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´ 98 M . Ferre- Masferrer et al. / Clinica Chimica Acta 279 (1999) 97 –105

1. Introduction

Reference values are necessary to compare patients’ results. The InternationalFederation of Clinical Chemistry (IFCC) has published recommendations on the

theory of reference values, the selection of individuals for obtaining referencevalues and the statistical treatment of data in order to estimate reference limits[1]. Several European societies of clinical chemistry have published documents

on this topic, concluding that every clinical laboratory should produce its ownreference values [2]; however, only a few laboratories do so. The selection of

reference individuals is difficult, time-consuming and costly. Furthermore, thecontinued evolution of measurement procedures requires this process to berepeated too often.

Thus, it is not surprising that, in many laboratories, reference values are takenfrom the scientific or commercial literature. However, reference limits included

in text books or in manufacturers’ package inserts should not be used fordiagnostic purposes; these texts usually contain no information about themetrological quality (systematic error and imprecision) with which the reference

values have been produced. In fact, the reliability of reference limits shown in atext book is usually inversely proportional to the between-laboratory coefficientof variation observed in an external quality assessment scheme [3].

An alternative to IFCC recommendations is the estimation of indirect1

reference limits by means of mathematical–statistical procedures applied to thepatients’ results obtained daily in the laboratory, after differentiating them into

‘pathological’ and ‘non-pathological’ (health-related) results [4–12]. The aim of this study is to apply, compare and validate three different procedures for this

alternative [8,10,12].

2. Materials and methods

2.1. Reference individuals

For validation purposes, 120 healthy reference individuals (the reference

sample) were selected according to IFCC recommendations. For practicalreasons, we enrolled only women aged 20–45 years because they were easily

available in our hospital. These women were not pregnant and had no history of either severe diseases or surgery in the previous 3 months. They were advised toavoid physical exercise and cigarette smoking the night before testing and any

alcohol consumption during the prior day. In the last 8 h they had neither eatensolid food nor drank any liquid except water, and they had remained seated for

1

This term has been proposed by Kairisto et al. [11].

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´ M . Ferre- Masferrer et al. / Clinica Chimica Acta 279 (1999) 97 –105 99

15 min before blood sampling.Venous blood was drawn between 8:00 and 10:00h, using evacuated blood-collection tubes with gel (Vacutainer, Becton Dickin-

son, ref. 368510). After 30 min, the tubes were centrifuged at 1200 g for 15 min.Serum samples were tested within 4 h of blood collection.

2.2. Patients

The hospital where the work was conducted has 1000 beds comprising allmain clinical medical specialities, except paediatrics and obstetrics. During

1995, the clinical biochemistry laboratory of the hospital received 119 583requests corresponding to 85 618 different patients, 67 565 of which were

outpatients (79%), and 18 053 (21%) were inpatients.All patients’ results have been stored during 1995 in a laboratory information

system (Omega, Boehringer Mannheim, Barcelona, Spain); among them, results

from 5578 women aged 20–45 years were selected and filed using a personalcomputer connected on-line to the laboratory information system. Only the firstresult for each patient was included (Table 1).

2.3. Measurement procedures

Biochemical quantities selected for this study were:

• Mass concentration of albumin and protein in serum• Substance concentration of bilirubins, calcium(II), creatininium, phosphate,

potassium ion, sodium ion, urate and urea in serum• Catalytic concentration of aspartate aminotransferase, alkaline phosphatase,

alanine aminotransferase and g-glutamyltransferase in serum

All measurements were made with a Hitachi 747 analyser (BoehringerMannheim, Germany); details of the measurement procedures are irrelevant forthis study and have been omitted. A human serum freeze-dried calibrator

(Boehringer Mannheim, Germany, ref. 759350) was used once a day forcalibration. During the study, internal quality control was made using Moni-TrolI-X and Moni-Trol II-X (Dade International Inc. Miami, FL).

