Error Aleatorio Critico

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CL IN . CHEM . 3 5/2 , 2 84 -2 88 ( 19 89 )

284 C LIN IC AL C HE MIST RY , V ol. 35, N o. 2, 1989

ChoosingQual i ty -ControlSystems to Detect Maximum Clinical lyAl lowableAnalyticalErrorsKrlstlanUnn.tCrit ical s ys tem at ic a nd ra nd om ana ly tic al e rr or s f or 1 7 com-mon clin ica l c he mica l co mp on en ts w ere e stim ate d fro mpublish ed va lu es for analy tic a l impr ec is ion , b io log ic a l v a ria -t ion , and med ica ll y important changes . Appropr ia te qua li ty -contro l system s for these analytes are discussed on thebasis o f power c on sid er atio ns . T he s im p le r ule 1 , w it h o necon tro l per run,is m i nima lly su ff ic ien t f o r t he anal yt es ( abouto ne q ua rte r o f th os e c on sid ere d h ere ) fo r w hic h th e m ag ni-tu de o f critica l e rro r is a t lea st 3 anal yt ica l s t andard devi-a tio ns. T he m ore p ow erfu l ru le 1 , w ith o ne co ntro l pe r run,is th e m in im al re qu ire me nt fo r a na ly tes fo r w hic h critica le rro rs a re a bo ut 2 a na ly tic al s ta nd ard d ev ia tio ns ; th es e a reabout h alf t he r em a in in g a na ly te s. G re ate r p owe r v alu es a rea ch ie ve d b y u sin g m ultip le ru le s b as ed o n s ev era l c on tro lsper ru n. In g en era l, th is s tu dy d oe s n ot s up po rt th e v ie w p utfo rw a rd b y s ome aut ho rs th at t he q ua lit y-c on tro l r ule s in u setoday are to o restrictive.

Commonly , th e d es ig n o f quality-control systems in clini-ca l che mistry is b ase d on convent ion r at he r than on consid-era tio n o f what size of a naly tical e rrors shou ld be detectedfo r clin ic al u tility. The ability of various quality-controlrules to reveal errors of a given magnitude w ith a statedp ro ba bility h as b ee n co nsid ere d by Westgard e t a l. (1,2). Itis difficult to de fine m ed ica lly im po rta nt e rro rs objectively,an d several investigators have ch ose n th e p ra gm atic ap -proach of in te rr og atin g c lin ic ia ns as to what changes inlaboratory re sults a re ju dg ed a s being important (3-8). Inth is paper, I use th e medically importantchanges recordedb y S ke nd ze l e t a l. (8 ) as a starting point a nd , b y taking bothpro-analytical and biologicalariat ion into account , deriveth e m ax im um a llo wa ble a na ly tic al errors fo r commonlym ea sure d a na lytes. F rom th ese va lu es, I sug ge st appropri -at e quality-control systems.Backg round and Assumpt ionsMedical ly Important D if fe rences Re la ted to Analyt ical andBiological Variation

T o p hysic ia ns in va rio us m edica l f ie ld s S ke nd ze l e t a l. (8 )p os ed 2 5 q ue st io ns co nce rning co mm on clinica l p ro ble ms,a sk ing th e ph ysic ian s to select from severalpossibil i t ies th echange in laboratory result f or a p at ie nt that would e lic it a na ct io n, i .e ., further esting or therapy. Mos t o f t he questionsconcerned a change in a patient being monitored fo r s om edisease; in s om e cases, a d if fe rence between a patients valueand a fixed lim it, e.g., a re fe re nc e interval lim it, wasc on sid ere d. F ro m 750 responses, S ke nd ze l e t a l. re co rd ed th emedian value of the answers to a given quest ion an dc on ve rte d th is to a r ela tiv e v alu e with respect to the ana ly tec on ce ntra tio n. F rom th es e m e dia n d iffe re nc es o f medicalimportance ( Imeci ) , so-called medically use fu l coe ff ic ien ts o fvariat ion (CV,,,) were derived:

