid fluctuated widely, which was attributable to 
      virtually flat goodness-of-fit profile for [lambda, alpha]. For highly skewed 
      distributions, 1pBC caused bias in estimating RI and lambda due to remotely peaked 
      goodness-of-fit profile. Real-world data analyses revealed that 2pBCopt and 1pBC 
      achieved Gaussian transformation (|Sk|<0.1 and |Kt|<0.3) in 82.4 % and 66.9 % 
      among 776 datasets, respectively. Fitting bias signified by Kt<-0.4 was more 
      common to 1pBC. The practical utility of 2pBCopt was unbiased prediction of 
      analyte-specific distribution-shape (lambda). Whereas nonparametric method gave highly 
      variable RIs for both simulated and real-world datasets. CONCLUSIONS: 2pBCopt is 
      suitable for calculating RIs and grasping distribution-shape from the estimated 
      lambda.
CI  - Copyright (c) 2023 The Authors. Published by Elsevier B.V. All rights reserved.
FAU - Ichihara, Kiyoshi
AU  - Ichihara K
AD  - Faculty of Health Sciences, Department of Clinical Laboratory Sciences, Yamaguchi 
      University Graduate School of Medicine, Minami-Kogushi 1-1-1, Ube, 755-0001, 
      Japan. Electronic address: ichihara@yamaguchi-u.ac.jp.
FAU - Yamashita, Teppei
AU  - Yamashita T
AD  - Department of Clinical Pharmacology, Tokai University School of Medicine, 
      Isehara, 259-1193, Japan.
FAU - Kataoka, Hiromi
AU  - Kataoka H
AD  - Faculty of Health Science and Technology, Kawasaki University of Medical Welfare, 
      Kurashiki, 701-0192, Japan.
FAU - Sato, Shoichi
AU  - Sato S
AD  - Faculty of Medical Sciences, Juntendo University, Urayasu, Chiba, 279-0021, 
      Japan.
LA  - eng
PT  - Journal Article
PT  - Multicenter Study
DEP - 20230919
PL  - Ireland
TA  - Comput Methods Programs Biomed
JT  - Computer methods and programs in biomedicine
JID - 8506513
SB  - IM
MH  - Humans
MH  - Reference Values
MH  - Computer Simulation
MH  - Normal Distribution
MH  - Bias
MH  - *Data Analysis
OTO - NOTNLM
OT  - Bias ratio
OT  - Clinical chemistry
OT  - Nonparametric method
OT  - Power transformation
OT  - Power-normal distribution
OT  - Reference values
COIS- Declaration of Competing Interest No authors have any competing interests to 
      declare in conducting this study and reporting the results.
EDAT- 2023/10/24 00:41
MHDA- 2023/11/14 06:43
CRDT- 2023/10/23 18:06
PHST- 2023/01/14 00:00 [received]
PHST- 2023/07/20 00:00 [revised]
PHST- 2023/09/15 00:00 [accepted]
PHST- 2023/11/14 06:43 [medline]
PHST- 2023/10/24 00:41 [pubmed]
PHST- 2023/10/23 18:06 [entrez]
AID - S0169-2607(23)00486-8 [pii]
AID - 10.1016/j.cmpb.2023.107820 [doi]
PST - ppublish
SO  - Comput Methods Programs Biomed. 2023 Dec;242:107820. doi: 
      10.1016/j.cmpb.2023.107820. Epub 2023 Sep 19.