ISO 20391-2:2019

Biotechnology — Cell counting — Part 2: Experimental design and statistical analysis to quantify counting method performance

This document provides a method for evaluating aspects of the quality of a cell counting measurement process for a specific cell preparation through a set of quality indicators derived from a dilution series experimental design and statistical analysis. The quality indicators are based on repeatability of the measurement and the degree to which the results conform to an ideal proportional response to dilution. This method is applicable to total, differential, direct and indirect cell counting measurement processes, provided that the measurement process meets the criteria of the experimental design (e.g. cells are suspended in a solution). This method is most suitable during cell counting method development, optimization, validation, evaluation and/or verification of cell counting measurement processes. This method is especially applicable in cases where an appropriate reference material to assess accuracy is not readily available. This method does not directly provide the accuracy of the cell count. This method is primarily applicable to eukaryotic cells. NOTE Several sector/application specific international and national standards for cell counting exist. Where applicable, consulting existing standards when operating within their scope can be helpful.

Biotechnologie — Dénombrement des cellules — Partie 2: Conception expérimentale et analyse statistique pour quantifier les performances de la méthode de dénombrement

General Information

• Status: Published
• Publication Date: 27-Aug-2019
• ICS: 07.080 - Biology. Botany. Zoology
• Technical Committee: ISO/TC 276 - Biotechnology
• Drafting Committee: ISO/TC 276/WG 3 - Analytical methods
• Current Stage: 9093 - International Standard confirmed
• Start Date: 26-Feb-2025
• Completion Date: 13-Dec-2025

Standards Content (Sample)

INTERNATIONAL ISO
STANDARD 20391-2
First edition
2019-08
Biotechnology — Cell counting —
Part 2:
Experimental design and statistical
analysis to quantify counting method
performance
Biotechnologie — Dénombrement des cellules —
Partie 2: Conception expérimentale et analyse statistique pour
quantifier les performances de la méthode de dénombrement
Reference number
©
ISO 2019
© ISO 2019
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ii © ISO 2019 – All rights reserved

Contents Page
Foreword .v
Introduction .vi
1 Scope . 1
2 Normative references . 1
3 Terms, definitions, symbols and abbreviated terms . 1
3.1 Terms and definitions . 1
3.2 List of abbreviated terms and symbols . 7
4 Principle . 8
4.1 General . 8
4.2 Proportionality . 9
4.3 Deviation from proportionality . 9
5 Experimental design .10
5.1 General .10
5.2 Considerations for the cell counting measurement process .10
5.3 Preparation of samples for the experimental design .11
5.3.1 General.11
5.3.2 Stock cell solution .11
5.3.3 Dilution fraction experimental design .12
5.3.4 Considerations for generating dilution fractions . .13
5.4 Test sample labelling .14
5.5 Measurement of the test sample.14
6 Statistical methods .15
6.1 General .15
6.2 Mean cell count .16
6.3 Measurement precision .16
6.4 Proportional model fit .16
6.5 Coefficient of determination .17
6.6 Proportionality index (PI) .17
6.6.1 General.17
6.6.2 Calculation of the smoothed residual (e ) .18
smoothed
6.6.3 Calculation of proportionality index (PI).18
6.7 Additional statistical analysis and quality metrics .19
6.8 Data interpretation .19
6.8.1 General.19
6.8.2 Interpretation of %CV .19
6.8.3 Interpretation of R .19
6.8.4 Interpretation of PI values .20
6.8.5 Comparison of PI values .20
7 Reporting .20
7.1 Reporting of quality indicators .20
7.2 Documentation of experimental design parameters and statistical analysis method .21
7.3 Additional reporting elements on the cell counting measurement process .22
Annex A (informative) Method to assess pipetting error contributions to dilution integrity .23
Annex B (normative) Method to calculate smoothed residual (e ) when a set of
smoothed
measured dilution fractions (DF ) is obtained .27
measured
Annex C (informative) Example formulae for calculating PI .29
Annex D (informative) Use case 1 — Evaluating the quality of a single cell counting
measurement process .31
Annex E (informative) Use case 2 — Comparing the quality of several cell counting
measurement processes .38
Bibliography .52
iv © ISO 2019 – All rights reserved

Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (ISO member bodies). The work of preparing International Standards is normally carried out
through ISO technical committees. Each member body interested in a subject for which a technical
committee has been established has the right to be represented on that committee. International
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ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of
electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www .iso .org/directives).
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www .iso .org/patents).
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and
expressions related to conformity assessment, as well as information about ISO's adherence to the
World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see www .iso
.org/iso/foreword .html.
This document was prepared by Technical Committee ISO/TC 276, Biotechnology.
A list of all parts in the ISO 20391 series can be found on the ISO website.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www .iso .org/members .html.
Introduction
Cell counting impacts many aspects of biotechnology, from biomanufacturing to medical diagnosis
and advanced therapy. The cell count can serve as an in-process quality control or be used in decision-
making. Cell count is also an important parameter in many cell-based assays, including activity and
potency, which are often normalized to the cell count to allow data comparison.
Cell count is generally expressed as a concentration and can reflect the total cell count of a cell
population (total cell count) or subpopulation (differential cell count). Advances in instrumentation
have resulted in a wide range of cell counting techniques/instruments for total and/or differential
cell counts. In the absence of a readily available reference material or ground truth, the accuracy of
a measurement method has been difficult to ascertain. This has been confounded by the complexity
of the biological preparation (e.g. cell type, sources, preparation, etc.). Several standards that address
sector/application-specific cell counting or the use of a specific measurement system exist (See
ISO 20391-1 and Reference [16] for further information). Some of these methods use a comparability
approach whereby the result from a newer cell counting test method is traced to the results obtained
from a more established cell counting method. While the comparability approach allows the data from
the second instrument to be benchmarked against those obtained from a primary (more established)
[17]
instrument, it does not address the quality of either measurement process . There remains a need to
develop strategies to provide assurance for the quality of a cell counting measurement process in the
[17]
absence of a reference material or reference method .
This document provides a method for evaluating aspects of the quality of a cell counting measurement
process through the use of a dilution series experimental design. From this experimental design, a set
of quality indicators are derived to assess the performance of a cell counting measurement process.
Specifically, the quality indicators assess precision and proportionality of cell counting measurement
processes. This approach is particularly useful when accuracy cannot be determined (i.e. in the absence
of a traceable reference method or traceable reference material) and is also relevant in aspects of
[17]
validating and monitoring the quality of cell counting measurement processes in general .
Information in this document is intended to provide confidence in the data produced by a chosen cell
counting measurement process. This approach can be useful for selecting or optimizing a measurement
process for a given cell preparation. This approach can also provide supporting performance parameters
that can be utilized during performance qualification of a particular cell counting measurement process.
vi © ISO 2019 – All rights reserved

