Comparison of microfluidic digital PCR and
conventional quantitative PCR for measuring
copy number variation
Alexandra S. Whale1, Jim F. Huggett1,*, Simon Cowen1, Valerie Speirs2, Jacqui Shaw3,
Stephen Ellison1, Carole A. Foy1and Daniel J. Scott1
1LGC Limited, Queens Road, Teddington, Middlesex TW11 0LY,2Leeds Institute of Molecular Medicine,
University of Leeds, St. James’s University Hospital, Leeds LS9 7TF and3Cancer Studies & Molecular
Medicine, University of Leicester, Robert Kilpatrick Clinical Sciences Building, Leicester Royal Infirmary,
Leicester LE2 7LX, UK
Received January 5, 2011; Revised and Accepted February 14, 2012
One of the benefits of Digital PCR (dPCR) is the
smaller fold change measurements. An example of
improved precision is the measurement of tumour-
associated copy number variation (CNV) in the cell
free DNA (cfDNA) fraction of patient blood plasma.
To investigate the potential precision of dPCR and
compare it with the established technique of quan-
titative PCR (qPCR), we used breast cancer cell lines
modelled a range of different CNVs. We showed
that, with equal experimental replication, dPCR
could measure a smaller CNV than qPCR. As
dPCR precision is directly dependent upon both
the number of replicate measurements and the
method to assist the design of dPCR experiments
(based on Poisson and binomial distributions) to
derive an expression for the variance inherent in
dPCR, we produced a power calculation to define
the experimental size required to reliably detect a
given fold change at a given template concentration.
This work will facilitate any future translation of
dPCR to key diagnostic applications, such as
cancer diagnostics and analysis of cfDNA.
A key measurement challenge in diagnostic research
involves identifying small changes in gene dosage or
nucleic acid sequence that are commonly associated with
genetic diseases. Copy number variations (CNVs) are
changes in the genomic DNA leading to an abnormal
number of copies of a DNA sequence (usually two
copies per diploid genome). CNVs are caused by deletions,
duplications or structural rearrangements of the genome.
CNVs are involved in a large number of complex human
diseases such as Down’s syndrome (trisomy 21) and many
cancers, for example HER2 gene amplification in breast
cancer (BC) (1–5). CNV measurements are used for
analysis can assist in subsequent prognostic monitoring
(6,7). Clinical diagnostic methods currently include fluor-
escence in situ hybridization (FISH), comparative genome
hybridisation (CGH), single nucleotide polymorphism
(SNP) arrays, deep sequencing and real-time quantitative
PCR (qPCR) (8–10).
Quantitative PCR (qPCR) is currently the most sensi-
tive approach able to resolve ?1.5-fold changes (11,12).
The discovery of cell free DNA (cfDNA) in blood plasma
has provided a simple source of genetic material for
pre-natal and tumour diagnosis (13–18) that could poten-
tially enable routine minimally invasive sampling for
subsequent CNV analysis. qPCR has recently identify
amplified HER2 molecules in breast cancer patients
with good correlation between the levels of amplification
detected in the primary tumour and cfDNA (19).
However, as only a proportion of the cfDNA is derived
from the embryo or tumour, identification of an
associated CNV is more challenging as the target DNA
is effectively ‘diluted’ in a background of normal DNA.
Consequently, a tumour-associated 5-fold increase in
CNV becomes a 1.2-fold increase if only 5% of the
cfDNA sample is derived from the tumour; this magnitude
of CNV would be undetectable by current approaches.
One method that has shown promise for improving the
limit of detection for nucleic acid quantification is digital
PCR (dPCR) with a number of reports highlighting the
*To whom correspondence should be addressed. Tel: +44 20 8943 7655; Fax: +44 20 8943 2767; Email: email@example.com
Published online 28 February 2012Nucleic Acids Research, 2012, Vol. 40, No. 11e82
? The Author(s) 2012. Published by Oxford University Press.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/
by-nc/3.0), which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
superior accuracy of dPCR for CNV analysis (20,21).
dPCR has been reported to detect a 1.25-fold difference
in copy number (21); however, to our knowledge, no direct
comparison between qPCR and dPCR has been per-
formed to ascertain if the latter is more sensitive.
Another aspect that is not extensively addressed in the
literature is that the ability of dPCR to measure small
CNVs is directly dependent upon template concentration.
