Note: Descriptions are shown in the official language in which they were submitted.
CA 02603389 2011-05-10
IDENTIFYING STATISTICALLY LINEAR DATA
BACKGROUND OF THE INVENTION
[0001] The present invention relates generally to data processing systems and
methods, and more
particularly to systems and methods for identifying statistically linear data
in a data set of an
amplification process, such as polymerase chain reaction (PCR).
[0002] Many experimental processes exhibit amplification of a quantity. For
example, in PCR, the
quantity may correspond to the number of parts of a DNA strand that have been
replicated, which
dramatically increases during an amplification stage or region. Other
experimental processes
exhibiting amplification include bacterial growth processes. The quantity is
detected from an
experimental device via a data signal, whose data points are analyzed to
determine information
about the amplification. As part of the data analysis, it is important to know
if amplification has
potentially occurred; otherwise, effort might be wasted on analyzing non-
amplifying data. If the
data is statistically linear, then amplification has not occurred.
[0003] Ideally, the data from the amplification detection device would be a
monotonic and
continuous signal, thus one could easily identify whether the data, or
portions thereof, has
statistically linear behavior. However, the signal from the amplification
device typically contains
noise, thus making identifying a behavior of the signal difficult. The noise
manifests itself in each
data point in the signal from the device having random fluctuations that occur
on top of the true
signal, e.g. the actual number of DNA strands. Thus, the data requires
processing to allow for
identifying of linear behavior.
[0004] A typical prior method for processing data to determine if it is
statistically linear is with a
linear least squares (LSQ) fit. The correlation value of the LSQ fit can be
used to determine whether
there is an adequate fit. By standard convention, a correlation value of 0 is
related to a bad fit, thus
the data is not linear, and a value of 1 suggests a good fit for linearity.
The problem is that in the
presence of noise, the correlation value can be close to 0 or 1 for data that
looks statistically linear.
Additionally, the correlation value does not correspond to a physical value
that may provide
additional insight and efficacy. Thus, the correlation value is not an
acceptable criterion,
particularly for data that can be extremely noisy.
[0005] Therefore it is desirable to provide systems and methods for processing
a data set having
noise, and for identifying whether the dataset is statistically linear, that
overcome the above and
other problems.
1
CA 02603389 2011-05-10
BRIEF SUMMARY OF THE INVENTION
[0006] Accordingly, embodiments of the present invention provide methods and
systems directed to
processing data to determine whether the data exhibits statistically linear
behavior. Statistically
linear data means that the data generally does not curve downward or upward or
otherwise display
amplification. Such data typically appears to be roughly linear with a large
noise signal superposed
upon it. The data may be received from real-time PCR processes or other
processes exhibiting
amplification or growth.
[0007] According to one exemplary embodiment of the present invention, a
method of processing
data is provided. The method typically includes receiving an original set of
data points having a
signal component and a noise component. The original data set is fit to a
linear function. In one
aspect, the fit is accomplished by calculating a linear least squares fit to
the data set. The method
also includes calculating a residual between the original data set and the
linear fit, and calculating a
measure of the residual between the original data set and the linear fit. In
one aspect, the measure is
a standard deviation.
[0008] The method also typically includes estimating the noise component
present in the data set by
calculating a smoothed data set and calculating the residual between the
smoothed data set and the
original data set. A smoothed data point is based on values of original data
points that are local to
that smoothed data point. In one aspect, a low pass filter is used to
calculate the smoothed data set.
Exemplary low pass filters include a Savitzy-Golay filter, a digital filter,
or digital smoothing
polynomial filter. In another aspect, a value of a smoothed data point is an
average of original data
points within a window around the smoothed data point.
[009] The method also typically includes calculating a measure of the residual
of the estimated
noise, and comparing the measures to determine whether the original data set
exhibits statistically
linear behavior. The comparing may include calculating a ratio of the first
and second measure to
determine if the ratio is smaller or greater than a pre defined value. In one
aspect, the pre-defined
value is of order 1.
[0010] In preferred aspects, the method is implemented in a processor, such as
a processor in a
stand-alone computer, a network attached computer or a data acquisition device
such as a real-time
PCR machine. One example of a real-time PCR machine is the iCycler iQ System
provided by Bio-
Rad Laboratories.