INTERNATIONAL STANDARD ISO 20391-2:2019(E)
Biotechnology — Cell counting —
Part 2:
Experimental design and statistical analysis to quantify
counting method performance
1 Scope
This document provides a method for evaluating aspects of the quality of a cell counting measurement
process for a specific cell preparation through a set of quality indicators derived from a dilution series
experimental design and statistical analysis. The quality indicators are based on repeatability of
the measurement and the degree to which the results conform to an ideal proportional response to
dilution. This method is applicable to total, differential, direct and indirect cell counting measurement
processes, provided that the measurement process meets the criteria of the experimental design (e.g.
cells are suspended in a solution).
This method is most suitable during cell counting method development, optimization, validation,
evaluation and/or verification of cell counting measurement processes.
This method is especially applicable in cases where an appropriate reference material to assess
accuracy is not readily available. This method does not directly provide the accuracy of the cell count.
This method is primarily applicable to eukaryotic cells.
NOTE Several sector/application specific international and national standards for cell counting exist. Where
applicable, consulting existing standards when operating within their scope can be helpful.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements of this document. For dated references, only the edition cited applies. For
undated references, the latest edition of the referenced document (including any amendments) applies.
ISO 20391-1, Biotechnology — Cell counting — Part 1: General guidance on cell counting methods
3 Terms, definitions, symbols and abbreviated terms
For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https: //www .iso .org/obp
— IEC Electropedia: available at http: //www .electropedia .org/
3.1 Terms and definitions
3.1.1
accuracy
closeness of agreement between a measured quantity value and a true quantity value
of a measurand
[SOURCE: ISO/IEC Guide 99:2007, 2.13, modified — Notes deleted]
3.1.2
bias
estimate of a systematic measurement error
[SOURCE: ISO/IEC Guide 99:2007, 2.18]
Note 1 to entry: Systematic measurement error is a component of measurement error that in replicate
measurements remains constant or varies in a predictable manner. A reference quantity value for a systematic
measurement error is a true quantity value, or a measured quantity value of a measurement standard of
negligible measurement uncertainty, or a conventional quantity value.
Note 2 to entry: Also defined as the difference between the expectation of the test results and an accepted
reference value (ISO 3534-1).
3.1.3
cell concentration
cell count per volume
Note 1 to entry: Typically used for cells in suspension (e.g. cell number per ml).
Note 2 to entry: Cell concentration can refer to the total cell count or the count of a specific subset of cells within
the volume (e.g. viable cell number per ml).
3.1.4
cell count
discrete number of measured cells
Note 1 to entry: Cell count for cells in suspension is typically expressed as cell concentration.
3.1.5
cell counting
measurement process to determine the cell count
3.1.6
cell suspension
single cells or aggregates of cells dispersed in a liquid matrix
3.1.7
debris
fragments of cells and/or particles of biological or non-biological origin
3.1.8
differential cell count
cell count of a subset of cells, which have been distinguished from other cell subpopulations by at least
one distinct cell attribute identified in the measurement
Note 1 to entry: The concentrations derived from a differential cell count can be expressed in absolute
concentration or as a relative measure (i.e. percentage) with respect to the total cell number or another
predefined population.
3.1.9
dilution fraction
ratio by which the concentration of solute in a solution has been reduced from an original concentration
Note 1 to entry: Dilution fraction can range from 0 to 1.
Note 2 to entry: Dilution fraction is also sometimes referred to as “dilution ratio” or “dilution factor”.
EXAMPLE The ratio by which the concentration of cells (solute) in a cell suspension (solution) has been
reduced from a starting concentration of cells in suspension.
2 © ISO 2019 – All rights reserved

3.1.10
dilution series
group of solutions that have increasing or decreasing concentrations of the same substance
Note 1 to entry: A dilution series can be generated by serial dilution or by independent dilution.
Note 2 to entry: For a cell suspension, a dilution series is a group of suspensions that have increasing or decreasing
concentrations of cells.
3.1.11
experimental design
process of planning a study to meet specified objectives
Note 1 to entry: Plan for assigning experimental conditions to participants and the statistical analysis associated
with the plan. Typically, this includes a specification of the independent variables, dependent variables, number
of participants and sampling strategy, procedure for assigning participants to experimental conditions, and
order in which test tasks are given.
3.1.12
independent dilution
dilution series where each dilution is conducted independently of other dilutions
Note 1 to entry: Generally independent dilution series are generated directly from a common stock solution at a
pre-specified (or target) dilution fraction.
3.1.13
intermediate precision
condition of measurement, out of a set of conditions that includes the same measurement procedure,
same location, and replicate measurements on the same or similar objects over an extended period of
time, but may include other conditions involving changes
Note 1 to entry: The changes can include new calibrations, calibrators, operators, and measuring.
Note 2 to entry: Operator bias refers specifically to error introduced by human operator experience.
[SOURCE: ISO/IEC Guide 99:2007, 2.22, modified — Note 3 deleted]
3.1.14
limit of quantitation
LOQ
lowest cell count in a sample that can be quantitatively determined with a suitable
precision and accuracy using a specific analytical method
Note 1 to entry: The limit of quantification describes quantitative assay for low levels of cells in sample matrices.
3.1.15
linearity
within a given range, ability of an analytical procedure to obtain test results which are directly
proportional to the concentration (amount) of analyte in the sample
[SOURCE: Reference [14], modified.]
Note 1 to entry: In cell counting the concentration of analyte refers to the concentration of cells (total or
differential) in the sample.
Note 2 to entry: When a set of measurements exhibits linearity over a range of a given input (while all other
inputs and measurement conditions are held constant), the expected value of the measurand can be expressed as
the sum of a constant bias term and the input parameter multiplied by a fixed constant.
3.1.16
measurand
quantity intended to be measured
[SOURCE: ISO/IEC Guide 99:2007, 2.3, modified — Notes and examples deleted.]
3.17
measured dilution fraction
dilution fraction verified by a traceable measurement
Note 1 to entry: For example, the volume of liquid can be verified by measuring the mass of the liquid (taking into
density) using a calibrated and traceable scale with appropriate sensitivity.
3.1.18
measurement process
entire process for obtaining a cell count
Note 1 to entry: A measurement process can include sample preparation procedures, the measuring system, its
settings (e.g. aperture choice, cell size gating, magnification, light exposure time etc.), and data analysis.
3.1.19
measurement precision
closeness of agreement between indications or measured quantity values obtained by replicate
measurements on the same or similar objects under specified conditions
Note 1 to entry: Measurement precision is usually expressed numerically by measures of imprecision, such as
standard deviation, variance, or coefficient of variation (CV) under the specified conditions of measurement.
Note 2 to entry: The ‘specified conditions’ can be, for example, repeatability conditions of measurement,
intermediate precision conditions of measurement, or reproducibility conditions of measurement (see
ISO 5725-1).
[SOURCE: ISO/IEC Guide 99:2007, 2.15, modified — Notes 3 and 4 deleted.]
3.1.20
proportionality
ability of an analytical procedure, irrespective of range, to obtain test results which are directly
proportional to the concentration (amount) of analyte in the sample
Note 1 to entry: In cell counting the concentration of analyte refers to the concentration of cells (total or
differential) in the sample.
Note 2 to entry: A collection of measurements exhibit proportionality with respect to a given input parameter
when the ratio of the expected value of the measurement to the value of the input parameter at which the
measurements were taken remains constant as the value of the input parameter changes (while all other inputs
and measurement conditions are held constant).
Note 3 to entry: When a set of measurements exhibits proportionality over a range of a given input, then, Y = cX
where Y, the expected value of the measurements is expressed as the input parameter (X) multiplied by a fixed
constant (c), with no bias term.
3.1.21
proportionality constant
constant multiplier that directly relates the measurand to an input parameter
3.1.22
proportionality index
measure of deviation from proportionality for a dilution series experimental design
Note 1 to entry: The proportionality index (PI) is specific to the cell preparation and cell counting measurement
process being evaluated.
4 © ISO 2019 – All rights reserved