This is a crucial consideration when considering cfDNA as
a template as its concentration can range considerably;
from 2 to 30ng/ml plasma in healthy individuals to
180–600ng/ml plasma both during pregnancy and in
cancer patients (13,16,18,22–24).
This study aimed to investigate this further using an
in vitro BC gene amplification model to identify when
a CNV is too small to be measured by qPCR and
dPCR. Subsequently, we developed a model, based on
the Poisson and binomial distributions, to determine the
variance inherent in dPCR, and used this to perform
power calculations which demonstrate the effects of the
DNA-template concentration on the sensitivity of CNV
MATERIALS AND METHODS
Genomic DNA (gDNA) from three BC cell lines with
different levels of HER2 gene amplification were used;
high-HER2 amplification (SK-BR-3; ATCC HTB-30),
low-level HER2 gain (T-47D; ATCC HTB-133) and one
with a single HER2 allele deletion (MCF-7; ATCC
HTB-22). Control experiments were performed using
commercially available gDNA from pooled healthy
females that have two copies of each gene per diploid
genome (Promega G1521). gDNA concentrations were
determined by A260 measurements (Nanodrop, Thermo
Scientific) and purity was measured by A260/A280measure-
ment (all gDNA samples were between 1.93 and 1.96).
Haploid copy number dilutions were calculated based on
the molecular weight of one normal haploid female
genome equalling 3.275 pg.
The TaqMan?copy number reference assay (Applied
Biosystems 4401631) contained 900nM each of RNase
P-specific forward and reverse primers and 250nM of a
VIC dye-labelled TAMRA hydrolysis probe. The RNase
P amplicon sequence was confirmed by clonal sequencing
(LGC Genomics; Supplementary Figure S1a). The HER2
assay, targeting intron 5 of the HER2 gene on chromo-
some 17q21.1, contained 900nM each of forward
(50-AAG CTA AGA AAT AAG GCC AGA TGG-30)
and reverse (50-CGC ACA GCA CCA AGG AAA
AG-30) primers and 200nM of hydrolysis probe (50
FAM-CAG CAG AAC
CCT-BHQ1 30) (20) (SIGMA). The amplification of a
single PCR product for both the RNase P and HER2
assays was confirmed using the 2100 Bioanalyzer and
DNA 1000 kit according to the manufacturer’s instruc-
tions (Agilent; Supplementary Figure S1b).
Real-time quantitative PCR
Real-time quantitative PCR was performed in accordance
with the MIQE guidelines (Supplementary Table S1 and
Supplementary Figure S1) (25). Ten microlitres reactions
contained 1? TaqMan?gene expression mastermix (ABI
4369016), 1? gene-specific assay and 2ml target DNA.
qPCR was performed using the Prism 7900HT Real
Time PCR system (ABI). Thermocycling conditions were
95?C for 10min, followed by 40 cycles of 95?C for 15s and
60?C for 60s. Quantification was performed with the
standard curve method using five standard dilutions, in
triplicate, of normal female gDNA ranging from 16.50
to 0.33ng (5000 to 100 haploid genome copies) per
reaction. Due to the differences in molecular weight
between the BC cell line gDNA, triplicate reactions were
performed on a range of gDNA concentrations (16.50 to
0.33ng per reaction) for HER2 and RNase P assays. This
allowed identification of the gDNA concentration that fell
within the range of the qPCR standard curves for both
HER2 and RNase P assays. Subsequently, eight HER2
and eight RNase P reactions (16 reactions in total) were
performed on the optimum weight of gDNA for each cell
line (normal female: 0.71ng, MCF-7: 0.60ng, SK-BR-3:
0.94ng and T-47D: 1.45ng). The SDS software v2.4 (ABI)
was used to calculate the quantification cycle (Cq) value,
that is defined as the number of cycles at which the fluor-
escence signal is significant above the threshold, which was
converted to copy number using the relevant standard
curve. Replicate HER2:RNase P ratios were calculated
by randomly pairing HER2 and RNase P copy numbers
and calculating the 95% confidence intervals (CI) from the
standard error of the mean and the two-tailed Student’s
t-test. No template control (NTC) reactions were per-
formed using water with no template; in all cases, no amp-
lification occurred (Supplementary Figure S1c and S1d).