CVmec i = med(1.65V)

When a p atie nt s v alu e wa s compared w ith a f ixed limit, th er ela tio n wa s a s f ollow s:

CVm = med1.65The CVm has been interpretedas a g oal fo r analyticalimprecis ion f or t he f ollow ing r ea so n. If th e a na ly tic al im p re -cision (Se) is th e only source o f ra ndo m v aria tio n, a nd th egoal is fulfilled, th e difference of medic al im p or ta nc e iss ta ti st ic a ll y s ig n if ic an t at th e 0 .0 5 l eve l ( one -s id ed t es t) . T hetest results given clinicians, h ow ev er, a re s ub je ct to a dd i-t ional sour ces o f va ri at io n : pre-analytical an d biologicalf ac to rs . The p ro -anal yt ic a l imp r ec is ion (sr) is th at in du ce db y th e venipuncture and the p re -p ro cess ing o f t h e sample . I nt he p resen t cont ex t, t he b io log ic a l v a ri at io n (Sb) i s t he intra-individual v ariatio n a bo ut a h om eo sta tic s et p oin t (9 ). T ote st wh et he r a n o bs er ve d c ha ng e in a p atie nt , o r a d iff er en cewith re sp ec t to a fixedpoint , in dic ate s a re al d iffe ren ce inth e b io lo gic al s ta te o f t h e in div id ua l, o ne h as t o calculate th eto ta l s tandard dev ia t ion (St), wh ic h s ho uld b e e xp re ss ed a s acoeffic ient of var iat ion:

St=y++sAn observed change (ii) in a monitored pat ient is stat is t ica l lysignif icant (one-sided te st) if:

.I(sV) >1.65T ab le 1 p re sen ts data for the com monly used analytes

examined by Skendzel e t a l. (8). The in tr a- in d iv idual b io log -i ca l va r ia t ion (coe f fi ci en tso f v ar ia tio n, c olum n 1) m ostly arethose a gre ed u po n a t c on fe re nc es in 1 97 6 a nd 1 97 8 (10). Theva lu e f or b ili ru b in o rig in a te s f ro m a report by W inkel et al.(11), an d th at fo r aspartate arninotransferase is th e a ve ra geo f th e re su lts o bta in ed in tw o stu die s (1 1, 1 2). For bloodhemog lob in , b lood leukocyte c ou nt, a nd p la sm a p ro th rom-bin tim e, the intra-individual v aria tio n w as e stim ate d a sdescribed i n t he Appendix.The analytical im p re cis io ns lis te d in Table 1 r ep re sen tmedian v alu es o f t he in tr a-la bo ra to ry c oe ffic ie nts o f v ar ia -tion recorded in surveys b y T he C olleg e o fAmerican Pathol-ogists (8 , 1 3), an d so may be regarded as representativestate o f th e a rt va lu es . T he to ta l s ta nda rd devia tio ns a reb as ed o n th e biological and the a na ly tic al s ta nd ard devi-a tio ns ; f or a ll analytes, I have assumed th e pre-analyt icalstandard deviation to be equal to one-half th e analyt icals tandard devia ti on , an intermediate va lu e o f t he p re -analy t-ic al s ta nda rd deviations recorded fo r v a rio u s analy te s (14,15). Thus, the formula for the totalstandard deviationbecomes :

= V1.25 s + sThe medical ly impor tan t d if fe rences in Table 1 repro-s en t th e difference b etw een a fi xed lim it and a patientsresult that elic its an action. These values are eq ua l tothe CV,, values of the study of Skendzel et a l. (8),multip lie d b y 1 .6 5. In th os e s itu atio ns w he re S ke nd ze l e t a l.

Department of C lin ica l C hemis try K K 4 05 1, R ig sh osp ita le t,Blegdamsvej9 , DK-2 100Copenhagen0, Denmark.Received Sep tember 29 , 1988 ; ac cep tedNovember 18, 1988. The c li n ica l ques t ionswere d ir ec tio na l, s o th e statistical testss ho u ld b e on e- si de d .