3.1.23
p-value
output of a statistical hypothesis test
Note 1 to entry: The p-value is obtained in the following manner: The distribution of the test statistic under the
assumption that the null hypothesis is true, called the null distribution, is determined. The p-value is computed
from the null distribution as the probability of observing a test statistic that is as or more extreme than the test
statistic obtained from the actual data.
3.1.24
quantity
property of a phenomenon, body, or substance, where the property has a magnitude that can be
expressed as a number and a reference
[SOURCE: ISO/IEC Guide 99:2007, 1.1, modified — Notes and example deleted.]
3.1.25
range
quantity interval bounded by rounded or approximate extreme indications
3.1.26
reference material
reference standard
material, sufficiently homogeneous and stable with reference to specified properties, which has been
established to be fit for its intended use in measurement or in examination of nominal properties
[SOURCE: ISO/IEC Guide 99:2007, 5.13, modified — Notes and examples deleted.]
3.1.27
reference method
reference measurement procedure
measurement procedure accepted as providing measurement results fit for their intended use in
assessing measurement trueness of measured quantity values obtained from other measurement
procedures for quantities of the same kind, in calibration, or in characterizing reference materials
[SOURCE: ISO/IEC Guide 99:2007, 2.7]
3.1.28
repeatability
precision of the results of measurement under defined conditions of measurement
Note 1 to entry: Repeatability can also be considered as the closeness of the agreement between results of
[17]
successive measurements of the same measurand carried out under the same conditions of the measurement .
3.1.29
residual
numerical difference between the observed value of a dependent variable and the
predicted value
3.1.30
sample
one or more parts taken from a system and intended to provide information on the system
Note 1 to entry: Often the sample serves as a basis for decision on the system or its production.
Note 2 to entry: For example, a smaller volume or aliquot of cell suspension taken from a larger volume of cell
[17]
suspension .
[SOURCE: ISO 15198:2004, 3.22, modified — “population” replaced by “system”, Notes added.]
3.1.31
serial dilution
stepwise dilution of a substance in solution where the reduction of concentration is cumulative,
lessening with each subsequent dilution
Note 1 to entry: In a serial dilution series, all dilutions except for the first are dependent on the preceding dilution.
3.1.32
stock cell solution
sufficiently stable (over time) cell suspension at sufficiently high concentration to allow dilution into
working concentrations during experimentation
3.1.33
systematic error
component of measurement error that in replicate measurements remains constant or varies in a
predictable manner
Note 1 to entry: A reference quantity value for a systematic measurement error is a true quantity value, or a
measured quantity value of a measurement standard of negligible measurement uncertainty, or a conventional
quantity value.
Note 2 to entry: Systematic measurement error, and its causes, can be known or unknown. A correction can be
applied to compensate for a known systematic measurement error.
Note 3 to entry: Systematic measurement error equals measurement error minus random measurement error.
[SOURCE: ISO/IEC Guide 99:2007, 2.17]
3.1.34
target dilution fraction
dilution fraction that is trying to be achieved by diluting with a specified volume of solution
3.1.35
test sample
small aliquot of the sample that is prepared for measurement in the method of interest
Note 1 to entry: Generally, test samples are representative of the sample they are prepared from and are
sometimes referred to as “representative test sample(s)”.
3.1.36
total cell count
cell count of all cells, independent of the attribute(s) of the cell
3.1.37
true count
true quantity value
quantity value consistent with the definition of a quantity
Note 1 to entry: In the error approach to describing measurement, a true quantity value is considered unique
and, in practice, unknowable. The uncertainty approach is to recognize that, owing to the inherently incomplete
amount of detail in the definition of a quantity, there is not a single true quantity value but rather a set of
true quantity values consistent with the definition. However, this set of values is, in principle and in practice,
unknowable. Other approaches dispense altogether with the concept of true quantity value and rely on the
concept of metrological compatibility of measurement results for assessing their validity.
Note 2 to entry: In the special case of a fundamental constant, the quantity is considered to have a single true
quantity value.
Note 3 to entry: When the definitional uncertainty associated with the measurand is considered to be negligible
compared to the other components of the measurement uncertainty, the measurand can be considered to have
an “essentially unique” true quantity value. This is the approach taken by the ISO/IEC Guide 98-3 and associated
documents, where the word “true” is considered to be redundant.
6 © ISO 2019 – All rights reserved

[SOURCE: ISO/IEC Guide 99:2007, 2.11, modified — “GUM” replaced by “ISO/IEC Guide 98-3”.]
3.1.38
validation
confirmation, through the provision of objective evidence, that the requirements for a specific intended
use or application have been fulfilled
[SOURCE: ISO 9000:2015, 3.8.13, modified — Notes deleted.]
3.1.39
variability
quantification of probability distribution function for variable, parameter, or condition
[SOURCE: ISO 16732-1:2012, 3.29]
3.2 List of abbreviated terms and symbols
List of abbreviations in order of citation.
Abbreviated term or
Description
symbol
β proportionality constant that can differ from k
ideal
β scalar coefficient estimated from the proportional model fitting
CV coefficient of variation
coefficient of variation for a set of K repeated observations of representative test
ij
CV
ij
sample j, at target dilution fraction df
i
mean percent CV for a set of n representative test samples, with target dilution frac-
i
%CV
df tions df
i
i
c ideal proportionality constant
ideal
tc theoretical/true count of sample j
j
DF dilution fraction
dilution fraction of sample j controlled by the measurement process or determined
DF
j
experimentally
tDF theoretical/true dilution fraction
DF set of unique target dilution fractions
DF set of measured dilution fractions
measured
df targeted dilution fraction
i
df measured dilution fraction
ij
e residual between data and modelled fit
smoothed smoothed residual between processed cell count and proportional model fit
e
smoothed residual when target dilution fraction is used in the analysis of proportion-
smoothed
e
ality (smoothed residual at each target DF)
i
smoothed residual when measured dilution fraction is used in the analysis of propor-
smoothed
e
ij tionality (smoothed residual for each representative test sample)
E(oc ) expected value of observed counts
j
i index for target dilution fraction
j index for replicate representative test sample
k index for replicate measurement made on a representative test sample
K number of repeated measurements of the representative test sample
ij
I number of target dilution fractions
n number of replicate representative test samples at the target dilution fraction
i
Abbreviated term or
Description
symbol
PI proportionality index
R coefficient of determination
observed value from measurement k of representative test sample j at target dilution
Y
ijk
fraction i
mean cell count for a set of n representative test samples, with target dilution frac-
i
Y
df tions (df )
i
i
th
mean over the set of K repeated observations for the j representative test sample of df
ij i
Y
ij⋅
mean of Y over independent representative test samples j for a set of n replicate
ij⋅ i
Y
⋅⋅⋅
representative test samples
proportional
proportional
λ
estimated cell count at DF using β obtained from proportional model fit λ
DF k 1 i
k
proportional
proportional model fit to Y versus df
λ
ij ij
ij
4 Principle
4.1 General
[15]
Achieving high confidence in cell counting implies that the measurement is both accurate and precise .
For a well-controlled dilution fraction series, the concept of proportionality may be used as an internal
reference and deviation from proportionality can serve as an alternative to the direct evaluation of
[16]
accuracy . Specifically, using experimental design and statistical analysis, quality indicators that
describe deviation from proportionality and coefficient of variation (CV) can be evaluated to assess
aspects of the quality of a cell counting measurement process.
The quality indicators evaluate the overall quality of a cell counting measurement process, where the
measurement process includes sample preparation and handling, data acquisition, and data processing/
correction.
Accuracy is ideally evaluated using a reference method and/or reference material with a known “true”
value (see ISO 5725-1 and ISO 5725-2 for further information). In the absence of an appropriate reference
material or reference method, the quality of a cell counting measurement can be indirectly assessed
through its adherence to or deviation from the fundamental principle of proportionality, which implies
that the measured cell count shall be proportional to the dilution fraction (DF) under ideal experimental
conditions. Deviation from proportionality would indicate that a systematic measurement error has
occurred to reduce the overall measurement confidence. This approach however does not directly
provide the accuracy of the cell count.
The precision of a cell counting measurement indicates the closeness of agreement between cell counts
obtained by replicate measurements on the same or similar cell preparation under specified conditions.
Experimental data with low precision but with average cell counts fitting well to proportionality would
reduce the quality of the measurement process. Importantly, low measurement precision (i.e. large
random measurement error) can mask deviations from proportionality.
8 © ISO 2019 – All rights reserved

