**Gemma Solé-Enrech, Xavier
Fuentes-Arderiu**

Laboratory Clínic

University Hospital de Bellvitge, L'Hospitalet de Llobregat,
Catalonia, Spain

**Correspondence**

Tel: +34 932 607 644

Fax: +34 932 607 546

e-mail: xfa@bellvitgehospital.cat

One of the requirements concerning the working instructions for
measurement procedures (or measuring systems) given in the
subclause 5.5.3 of the standard ISO 15189:2007 (1) states that the
clinical laboratory documentation should include the reportable
interval of examination results, and in the subclause B.5.6 of the
Annex B states that, for each examination procedure, a range
[interval] of values should be predefined to detect *absurd*
or *impossible* results. Thus, any laboratory seeking
accreditation for compliance with the mentioned standard shall
establish the limits for these intervals.

On the other hand, the same standard, in the subclause 5.7.1,
states that authorized personnel shall review systematically the
results of examinations in the post-examination phase. One way of
performing this systematic review is the plausibility control (2),
using alert limits, among other tools, in order to detect
*doubtful results*. Some of these doubtful results detected
using this way could be results with a very low probability of
belonging to the patient, here named *unlikely
results.*

Bearing in mind these two objectives, it is advisable to set a
criterion to estimate *unlikeliness limits* which will
define the unlikely results, aside from the clinical implication of
these results.

As there are not scientifically rigorous procedures to set
unlikely limits, the establishment of such limits will be more or
less arbitrary. The current text discusses several strategies that
can be used to estimate the unlikeliness limits as well as the
problems appeared in this estimation. The manuscript describes and
compares different methods for the definition of the reportable
interval of an examination procedure.

In order to establish the unlikeliness limits of several
biological quantities measured in the clinical laboratory of the
Hospital Universitari de Bellvitge (
Table 1), for each quantity, the measured values reported
during years 2006 and 2009, and stored in the laboratory
information system Omega 3000 (Roche Diagnostics España S.L., Sant
Cugat del Vallès, Catalonia, Spain) were used, as long as 10 000
data or more were available.

Among the different procedures proposed to estimate the
unlikeliness limits, it is necessary to find out which one, despite
of its arbitrariness, allows the establishment of these limits
taking care that the number of unlikely results be reasonable under
a professional point of view.

One of the proposed procedures to get a limit is based in the
estimation of fractiles beyond which will be very unlikely to find
a result, although the choice of this fractile is completely
arbitrary (3).

Another proposed procedure is based on considering unlikely any
result outside the range defined by the higher and the lower of the
cumulated reported (validated) results, after excluding possible
outliers (4).

On the other side, if the definition of unlikely value is
considered under a statistical point of view, this definition is
equivalent to the definition of outlier (5). Thus, a statistical
test for outlier detection may be adapted to estimate unlikeliness
limits.

In accordance with the Dixon's test for outliers detection (5), in
a series of results (containing outliers) sorted from lowest to
highest:

*xn* is an outlier when *x*n -*x*n-1 >
(*x*n-*x*1)/3

*x*1 is an outlier when *x*2 -*x*1 >
(*x*n-*x*1)/3

Thus, any result being ≤ *x*1 or ≥ *x*n will be
considered outlier and, consequently, *x*2 will be the first
non outlier value and *x*n-1 the last non outlier
value.

Therefore, in a series of results sorted from lowest to highest,
the value of the first hypothetical outlier in the right side,
*x*n, can be calculated as follows:

*x*n - *x*n-1 = (*x*n - *x*1)/3;
3*x*n - 3*x*n-1 = *x*n-*x*1;
*x*n = (3*x*n-1 - *x*1)/2

The hypothetical first outlier in the left side, *x*1, is
calculated similarly:

*x*2 - *x*1 = (*x*n - *x*1)/3;
3*x*2 - 3*x*1 = *x*n - *x*1;
*x*1 = (3*x*2 - *x*n)/2

Thus, the hypothetical first outlier in the left side
corresponds to the lower unlikeliness limit and the first outlier
in the right side corresponds to the upper unlikeliness
limit.

