Determination of the Limit of Detection
and the Limit of Quantitation during
Assay Development
Eloi P. Kpamegan, Ph.D., MSF
Director, Clinical and Nonclinical Biostatistics
Introduction
¾ The Limit of detection (LOD) and the limit of
quantitation (LOQ) are important parameters that
need to be determined during assay development.
¾ The usefulness and optimal throughput of an assay
may depend on the appropriate determination of
the LOD and the LOQ
¾ The experiment design and statistical method used
for the determination of LOD and LOQ is
dependent on the assay type (e.g., ELISA,
Functional or PCR)
¾ This presentation describes the design, testing and
statistical procedures required to determine the
LOD and LOQ during assay development. The
procedures to be used to confirm the LOD and the
LOQ during assay validation are discussed
Definition
“Validation
of Analytical Procedures
is the process of determining the
suitability of a given methodology
for providing useful analytical data.
A method that is valid in one
situation could well be invalid in
another.”
J. Guerra, FDA, Pharm. Technology, March 1999
Definition
Validation of an analytical method is
primarily concerned with:
• the identification of the sources of
potential errors
• quantification of the potential errors
in the method
An Assay Validation describes in
mathematical and quantifiable terms
the performance characteristics of an
assay
Common Misconceptions
Assay Validation ≠ Assay Optimization ≠
Assay Qualification
A Validated Method is NOT necessarily a
“tight” method
Repeating an assay a number of time does
not constitute validation
Evolvement of an Assay
Development
Optimization
Qualification
Pre-Validation
Revalidation
Validation
Implementation
Assay Validation Parameters: USP &
ICH
Accuracy
Precision
Limit of Detection
Method
Validation
Limit of Quantitation
Specificity
Linearity and Range
Ruggedness/Robustness
System Suitability
Assay Qualification
¾ An assay is qualified when the following
parameters are assessed and the performance
documented in a qualification (or Prevalidation) report
ƒ
ƒ
ƒ
ƒ
ƒ
ƒ
ƒ
LOB/LOD/LOQ
Limited Precision/Reproducibility
Accuracy
Dilutability or Internal Accuracy
Specificity
Robustness
Short-Term Stability
Two Assay Types
¾Continuous Assays
ƒ ELISA
ƒ RIA
ƒ Total IgG assay
ƒ Etc
¾Functional assays
ƒ Neutralization Assay
ƒ PRNT Assay
ƒ HAI Assay
ƒ Etc
Continuous Assays
¾Limit of Blank (LOB)
– The LOB is the highest measurement result that is likely to be observed
(with a stated probability) for a blank or negative sample
¾Limit of detection (LOD)
– The LOD is the lowest amount of analyte in a sample that can be
detected with (stated) probability, although not quantified as an exact
value. Also called minimum detectable concentration (MDC)
– The reliable detection limit (RDL) is an estimate of LOD that has a high
probability of producing a response significantly greater than the
response at zero concentration of analyte
Æ When using a four parameter logistic reference curve the MDC and the
RDL are two different estimates of the LOD
¾Limit of Quantitation (LOQ)
– The LOQ is the lowest amount of analyte in a sample that can be
quantitatively determined with a stated acceptable precision and
accuracy, under stated experimental conditions
Determination of LOB
¾The assumption in the determination of the
LOB is that values exceeding the 95th
percentile of the distribution of values on truly
blank or negative samples deviate significantly
from blank or negative measurements. When a
sample produces an observed value that
exceeds this limit, it may be declared to contain
an amount of analyte that exceeds zero
Æ NCCLS document EP17-A
Determination of LOB Cont’
• A α value of 5% corresponds to using the 95th
percentile of the distribution of blank or negative
values as the limit for declaring a measured value
significantly higher than the blank or negative
• Given a Gaussian distribution of blank or negative
values, this limit corresponds to:
LOB = μ B + 1.645σ B
where μB and σB are the mean and standard deviation
of the blank or negative measurements, respectively
LOD Experiment Design
¾ A minimum of 10 individual samples with
concentrations ranging from the LOB to approximately
4xLOB shall be tested at least 10 times by at least two
technicians in a minimum of two days or runs
¾ A pooled SDS estimate can be derived from repeated
measurements with the set of samples (a minimum of
10 measurements of at least 10 samples)
Measurements shall be carried out by different
technicians in different days or runs to be able to
capture the true variability of the analytical method.
¾ The SDS is the pooled estimate after checking the
statistical assumption of homogeneity of variance
LOD Estimation Cont’
An estimate LOD is then obtained as:
LOD = LOB + cβSDS
¾ SDS is the estimated standard deviation of
the sample distribution at a low level.