4.2 Proportionality
The theoretical true counts of samples extracted from a common, ideally homogenized, stock
solution are related by their respective dilution fractions in accordance with the expression shown in
Formula (1):
tc =×ctDF (1)
jjideal
where
tc is the theoretical true count for the sample j;
j
c is an unknown proportionality constant equal to the theoretical true count for an
ideal
undiluted sample;
tDF is the true dilution fraction for sample j.
j
By rigorously controlling the dilution fraction, the theoretical tDF may be approximated by DF . See
j j
Formula (2):
tDFD≅ F (2)
jj
where DF is the dilution fraction of sample j controlled by the measurement process or determined
j
experimentally.
An uncalibrated, but otherwise ideal, measurement process would exhibit a proportional relationship
between the expected value of observed counts, E(oc ), and the dilution fraction. That is, in the absence
j
of systematic measurement errors, E(oc ) is given by Formula (3):
j
EocD=×β F (3)
()
jj
where β is a proportionality constant that can differ from c .
ideal
Combining Formula (1) and Formula (3) provides the basis for directly relating tc to E(oc ) through a
j j
constant; see Formula (4):
c
 
ideal
tc = ×Eoc (4)
()
jj 
β
 
If β is known (e.g. through the use of a reference material) and β ≅ c , then E(oc ) ≅ tc (i.e. the
ideal j j
accuracy of the observed counts could be established).
If β is not known, the closeness in agreement between the expected proportional relationship
[Formula (3)] and the measured relationship may be used to assess the quality of a cell counting
measurement process, since any deviation from the proportionality is indicative of the presence of
measurement errors.
NOTE Measurement errors that scale proportionally with dilution will not result in significant changes to
proportionality and therefore will not be detected in an analysis of deviation from proportionality.
4.3 Deviation from proportionality
Deviation from proportionality is assessed by summarizing the deviation of processed cell count data
from a proportional model fit (see Figure 1).
Key
X dilution fraction
Y cell concentration (cells/ml)
average cell count data across replicate observations
proportional model fit to the data
deviations or residuals (e) between the cell count data and the proportional fit
NOTE This is a schematic representation of a hypothetical study with five target dilution fractions and three
test samples at each target dilution fraction.
Figure 1 — Schematic of a hypothetical cell counting results from a dilution series
experimental design
Residuals (e) can occur as the result of systematic errors, random errors, or a combination thereof in
the measurement process. As such, functions of residuals are sensitive to changes in both bias and
precision.
A proportionality index will be calculated based on an analysis of smoothed residuals (e ) from
smoothed
the proportional model fit (see 6.4).
NOTE Evaluating deviation from proportionality via a hypothesis test (producing a p-value) in which the
null hypothesis presumes the behaviour of expected counts to be proportional to dilution fraction and the
alternative hypothesis is a more flexible (e.g. linear or quadratic) model p-value evaluation, is not considered
here because high random measurement error will reduce the ability to detect statistically significant deviations
from proportionality.
5 Experimental design
5.1 General
Cell counting method selection, considerations for performing a cell counting measurement, possible
sources of uncertainty, as well as instrument qualification, method validation and reporting are
described in ISO 20391-1.
The cell counting method selection, method validation and reporting shall be carried out in accordance
with ISO 20391-1.
5.2 Considerations for the cell counting measurement process
The experimental design and statistical analysis methods described in this document may be used
to evaluate the quality of cell counting measurement processes in which the test sample is in a
suspension format.
10 © ISO 2019 – All rights reserved

This method may be applied to total, differential, direct and indirect cell counting measurement
processes.
NOTE 1 If significant cell processing is required prior to counting, for example in the case of cells grown in
aggregates that are individualized prior to counting, the processing steps to individualize cells can be considered
a part of the cell counting measurement process. In this case the stock cell solution will contain the cell aggregates
which are then diluted into the independent test samples. Each independent test sample can then undergo the
processing steps to individualize cells prior to measurement. Challenges in this case include maintaining dilution
integrity when samples contain aggregates.
NOTE 2 In the case that cells are embedded in a matrix or adhered to a surface, the process to bring the cells
into a suspension format is not considered a part of the cell counting measurement process for the purpose of
this document.
In the case of a measurement process where rare cell events or low numbers of cells will be counted
relative to large background populations of cells, additional considerations beyond the experimental
design and statistical analysis described in this document may apply.
5.3 Preparation of samples for the experimental design
5.3.1 General
The test material for the experimental design shall be cells in suspension. Cells can be in conditions that
reflect the behaviour of the cells (i.e. single cells, cell aggregates, or cell agglomerates).
Sample preparation and handling procedures used to generate representative test samples for the cell
counting measurement process should be optimized to maintain the properties of the test samples for
counting.
Sample preparation procedures should avoid damaging cells in ways that change their ability to be
counted or in ways that introduce/reduce debris that can interfere with or artificially improve the cell
counting measurement process.
NOTE 1 References [18], [19], [20], [21] provide further guidance on sample preparation procedures for
particular cell types and cell samples.
Sample preparation procedures should be conducted in an amount of time and under conditions that
maintain the stability of the cells sample with respect to properties that can affect the cell counting
measurement process. See ISO 20391-1 for further information.
NOTE 2 Samples containing live cells are dynamic and therefore can be unstable with regards to properties
that can affect a cell count. Interactions such as cell-cell interactions and cell-material interactions can cause
changes in the cell sample that can affect a cell count.
Samples for cell counting measurement processes resulting in a differential cell count (e.g. concentration
of viable cells) will have some level of heterogeneity that can be affected by the dilution process.
Sample preparation procedures should aim to generate test samples that are representative of the
heterogeneity of the stock cell solution.
NOTE 3 For heterogenous cell samples, some cells can be more affected by conditions of the culture/sample
environment than others, thus affecting representativeness of test samples.
5.3.2 Stock cell solution
A single stock cell solution should be used to generate all representative test samples. Additional stock
cell solutions may be used if the concentration and composition of the stock cell solutions are nominally
equivalent.
The cell concentration of the stock cell solution should be estimated using
...