3. Procedures for dividing mixed distributions

3.1. Bhattacharya procedure

The Bhattacharya procedure, as modified by Naus et al. [6], assumes that

health-related distributions can be described by a gamma function. Health-

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Table 1

Distributions of patients’ results used to estimate reference limits

Quantity n Refererence limit re-

¯ sults (%) x s G G1 2

Lower Upper

limit limit

r S–Albumin (g/ l) 5067 23 1 45 5 21.7 4.8

cS–Bilirubins (mmol/ l) 3391 NC 4 9 10 13 240

cS–Calcium(II) (mmol/ l) 4993 7 4 2.30 0.1 20.4 4.8

cS–Creatininium (mmol / l) 5711 NC 7 86 65 12 159

cS–Phosphate (mmol / l) 2177 8 9 1.17 0.3 1.8 11

cS–Potassium ion (mmol/ l) 5578 2 9 4.37 0.4 0.8 5.2

r S–Protein (g/ l) 2947 10 6 70 7 20.3 4.4

cS–Sodium ion (mmol/ l) 5578 5 2 141 3 20.2 6.9

cS–Urate (mmol/ l) 5104 NC 9 236 79 1.4 5.9

c

S–Urea (mmol/ l) 3128 NC 11 5.7 3.6 5.8 49S–Alanine aminotransferase 5722 NC 15 0.50 1.2 25 925

a(mkat/l)

S–Aspartate aminotransferase 3297 NC 18 0.65 1.2 1.3 1.5a

(mkat/l)

S–Alkaline phosphatase 5098 NC 8 1.1 0.7 7 85a

(mkat/l)

S–g-Glutamyltransferase 5098 NC 24 0.53 1.0 9 109a

(mkat/l)

Lower limit, lower reference limit obtained in reference sample according to IFCC recommendation; upper limit, upper reference limit obtained in

reference sample according to IFCC recommendation.

¯ n, number of patients used; x, mean value of mixed population; s, standard deviation of mixed population; G , skewness coefficient of mixed1

population; G , kurtosis coefficient of mixed population; NC, not calculated, because they have no diagnostic utility.2a

Catalytic concentration.c

Substance concentration.r

Mass concentration.

related and disease-related distributions from patients’ results can be separatedmathematically if the two subpopulations do not overlap too much and if thesample size is large enough. The total frequency distribution is divided into anumber of classes with the same width. When the logarithm of the ratio of the

frequencies in two sequential classes is plotted against the centre of the firstclass, a gamma distribution will display a straight line, their statistics (m and a )can be calculated, and the fractiles 0.025 and 0.975 can be estimated from a

chi-squared distribution.To estimate indirect reference limits based on the Bhattacharya procedure, a

computer program developed by H.F.M. Borgonjen (ZCA, Juliana Hospital,

7300DV Apeldoorn, Holland) was used.

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statistical test comparing an observed fractile with a theoretical one [15] wasused.

4. Results

The distribution of patients’ results for each quantity has been reported by

some statistics (Table 1). In order to calculate the proportion of pathologicalresults in the mixed distribution, the reference limits obtained following IFCC

recommendations with the reference sample have been used. The results outsidethe reference intervals defined by these reference limits have been considered asdisease-related.

The indirect reference limits estimated from patients’ results using the threeprocedures and the reference limits estimated following to IFCC recommenda-

tions are given in Table 2.In this work, the three procedures studied gave indirect reference limits

similar to those obtained in a reference sample according to IFCC recom-

mendations. However, after validating the indirect reference limits, statisticaldifferences have been found for some quantities.

As regards serum concentration of bilirubins, creatinium, urate and urea, we

have only validated the upper indirect reference limit, because this is the onlyone having diagnostic utility in our hospital.

The upper indirect reference limits for substance concentration of bilirubins

and catalytic concentration of alanine aminotransferase in serum obtained by thethree procedures are significantly different (P , 0.05) from fractile 0.975 of the

reference distribution.The upper indirect reference limit for catalytic concentration of aspartate

aminotransferase in serum obtained using the Kairisto et al. procedure [11] is

statistically different (P , 0.05) from fractile 0.975 of the reference distribution.The lower indirect reference limit for substance concentration of potassium

ion in serum obtained using Martin et al. [10] and Kairisto et al. procedures [11]

is statistically different (P , 0.05) from fractile 0.025 of the reference dis-tribution.