About 4.5ml reactions containing 1? TaqMan?gene
expression mastermix, 2? GE sample loading reagent
(Fluidigm 85000746), 1? gene-specific assay and 1.35ml
target gDNA was pipetted into each loading inlet of a
48.770 digital PCR array (Fluidigm). The BioMark IFC
controller MX (Fluidigm, San Francisco, CA) was used to
uniformly partition the reaction from the loading inlet
into the 770?0.84 nl chambers. dPCR was performed
(Fluidigm). Thermocycling conditions were set as for
qPCR. For BC cell line gDNA analysis, reactions were
performed in quadruplicate panels for HER2 and RNase
P assays (eight panels in total) on 0.6ng BC cell line
gDNA, estimated using A260measurements. The Digital
PCR Analysis software (Fluidigm) was used to set the Cq
threshold and range (Supplementary Figure S2), and to
count the number of positive chambers (H) out of the
total number chambers (C) from which the Poisson distri-
bution was used to estimate the average number of mol-
ecules per chamber (l) so that l=?ln (1 ? H/C) (26).
HER2:RNase P ratio (lt/lr) and 95% CI were calculated
as described in this publication (Table 1). NTC reactions
were performed using water with no template; in all cases,
e82 Nucleic Acids Research, 2012,Vol. 40,No. 11PAGE 2 OF 9
no positive chambers were observed (Supplementary
Establishment and analysis of copy number
The in vitro gene amplification model was established
by spiking T-47D gDNA into normal female gDNA at
various percentages to generate a theoretical range of
HER2:RNase P ratios between 1.00 and 2.00 based on
the dPCR analysis (Supplementary Table S2). All ratios
were diluted to give approximately 720 RNase P copies/ml.
For qPCR, four replicates were performed per ratio for
both HER2 and RNase P assays in two independent
experiments (16 reactions in total). All CNV ratios were
calculated by conversion of Cq values to copy numbers of
HER2 and RNase P using a standard curve generated
from five dilutions, in triplicate, of normal female
gDNA ranging from 1,000 to 20 haploid genome copies/
ml (Supplementary Figure S1c and S1d). For dPCR, four
panels were performed per ratio for both HER2 and
RNase P assays in two independent experiments (16
panels in total) to give approximately 155 RNase
P copies per panel (lr=0.2) where one panel on a
48.770 dPCR array contains 0.195ml of template. CNV
ratios were calculated using the equations described in
this paper (Table 1).
To investigate the number of dPCR panels (containing
770 chambers each) needed
differences, a pseudo-random number generator (the
assign a number to each HER2 and RNase P panel. In
each case, the required numbers of panels were selected
from the eight panel data set.
to detectsmall ratio
Statistical analysis and power calculations
Statistical analysis was performed using the MS Office
Excel software (2003). Statistical comparisons to establish
CNV limit of measurement were performed using
the one-way analysis of variance test to compare the
RNase P counts (dPCR) or copy number (qPCR)
between the samples (in vitro gene amplification model
ratio). Two-way analysis of variance was used to test for
differences in the mean copy number between the respect-
ive replicate qPCR experiments. The two-tailed Student’s
t-test was used to analyse the difference in HER2 counts
or copy number between the sample and the calibrator
(normal female gDNA). Power and associated calcula-
tions reported in this paper were carried out using the R
statistical programming language (version 2.13, http://
www.r-project.org). All scripts were written and run on
a standard desktop personal computer (Optiplex, Dell
Corporation). Further details of the methods and theory
are given in the Statistical Supplementary Information.
CNV measurement by dPCR and comparison with qPCR
In order to investigate the accuracy of dPCR for CNV
measurement, we used three BC cell lines with different
HER2 gene copy number as a model of gene amplification.
The RNase P assay was used as the reference gene for the
diploid control. Assay optimization was performed using
qPCR for HER2 and RNase P assays (Supplementary
Figure S1). For dPCR, absolute quantification of HER2
and RNase P molecules were calculated from the number
of positive counts per panel based on the Poisson distri-
bution for the number of molecules in each chamber
dPCR analysis of normal female gDNA had a
HER2:RNase P ratio of 1.03 and was not significantly
different from qPCR analysis that had a HER2:RNase P
ratio of 1.00 (P=0.39; Figure 1b). Analysis of MCF-7
gDNA, which has a single HER2 allele deletion, gave a
ratio of 0.44 by both dPCR and qPCR. T-47D gDNA,
which has low-HER2 copy gain had a HER2:RNase P
ratio of 2.00 and 1.96 for dPCR and qPCR, respectively.