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2019-08
ISO/TC 276/WG 3
Secretariat: DIN
Biotechnology — Cell counting — Part 2: Experimental design and statistical analysis to
quantify counting method performance
Biotechnologie — Dénombrement des cellules — Partie 2: Conception expérimentale et analyse
statistique pour quantifier les performances de la méthode de dénombrement
© ISO 2019 – All rights reserved i

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© ISO 2019
All rights reserved. Unless otherwise specified, or required in the context of its implementation,
no part of this publication may be reproduced or utilized otherwise in any form or by any means,
electronic or mechanical, including photocopying, or posting on the internet or an intranet,
without prior written permission. Permission can be requested from either ISO at the address
below or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH‐1214 Vernier, Geneva
Phone: [phone]
Fax: [phone]
Email: [e-mail]
Website: www.iso.org
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Published in Switzerland
ii © ISO 2019 – All rights reserved

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Deleted: Error! Hyperlink
reference not valid.¶
Contents
Introduction 6¶
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valid.¶
Foreword . 5
2 Normative references 1¶
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Introduction. 6
valid.¶
3.1 Terms and definitions 1¶
1  Scope . 1
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2  Normative references . 1
valid.¶
4 Principle 9¶
3  Terms, definitions, symbols and abbreviated terms . 1
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3.1  Terms and definitions . 1
valid.¶
3.2  List of abbreviated terms and symbols . 7  4.2 Proportionality 9¶
Error! Hyperlink reference not
4  Principle . 9
valid.¶
4.1  General . 9  5 Experimental design 11¶
Error! Hyperlink reference not
4.2  Proportionality. 9
valid.¶
4.3  Deviation from proportionality . 10
5.2 Considerations for the
cell counting measurement
5  Experimental design . 11
process 11¶
5.1  General . 11
Error! Hyperlink reference not
5.2  Considerations for the cell counting measurement process . 11
valid.¶
5.3  Preparation of samples for the experimental design . 12
5.3.1 General 12¶
5.3.1  General . 12  Error! Hyperlink reference not
valid.¶
5.3.2  Stock cell solution . 12
5.3.3 Dilution fraction
5.3.3  Dilution fraction experimental design . 13
experimental design 13¶
5.3.4  Considerations for generating dilution fractions . 14
Error! Hyperlink reference not
5.4  Test sample labelling . 15
valid.¶
5.4 Test sample
5.5  Measurement of the test sample . 15
labelling 15¶
6  Statistical methods . 16
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valid.¶
6.1  General . 16
6 Statistical methods 16¶
6.2  Mean cell count . 16
Error! Hyperlink reference not
6.3  Measurement precision . 17
valid.¶
6.4  Proportional model fit . 17
6.2 Mean cell count 16¶
6.5  Coefficient of determination . 18
Error! Hyperlink reference not
valid.¶
6.6  Proportionality Index (PI ) . 18
6.4 Proportional model
6.6.1  General . 18
fit 17¶
6.6.2  Calculation of the smoothed residual (esmoothed) . 19
Error! Hyperlink reference not
6.6.3  Calculation of proportionality index (PI) . 19
valid.¶
6.7  Additional statistical analysis and quality metrics . 20
6.6 Proportionality Index
(PI) 18¶
6.8  Data Interpretation . 20
Error! Hyperlink reference not
6.8.1  General . 20
valid.¶
6.8.2  Interpretation of %CV . 20
6.6.2 Calculation of the
6.8.3  Interpretation of R . 20
smoothed residual
6.8.4  Interpretation of PI values . 21
(esmoothed) 19¶
Error! Hyperlink reference not
6.8.5  Comparison of PI values . 21
valid.¶
7  Reporting . 21  6.7 Additional statistical
analysis and quality
7.1  Reporting of quality indicators . 21
metrics 20¶
7.2  Documentation of experimental design parameters and statistical analysis method . 22
Error! Hyperlink reference not
7.3  Additional reporting elements on the cell counting measurement process . 23
valid.¶
6.8.1 General 20¶
Annex A (informative)  Method to assess pipetting error contributions to dilution integrity . 24
Error! Hyperlink reference not
valid.¶
A.1  General . 24
6.8.3 Interpretation of
R 20¶
... [1]
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A.2 Example procedure for pre-evaluating pipetting error contributions to dilution
integrity using a calibrated scale to obtain accurate volume estimates upon
pipetting . 24
A.3 Example procedure for obtaining a measured DF during the evaluation of PI using a
calibrated scale to obtain accurate volume estimates . 26
Annex B (normative) Method to calculate smoothed residual (e ) when a set of
smoothed
measured dilution fractions (DFmeasured) is obtained . 28
Annex C (informative) Example formulae for calculating PI . 30
C.1 Detailed example of the calculation of PI based on sum of the absolute value of
scaled smoothed residuals . 30
C.2 Detailed example of the calculation of PI based on R of smoothed residuals . 30
C.3 Additional examples of the calculation of PI when measured dilution fraction is
utilized . 31
Annex D (informative) Use case 1 — Evaluating the quality of a single cell counting
measurement process . 32
D.1 General . 32
D.2 Description of experimental design and statistical analysis . 32
D.3 Raw Data and Data Analysis for Use Case 1 . 33
D.4 Example Report for Use Case 1 . 33
D.5 Interpretation . 38
Annex E (informative) Use case 2 — Comparing the quality of several cell counting
measurement processes . 39
E.1 General . 39
E.2 Description of experimental design and statistical analysis . 39
E.3 Raw Data and Data Analysis for Use Case 2 . 40
E.4 Example Report for Use Case 2 . 42
E.5 Comparison of cell counting methods evaluated in Use Case 2 . 50
E.5.1 Comparing quality indicators between cell counting methods . 50
E.6 Interpretation . 51
E.7 Consistency of results with underlying simulated model . 52
Bibliography . 54
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Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national
standards bodies (ISO member bodies). The work of preparing International Standards is normally
carried out through ISO technical committees. Each member body interested in a subject for which a
technical committee has been established has the right to be represented on that committee.
International organizations, governmental and non‐governmental, in liaison with ISO, also take part in
the work. ISO collaborates closely with the International Electrotechnical Commission (IEC) on all
matters of electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).
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Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www.iso.org/patents).
Deleted: www.iso.org/patents
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and
expressions related to conformity assessment, as well as information about ISO's adherence to the
World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT),
see www.iso.org/iso/foreword.html.
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d.html
This document was prepared by Technical Committee ISO/TC 276, Biotechnology.