5. Discussion

The establishment of reference values is difficult, time-consuming and costly;

consequently, it is not surprising that only a few laboratories do it. Probably, oneof the main problems is to obtain a sufficient number of adequate samples forobtaining reference values, particularly for quantities that are not distributed

according to Laplace–Gauss’ law and for which partitioning criteria should be

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Table 2

Indirect reference limits obtained from patients’ results using Bhattacharya [4], Martin et al. [10],

and Kairisto et al. [11] procedures

Quantity (units) Procedure

a

Bhattacharya Martin at al. Kainsto at al. IFCC [1]

[4] [10] [11]

r

S–Albumin (g/ l) 41–52 39–51 39–52 41–53c

S–Bilirubins (mmol/ l) 3–14* 3–16* 2–13* 4–18c

S–Calcium(II) (mmol / l) 2.13–2.48 2.12–2.48 2.11–2.47 2.15–2.46c

S–Creatininium (mmol/ l) 64–96 62–93 62–95 65–96c

S–Phosphate (mmol/ l) 0.84–1.55 0.82–1.52 0.84–1.56 0.87–1.45c

S–Potassium ion (mmol/ l) 3.74–4.95 3.78*–5.04 3.80*–5.05 3.66–4.89r

S–Protein (g / l) 63–81 63–81 61–80 64–79c

S–Sodium ion (mmol/ l) 138–146 138–146 136–146 138–146c

S–Urate (mmol / l) 129–366 120–345 120–337 134–325c

S–Urea (mmol / l) 2.9–8.2 2.6–7.8 2.3–7.5 3.0–7.3S–Alanine aminotransferase ,0.47* ,0.52* ,0.51* ,0.60

b

(mkat/l)

S–Aspartate aminotransferase ,0.45 ,0.49 ,0.41* ,0.46b

(mkat/l)

S–Alkaline phosphatase ,1.5 ,1.7 ,1.5 ,1.4b

(mkat/l)

S–g-Glutamyltransferase ,0.41 ,0.48 ,0.44 ,0.43b

(mkat/l)

a

Reference limits obtained from reference sample were produced according to the FCC recommendations.b

Catalytic concentration.c

Substance concentration.r

Mass concentration.* Significantly different (P#0.05) than fractile 0.975 of the reference distribution.

used. For this reason, there are three alternatives to solve this problem: (i)

adoption of reference limits produced by other laboratories after verifying their

transferability [1], (ii) the multicentric production of reference values [16], and

(iii) the use of patients’ results to estimate reference limits by direct or indirect

methods [4–14].In any case, the ideal situation is to have true interchangeability of reference

limits, and consequently, common interpretation of results coming from different

laboratories.Among these alternatives, the estimation of reference limits from patients’

results has many advantages:

• It is the easiest procedure

• It is the cheapest procedure

• Reference limits are derived from values obtained with the same pre-

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metrological conditions as the patients’ results which will be compared withreference limits

• Patients’ results can be easily selected according to biological variationfactors when it is necessary.

The upper indirect reference limits for substance concentration of bilirubins

and catalytic concentration of alanine aminotransferase in serum obtained by thethree procedures have not been used for diagnostic purposes. This is probably

due to the shapes of the mixed distributions; these distributions have coefficientsof skewness and kurtosis greater than the other quantities studied (Table 1). Theshape of mixed distributions seems to have an influence on the reliability of

these procedures. We observed that the three procedures are reliable whendistribution of patients’ result has a coefficient of skewness of 12 or lower and a

coefficient of kurtosis of 159 or lower, but they are not reliable when these

values are 13 and 240 or higher, respectively.The upper indirect reference limit for catalytic concentration of aspartate

aminotransferase in serum obtained by the Kairisto et al. procedure [11] and thelower indirect reference limit for substance concentration of potassium ion inserum obtained by the Martin et al. [10] and Kairisto et al. [11] procedures are

not valid, but we do not have an explanation for these differences.We conclude that the three procedures used to estimate reference limits from

patients’ results are good enough for the following quantities: substanceconcentrations of calcium(II), creatininium, phosphate, sodium ion, urate andurea in serum; mass concentration of albumin and protein in serum; and catalytic

concentration of alkaline phosphatase and g-glutamyltransferase in serum.

The most effective procedure studied is the one proposed by Bhattacharya [4]modified for gamma distributions.

References

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