NORMALITY vs LOG-NORMALITY in CLINICAL CHEMISTRY

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TRU Mathematics 15−1 （1979）

NORMALITY vs LOG−NORMALITY in

CLINICAL CHEMISTRY

Motosaburo MASUYAMA

（Received June 22， 1979） The Hbffmann methods of dete】rrnining no〕Cmal ranges in clinical chemistr）r ［1，2］ are based on a wrong assumption of lthe normality， 14］ and give actually miserable results for many substances in blood 正3］． According to my own experience， the concenYration O of a nonnal constituent in blood follows m◎stly a logarithmico，no皿1 1aw （Llv）， at least apProxi皿ately， and a few constituents foilow・apProximately no”naユ 1aws （N）・ There hold two empirical laws， i．e． a pri皿itive or fundamental sd）stance whose standard deviation 〔SD〕 of X＝ Zog O is sufficiently small follows a normal law and the formal correlation coefficient ρ between the meanμc and

th・SD・。−g 14・騨血・・t・・㎞・li・n ・ni・・1…d・hi・ken is als°small

［5］．Ithought that an apParent nomal case皿ight be孤apProx迦ation to a

logarithmico−nonna1 case， since the skewness of a logarithmico−no㎜1 di・t・ib・・i・n i・n・ar・y・er・，・h・n・一％2 is suffi・i・n・・y・ma・・， i．・．・、一・・、・、…了一e・rp．・。工頃…a）一卿・…ノ・・expr・…ノ］。。ρ。。t，。2．．．． The guess is actually true． Let∫（C／ and φ（u／ be the density functions of c and the unit noriiial distribution respectively． ’lhen the characteristic func℃ion of C is given by 9（cノ＝E［e‘tP（itCノ］＝∫°°wrけexp．x／frc／dC oOD ＝1。。eap ［it exprPx≠uσxノ］tpru／du −・評瞬㌦一t2・。2・rpc・・。ノ／・］・… for sufficiently sma11 σoc． TJhis shows that O distributes approximately

ご，wl：h隠隠tμ：。1。隠；hl欝leσき1詫㌦’と％2μ・2≡σ・2’

67

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68 _M．MASUYAMA

Sodiu皿

Ch10ride

Calci㎜

Total protein

Potassium

Glucose

Albumin

Phosphorus★

Cholinesterase

Phospholipids

σ ρ

0．010．04

0．01 0．27 0．02 0．65 0．05 0．ヱ2

0．030．00

0．05 0．39 0．06 0．07 0．07 0．07

N

LN

．π

N」LN

LN

CholesteTOl

Uric acid

TTT

Urea

CTeatinine

ALP

GOT

Bilirubin

LDH

GPT

σ ρ

θ．080．57LIV

0．O．80．77 LIV 0．10

LN

0．ヱユ0．84L∼V 0．1ユ 0．54 Z｝N

0．130．40Lru

0．13 ヱ｝N

0．ヱ40．90LN

0．ユ60．89乙1r

0，ヱ7 （★ inorganic〕 LIv

REFERENCES

1． 2． 3． ● ・ 4ζり Hoffinann，R．G．．〔1963〕：Statistics in the practice of medicine， JAMA， Sept． 14， 864−873． Hoffinann，R．G．（1974）：New Clinical Laboratory Standardization MethodS， Exposition． Kitamura；M． et a1．（1978〕：Katizya D6ta kara motomeru Kizyunti Sakuseih6 no Hy6ka， Rinsy6by6ri， 26， Supp1．， 36． Masu）ra皿va，M．〔1977）：S）r6識ei no Mat㎝ekata， I I， Takeuti−Syoten． Masuヴama，M．〔1978）：Species difference of biochemical individual variabilities etc．，TRU Math．，14−2， 61・・70．

Department of Applied Mathematics

Science University of Tokyo

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