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A list of all parts in the ISO 20391 series can be found on the ISO website.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www.iso.org/members.html.
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ml
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Introduction
Cell counting impacts many aspects of biotechnology, from biomanufacturing to medical diagnosis and
advanced therapy. The cell count can serve as an in‐process quality control or be used in decision‐
making. Cell count is also an important parameter in many cell‐based assays, including activity and
potency, which are often normalized to the cell count to allow data comparison.
Cell count is generally expressed as a concentration and can reflect the total cell count of a cell
population (total cell count) or subpopulation (differential cell count). Advances in instrumentation
have resulted in a wide range of cell counting techniques/instruments for total and/or differential cell
counts. In the absence of a readily available reference material or ground truth, the accuracy of a
measurement method has been difficult to ascertain. This has been confounded by the complexity of the
biological preparation (e.g. cell type, sources, preparation, etc.). Several standards that address
sector/application‐specific cell counting or the use of a specific measurement system exist (See
ISO 20391‐1 and Reference [16] for further information). Some of these methods use a comparability
approach whereby the result from a newer cell counting test method is traced to the results obtained
from a more established cell counting method. While the comparability approach allows the data from
the second instrument to be benchmarked against those obtained from a primary (more established)
[17]
instrument, it does not address the quality of either measurement process . There remains a need to
develop strategies to provide assurance for the quality of a cell counting measurement process in the
[17]
absence of a reference material or reference method .
This document provides a method for evaluating aspects of the quality of a cell counting measurement
process through the use of a dilution series experimental design. From this experimental design, a set of
quality indicators are derived to assess the performance of a cell counting measurement process.
Specifically, the quality indicators assess precision and proportionality of cell counting measurement
processes. This approach is particularly useful when accuracy cannot be determined (i.e. in the absence
of a traceable reference method or traceable reference material) and is also relevant in aspects of
[17]
validating and monitoring the quality of cell counting measurement processes in general .
Information in this document is intended to provide confidence in the data produced by a chosen cell
counting measurement process. This approach can be useful for selecting or optimizing a measurement
process for a given cell preparation. This approach can also provide supporting performance
parameters that can be utilized during performance qualification of a particular cell counting
measurement process.
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INTERNATIONAL STANDARD ISO 20391-2:2019(E)
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Biotechnology — Cell counting — Part 2: Experimental design and
statistical analysis to quantify counting method performance
1 Scope
This document provides a method for evaluating aspects of the quality of a cell counting measurement
process for a specific cell preparation through a set of quality indicators derived from a dilution series
experimental design and statistical analysis. The quality indicators are based on repeatability of the
measurement and the degree to which the results conform to an ideal proportional response to dilution.
This method is applicable to total, differential, direct and indirect cell counting measurement processes,
provided that the measurement process meets the criteria of the experimental design (e.g. cells are
suspended in a solution).
This method is most suitable during cell counting method development, optimization, validation,
evaluation and/or verification of cell counting measurement processes.
This method is especially applicable in cases where an appropriate reference material to assess
accuracy is not readily available. This method does not directly provide the accuracy of the cell count.
This method is primarily applicable to eukaryotic cells.
NOTE Several sector/application specific international and national standards for cell counting exist. Where
applicable, consulting existing standards when operating within their scope can be helpful.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements of this document. For dated references, only the edition cited applies. For
undated references, the latest edition of the referenced document (including any amendments) applies.
ISO 20391‐1, Biotechnology — Cell counting — Part 1: General guidance on cell counting methods
3 Terms, definitions, symbols and abbreviated terms
For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https://www.iso.org/obp
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p
— IEC Electropedia: available at http://www.electropedia.org/
Deleted: http://www.electropedi
a.org/
3.1 Terms and definitions
3.1.1
accuracy
closeness of agreement between a measured quantity value and a true quantity value
of a measurand
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[SOURCE: ISO/IEC Guide 99:2007, 2.13, modified — Notes deleted]
3.1.2
bias
estimate of a systematic measurement error
[SOURCE: ISO/IEC Guide 99:2007, 2.18]
Note 1 to entry: Systematic measurement error is a component of measurement error that in replicate
measurements remains constant or varies in a predictable manner. A reference quantity value for a systematic
measurement error is a true quantity value, or a measured quantity value of a measurement standard of negligible
measurement uncertainty, or a conventional quantity value.
Note 2 to entry: Also defined as the difference between the expectation of the test results and an accepted
reference value (ISO 3534‐1).
3.1.3
cell concentration
cell count per volume
Note 1 to entry: Typically used for cells in suspension (e.g. cell number per ml).
Note 2 to entry: Cell concentration can refer to the total cell count or the count of a specific subset of cells within
the volume (e.g. viable cell number per ml).
3.1.4
cell count
discrete number of measured cells
Note 1 to entry: Cell count for cells in suspension is typically expressed as cell concentration.
3.1.5
cell counting
measurement process to determine the cell count
3.1.6
cell suspension
single cells or aggregates of cells dispersed in a liquid matrix
3.1.7
debris
fragments of cells and/or particles of biological or non‐biological origin
3.1.8
differential cell count
cell count of a subset of cells, which have been distinguished from other cell subpopulations by at least
one distinct cell attribute identified in the measurement
Note 1 to entry: The concentrations derived from a differential cell count can be expressed in absolute
concentration or as a relative measure (i.e. percentage) with respect to the total cell number or another
predefined population.
3.1.9
dilution fraction
2 © ISO 2019 – All rights reserved