2
CA 02603389 2011-12-06
[0011] According to another exemplary embodiment of the present invention, an
information storage medium having a plurality of instructions adapted to
direct an information
processing device to perform an operation of processing data to determine
whether the curve
exhibits linear behavior is provided. In one aspect, the information storage
medium is a RAM or
ROM unit, hard drive, CD, DVD or other portable medium.
[0012] According to another exemplary embodiment of the present invention, a
PCR
detection system is provided. The PCR detection system includes a detector for
producing an
original set of data points having a signal component and a noise component
and includes logic for
processing data to determine whether the data exhibits linear behavior.
[0013] In accordance with another exemplary embodiment, a method of processing
a data
set to determine whether the data set exhibits statistically linear behavior
includes receiving an
original set of data points having a signal component and a noise component.
Each data point
represents a physical quantity of a substance during an amplification process.
The method further
includes fitting the original data set to a linear function, calculating a
residual between the original
data set and the fitted linear function, and calculating a first measure of
the residual between the
original data set and the fitted linear function. The method further includes
estimating the noise
component present in the original data set, by calculating a smoothed data set
by determining a set
of smoothed data points wherein a value of a smoothed data point is based on
values of a plurality
of original data points that are local to that smoothed data point, and by
calculating a residual
between the smoothed data set and the original data set. The method further
includes calculating a
second measure of the residual between the smoothed data set and the original
data set, and
comparing the first measure to the second measure to determine whether the
original data set
exhibits statistically linear behavior. The method is implemented using a
processor.
[0013a] In accordance with another illustrative embodiment, a computer-
readable
information storage medium stores a plurality of instructions adapted to
direct an information
processing device to perform an operation of processing data to determine
whether the data exhibits
linear behavior. The operation includes receiving an original set of data
points having a signal
component and a noise component. Each data point represents a physical
quantity of a substance
during an amplification process. The operation further includes fitting the
original data set to a
linear function, calculating a residual between the original data set and the
fitted linear function, and
calculating a first measure
3
CA 02603389 2011-05-10
of the residual between the original data set and the fitted linear function.
The operation further
includes estimating the noise component present in the original data set, by
calculating a smoothed
data set by determining a set of smoothed data points wherein a value of a
smoothed data point is
based on values of a plurality of original data points that are local to that
smoothed data point, and
by calculating a residual between the smoothed data set and the original data
set. The operation
further includes calculating a second measure of the residual between the
smoothed data set and the
original data set, and comparing the first measure to the second measure to
determine whether the
original data set exhibits statistically linear behavior.
[0013b] In accordance with another illustrative embodiment, a polymerase chain
reaction
(PCR) detection system includes a detector for producing an original set of
data points having a
signal component and a noise component, wherein the data represents a PCR
amplification curve.
The system further includes means for processing data to determine whether the
data exhibits linear
behavior, by fitting the original data set to a linear function, calculating a
residual between the
original data set and the fitted linear function, calculating a first measure
of the residual between the
original data set and the fitted linear function, and estimating the noise
component present in the
original data set. Estimating the noise component includes calculating a
smoothed data set by
determining a set of smoothed data points, wherein a value of a smoothed data
point is based on
values of a plurality of original data points that are local to that smoothed
data point, and calculating
a residual between the smoothed data set and the original data set.
Determining further includes
calculating a second measure of the residual between the smoothed data set and
the original data set,
and comparing the first measure to the second measure to determine whether the
original data set
exhibits statistically linear behavior.
[0014] Reference to the remaining portions of the specification, including the
drawings and claims,
will realize other features and advantages of embodiments of the present
invention. Further features
and advantages of embodiments of the present invention, as well as the
structure and operation of
various embodiments are described in detail below with respect to the
accompanying drawings. In
the drawings, like reference numbers indicate identical or functionally
similar elements.
3A
CA 02603389 2007-09-28
WO 2006/124673 PCT/US2006/018549
BRIEF DESCRIPTION OF THE DRAWINGS
[0015] Figure 1 illustrates an example of a PCR amplification curve.
[0016] Figure 2 illustrates a real-time PCR data set exhibiting noise and
statistically linear
behavior.
[0017] Figure 3 illustrates a real-time PCR data set exhibiting noise and
amplification.
[0018] Figure 4 illustrates a method of processing a data set to determine
whether the data
set exhibits statistically linear behavior according to an embodiment of the
present invention.