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Tab le 1 . I nt ra -I nd lv idual B iolog ica l Va ria ti on (se,), Analyt ica l Imprec ision (Sa), To ta l S t andard Dev ia ti on (sJ,Medically Important D ifference and for 17 Analyteslntra-Indlv. Anal. Total at .

Analytea var. (Sb) var . (s ) dev. (St) A,,,.,Aspartate aminotransferase 0.140 0.061 0.156 0.335 2. 2Biiirubin 0.230 0.109 0.260 0.431 1.7Cholesterol 0.048 0.038 0.064 0.203 3. 2Triglyceride 0.260 0.054 0.267 0.266 1.0Creatinine 0.044 0.061 0.081 0.259 3. 2Urea 0.124 0.046 0.134 0.308 2.3Glucose 0.044 0.035 0.059 0.224 3.8Iron 0.260 0.032 0.262 0.284 1. 1Phosphate 0.058 0.035 0,070 0.257 3. 7Total protein 0.030 0.022 0.039 0.137 3. 5Thyroxin 0.076 0.089 0.125 0.380 3.0Hemogiobin 0.045 0.011 0.047 0.076 1. 6Leukocytecount 0.147 0.025 0.150 0.251 1. 7Prothrombin time 0.045 0.038 0.062 0.251 4. 0Calcium 0.018 0.024 0.032 0.097 3. 0Potassium 0.044 0.021 0.050 0.119 2.4SodIum 0.008 0.012 0.016 0.036 2.3

a Measured in serum,plasma,or blood.Al lesultsareexpresseds relativeoanalyteconc entration s.

P robab S t ydensityProbabilitydensity

0A A

CL IN ICALCHEM IS TRY , V ol. 35 , N o . 2 , 1 98 9 2 85

gave two o r t hr ee v alu e s fo r t he s ame analy te , correspond-in g to different clinical problems, I have selected th e m ea nvalue. M edically important changes in a patient beiflgmonitored ar e obtained b y m u ltip ly in g th es e v alu es b y V 2.Finally, for most (15/17) of these values are equal toor exceed 1.65.T he Me an in g o f t he Requ ir em ent f or S ta tis tic al S ig nific an ce

How important is th e re qu ireme nt fo r s ta tis tic al signifi-cance?Al though clinicians u su ally d o n o t c ar ry o ut f orma llys ta tis tic al te sts o f significance in e ve ry da y w or k, this con-cept is n eve rt he le ss o f r e a l impo rt ance. f fm&j/St is >1 .6 5 fo ra n a na ly te , observed changes () that are larger than theaction lim it w ill occur in


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ATest result

Probabhi l tydensity

Fig.2. DistributIonofobservedanaly t ical resul tsabout th e target va lu e ( a) f o r th e i n -cont ro l ta te ;(b ) in the presence o fa sys temat icerror, ASE;and (C ) when th e s ta nd ar d d e vi at io n i s increasedfrom s to s,

ii Test resu l t

2 86 CL IN ICALCHEM IS TRY , V o l. 3 5, N o . 2 , 1989

Because a lte rn ative sta te s fo r h et ero ge ne ou s e ve ry da yclinical problems are difficulto s pe cify , I h av e chosen tofollow th e pragmatic a pp ro ac h o f S ke nd ze l e t a l., focusing onth e type I error problem and retaining th e requirementA,/s 1.65 as a reasonablea pp ro ac h in consideringhemaximum allowable analytical errors (see below). Thiscon ditio n see ks to keep th e fa ls e- po s itiv e a la rm f requencyreasonably low and ensures that only up to 5% of theo bse rved A valu es are in th e o pp osite direction o f t he true Aw hen th e true A equals A .ResultsCr it ic a l Ana ly ti ca l E rr or s De riv ed f rom Med ica lly Impo rt an tDifferences