ISO/FDIS 20391-2:2019(E)
ratio by which the concentration of solute in a solution has been reduced from an original concentration
Note 1 to entry: Dilution fraction can range from 0 to 1.
Note 2 to entry: Dilution fraction is also sometimes referred to as “dilution ratio” or “dilution factor”.
EXAMPLE The ratio by which the concentration of cells (solute) in a cell suspension (solution) has been reduced
from a starting concentration of cells in suspension.
3.1.10
dilution series
group of solutions that have increasing or decreasing concentrations of the same substance
Note 1 to entry: A dilution series can be generated by serial dilution or by independent dilution.
Note 2 to entry: For a cell suspension, a dilution series is a group of suspensions that have increasing or
decreasing concentrations of cells.
3.1.11
experimental design
process of planning a study to meet specified objectives
Note 1 to entry: Plan for assigning experimental conditions to participants and the statistical analysis associated
with the plan. Typically, this includes a specification of the independent variables, dependent variables, number of
participants and sampling strategy, procedure for assigning participants to experimental conditions, and order in
which test tasks are given.
3.1.12
independent dilution
dilution series where each dilution is conducted independently of other dilutions
Note 1 to entry: Generally independent dilution series are generated directly from a common stock solution at a
pre‐specified (or target) dilution fraction.
3.1.13
intermediate precision
condition of measurement, out of a set of conditions that includes the same measurement procedure,
same location, and replicate measurements on the same or similar objects over an extended period of
time, but may include other conditions involving changes
Note 1 to entry: The changes can include new calibrations, calibrators, operators, and measuring.
Note 2 to entry: Operator bias refers specifically to error introduced by human operator experience.
[SOURCE: ISO/IEC Guide 99:2007, 2.22, modified — Note 3 deleted]
3.1.14
limit of quantitation
LOQ
lowest cell count in a sample that can be quantitatively determined with a suitable
precision and accuracy using a specific analytical method
Note 1 to entry: The limit of quantification describes quantitative assay for low levels of cells in sample matrices.
3.1.15
linearity
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within a given range, ability of an analytical procedure to obtain test results which are directly
proportional to the concentration (amount) of analyte in the sample
[SOURCE: Reference (14), modified.]
Note 1 to entry: In cell counting the concentration of analyte refers to the concentration of cells (total or
differential) in the sample.
Note 2 to entry: When a set of measurements exhibits linearity over a range of a given input (while all other inputs
and measurement conditions are held constant), the expected value of the measurand can be expressed as the
sum of a constant bias term and the input parameter multiplied by a fixed constant.
3.1.16
measurand
quantity intended to be measured
[SOURCE: ISO/IEC Guide 99:2007, 2.3, modified — Notes and examples deleted.]
3.17
measured dilution fraction
dilution fraction verified by a traceable measurement
Note 1 to entry: For example, the volume of liquid can be verified by measuring the mass of the liquid (taking into
density) using a calibrated and traceable scale with appropriate sensitivity.
3.1.18
measurement process
entire process for obtaining a cell count
Note 1 to entry: A measurement process can include sample preparation procedures, the measuring system, its
settings (e.g. aperture choice, cell size gating, magnification, light exposure time etc.), and data analysis.
3.1.19
measurement precision
closeness of agreement between indications or measured quantity values obtained by replicate
measurements on the same or similar objects under specified conditions
Note 1 to entry: Measurement precision is usually expressed numerically by measures of imprecision, such as
standard deviation, variance, or coefficient of variation (CV) under the specified conditions of measurement.
Note 2 to entry: The ‘specified conditions’ can be, for example, repeatability conditions of measurement,
intermediate precision conditions of measurement, or reproducibility conditions of measurement (see
ISO 5725‐1).
[SOURCE: ISO/IEC Guide 99:2007, 2.15, modified — Notes 3 and 4 deleted.]
3.1.20
proportionality
ability of an analytical procedure, irrespective of range, to obtain test results which are directly
proportional to the concentration (amount) of analyte in the sample
Note 1 to entry: In cell counting the concentration of analyte refers to the concentration of cells (total or
differential) in the sample.
Note 2 to entry: A collection of measurements exhibit proportionality with respect to a given input parameter
when the ratio of the expected value of the measurement to the value of the input parameter at which the
measurements were taken remains constant as the value of the input parameter changes (while all other inputs
and measurement conditions are held constant).
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ISO/FDIS 20391-2:2019(E)
Note 3 to entry: When a set of measurements exhibits proportionality over a range of a given input, then, Y = cX
where Y, the expected value of the measurements is expressed as the input parameter (X) multiplied by a fixed
constant (c), with no bias term.
3.1.21
proportionality constant
constant multiplier that directly relates the measurand to an input parameter
3.1.22
proportionality index
measure of deviation from proportionality for a dilution series experimental design
Note 1 to entry: The proportionality index (PI) is specific to the cell preparation and cell counting measurement
process being evaluated.
3.1.23
p-value
output of a statistical hypothesis test
Note 1 to entry: The p‐value is obtained in the following manner: The distribution of the test statistic under the
assumption that the null hypothesis is true, called the null distribution, is determined. The p‐value is computed
from the null distribution as the probability of observing a test statistic that is as or more extreme than the test
statistic obtained from the actual data.
3.1.24
quantity
property of a phenomenon, body, or substance, where the property has a magnitude that can be
expressed as a number and a reference
[SOURCE: ISO/IEC Guide 99:2007, 1.1, modified — Notes and example deleted.]
3.1.25
range
quantity interval bounded by rounded or approximate extreme indications
3.1.26
reference material
reference standard
material, sufficiently homogeneous and stable with reference to specified properties, which has been
established to be fit for its intended use in measurement or in examination of nominal properties
[SOURCE: ISO/IEC Guide 99:2007, 5.13, modified — Notes and examples deleted.]
3.1.27
reference method
reference measurement procedure
measurement procedure accepted as providing measurement results fit for their intended use in
assessing measurement trueness of measured quantity values obtained from other measurement
procedures for quantities of the same kind, in calibration, or in characterizing reference materials
[SOURCE: ISO/IEC Guide 99:2007, 2.7]
3.1.28
repeatability
precision of the results of measurement under defined conditions of measurement
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Note 1 to entry: Repeatability can also be considered as the closeness of the agreement between results of
[17]
successive measurements of the same measurand carried out under the same conditions of the measurement .
3.1.29
residual
numerical difference between the observed value of a dependent variable and the
predicted value
3.1.30
sample
one or more parts taken from a system and intended to provide information on the system
Note 1 to entry: Often the sample serves as a basis for decision on the system or its production.
Note 2 to entry: For example, a smaller volume or aliquot of cell suspension taken from a larger volume of cell
[17]
suspension .
[SOURCE: ISO 15198:2004, 3.22, modified — “population” replaced by “system”, Notes added.]
3.1.31
serial dilution
stepwise dilution of a substance in solution where the reduction of concentration is cumulative,
lessening with each subsequent dilution
Note 1 to entry: In a serial dilution series, all dilutions except for the first are dependent on the preceding dilution.
3.1.32
stock cell solution
sufficiently stable (over time) cell suspension at sufficiently high concentration to allow dilution into
working concentrations during experimentation
3.1.33
systematic error
component of measurement error that in replicate measurements remains constant or varies in a
predictable manner
Note 1 to entry: A reference quantity value for a systematic measurement error is a true quantity value, or a
measured quantity value of a measurement standard of negligible measurement uncertainty, or a conventional
quantity value.
Note 2 to entry: Systematic measurement error, and its causes, can be known or unknown. A correction can be
applied to compensate for a known systematic measurement error.
Note 3 to entry: Systematic measurement error equals measurement error minus random measurement error.
[SOURCE: ISO/IEC Guide 99:2007, 2.17]
3.1.34
target dilution fraction
dilution fraction that is trying to be achieved by diluting with a specified volume of solution
3.1.35
test sample
small aliquot of the sample that is prepared for measurement in the method of interest
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ISO/FDIS 20391-2:2019(E)
Note 1 to entry: Generally, test samples are representative of the sample they are prepared from and are
sometimes referred to as “representative test sample(s)”.
3.1.36
total cell count
cell count of all cells, independent of the attribute(s) of the cell
3.1.37
true count
true quantity value
quantity value consistent with the definition of a quantity
Note 1 to entry: In the error approach to describing measurement, a true quantity value is considered unique and,
in practice, unknowable. The uncertainty approach is to recognize that, owing to the inherently incomplete
amount of detail in the definition of a quantity, there is not a single true quantity value but rather a set of true
quantity values consistent with the definition. However, this set of values is, in principle and in practice,
unknowable. Other approaches dispense altogether with the concept of true quantity value and rely on the
concept of metrological compatibility of measurement results for assessing their validity.
Note 2 to entry: In the special case of a fundamental constant, the quantity is considered to have a single true
quantity value.
Note 3 to entry: When the definitional uncertainty associated with the measurand is considered to be negligible
compared to the other components of the measurement uncertainty, the measurand can be considered to have an
“essentially unique” true quantity value. This is the approach taken by the ISO/IEC Guide 98‐3 and associated
documents, where the word “true” is considered to be redundant.
[SOURCE: ISO/IEC Guide 99:2007, 2.11, modified — “GUM” replaced by “ISO/IEC Guide 98‐3”.]
3.1.38
validation
confirmation, through the provision of objective evidence, that the requirements for a specific intended
use or application have been fulfilled
[SOURCE: ISO 9000:2015, 3.8.13, modified — Notes deleted.]
3.1.39
variability
quantification of probability distribution function for variable, parameter, or condition
[SOURCE: ISO 16732‐1:2012, 3.29]
3.2 List of abbreviated terms and symbols
List of abbreviations in order of citation.
Abbreviated term or
Description
symbol
β proportionality constant that can differ from k
ideal
β scalar coefficient estimated from the proportional model fitting
CV coefficient of variation
coefficient of variation for a set of Kij repeated observations of representative test
CV
ij
sample j, at target dilution fraction df
i
%CV mean percent CV for a set of n representative test samples, with target dilution
df i
i
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fractions df
i
cideal ideal proportionality constant
tc theoretical/true count of sample j
j
DF dilution fraction
dilution fraction of sample j controlled by the measurement process or determined
DFj
experimentally
tDF theoretical/true dilution fraction
DF set of unique target dilution fractions
DF set of measured dilution fractions
measured
df targeted dilution fraction
i
df measured dilution fraction
ij
e residual between data and modelled fit
smoothed
smoothed residual between processed cell count and proportional model fit
e
smoothed residual when target dilution fraction is used in the analysis of
smoothed
e
i
proportionality (smoothed residual at each target DF)
smoothed residual when measured dilution fraction is used in the analysis of
smoothed
e
ij
proportionality (smoothed residual for each representative test sample)
E(ocj) expected value of observed counts
i index for target dilution fraction
j index for replicate representative test sample
k index for replicate measurement made on a representative test sample
K number of repeated measurements of the representative test sample
ij
I number of target dilution fractions
n number of replicate representative test samples at the target dilution fraction
i
PI proportionality index
R coefficient of determination
observed value from measurement k of representative test sample j at target dilution
Y
ijk
fraction i
mean cell count for a set of n representative test samples, with target dilution
i
Y
df
i
fractions (df)
i
th
mean over the set of K repeated observations for the j representative test sample of
ij
Y
ij
df
i
mean of Y over independent representative test samples j for a set of n replicate
i
ij
Y