¾ As an example, if 5 low samples are tested,
then where cβ =1.645/(1-1/(4f)) is derived
from the 95th percentile of the standard
Gaussian distribution (and the correction
factor), which is applied because the SDS is a
biased estimate for the population standard
deviation σS
LOD Determination Example
sqrt(0.0119)
cp = 1.645/(1-1/(4xf))
= 1.645/(1-1/4x60)
= 1.6519
LODt = LOB +
cβ x SDs
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Expected
MEAN
STD
%CV
Bias
STD^2
SDs
cbeta
LOB/LON
LOD
L1
L2
L3
L4
3.28
3.20
3.34
3.37
3.22
3.30
3.20
3.30
3.02
3.22
3.19
3.36
3.26
3.39
3.22
3.21
3.20
3.26
0.09
3
5.53%
0.0085
0.1092
1.6519
1.2
1.38
1.94
2.02
1.97
2.12
2.13
2.01
1.96
1.95
2.19
1.99
2.15
2.11
2.19
1.94
1.98
2.10
1.92
2.05
0.09
4
12.68%
0.0083
1.44
1.42
1.51
1.66
1.51
1.50
1.54
1.90
1.53
1.45
1.54
1.90
1.62
1.62
1.48
1.51
1.60
1.57
0.14
9
-2.90%
0.0209
1.40
1.43
1.49
1.46
1.41
1.40
1.36
1.14
1.31
1.27
1.36
1.25
1.20
1.25
1.41
1.28
1.37
1.34
0.10
7
-3.25%
0.0100
3.01%
0.0119
SD2S = (15*0.0085 + 15*0.0083
+15*0.0209 + 15*0.01) / 60
Considerations Using 4PL
Conrad P. Quinn, Vera A. Semenova, Cheryl M. Elie et al (2002).
¾ When 4PL is used to model the characteristic curve for the
standard data two estimates of LOD can be obtained: the
MDC and the RDL. The position of the LOB with respect
to the MDC and the RDL will determine the true LOD
Definition of MDC and RDL
¾ The minimum detectable concentration
(MDC) is the concentration of the
analyte corresponding to the
interpolated intersection of the lower
asymptote of the upper 95% confidence
interval (95% CI) with the 4-PL fit of
the standards data
¾ The reliable detection limit (RDL) is
the concentration of the analyte
corresponding to the interpolated
intersection of the upper 95% CI
asymptote with the lower 95% CI of the
standards data
LOD Design and Analysis
¾ At a minimum, data from at least 30
reference curves shall be used to estimate
the MDC and the RDL
¾ If the LOB is an OD value, it should be
converted to the analyte concentration by
using the standard curve calibration factor.
ƒ If the LOB ≤ MDC then the LOD = MDC
ƒ If the MDC ≤ LOB ≤ RDL then the LOD =
RDL
LOD Determination Example
LoD
Antigen
Number of
curves
Number of
Concentrations
LoB
(μg/mL)
MDC
RDL
Tetanus
60
8
0.000
0.00031
0.00045
LoD
(μg/mL)
0.0016
LOQ Experiment Design
¾The LOQ is the lowest amount of analyte in a
sample that can be quantitatively determined
with a stated acceptable precision and accuracy,
under stated experimental conditions
¾The test results from the LOD study can be used
to estimate the LOQ. At least 10 low levels
samples with concentrations in the ranging from
the LOD to approximately 4xLOD shall be tested
at minimum of 5 to 10 times by at least two
technicians in a minimum of two days or runs
LOQ Estimation
¾ The procedure described for the estimation of
the LOD will be used to determine the LOQ. The
estimated LOQ is obtained as:
LOQ = LOD + cβxSDS
where SDS is the pooled estimate of the standard
deviation of the low samples in the range of the
LOD to 4xLOD after checking the statistical
assumption of homogeneity of variance
The LLOQ is estimated during Qualification/Prevalidation experiment!!!
LLOQ Challenge During Validation
WARNINGS!!! LLOQ cannot be estimated during
validation experiments
¾A minimum of ten validation samples ranging
from below the LOD to four times the LOD will be
tested
¾Each sample will have a minimum of 10
independent determinations generated as
described by the method
¾Verification of the LLOQ by inspection of
precision profile (%CV) for point-at-which the
assay deviates from acceptable performance (i.e.
%CV ≤ 20%)
LLOQ Challenge Example
LLOQ – Precision Profile from <7 to 60 EU/ml
SAMPLE #
MEAN
STANDARD DEVIATION
CV (%)
4
13.41
2.7393
20.43
1
13.41
0.6820
5.08
5
14.07
3.7958
26.97
2
15.75
1.8806
11.94
3
15.83
1.7192
10.86
6
16.63
2.0629
12.40
Antigen
Number
of
Reference
Curves
AAA
10
Test for Homogeneity
P-value
Conclusion
LoD
(EU/mL)
0.0011
Fail
5.77
LoQ
SDs
Cβ or DS
LoQ
(EU/mL)
-
8.88
14.61
LLOQ – Precision Profile from <15 to 60 EU/ml
SAMPLE #
9
5
4
8
3
7
10
2
6
1
N
8
13
15
15
15
14
15
15
14
15
MEAN
12.47
16.08
24.61
24.64
32.38
39.16
42.08
48.26
51.62
60.22
STANDARD DEVIATION
2.3343
2.7185
3.6272
3.1005
5.6747
3.8095
5.3051
7.5851
5.6713
5.9099
CV (%)
18.72
16.91
14.74
12.58
17.52
9.73
12.61
15.72
10.99
9.81
LLOQ Considerations for
Functional Assays
¾ In functional assays LLOD and LLOQ are
identical
¾ The LLOQ is the lowest level of antibody
present in a sample that can be consistently
detected with suitable precision and accuracy
by applying the test procedure
¾ 5 to 10 low human sera (non-specific, e.g.