An analyt ical method ordinarily produces resu l ts th at a rescattered about a target value, , with a standard deviat ion,S ( Fi gu re 2 a) . This in -contro l sta te may be disturbed byerrors. A system atic error (inaccuracy) is a co nsta nt b ia s(ASE) thatshiftshe target value from to 1& + ASE (Figure2b). A random error represents an increase o f th e basel inescatter a bo ut th e targetv alu e (F ig ure 2 c). Analyt ical meth-ods for w hich A .Jst is >1.65 for the in-contro l state m ays till, in a n o ut- of -c on tro l s ta te , f ulf ill t he b as ic r eq uir em ento f < 5% fa ls e-p os itiv e alarms in th e c lin ic ally s ta tio na rystate. Figure 3 i l lustrates th e max imum systematic error(ASE) at which this condition is just fulfille d. A SE C isd efin ed b y th e f ollow in g r ela tio n:

ASE = AmM - 1.65 StIt is c on ve nie nt to express th e c ritic al s ys tem at ic error ina na ly tic al sta nd ard d ev ia tio n u nits . The standardized criti-ca l systematic error is :

ASEct) = ASEdSa = [A - 1.65StJfST he a bo ve -m en tio ned a pp ro ac h is va lid fo r a ll an alyte s inTable 1 fo r which Am,/St substantial ly exceeds 1 .6 5 , i .e ., f or12 of 17 analytes (Table 2). Tw o of the 12 analy tes haveASE v alu es o f about 1, half exhibit values o f a b ou t 2 , a nda th ird have values equal to or greater than 3 (maximum4.0).T he s ta nd ar diz ed c rit ic al r an dom error (AR E) is d e te r-mined as follows.An increase o f th e a na ly tic al standarddeviation from s to s changes the to ta l s ta nda rd deviationsto s. T o a vo id having >5% of o bs er ve d A va lu es exceedA,, (in the same d irect ion ), w hen the true A is z ero , th ef ol low in g cond it io n should b e fu lifiled (F igu re 4):

AmJS = 1.65Ha vin g d ete rm in ed s, s is obta ined as fo ll ows (suppos ingth e p re -a na ly tic al e rro r (s = 0. 5 Sa ) t o b e constant):

s = Vs + 0. 5 s + s

wh ic h re arr an ge s tos = Vs - s - 0.5 s

The critical random error i s f ina ll y standardized:AREC(8t )= S/sa

Abou t hal f of the 12 analytes considered have AREvalues between 2 a nd 3 (T ab le 2 ). S od ium h as th e m in im umv alu e (1 .6 ) a nd p ho sp ha te th e maximum (4.1).Qua lit y-Con tr ol Des igns App rop ria te f or De tec ti on o f C r it ic a lErrors

H a vin g e stim a te d th e critical errors ASE) and ARE ,one can s ele ct a quality-control system that is a ble to detectthese errors w ith a reasonable probability (pow er). Then ot at io n AL fo r quality-control rules is u sed , w he re A is th enumber of control obse rva ti ons tha t mus t exceed the lim it Lt o in dic at e a n o ut -o f- co nt ro l s ig na l. T ab le 3 p re se nt s p owe rsfo r some com mon contro l ru les: tw o sim ple ru les, 1 for n =1 control per run and 1 (n = 1) , and a mu l ti -r u le , 1/2/R(n = 2, 4, o r 6 ) (h ere , s refers t o t he a na ly tic al standardd ev ia tio n) . T he mu lt i- ru le g iv es a r eje ct s ig na l if o ne c on tr ole xceedsa 3s limit, tw o consecut ive contro ls exceed th e same2s limit, o r th e max imum and the m inim um values of thecontro ls deviate by m ore than 4s. The 2 component issensitive towards systematic e rro rs , w he rea s R in p artic u-la r d ete cts ra nd om e rro rs . T he p ow ers h av e been read fromth e p ow er graphs presented by Westgard e t a l. ( 1, 2 ).