There was no significant difference in HER2:RNase P
ratios between the two techniques when measuring
Table 1. Summary of equations derived in this study
DescriptionSymbolEquation Equation in MS ExcelWorked example
Number of chambers analysed
Number of positive chambers for reference
Number of positive chambers for target
Number of reference molecules per chamber
Number of target molecules per chamber
Log ratio estimate
?ln (1 ? Hr/C)
?ln (1 ? Ht/C)
1 ? e??t
R ? 1:960?R
?ln(1 ? (Hr/C))
?ln (1 ? (Ht/C))
Variance for Log ratio estimate
te??t+1 ? e??r
(1 ? EXP(?lt))/(C?lt2* EXP(?lt))
+(1 ? EXP(?lr))/(C * lr2 * EXP(?lr))
Standard deviation for Log ratio estimate
1 ? e??t
te??t+1 ? e??r
Log ratio 95% CI (one-tailed) - high
Log ratio 95% CI (one-tailed) - low
Ratio 95% CI (one-tailed) - high
Ratio 95% CI (one tailed) - low
R+NORMSINV(0.975) * sR
R+NORMSINV(0.025) * sR
For equations in MS Excel, an ‘equals’ sign must be inserted before the formula and symbols should be replaced with the experimental values.
A worked example is provided, with the values used to generate the variance model and to ensure correct equations are transferred
PAGE 3 OF 9Nucleic Acids Research,2012, Vol.40, No. 11e82
MCF-7 (P=0.71) and T-47D (P=0.52). SK-BR-3
gDNA, which has high HER2 gene amplification, had a
HER2:RNase P ratio of 7.15 when measured by dPCR
which was significantly lower than the HER2:RNase P
ratio 9.43 observed by qPCR (P=0.00005). For all meas-
urements, the 95% CIs were slightly larger for dPCR,
where four dPCR panels were analyzed, when compared
with qPCR, where eight reaction wells were analyzed
Limit of detection for analysing copy number variations
To determine the limit of detection for analysis of CNVs
by dPCR, an in vitro gene-amplification model was used,
whereby T-47D gDNA was spiked into normal female
gDNA to generate a theoretical range of HER2:RNase P
ratios between 1.00 and 2.00 at low copy number (2.1ng/
ml) for analysis using dPCR and qPCR (Supplementary
Table S2). Using dPCR, a ratio of 1.17 or more was sig-
nificantly different from the experimentally derived
normal female gDNA ratio of 1.03 (P<0.0003) when
eight panels where used (Figure 2a). There was good
linear correlation between the expected and the observed
ratios when measuring a CNV of ?1.17 (R2=0.9974) and
this linear correlation was maintained when the line was
extrapolated through the observed ratio for normal female
gDNA (Figure 2a; dashed line). Furthermore, the slope
and intercept of the linear correlation were measured as
1.05 and 0.05, respectively, demonstrating the accuracy in
the measured ratios, and that no bias was introduced. An
expected ratio of 1.12 was not significantly different from
normal female gDNA when using eight panels (P=0.67;
Figure 2a). In all cases, the RNase P counts observed for
each measurement were not significantly different from
gene-amplification model with qPCR demonstrated that
ratios of 1.27 or more were significantly different from
R2 = 0.9949
y = 1.01x + 0.0003
Observed ratio (95% CI)
R2 = 0.9949
y = 1.05x - 0.05
Observed ratio (95% CI)
Figure 2. Determination of CNV detection of digital and quantitative
real-time PCR. Quantitation of HER2:RNase P ratios using (a) dPCR
and (b) qPCR generated from the in vitro gene-amplification model.
The x-axis shows the expected HER2:RNase P ratio and the y-axis
shows the observed HER2:RNase P ratios with the 95% CI. (a) For
dPCR, four panels for each assay were analyzed for ratios>1.5
(daggered symbol) and eight panels for each assay for ratios <1.5. In
all cases, lrwas approximately 0.2. The error bars represent the 95%
CIs. (b) For qPCR, eight reactions were performed for each assay and
all ratios. The error bars represent the 95% CIs calculated from the
standard error of the mean and associated T-value with 95% confi-
dence and seven degrees-of-freedom. Key: black triangle: normal
female gDNA, black diamond: significantly different from normal
female gDNA (P<0.05), gray diamond: not significantly different
from normal female gDNA (P>0.05). Solid line of linear correlation
is shown for those ratios that were significantly different from normal
female gDNA. Dashed line is the extrapolation of the linear correlation
showing intersection with HER2:RNase P ratio of 1.0. R2and equa-
tions are given for the linear correlation.