[0019] Figure 5A illustrates a linear fit to a data set exhibiting
statistically linear behavior.
[0020] Figure 5B illustrates a linear fit to a data set exhibiting amplifying
behavior.
[0021] Figure 6A illustrates a smoothed data set of real-time PCR data
according to an
embodiment of the present invention.
[0022] Figure 6B illustrates an estimated noise of real-time PCR data
according to an
embodiment of the present invention.
[0023] Figure 7 illustrates a system that processes real-time PCR data
according to an
embodiment of the present invention.
DETAILED DESCRIPTION OF THE INVENTION
[0024] The present invention provides techniques for processing a data set and
identifying
whether the data set is statistically linear, as well as distinguishing such a
linear data set from
a data set containing an amplification signal. In preferred aspects, the
present invention is
particularly useful for processing data from PCR growth or amplification
processes to
identify and remove statistically linear data prior to further analysis of the
data. It should be
appreciated, however, that the teachings of the present invention are
applicable to processing
any data set or curve that may include noise, and particularly curves that
should otherwise
exhibit growth or amplification such as a bacterial growth process.
[0025] Figure 1 shows an example of a PCR curve 100, where intensity values
110 vs.
cycle number 120 are plotted for a typical PCR process. The values 110 may be
any physical
quantity of interest, and the cycle number may be any unit associated with
time or number of
4
CA 02603389 2007-09-28
WO 2006/124673 PCT/US2006/018549
steps in the process. Such amplification curves typically have a linear region
130 followed
by an amplification region 140 and then by an asymptotic region 150, as shown
in FIG. 1.
There also might be additional types of behavior such as downward curving
data. An
amplification region may have exponential, sigmoidal, high order polynomial,
or other type
of logistic function or logistic curve that models growth.
[0026] To understand the experimental process involved, it is important to
identify the
position and shape of amplification region 140. For example, in a PCR process,
it may be
desirable to identify the onset of amplification, which occurs at the end of
the baseline region
(linear region 130). A step in identifying the location is to identify if a
possible amplification
region even exists, as a PCR process may not show any amplification. However,
since real-
time PCR data has noise, the identification of whether the data set might
exhibit
amplification, or equivalently that it is not statistically linear, can be
difficult.
[0027] For example, Figure 2 illustrates a linear region 230 of a real-time
PCR curve 200
made from a data set with data points 240 that include a signal and noise.
Note that even for
devices that produce a constant signal, this data must be broken into data
points for analysis.
The noise causes the fluctuations in the data points. Overall, the data is
generally moving
upward (i.e. positive slope) in a linear fashion. However, as curve 200 is
very non-linear
from point to point, the generally linear behavior cannot be determined by
directly analyzing
curve 200 at any one point along the curve. A direct analysis of curve 200
would falsely
determine that the data does not exhibit statistically linear behavior.
Embodiments of the
present invention effectively determine whether data exhibits statistically
linear behavior.
[0028] Additionally, it is important to differentiate data curves having
linear behavior and
data curves having amplifying behavior. Figure 3 illustrates a real-time PCR
curve 300 that
exhibits amplification. Initially, the data exhibits linear behavior in region
330 and in later
cycles there is amplification in region 340. Embodiments of the present
invention robustly
and with. consistent accuracy differentiate between PCR curve 200 having only
linear
behavior and PCR curves possibly having an amplifying region, such as PCR
curve 300.
[0029] Figure 4 illustrates a method 400 of processing data to determine
whether the data
exhibits statistically linear behavior according to an embodiment of the
present invention.
The data set is composed of data points and represents a curve having a signal
component and
a noise component.
5
CA 02603389 2007-09-28
WO 2006/124673 PCT/US2006/018549
[0030] In step 405, the data set is first collected or received. The data set
may be received
through many mechanisms. For example, the data set may be acquired by a
processor
(executing instructions) resident in a PCR data acquiring device such as an
iCycler iQ device
or similar PCR analysis device. The data set may be provided to the processor
in real time as
the data is being collected, or it may be stored in a memory unit or buffer
and provided to the
processor after the experiment has been completed. Similarly, the data set may
be provided
to a separate system such as a desktop computer system via a network
connection (e.g., LAN,
VPN, intranet, Internet, etc.) or direct connection (e.g., USB or other direct
wired or wireless
connection) to the acquiring device, or provided on a portable medium such as
a CD, DVD,
floppy disk or the like to a stand-alone computer system. After the data set
has been received
or acquired, the data may be analyzed.
