Data processing: measuring – calibrating – or testing – Measurement system in a specific environment – Biological or biochemical
Reexamination Certificate
2000-10-20
2003-05-20
Brusca, John S. (Department: 1631)
Data processing: measuring, calibrating, or testing
Measurement system in a specific environment
Biological or biochemical
C435S006120
Reexamination Certificate
active
06567750
ABSTRACT:
FIELD OF THE INVENTION
The present invention relates to a process for making evaluations which objectify analyses of data obtained from hybridization arrays. The present invention is in one aspect a method for making inferences as to the extent of random error present in replicate genomic samples composed of small numbers of data points, and in another aspect is a method for distinguishing among different classes of probe intensities (e.g., signal versus nonsignal).
BACKGROUND OF THE INVENTION
Array-based genetic analyses start with a large library of cDNAs or oligonucleotides (probes), immobilized on a substrate. The probes are hybridized with a single labeled sequence, or a labeled complex mixture derived from a tissue or cell line messenger RNA (target). As used herein, the term “probe”, will therefore be understood to refer to material tethered to the array, and the term “target” will refer to material that is applied to the probes on the array, so that hybridization may occur.
There are two kinds of measurement error, random and systematic. Random error can be detected by repeated measurements of the same process or attribute and is handled by statistical procedures. Low random error corresponds to high precision. Systematic error (offset or bias) cannot be detected by repeated measurements. Low systematic error corresponds to high accuracy.
Background correction involves subtracting from the probe the intensity of an area outside of that probe. Areas used for calculation of background can be close to the probe (e.g. a circle lying around the probe), or distant. For example, “blank” elements can be created (i.e., elements without probe material), and the value of these elements can be used for background estimation.
Normalization procedures involve dividing the probe by the intensity of some reference. Most commonly, this reference is taken from a set of probes, or from the mean of all probes.
Once systematic error has been removed by background removal and normalization procedures (or others, as required), any remaining measurement error is, in theory, random. Random error reflects the expected statistical variation in a measured value. A measured value may consist, for example, of a single value, a summary of values (mean, median), a difference between single or summary values, or a difference between differences. In order for two values to be considered reliably different from each other, their difference must exceed a threshold defined jointly by the measurement error associated with the difference and by a specified probability of concluding erroneously that the two values differ (Type I error rate).
Of primary interest are differences between two or more quantified values, typically across different conditions (e.g., diseased versus non-diseased cell lines, drug versus no drug). The desired estimate of expected random error ideally should be obtained from variation displayed by replicate values of the same quantity. This is the way that such estimates are normally used in other areas of science. Hybridization studies, however, tend to use a very small number of replicates (e.g., two or three). Estimates of random error based on such small samples are themselves very variable, making comparisons between conditions using standard statistical tests imprecise and impractical for all but very large differences.
This difficulty has been recognized by Bassett, Eisen, & Boguski in, “Gene expression informatics: It's all in your mine”,
Nature Genetics,
21, 51-55 (1999), who have argued that the most challenging aspects of presenting gene expression data involve the quantification and qualification of expression values and that qualification would include standard statistical significance tests and confidence intervals. They argued further that “ideally, it will be economically feasible to repeat an experiment a sufficient number of times so that the variance associated with each transcript level can be given” (p. 54). The phrase “sufficient number of times” in the preceding quote highlights the problem. The current state-of-the-art in array-based studies precludes obtaining standard statistical indices (e.g., confidence intervals, outlier delineation) and performing standard statistical tests (e.g., t-tests, analyses-of-variance) that are used routinely in other scientific domains, because the number of replicates typically present in studies would ordinarily be considered insufficient for these purposes. A key novelty in the present invention is the circumvention of this difficulty.
Statistical indices and tests are required so that estimates can be made about the reliability of observed differences between probe/target interactions across different conditions. The key question in these kinds of comparisons is whether it is likely that observed differences in measured values reflect random error only or random error combined with treatment effect (i.e., “true difference”)? In the absence of formal statistical procedures for deciding between these alternatives, informal procedures have evolved in prior art. These procedures can be summarized as follows:
1. Arbitrary Thresholds
Observed differences across conditions differ by an arbitrary threshold. For example, differences greater than 2- or 3-fold are judged to reflect “true” differences.
2. Thresholds Established Relative to a Subset of Array Elements
A subset of “reference” genes is used as a comparison point for ratios of interest. For example, relative to the reference gene, a gene may show a 2:1 expression ratio when measured at time 1, a 2.8:1 ratio when measured at time 2, and so on.
3. Thresholds Established Based on Observed Variation in Background
The standard deviation of background values is used as a proxy for the measurement error standard deviation associated with probe values of interest. If a probe intensity exceeds the background standard deviation by a specified number (e.g., 2.5), the probe is considered “significant.” None of the above approaches is optimal, because each relies on a relatively small number of observations for deriving inferential rules. Also, assessments of confidence are subjective and cannot be assessed relative to “chance” statistical models. Approaches 1 and 2 are especially vulnerable to this critique. They do not meet standards of statistical inference generally accepted in other fields of science in that formal probability models play no role in the decision-making process. Approach 3 is less subject to this latter critique in that a proxy of measurement error is obtained from background. It is nonetheless not optimal because the measurement error is not obtained directly from the measured values of interest (i.e., the probes) and it is not necessarily the case that the error operating on the background values is of the same magnitude and/or model as the one operating on probe values.
Other informal approaches are possible. For example, the approaches described in 2 above could be modified to estimate the standard deviations of log-transformed measurements of reference genes probed more than once. Because of the equality [log(a)−log(b)=log(a/b)], these proxy estimates of measurement error could then be used to derive confidence intervals for differential ratios of log-transformed probes of interest. This approach would nonetheless be less than optimal because the error would be based on proxy values and on a relatively small number of replicates.
Chen et al. (Chen, Dougherty, & Bittner) in “Ratio-based decisions and the quantitative analysis of cDNA microarray images”,
Journal of Biomedical Optics,
2, 364-374 (1997) have presented an analytical mathematical approach that estimates the distribution of non-replicated differential ratios under the null hypothesis. Like the present invention, this procedure derives a method for obtaining confidence intervals and probability estimates for differences in probe intensities across different conditions. However, it differs from the present invention in how it obtains these estimates. Unlike the prese
Nadon Robert
Ramm Peter
Brusca John S.
Darby & Darby
Imaging Research Inc.
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