2REHPe s aNR
HER2:RNaseP (95% CI)
Figure 1. Comparison of HER2:RNase P ratio in breast cancer cell
line genomic DNA using digital and quantitative real-time PCR.
(a) Software-generated heat map showing a single panel in a 48.770
dPCR array that contains 770 chambers with positive (white) and
negative (black) amplification signals. One representative dPCR panel
is shown for each gDNA sample and assay with the number of positive
chambers shown in the top right corner of the panel. Positive and
negative chambers were used to calculate the number of molecules
per panel and the HER2:RNase P ratio for the gDNA sample. The
NTC panels for both assays had no positive chambers. (b) qPCR (n=8
wells) and dPCR (n=4 panels) gave similar HER2:RNase P ratios for
all BC gDNA except the SK-BR-3 gDNA that was significantly higher
by qPCR compared with dPCR (asterisk). Data is presented on a log
scale and error bars represent 95% CIs.
e82Nucleic Acids Research, 2012,Vol. 40,No. 11PAGE 4 OF 9
normal female gDNA (P<0.0005) and maintained a
linear correlation (R2=?0.99; Figure 2b; dashed line).
As was observed with the dPCR analysis, the observed
ratios were accurate with no introduced bias as shown
by the slope (1.01) and intercept (<0.001) of the linear
correlation. Ratios of ?1.22 did not differ significantly
from female gDNA (P>0.05; Figure 2b). As with
dPCR, in all cases, the RNase P counts observed for
each measurement were not significantly different from
one another (P?0.27). Furthermore, no statistically sig-
nificant inter-run variability was observed for either the
RNase P or the HER2 assays (P?0.99 and P?0.15,
Determination of the number of dPCR panels needed to
confidently detect small changes in copy number variation
From our data, when the CNV to be measured is
>1.5-fold, then four dPCR panels were sufficient while
CNVs<1.5-fold could be detected with up to eight
dPCR panels (Figures 1b and 2a). As CNVs of <1.17
were not measurable using eight dPCR panels, it would
be useful to be able to predict how many dPCR panels
would be needed to detect such small CNVs. For such a
prediction, we would need to assess discriminating power,
and therefore, the true copy number difference at which
we would reliably judge two materials to be different. This
was achieved with a statistical power calculation, which
required a test statistic and associated distribution.
The domain of interest in this study involved the refer-
ence RNase P assay adjusted to give an observed number
of positive chambers in the region of 100–200 per panel
(2.1ng/ml) to mimic the low concentration observed in
cfDNA samples (18). Based on the Poisson distribution,
this can be used to estimate the number of molecules per
chamber (l), and in this case, l was approximately 0.2 in a
48.770 dPCR array (Table 1). At this concentration, the
probability P that a chamber will give a positive signal is
1 ? e??and is the same for every chamber (26). The CNV
is the ratio of l estimates for the two groups being
compared and as such, it is highly non-Normal. By
taking the logarithm of the ratio for these two groups
(R), the data is transformed to produce a variable whose
distribution is very close to Normal (Supplementary
Figure S3a) and is given by the equation:
R ¼ ln?t
where ltand lrcorrespond to the l values of the target
and reference genes, respectively, and l=?ln (1 ? H/C)
[Table 1; (26)]. Consequently, power calculations can be
based on a t-test for a difference in the logarithm of the
observed ratio of target to reference gene from zero.
To calculate power, we first need an expression for
the variance (?2
R) of the log ratio R. This was derived
Supplementary Information’) and is given here as:
R?1 ? e??t
te??t+1 ? e??r
Comparison of the theoretical standard deviation of R
[estimated from Equation (2) as ˇ?2
standard deviation of the experimental data (Figure 2a)
demonstrated good concordance (Supplementary Figure
S3b). With a valid estimate of the variance ?2
ratio, the upper and lower 95% CI can be calculated
(Table 1). Power calculations can also be derived to deter-
mine the number of chambers required for an experiment
capable of detecting a log ratio R with a defined test power
of 1 ? ? and at the 1 ? ? confidence level, where ? and ?
are the false-positive and false-negative rates, respectively.