[0031] In step 410, a linear fit to the data set is calculated. Typically, a
fit defines a merit
function S that measures the agreement or difference between the data set and
the fit, where
small values of the merit function typically represent better parameters for
the fit. For
example, in a linear least squares fit, the merit function is the squares of
the difference
between the data values Y and the fit function f (xi), where for N data
N
points S = (Y; - f (Xi)) 2. In a PCR process, Y is the data intensity and x is
the cycle
number. Figure 5A shows a linear fit 510 of the PCR curve 200. Figure 5B shows
a linear fit
550 of PCR curve 300.
[00321 Merit functions may include different weight contributions or
normalization factors
to the merit function for different data points. Merit functions may also
scale data point
values or take a function of data points before a difference is taken. The
difference may be
taken between the data at one x value and f (x) at a different x value. For
example, a term in
the merit function may represent the length of a line from data curve to the
linear fit, such
that the line is perpendicular to the linear fit. This occurs at a difference
cycle number unless
the linear fit has a slope of 0. One skilled in the art will recognize the
many different merit
functions that could be used.
[0033] In step 415, a residual R between the data and the linear fit is
calculated. The
residual R is a set of values corresponding to an error in the data points
from the linear fit.
For example, the residual may be the difference in the linear fit value and
the actual data
point for each cycle number, giving R. = Y; - f (xi), which is a standard form
of the residual.
6
CA 02603389 2007-09-28
WO 2006/124673 PCT/US2006/018549
In some embodiments, the residual is related to the values used to determine
the merit
function of the linear fit. In other embodiments, the residual is a different
value. In Figure
5A, errors 520 are used to calculate values of the residual R between curve
200 and linear fit
510. In Figure 5B, errors 560 are used to calculate values of the residual R
between curve
300 and linear fit 550.
[0034] In step 420, a measure cs, of the residual between the data and the
linear fit is
calculated. The measure is a single value made from the set of values that are
the residual.
N
In one embodiment, the residual is a standard deviation, giving o'1 = 1 ~R? .
Some
N i_1
embodiments may have a weighting value for each value of the residual, and
other
embodiments may subject each residual value or all residual values to
additional or other
functions. One skilled in the art will recognize the many different measures
that could be
used.
[0035] In step 425, an estimated noise component present in the data set is
calculated. The
data is presumed to consist of two components, a true signal and noise. Thus,
the noise is the
difference between the true signal and the actual data point. However, the
true signal can
never be directly measured as noise is always added or present when a signal
is detected.
[0036] The true signal is estimated as a smoothed data set composed of
smoothed data
points. Figure 6A shows a smoothed data set 670 of PCR curve 300. A value of a
smoothed
data point is based on a function G of a plurality of original data points
that are local to that
smoothed data point. The term local relates to how far away the x value of the
data points are
from the data point being calculated. For example, a point may be local to
another point if
they differ by a preset number (window) of cycles. A window of three and five
cycles has
proved adequate, but other windows may be used, such as 10 or 20 cycles or
more. A
variable window value may also be used, i.e. each smoothed data point may be
calculated
with a different window. Additionally, a window having fractions of a cycle
may be used,
for example where fractional data points are interpolated. A window may also
not be
symmetric around a data point, i.e. one point before and three points after
that data point may
be used. A point ceases to be local once the difference in the x value
approaches the total
scale used, i.e. total number of cycles.
[0037] In one embodiment, the function G is a moving average or low pass
filter. For
example, the function G may take an average of the original data points within
a prescribed
7
CA 02603389 2007-09-28
WO 2006/124673 PCT/US2006/018549
L+K
number of cycles, e.g. a centered mean. Thus in one embodiment, G(xL) = 1 IY2
2K + 1;_L-K
where L is the index of the smoothed data point being calculated and K is the
window used.
[0038] Also, in step 425, a residual between the smoothed data and the
original data is
calculated. This residual is defined to be the estimated noise. The residual
between the
smoothed data and the original data may be defined in the same manner as the
residual
between the original data and the linear fit, or the residuals may be defined
in a different
manner. Figure 6B shows an estimated noise component 680 associated with PCR
curve 300
and smoothed data set 670. A superposition of noise component 680 on signal
670 gives the
data curve 300.