Combining T ab le s 2 an d 3 g uid es u s t o select an approp ri-ate q ua lity -c on tr ol sy ste m fo r a g iv en a na ly te . Several o f t h eanalytes (potass ium, c alc ium , u re a, thyroxin, and creati-nine) have ASE) values of about 2 and ARE valuesfrom 2.3 to 3. For t hese ana ly tes the 1 (n = 1) ru le d ete ctsboth error types w ith the pow er f ro m 0 .4 0 t o 0.50. Higherpower va lu es ( 0. 65 - 0 .8 5) a re a ch ie ve d b y u sin g th e 1 ,/2 /R(n = 4 ) r ule . The 1(n = 1) ru le ha s lo w p ow er h ere andis insuf fi cien t.

O ne s ho ul dgeneral ly strive fo r h ig h le ve ls o f p o w er w he ne rr or s a re fr eq ue nt; o n th e o th er hand, o ne c an accept lowerle ve ls wh en errors are rare (16). Th e e rro r fre qu en cy isseldom known, b ut p ast experience may g iv e s om e in dic a-tion. For example, elect rochemical determinat ion of electro-lytes is a n a nalysis su bje ct to f re quen t e rr or s. For potassiumassayed by this principle, th e multi-rule w ith n = 4 thusma y be p re fe ra ble to th e s im ple 1 (n = 1) rule. For the fewanaly tes w ith ASE) about 1 (sodium , a sp arta te amin o-tr an sfe ra se ), a low level of pow er has to be accepted, evenw ith n = 6 cont ro ls an d the mu l ti -ru le . Using a multi-ruleover s ev er al ru ns may increase s omewha t t he p ro ba bilit yfo r detecting persisting errors (17).A ASE) value of about 3 is detected w ith pow ers 0.50and 0.84 w ith use of the sim ple ru les 1 and 1(n = 1),

Probabil i tydensity

Probabilitydensi ty

ji Test resu l t


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Probabilitydensity Probabil i tydensity

5%

Test result* ME D #{149} ME D

Test resu lt

1J2R4,

0.81. 31.81.81. 92. 02. 12. 63. 33. 63. 94. 0

CL IN ICALCHEM ISTRY, Vo l.3 5 , No . 2 , 1 989 28 7

FIg .3 . Distributionf observed pat ients resu l tsabout + ASECwi thas ta nd ard d ev ia tio n , g ive n a homeostaticetp oi nt a nd a systematicanalyt icalerrorASEC5 % o f t he valuesexceed +re sp ec tiv ely . T he a bility to re ve al a critical random error ofabout 3 is not quite as high for these ru les, 0 .30 an d 0.50,respectively. Very h ig h p owe r le ve ls fo r b oth e rr or ty pe s a reachieved by using the m ulti-ru le (n = 4 ). T he an aly te schole s te ro l, t ot al p ro te in , and g lu co se h av e ASE) andARE) values of a bou t 3.For analy tes with A,/s


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Sb(intra)0.0450.1470.045

2 88 CL IN ICALCHEM IS TRY , V ol. 3 5, N o . 2, 1989

reserved fo r analy tes in w hic h A SE ) and ARE exceed3.The advantage of the 1(n = 1) rule is the very lowf re qu en cy o f f a ls e r eje ct io ns ( 0.0 02 7). T he mu lt i- ru le o ff er s ag re ate r e ffic ie nc y fo r a g iv en number o f c on tro ls , b ut it isa ls o mo re complicated to apply. N otice that the powers ofTable 3 have been obtained under the assum ption of nobetween-run analytical componen t o f variation. If this com-ponent is o f a b ou t th e s am e s iz ea s th e within-run variation,th e actual powers are somewhat smaller (22).Some authors (13) have argued that qu ali ty -c on tr ol li m it s