Our experiment was one in which a positive R was the
expected result (an increase in copy number, so lt>lr),
so a one-tailed test was appropriate. Statistical significance
was declared at a P-value of ? or lower (<0.05) and the
Supplementary Figure S4). Power calculations involving
a test statistic which has a Normal distribution can only be
carried out numerically, as there is no analytical solution
and details of the method are given in the ‘Statistical
Using the power curve, where lr=0.2, we found that
with 95% power, a fold change of 1.2 was easily detectable
with five 770-chamber panels per gene assay, while ratios
of 1.1 and below required greatly increased numbers of
panels (>15 panels; Figure 3a). Using the curve to
compare the data from the HER2 in vitro gene-
amplification model with the number of panels required
demonstrates that a ?1.17 ratio can be measured with
eight or fewer panels (Figure 3a); this is shown experimen-
tally (Figure 2a). However, from the curve, a ratio of 1.12
was predicted to need more than 10 panels (Figure 3a),
which is supported by our inability to measure with con-
fidence a 1.12 ratio with only eight panels (Figure 2a). Our
power curve predicts that when lris 0.2, the smallest CNV
ratio that could be measured using eight dPCR panels is
approximately 1.15 (Figure 3a). This lies between our two
experimental data points and therefore confirms the fitness
of our model for this template concentration.
To further test the power calculations, each HER2
dPCR panel was randomly paired with an RNase P
panel and the desired number of paired panels (1–8)
were selected and used to calculate their CNV ratio and
associated 95% CI (Figure 3b). Our power curve suggests
that approximately three panels are needed to detect a
ratio of 1.27 when lr=0.2 (Figure 3a) which was experi-
mentally measurable with four or more panels (Figure 3b).
Analysis of a fold difference of 1.17 predicted that
approximately six panels are needed (Figure 3a), which
is concordant with our experimental data (Figure 3b).
Power calculations were also performed for qPCR using
the Student’s t-statistic (see ‘Supplementary Statistical
Information’ for details) and the resulting power curves
demonstrated that ratios greater than 1.25 can be
measured with 95% power and eight replicate qPCR
wells (Supplementary Figure S7). This compared well
with the experimental data generated from the in vitro
gene amplification model where a ratio of 1.27 was
measured with eight qPCR wells but small ratios
were not (Figure 2b). From the power curve, it was
shown that using gDNA at the experimental defined
R] with the observed
Rin the log
PAGE 5 OF 9 Nucleic Acids Research,2012, Vol.40, No. 11e82
concentration, an excess of 20 qPCR wells would be
needed to measure ratios of 1.17 or fewer (Supplementary
We have investigated the measurement capabilities of
dPCR when investigating changes in CNV, described the
limit of detection for a given experiment and demonstrate
that dPCR exhibits greater sensitivity than qPCR when
investigating subtle fold-differences. The potential of
cfDNA as a source of template in minimally invasive diag-
nostics is becoming increasingly apparent. The measurable
resolution of qPCR in our gene-amplification model for
cfDNA, which we describe here as a ratio of 1.27, offers a
theoretical diagnostic potential, however, the reality is
that smaller CNVs, where the tumour contribution to
the cfDNA can be as little as 5% of the total cfDNA
(16,17) are still technically out of reach using qPCR.
Furthermore, one of the major differences between
qPCR and dPCR is that technical variability of qPCR
can be high between and within laboratories (27). dPCR
is notably less variable between experiments (28,29), which
offers the possibility of reproducibly more accurate
results. In this study, a CNV ratio of 1.17 was significantly
detected using eight panels and therefore, the ability of
dPCR to detect incrementally smaller fold differences
than qPCR demonstrates the potential of this method
for future CNV clinical diagnostics.
Recently, an error model relating to the 95% theoretical
CI for copy number versus number of chambers was pub-
lished (21). According to this model, approximately 1,200
chambers (equates to 1.5 panels) would be needed to
detect a CNV ratio of 1.25. However, when the authors
performed this in a real experiment, they were unable to
realise this predicted precision, requiring twice the number
of chambers/panels to measure the targeted difference
(21). The authors explain that this was directly due to
the fact that, for their model, they fixed the lrat a value
of 0.6, whereas the real experiment (where lrvalues were
0.18 and 0.37 for their two samples) was below this value
and so did not have sufficient power to resolve the given
difference with the predicted number of chambers.
When we used this model to estimate the number of
chambers needed for our experiments, we found that
this was also underestimated and due to the smaller lr,
which in the case of our experiment was about 0.2.