It is well known that, in order to be sure that the estimation of
limits is acceptable, it is very important that all the measured
values used belong to the selected population, that is, they are
not outliers. However, there is not literature enough with proper
information regarding the most appropriate procedure to detect
outliers, especially in populations with such large number of data
and with non Gaussian distribution as the used in the current
study.

In this work, we selected a modification of the Dixon's test,
modified according to Reed, Henry, and Mason (5, 6), for the
detection of outliers, because, despite presenting some limitations
(masking outliers when instead of a single outlier result is a
collection of data that is not part of the sample), this test is
one of the recommended criterion by the American organization
*Clinical and Laboratory Standards Institute (CLSI)* for the
establishment of reference values (7), which is a situation with
some analogy with that presented in this article.

In Table 1, different unlikeliness limits for
each biological quantity considered are showed. These limits have
been estimated using the three strategies mentioned above
(fractile, lowest and highest non outlier value, estimation of the
minimum hypothetical outlier value using the Dixon's inequation).
We have to take into account that increasing the number of
available data means that the established unlikeliness limits will
be more reliable, so, it is reasonable to review them once a
year.

It should be remarked that for kinds of quantity related with
fractions (substance fraction, mass fraction, volume fraction,
etc.), the Dixon's inequation is not applicable. Because the actual
measurement results belong to the interval between 0 and 100 (or 0
and 1), and the Dixon's inequation may give unlikeliness limits
outside this range.

Moreover, this strategy will not be applicable in the estimation
of the lower unlikeliness limit, particularly in such cases where
the corresponding numerical value is close to 0, and after applying
the corresponding equation, the theoretical outlier values will
correspond to a negative value. Nevertheless, bear in mind that in
most cases, there are biological quantities for which ones the
establishment of a lower unlikeliness limit makes no sense. There
are biological quantities that in some patients have values below
the detection limit of the measurement procedure (and therefore
must be reported with the relational operator "£" followed by the
detection limit value and the corresponding unit).

The Dixon's inequation strategy, although provides a reasonable
number of unlikeliness values, it presents some limitations. In
fact, the main problem of this approach is that it can produce
results so abnormal to be completely useless for the scope of
avoiding inappropriate reporting; thus, an unlikeliness limit found
following this approach may be a value incompatible with life
(although it is very difficult to find information about which
values are incompatible with life).

Probably, as the setting of unlikeliness limits is, by definition,
arbitrary, any of the three approaches could be equally valid.

*References*

- International Organization for Standardization. Medical laboratories - Particular requirements for quality and competence. ISO 15189. Geneve: ISO; 2007.
- Fuentes-Arderiu X, Basart-Arraut M, Bosch-Ferrer À, Castiñeiras-Lacambra MJ, López-Martínez R, Miró-Balagué J. Proposed guidelines for the final review of measurement results in the clinical laboratory. Accred Qual Assur 2008;13:537-42.
- Suárez-Vega I, Fuentes-Arderiu X. Reportable interval of patient examination results and ISO 15189. Clin Chem Lab Med 2005; 43:1278.
- Pérez Contreras ME, Blanco Font A, Fuentes Arderiu X. Resultats inversemblants i la norma ISO 15189. In vitro veritas 2006;7: <http://www.acclc.cat/invitroveritas/vol7/art89.html>
- Dixon WJ. Processing data for outliers. Biometrics 1953; 9:74-89.
- Reed AH, Henry RJ, Mason WB. Influence of statistical method used on the resulting estimate of normal range. Clin Chem 1971;17:275-84.
- Clinical and Laboratory Standards Institute. Defining, establishing, and verifying reference intervals in the clinical laboratory; Approved Guideline. CLSI document C28-A3. Wayne: CLSI; 2008.

**Copyright © 2010 International Federation of Clinical
Chemistry and Laboratory Medicine (IFCC). All rights
reserved.**