representative test samples
proportional
proportional

estimated cell count at DF using β obtained from proportional model fit 
k 1
DF
i
k
proportional
 proportional model fit to Y versus df
ij
ij
ij
8 © ISO 2019 – All rights reserved

ISO/FDIS 20391-2:2019(E)
4 Principle
4.1 General
Achieving high confidence in cell counting implies that the measurement is both accurate and
[15]
precise . For a well‐controlled dilution fraction series, the concept of proportionality may be used as
an internal reference and deviation from proportionality can serve as an alternative to the direct
[16]
evaluation of accuracy . Specifically, using experimental design and statistical analysis, quality
indicators that describe deviation from proportionality and coefficient of variation (CV) can be
evaluated to assess aspects of the quality of a cell counting measurement process.
The quality indicators evaluate the overall quality of a cell counting measurement process, where the
measurement process includes sample preparation and handling, data acquisition, and data
processing/correction.
Accuracy is ideally evaluated using a reference method and/or reference material with a known “true”
value (see ISO 5725‐1 and ISO 5725‐2 for further information). In the absence of an appropriate
reference material or reference method, the quality of a cell counting measurement can be indirectly
assessed through its adherence to or deviation from the fundamental principle of proportionality,
which implies that the measured cell count shall be proportional to the dilution fraction (DF) under
ideal experimental conditions. Deviation from proportionality would indicate that a systematic
measurement error has occurred to reduce the overall measurement confidence. This approach
however does not directly provide the accuracy of the cell count.
The precision of a cell counting measurement indicates the closeness of agreement between cell counts
obtained by replicate measurements on the same or similar cell preparation under specified conditions.
Experimental data with low precision but with average cell counts fitting well to proportionality would
reduce the quality of the measurement process. Importantly, low measurement precision (i.e. large
random measurement error) can mask deviations from proportionality.
4.2 Proportionality
The theoretical true counts of samples extracted from a common, ideally homogenized, stock solution
are related by their respective dilution fractions in accordance with the expression shown in
Formula (1):
tcc tDF (1)
j ideal j
where
tc is the theoretical true count for the sample j;
j
c is an unknown proportionality constant equal to the theoretical true count for an
ideal
undiluted sample;
tDF is the true dilution fraction for sample j.
j
By rigorously controlling the dilution fraction, the theoretical tDF may be approximated by DF. See
j j
Formula (2):
tDF  DF
(2)
j j
where DFj is the dilution fraction of sample j controlled by the measurement process or determined
experimentally.
© ISO 2019 – All rights reserved 9

Deleted: /FDIS
An uncalibrated, but otherwise ideal, measurement process would exhibit a proportional relationship
between the expected value of observed counts, E(ocj), and the dilution fraction. That is, in the absence
of systematic measurement errors, E(ocj) is given by Formula (3):
E oc  DF (3)
j j
where β is a proportionality constant that can differ from c .
ideal
Combining Formula (1) and Formula (3) provides the basis for directly relating tcj to E(ocj) through a
constant; see Formula (4):
c
ideal
tcEoc (4)
 
j j


If β is known (e.g. through the use of a reference material) and β ≅ c , then E(oc) ≅ tc (i.e. the
ideal j j
accuracy of the observed counts could be established).
β is not known, the closeness in agreement between the expected proportional relationship
If
[Formula (3)] and the measured relationship may be used to assess the quality of a cell counting
measurement process, since any deviation from the proportionality is indicative of the presence of
measurement errors.
NOTE Measurement errors that scale proportionally with dilution will not result in significant changes to
proportionality and therefore will not be detected in an analysis of deviation from proportionality.
4.3 Deviation from proportionality
Deviation from proportionality is assessed by summarizing the deviation of processed cell count data
from a proportional model fit (see Figure 1).

Key
X dilution fraction
Y cell concentration (cells/ml)
average cell count data across replicate observations

proportional model fit to the data

deviations or residuals (e) between the cell count data and the proportional fit

10 © ISO 2019 – All rights reserved

ISO/FDIS 20391-2:2019(E)
NOTE This is a schematic representation of a hypothetical study with five target dilution fractions and three
test samples at each target dilution fraction.
Figure 1 — Schematic of a hypothetical cell counting results from a dilution series experimental
design
Residuals (e) can occur as the result of systematic errors, random errors, or a combination thereof in
the measurement process. As such, functions of residuals are sensitive to changes in both bias and
precision.
A proportionality index will be calculated based on an analysis of smoothed residuals (e ) from the
smoothed
proportional model fit (see 6.4).
NOTE Evaluating deviation from proportionality via a hypothesis test (producing a p‐value) in which the null
hypothesis presumes the behaviour of expected counts to be proportional to dilution fraction and the alternative
hypothesis is a more flexible (e.g. linear or quadratic) model p‐value evaluation, is not considered here because
high random measurement error will reduce the ability to detect statistically significant deviations from
proportionality.
5 Experimental design
5.1 General
Cell counting method selection, considerations for performing a cell counting measurement, possible
sources of uncertainty, as well as instrument qualification, method validation and reporting are
...