Probabilistic approach to confidence intervals of linear calibration

Hayashi, Yuzuru; Matsuda, Rieko; Poe, Russell B.

doi:10.1039/an9962100591

Cited by 26 publications

(44 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(1) has wide applicability. Examples are LOD, 21,24,26,28 confidence intervals of linear calibration 28 and tests of significant differences. 3,4,6 Theoretical SD descriptions elaborated so far include Winefordner's theory, [18][19][20] Ingle's theory, [15][16][17] Bouman's theory 21,22 and FUMI theory (FUnction of Mutual Information).…”

Section: Introductionmentioning

confidence: 99%

Test of Significant Differences with a priori Probability in Microarray Experiments

et al. 2003

Self Cite

View full text Add to dashboard Cite

The advent of high-throughput array technology has now made it possible to collect data on thousands to tens of thousands of genes simultaneously. However, methods for detecting the genuine changes in the gene expression levels in cells or tissues are still evolving. [1][2][3][4][5][6][7][8][9][10][11] A straightforward method for comparing two expression levels of genes is the traditional two-sample t-test. The basic problem with the t-test in microarray experiments, however, is that the repetition is restricted within a small number in most cases, because experiments are costly or tedious to repeat. Although the importance in replication has been illustrated, 1,3,6,9 situations often arise where only single or duplicate experiments for each condition are allowed.The purpose of this paper is to put forward a method for testing the significant differences of the gene expression levels under a single pair of experiments (a control experiment and treatment experiment). In order to take into account the stochastic aspects of gene expressions, we model our algorithm on the t-test. In our approach and the t-test, the SD estimates of the gene expression levels are a criterion for the statistical judgment, but one of the key differences is how to estimate the SD for each gene.In the t-test, the SD estimates are derived from the same data set as those to be judged by the t-test, itself. This fact can be closely connected with the above-mentioned problem of replication. In our approach, the SD estimates, referred to here as a priori SD, are obtained from experimental results which are different from the target data set of the judgment.Statistics tells that the variability in the estimates of SD obeys the chi-squares distribution and is much larger than the variability in the estimates of averages, as long as the estimates are obtained by repetition. That is, the estimates of averages are more reliable. The t-test uses the SD estimates directly, but in this paper, the a prior SD is given as a function of the average of the gene expression levels. Then, we can easily expect that our approach can provide more stable judgment, but needs a sound model for the a prior SD.The idea of the a priori SD is not novel in the area of analytical chemistry. Since more than three decades ago, there have been published many theories and methods for estimating SD with no recourse to repetition, especially in instrumental analyses. [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] In spite of varied symbols and terminology in the literature, the largest part of uncertainty equations proposed can take a universal form:where RSD denotes the relative standard deviation of measurements, sB denotes blank SD, A measurements (e.g., area), and I independent error. To our knowledge, Huber et al. A traditional method for comparing two expression levels of genes in microarray experiments is the two-sample t-test. Because of the difficulty in using a large number of microarrays, an alternative method is required which can provide a relia...

show abstract

Section: Introductionmentioning

confidence: 99%

Test of Significant Differences with a priori Probability in Microarray Experiments

et al. 2003

Self Cite

View full text Add to dashboard Cite

show abstract

“…However, the reliability of the measurement RSD (n = 1) by ISO 11843-7 is statistically equal to that of the measurement RSD from repetitive measurements (n = 40). 18 The present assessment repeatability method using ISO 11843-7 is also useful to examine the allowable limit test of the "System repeatability" in "Liquid Chromatography" by saving not only considerable chemical amounts, but also the experimental time.…”

Section: Discussionmentioning

confidence: 99%

“…On the other hand, an experiment to examine the repeatability was finished in 70 min with chromatographic measurement (n = 1) using ISO 11843-7. Since the confidence interval of the RSD by ISO 11843-7 was ±20%, which is equal to the SD error from repetitive measurements (n = 40), 18 an RSD by ISO 11843-7 is more reliable than that of repetitive measurements (n = 6). Furthermore, it shows that in this study the experimental time to estimate the repeatability was remarkably reduced by the application of ISO 11843-7.…”

Section: Estimation Of Repeatability In Quantitative Lc-3ecd By Iso 1mentioning

confidence: 96%

“…Also, the measurement RSD of stochastic ways by ISO 11843-7 had 95% confidence intervals corresponding to those for about 40 measurements (±20% of the true RSD). 18 Although ISO 11843-7 has been recently applied to examine the detection limits and predict measurement precision in HPLC-ECD for synthetic drugs, 19 the other application of ISO 11843-7 has hardly been reported to obtain an allowable limit of the "System repeatability" in quantitative HPLC-UV for herbal medicines, and to estimate the repeatability in LC with multi-channel detections, such as LC-3ECD. If ISO 11843-7 is applied to estimate the measurement precision in quantitative HPLC-UV and LC-3ECD of herbal medicines, the number of chromatographic measurements would be one without reducing the reliability of the measurement RSD.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Repeatability Assessment by ISO 11843-7 in Quantitative HPLC for Herbal Medicines

et al. 2015

Self Cite

View full text Add to dashboard Cite

We have proposed an assessment methods to estimate the measurement relative standard deviation (RSD) of chromatographic peaks in quantitative HPLC for herbal medicines by the methodology of ISO 11843 Part 7 (ISO 11843-7:2012), which provides detection limits stochastically. In quantitative HPLC with UV detection (HPLC-UV) of Scutellaria Radix for the determination of baicalin, the measurement RSD of baicalin by ISO 11843-7:2012 stochastically was within a 95% confidence interval of the statistically obtained RSD by repetitive measurements (n = 6). Thus, our findings show that it is applicable for estimating of the repeatability of HPLC-UV for determining baicalin without repeated measurements. In addition, the allowable limit of the "System repeatability" in "Liquid Chromatography" regulated in a pharmacopoeia can be obtained by the present assessment method. Moreover, the present assessment method was also successfully applied to estimate the measurement RSDs of quantitative three-channel liquid chromatography with electrochemical detection (LC-3ECD) of Chrysanthemi Flos for determining caffeoylquinic acids and flavonoids. By the present repeatability assessment method, reliable measurement RSD was obtained stochastically, and the experimental time was remarkably reduced.

show abstract

“…confidence intervals of calibration lines 23 and standard addition method. 24 As is well-known, refractive index detectors are useful for detecting materials possessing no absorbance in liquid chromatography (LC), but are susceptible to the flow pulsation of pumps.…”

mentioning

confidence: 99%

Prediction of Measurement Precision by Chemometric Invalidation of Flow Pulsation in Refractive Index Detection of Liquid Chromatography

et al. 1999

Self Cite

View full text Add to dashboard Cite

Probabilistic approach to confidence intervals of linear calibration

Cited by 26 publications

References 39 publications

Test of Significant Differences with a priori Probability in Microarray Experiments

Test of Significant Differences with a priori Probability in Microarray Experiments

Repeatability Assessment by ISO 11843-7 in Quantitative HPLC for Herbal Medicines

Prediction of Measurement Precision by Chemometric Invalidation of Flow Pulsation in Refractive Index Detection of Liquid Chromatography

Contact Info

Product

Resources

About