Weaver and co-workers (21) used the point (in observed
number of panels) at which calculated 95% CIs just
overlap, assuming a Poisson distribution for individual
counts. The point of theoretical CI overlap is an indicator
of discriminating power, in that it increases as precision
degrades and allows comparison
However, basic statistical theory shows that a significant
difference at the 95% confidence level would usually show
substantially overlapping CIs for the two independent
observations. In this case, statistical significance focuses
on the error rate under the null hypothesis; the probability
of wrongly declaring a result significant, or the false-
positive rate. In contrast, we were interested in assessing
discriminating power and therefore, the true copy number
difference at which will we reliably judge two materials to
be different, that is the false-negative rate. Therefore, we
generated a power calculation based on the variance and
false-negative rate of a given measurement of copy
Our power calculation method takes the DNA-template
concentration into consideration using the corresponding
lr and estimating the number of panels required.
Validation of the theory is demonstrated with our experi-
mental data (Figure 3b). Based on this, further theoretical
were derived and are given in Supplementary Figure S5
for researchers to use for future experimental design.
From these power curves, we predict that to investigate
(approximate values for lrof 0.18 and 0.37) with 95%
Ratio (95% CI)
Number of dPCR panels
Number of 770-chamber panels required
1.11.3 1.41.56 . 12 . 1
Figure 3. Determination of the number of dPCR panels needed to
measure HER2:RNase P ratios. (a) Power curve to determine the
number of panels required to detect different ratios of ltto lr, where
lt>lrwith 95% power at a confidence level of 95% and lr=0.2. The
two horizontal lines show a single-panel and eight-panel experiment
where the intersections with the power curve indicates the lowest de-
tectable CNV. The vertical line shows the smallest CNV detectable is
approximately 1.15 when lr=0.2 and the number of panels is 8.
(b) The relevant number of dPCR panels (1–8) were selected and the
HER2:RNase P ratio and associated 95% CIs were calculated.
The graphs for the different ratios are slightly staggered to allow iden-
tification of the 95% CI error bars for each ratio. Ratios that are
statistically different from the normal female gDNA are shown for
ratios of 1.27 (gray asterisk) and 1.17 (black asterisk).
e82Nucleic Acids Research, 2012,Vol. 40,No. 11PAGE 6 OF 9
respectively (Supplementary Figure S5), which was con-
sistentwith Weaver and
The power calculations described in this publication are
based on a one-tailed test as we were interested detecting
HER2 amplification (where lt>lr) which has clinical and
prognostic relevance (30,31). Further applications of this
model would include detection of trisomy, e.g. in Down’s
syndrome (32). However, a modification of this model to
include detection of both amplification and deletion of
gene copies would have a wider scope, e.g. in character-
ization of in vitro culture cells over time (33), detection of
polyploidy in plants (34) or as an alternative to CGH
analysis or FISH for cancer diagnostics. Therefore, we
have expanded our model to incorporate a two-tail test
(Supplementary Figure S6).
We also generated power curves for qPCR based on a
one- or two-tailed test (Supplementary Figure S7). These
curves demonstrates that while dPCR appears to detect
only incrementally smaller fold differences than qPCR
using a one-tailed test and eight replicate measurements
(1.17 versus 1.27 in this study), an additional 12 qPCR
wells per assay or more would be needed before qPCR
could potentially measure a similarly small ratio to
dPCR. This is dependent upon the standard deviation of
the qPCR (in this case, was approximately 10% for both
assays across all experiments) as the number of replicates
needed will increase if precision is reduced. The binary
nature of dPCR means that the precision is more inde-
pendent of variation in assay amplification, making it
easier to optimize and standardize between laboratories.
As conventional qPCR is currently approximately one
20th of the expense of an equivalent dPCR analysis, it
does still offer a practical alternative method to measure
smaller CNVs. However, the increased template required
to perform the larger number of replicate measurements
could be a disadvantage where sample is limiting. qPCR
has the benefit of being able to measure lower plasma
template concentration than the dPCR method used
here as its larger reaction volume facilitates the addition
of more template. qPCR is also scalable offering the
option of adding even more template, where sample
permits,by further increasing
reaction. This is not currently possible with the dPCR
approach used here; however, with the development of
higher volume and throughput dPCR methods this
option will also be possible (35–37) with comparable
Improvements to qPCR using similar technologies to
those advancing dPCR will increase the throughput of
qPCR, as has already been described (21), although this
is also at the cost of smaller input volume which often
requires pre-amplification (39); this is not routinely
needed for dPCR. It should also be noted that for
qPCR (conventional or high throughput) to measure
such small fold changes, it is not only important that
precise well-optimized assays are used, but it is also essen-
tial that some estimation of efficiency is made (25). This
can be done by standard curves to estimate copy number,
as described here, or by performing efficiency corrected
??Cq (40). However, this fact further complicates using
qPCR for small fold change measurement.