b ein g u sed today ar e gen era lly too narrow, being based onthe anal yt ic a l standard deviation, which has d ec lin ed inr ec en t y ea rs . C la im in g t ha t a q ua lity -c on tr ol system is to origidis th e same as saying that th e p ow er is unnecessari lyh ig h fo r d ete ctio n o f medicallyimportanterrors , i .e . , 0.99org re ate r. If this is th e c as e, w id en in g o f th e c on tro l lim itswould reduce th e fre qu en cy o f fals e re je ctio ns (a nd s o th ec os ts ), w hile m a in ta in in g a s uffic ie nt degree of power (areduction from 0.99 to 0.90 would b e fu lly a cc ep ta ble ).According t o t he p re se nt a na ly sis , s uita ble q ua lit y- co ntr ols ys tems c an b e s ele cte d from the set of trad itional ru lesbeing based o n th e analytical standard d ev ia tio n. F or n on eo f th e a na ly te s is th e p ow er o f t he m os t lib era l c on tro l rule[138(n = 1) ] unnecessarily high, justifying a w id en in g o f th econtrol limits t o f ou r o r mo re analy ti ca l standard deviations.Thus , t he c rit ic ism (13) o f t h e t rad it io n al cont ro l- ru le p rin c i-p le , fo un de d o n th e a na ly tic al standard d ev iatio n, is n ott en ab le . N or i s t h e approach adopted by Schoen e t a l. (23),wh ic h c on sis ts o f u sin g clinically usefu l contro l lim its. Aquality-control rule is a sta tistica l te st o f th e n ull h yp oth e-s is -t he a na ly sis is in c on tro l-a ga in st th e a lt ern at iv e-t heanalysis is o ut o f c on tro l. T he d es ig n s ho uld b e based on ac on sid era tio n o f th e fre qu en cy o f fa ls e re je ctio ns (typ e Ie rro r) a nd t he p owe r. Only when th e p ow er fo r a m ed ic allyimportant error turns out to be far too large should thecontrollimitsbe widened.AppendIx

Concerning biological variation,the focus has been onserum constituents.T o d erive e stim ates fo r h em og lo bin ,leukocyte count, an d p la sm a p ro th ro mb in tim e, th e g ro up0 .9 5- re fe re nc e in te rv als p re se nt ed in r ef. 24 w ere used as asta rtin g p oint. A ssu min g gauss ian d is tr ibu ti ons , th e rangeof th e 0 .9 5 -r ef er ence in te rv a l corresponds to four totalstandard d ev ia tio ns , wh er e th e t ot al standard devia ti on i s:

St = + S + Sjny) + S& inter)Notice that here we have both an intra- and an inter-in div id ua l b io lo gic al c om po ne nt o f v aria tio n (9 ). B y a rb i-trarily se ttin g = S) and 5p = O.SSa, Sl,(j,,t.a) 1b e c omp ute d and converted to a re la tiv e v alu e w ith respectto the mean of the reference interval. We did so, obtainingth e f oll ow in g v alu es :HemoglobinLeukocyte countProthrombin t imeReferences1. Westgard JO , Groth T. Power funct ions fo r s ta ti st ic al c on tr olrules.Clin Chem 1979 ;25 :863 -9 .2 . Westgard JO , Barry FL Cost-effective qual it y c on tr ol : managing