[0039] In step 430, a measure 62 of the residual between the smoothed data and
the original
data is calculated. The 62 value is used as a measure of the amplitude of
intrinsic noise. In
one embodiment 62 is a standard deviation. The measures 61 and G2 may be
defined in a
similar or different fashion.
[0040] In step 435, the first measure 61 is compared to the second measure 62
to determine
whether the data set exhibits linear behavior. In one embodiment, a ratio of
61 and 62 is
taken. If the ratio is smaller or greater than a pre-defined value then the
data is determined to
exhibit linear behavior. For example, if 61/62 is less than a value of order
one, e.g. 1.5, the
data is determined to be linear. Equivalently, the expression 61< co* 62 may
be used. This
expression states that the measure of the difference between the data and a
linear fit must be
less than a constant times the measure of the estimated noise present in the
data. In some
embodiments, the value of co may vary.
[0041] The constant co is related to the fact that the definition of noise, as
well as other
values, is not unique. The value for co may be obtained by examining large
numbers of data
sets to obtain a reasonable value for this number. Studies have indicated a
value of 1.5 works
well for the constant (co), when a standard deviation of a standard residual
is used. When
other residuals and measures of the residual are used, other values might be
more suitable. In
general, a value of co on the order of 1 should work well.
[0042] Once the data has been identified as statistically flat (linear), e.g.
not curving
downward or upward or otherwise displaying amplification, the data may be
discarded from
further analysis.
8
CA 02603389 2007-09-28
WO 2006/124673 PCT/US2006/018549
[0043] In certain aspects, code and instructions for controlling a processor
to implement the
data processing techniques of the present invention are stored on a computer-
readable or
information storage medium such as a RAM or ROM unit, hard drive, CD, DVD or
other
portable medium.
[0065] Figure 7 illustrates a system 700 according to one embodiment of the
present
invention. The system as shown includes a sample 705, such as bacteria or DNA,
within a
sample holder 710. A physical characteristic 715, such as a fluorescence
intensity value,
from the sample is detected by detector 720. A signal 725, including a noise
component, is
sent from detector 720 to logic system 730. The data from signal 725 may be
stored in a
local memory 735 or an external memory 740 or storage device 745. In one
embodiment, an
analog to digital converter converts an analog signal to digital form.
[0066] Logic system 730 may be, or may include, a computer system, ASIC,
microprocessor, etc. It may also include or be coupled with a display (e.g.,
monitor, LED
display, etc.) and a user input device (e.g., mouse, keyboard, buttons, etc.).
Logic system 730
and the other components may be part of a stand alone or network connected
computer
system, or they may be directly attached to or incorporated in a thermal
cycler device. Logic
system 730 may also include optimization software that executes in a processor
750.
[0067] According to one embodiment, logic system 730 includes instructions for
processing data and identifying statistically flat data. The instructions are
preferably
downloaded and stored in a memory modules 735, 740, or 745 (e.g., hard drive
or other
memory such as a local or attached RAM or ROM), although the instructions can
be provided
on any software storage medium such as a floppy disk, CD, DVD, etc. It should
be
understood that computer code for implementing aspects of the present
invention can be
implemented in a variety of coding languages such as C, C++, Java, Visual
Basic, and others,
or any scripting language, such as VBScript, JavaScript, Perl or markup
languages such as
XML. In addition, a variety of languages and protocols can be used in the
external and
internal storage and transmission of data and commands according to aspects of
the present
invention.
[0044] It will be appreciated that the process described herein is
illustrative and that
variations and modifications are possible. Steps described as sequential may
be executed in
parallel, order of steps may be varied, and steps may be modified or combined.
9
CA 02603389 2007-09-28
WO 2006/124673 PCT/US2006/018549
[0045] While the invention has been described by way of example and in terms
of the
specific embodiments, it is to be understood that the invention is not limited
to the disclosed
embodiments. To the contrary, it is intended to cover various modifications
and similar
arrangements as would be apparent to those skilled in the art. Therefore, the
scope of the
appended claims should be accorded the broadest interpretation so as to
encompass all such
modifications and similar arrangements.