Our model also raises the question of why variable
lrshould need to be considered at all when performing
dPCR. The alternative would be to ensure the optimum
concentration in the first place. However, this is only
possible when the sample DNA is at or higher than this
value, and if the concentration is lower than the optimum
lrthen more chambers would be needed, and therefore,
our model would provide an idea of how many. This issue
is applicable when using cfDNA as a template, which is by
nature low in concentration; around 2–30ng/ml blood
plasma in normal healthy humans (13,16–18,22,23),
which corresponds to approximately 600–9900 normal
haploid genomes per ml. Measuring HER2 status using
cfDNA offers considerable potential as a diagnostic and
prognostic test (19,30,31).
Our power calculation provides a good foundation
from which to design subsequent experiments; in our as-
sessment, we have used a high-quality DNA template in
our proof-of-principle experiments to model the cfDNA.
Additional factors that will need to be considered,
building on the findings of this study, include template
integrity, PCR-assay efficiency and the impact of matrix
effects as integral parts of subsequent translational
research, if this approach is to be used in the context of
HER2 and other clinical measurements. Recently, power
calculations based on a multivolume dPCR assays were
generated and demonstrated that different reaction
volumes influence the dynamic range and precision of
dPCR, could minimize the total number of dPCR reac-
tions needed and separated the upper and lower limits of
quantification. This would allow samples of differing con-
centration to be analyzed in parallel without compro-
mising one sample over the other (37).
An additional function of this study was to directly
compare microfluidic dPCR with conventional qPCR for
CNV using the same gDNA template and reaction assays.
Both methods gave similar HER2 CNV results using BC
cell line gDNA with varying numbers of HER2 gene
copies per diploid genome. Two BC cell lines were con-
current with the published data; MCF-7 gDNA, that has
monosomy for chromosome 17 assigned a HER2:RNase P
ratio of<0.5 (one copy per diploid genome) (41,42) and
T-47D gDNA gave a HER2:RNase P ratio of<2 (3–4
copies per diploid genome) (43–46). Analysis of the
SK-BR-3 gDNA identified high levels of HER2 amplifica-
tion that corresponds with the published copy number
range (14–24 copies per diploid genome) (41,43–45,47).
HER2:RNase P ratio obtained by dPCR (7.15) and
This difference could be attributed to the large number
of HER2 gene amplifications occurring on the same
molecule (concatamers of HER2 molecules inserted at
the same point in the genome) that are observed in this
cell line using FISH (48,49) but do not occur in the
MCF-7 or T-47D cell lines. Unlike qPCR, dPCR may
be unable to accurately quantify this type of gene ampli-
fication as linked genes cannot be separated into individ-
ual chambers. Qin and co-workers (20) have suggested
that this problem can be overcome by a pre-amplification
step using gene-specific primers to separate the linked
PAGE 7 OF 9 Nucleic Acids Research,2012, Vol.40, No. 11e82
copies before performing dPCR. However, such a step
requires careful validation because of the potential bias
that can be introduced that may outweigh the necessary
precision for detecting small CNVs (29).
In conclusion, our data suggests as microfluidic dPCR
becomes more established, it will offer a new level of pre-
cision and the clinical benefits of measuring smaller CNVs
in more challenging samples like cfDNA, will become
possible. However, the pre-clinical and translational
research necessary for this to be realized will need to
consider the issues explored by this study. The model we
describe here both provides a mechanism to facilitate this
research and highlights the issues around ensuring the
template concentration is included as a central consider-
ation when preparing CNV studies using dPCR. This will
better enable dPCR experiments to be designed, increasing
the impact of future research.
Supplementary Data are available at NAR Online:
Supplementary Tables 1–2, Supplementary Figures 1–7
and Supplementary Statistical Information.
The authors would like to acknowledge Dr Malcolm
Burns and Dr Alison Devonshire for critical review of
The UK National Measurement System. Funding for
open access charge: UK National Measurement System
Conflict of interest statement. None declared.
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