th e qualityand productivityf analytica l processes. Washington,D C: A m A ssoc f or C lin C h em , 1 98 6.3. Barnett RN. Med ic al s ig n if ic an ce of laboratory re su lts . Am JClin Pathol 1968;50:671-6.4. C am pbe ll D G, O we n JA . T he p hy sic ia nsview o f l aborato ryperformance. Aust Ann M ed 1969;18:4-6.5. S ke nd ze l L P. How phys ic i ansus e laboratory tests. J Am MedAssoc 1978;239:1077-80.6. Barret t AE , C ame ro n S J, Fraser CG , Panberthy LA , ShandKL .A c lin ic al v ie w of analytical g oa ls in clinicaliochemistry. J ClinPathol 1979;32 :893 -6 .7. Elion-Gerritzen WE. Analyticprecisionn clinical chem is tr y andmedica l decisions.Am J C li n P at ho l 1 98 0; 73 :1 83 -9 5.8. Skendzel LP , Barnet t RN , Platt R Me dic ally use fu l c r it e ri a fo ranalyticperformance o f la bo ra to ry te st s. Am J Clin Pathol1985;83:200-5.9 . Harris EK . Statistical principlesunderlying anal yt ic g oal -s e t-t in g in c lin ic al c hemis try. Am J C li n Pa tho l 1 979 ;7 2 :3 74- 82 .10 . Subcommit tee on Analytical Goals in C lin ic al C h em is tr y,WASP, C IBA Foundat ion , London , Engl and , 1 978 , P ro ceed ingsAnalyt ica l goalsin cl inicalchemistry:their relationshipto medica lca re . Am J C lin Pa tho l 1 979 ;7 1 :6 24- 30 .11 . Winkel P , S ta tla nd BE , Bo ke lu nd H . Factorscontributing tointra-individual var iat ion of serum con stituents :5. Sho rt-term day-to-day an d within-hour var iat ion of serumconst i tuentsin healthysubjects .Cl in Chem 1974;20:1520-7 .12 . Young DS , Harris E K, C otlo ve E . B io lo gic al a nd analyticcom pon entsof variation in long-termstudiesof serum consti tuentsin normalsubjects .4 . Resul tsof a studydesignedto eliminate long-term analyticdeviations.Cl in Chem 1971;17:403-10.1 3. R os sJW , Fraser MD. Cl in ical laboratoryprecis ion.The stateofth e ar t and medical use fu ln e ss based i nte rna l q ual it y cont ro l . Am JCl ii i Pa thol 1982;78(Suppl) :578 -86 .14. B oke lu nd H , W in ke l P , S ta tla nd BE. Factorscontributingountra-individual variat ion of serumconst i tuents:3 . Use of random-ized dupl icateserum specimens to eva lua te sou rces of analyt icalerror. Cl in Chem 1974 ;20 :1507 -12 .1 5. W in ke l P , S ta tla nd BE , N ie ls en MK . B iol og ic a l and analyticc om po ne nts o f variat ion of concentrationvaluesof selectedserumproteins.Scand J Clin La b Inves t 1976;36:531 -7.16 . Westgard JO , G ro th T . The predictive value theory of qualityc on tr ol. Am J C lin Pa tho l 1983;80:49-56.17 . Westgard JO , Barry FL , H unt M R, G roth T. A m ulti-ru leShewhar t chart fo r qua li ty c on tro l in c l in ical c hem is tr y [ Pr oposedSelected Method ] .C l ii i Chem 1981;27:493-501.18 . F ra se r C G . Better criteriaor desirable laboratory performanceexist [L ette r]. Am J ClinPathol 1986;85:251.19. ShephardMDS , P en be rth y L A, Fraser CG. Ana ly tic al g oa ls fo rquantitativeur ine ana lys is : a clinical view [Letter]. Clin Chem1981;27:1939-. .40.20 . Groth T , Ljunghall S , D e Verdier C -H . O ptim al screening fo rpatients with hyperparathyroidismwith use o f s erum c alciu mo bs erv atio ns. A d ec isio n-th eo re tic al a na ly sis. S ca nd J C lin LabInvest 1983;43:699-707.21 . Petersen PH , Roslef fF, RasmussenJ, Hobo lth N . S tud ie s on th erequired analytical quality of TS H measur ement s i n s cr ee ni ng f orcongenitalypothyroidism. Scand J Clin La b Invest 1980;40(Supp155):85-93.22 . Westgard JO , F al k H , G ro th T. In fluence of a between-runcomponent of var ia t ion , choice of control l imits, and shapeof errordistribution o n th e performance characteristics of rulesfor in te rna lqua li ty con tro l. Ch in Chem 1979 ;25 :394- 400 .23 . S cho en I, C uster E , Graham G,BandiZ, S uro vik M H. Q ualitycontrol lo g with CUSUM and clinicallysefulim its c rite ria , A rc hPathol Lab Med 1985;109 :333 -9 .24 . T ie tz NW , e d. T ex tb oo k of c li n ica l chemis try . Philadelphia,PA:WB Saunders & Co., 1986:1829-44.

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