sheep sera) can be tested a minimum of 11
times to confirm the LLOQ
Statistical Methods for Functional
Assays
¾Method 1: Wood and Durham (2000)
– The probability that the maximum ratio of two distinct
titers (obtained in the blind) on the same specimen will
not exceed 2
¾Method 2: Median Method
– The percent of the results within one 2-fold dilution
from the median titer
¾Method 3: Replicate within 4-fold range
– The probability that the maximum ratio of two distinct
titers on the same specimen will not exceed 4
Functional Assays Sample
Precision
¾For the median method, a sample or a specimen
with a given targeted titer is reproducible if “no
more than 10% of the sample tested would have
titers outside of a two-fold difference from their
median titer upon repeat testing”.
¾For the probability method, a sample with
probability greater or equal to 0.9 is deemed to
be acceptably reproducible.
Comparison of Precision Method
Acceptance Criterion
ƒ > 80% of the samples have no more than 10% of titers
outside of a two-fold difference from their median titer upon repeat
testing
ƒ > 80% of the samples have precision probability > 0.9
Example LLOQ Estimation During
Qualification Experiment
1:20 is the level of antibody present in a sample that can
be consistently detected with suitable precision and
accuracy by applying the test procedure
The LLOQ of this assay is can be chosen to be 20
LLOQ Challenge for Functional
Assays During Validation
¾A minimum of ten validation samples ranging from
below the LOQ to four times the LOQ will be tested
¾Each sample will have a minimum of 11
independent determinations generated as described
by the method
¾Verification of the LLOQ by inspection of precision
profile for point-at-which the assay deviates from
acceptable performance (i.e. (>=90% of results are
within ± 2-fold of the Median)
Example of LLOQ Challenge
During Validation
Titer
Median
Percent of results within
± 2-fold of the Median
1 40 40 40 80 40 40 40 20 80 40 40
40
100%
2 80 20 40 40 40 80 40 20 20 20 40
40
100%
3 40 40 40 40 20 40 40 20 20 40 40
40
100%
4 80 160 80 80 80 80 160 160 80 80 80
80
100%
5 20 40 40 20 20 20 20 40 20 20 40
20
100%
6 10 40 10 40 10 10 20 10 10 40 <10 10
73%
Sample
1 2 3 4 5 6 7 8 9 10 11
Verification of the LLOQ (1:20) by inspection of precision profile
for point-at-which the assay deviates from acceptable performance
(i.e. >=90% of results are within ± 2-fold of the Median)
Conclusion
¾The experiment design and statistical method
used for the determination of LOD and LOQ is
dependent on the assay type (e.g., ELISA,
Functional or PCR)
¾Appropriate determination of LOD/LOD is
increasingly becoming a regulatory concern for
calculation of sero-conversion, sero-protection or
geometric mean when licensing a vaccine or drug
products
Reference
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Code of Federal Regulation - 21 CFR 211.165(e), 211.194(a)(2)
Official Journal of the European Union - Commission Directive 2003/94/EC
ICH Harmonized Tripartite Guideline – Validation of Analytical Procedures:
Text and Methodology – Q2 (R1) – October 1994 – November 1996
European Pharmacopoeia – Technical Guide – December 1999
United States Pharmacopoeia - <1225> Validation of compendial
procedures
FDA Guidance for Industry – Analytical Procedures and Methods Validation
– Draft Guidance, August 2000
FDA Guidance for Industry – Bioanalytical Method Validation – May 2001
NCCLS – Protocols for Determination of Limits of Detection and Limit of
Quantitation; Approved Guideline – NCCLS document EP17-A – Clinical
and Laboratory Standards Institute Volume 24, Number 34, October 2004
Conrad P. Quinn, Vera A. Semenova, Cheryl M. Elie et al (2002). “Specific,
Sensitive, and Quantitative Enzyme-Linked Immunosorbent Assay for
Human IgG Antibodies to Anthrax Toxin Protective Antigen” Emerging
Infectious Disease Vol. 8 (10).
Dominique Pifat, Assay Validation Presentation
R.J. Wood & T. M. Durham, CDC, Atlanta, Georgia (2000). Reproducibility
of Serological Titers, Journal of Clinical Microbiology, 1980 p. 541-545