WordNet

an investigation of the component parts of a whole and their relations in making up the whole
the abstract separation of a whole into its constituent parts in order to study the parts and their relations (同)analytic thinking
a branch of mathematics involving calculus and the theory of limits; sequences and series and integration and differentiation
a form of literary criticism in which the structure of a piece of writing is analyzed
the use of closed-class words instead of inflections: e.g., `the father of the bride instead of `the brides father

PrepTutorEJDIC

(内容・状況などの)『分析』,分解;(詳細な)検討 / (化学・物理で)分析;《米》(心理学で)[精神]分析;(数学で)解析
引き続いて起こる,結果として起こる

Wikipedia preview

出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2016/05/16 18:01:11」(JST)

wiki en

[Wiki en表示]

In statistics, sequential analysis or sequential hypothesis testing is statistical analysis where the sample size is not fixed in advance. Instead data is evaluated as it is collected, and further sampling is stopped in accordance with a pre-defined stopping rule as soon as significant results are observed. Thus a conclusion may sometimes be reached at a much earlier stage than would be possible with more classical hypothesis testing or estimation, at consequently lower financial and/or human cost.

History

Sequential analysis was first developed by Abraham Wald^[1] with Jacob Wolfowitz, W. Allen Wallis, and Milton Friedman^[2] while at Columbia University's Statistical Research Group as a tool for more efficient industrial quality control during World War II. Its value to the war effort was immediately recognised, and led to its receiving a "restricted" classification.^[3] Another early contribution to the method was made by K.J. Arrow with D. Blackwell and M.A. Girshick.^[4]

A similar approach was independently developed at the same time by Alan Turing, as part of the Banburismus technique used at Bletchley Park, to test hypotheses about whether different messages coded by German Enigma machines should be connected and analysed together. This work remained secret until the early 1980s.^[5]

Applications of sequential analysis

Clinical trials

In a randomized trial with two treatment groups, group sequential testing may for example be conducted in the following manner: After n subjects in each group, i.e., a total of 2n subjects, are available, an interim analysis is conducted. That means, a statistical test is performed to compare the two groups, if the null hypothesis is rejected, the trial is terminated. Otherwise, the trial continues. Another n subjects per group are recruited. The statistical test is performed again, now including all 4n subjects. If the null is rejected, the trial is terminated. Otherwise, it continues with periodic evaluations until a maximum number of interim analyses have been performed. At this point, the last statistical test is conducted, and the trial is discontinued.^[6]

Other applications

Sequential analysis also has a connection to the problem of gambler's ruin that has been studied by, among others, Huyghens in 1657.^[7]

Step detection is the process of finding abrupt changes in the mean level of a time series or signal. It is usually considered as a special kind of statistical method known as change point detection. Often, the step is small and the time series is corrupted by some kind of noise, and this makes the problem challenging because the step may be hidden by the noise. Therefore, statistical and/or signal processing algorithms are often required. When the algorithms are run online as the data is coming in, especially with the aim of producing an alert, this is an application of sequential analysis.

Bias

The statistics of a trial that is stopped early at only n samples are different than a similar trial that is run for a predetermined number of trials, even if they end up collecting the same number of samples. If this is not accounted for when interpreting the sequential trial, the results will be biased. Therefore, it is important that proper methodology is followed in order to avoid false conclusions. See ^[8] for a discussion.

Notes

^ Wald, Abraham (June 1945). "Sequential Tests of Statistical Hypotheses". The Annals of Mathematical Statistics 16 (2): 117–186. doi:10.1214/aoms/1177731118. JSTOR 2235829.
^ Berger, James (2008). "Sequential Analysis". The New Palgrave Dictionary of Economics, 2nd Ed. doi:10.1057/9780230226203.1513.
^ [1]
^ Kenneth J. Arrow, David Blackwell and M.A. Girshick (1949). "Bayes and minimax solutions of sequential decision problems". Econometrica 17 (3/4): 213–244. doi:10.2307/1905525. JSTOR 1905525.
^ Randell, Brian (1980), "The Colossus", A History of Computing in the Twentieth Century (PDF), p. 30, retrieved 22 March 2011
^ Korosteleva, Olga (2008). Clinical Statistics: Introducing Clinical Trials, Survival Analysis, and Longitudinal Data Analysis (First ed.). Jones and Bartlett Publishers. ISBN 0-7637-5850-7.
^ Gosh, B. K.; Sen, P. K. (1991). Handbook of Sequential Analysis. New York: Marcel Dekker. ISBN 9780824784089. ^{[page needed]}
^ [2]

References

Wald, Abraham (1947). Sequential Analysis. New York: John Wiley and Sons.
Bartroff, J., Lai T.L., and Shih, M.-C. (2013) Sequential Experimentation in Clinical Trials: Design and Analysis. Springer.
Ghosh, Bhaskar Kumar (1970). Sequential Tests of Statistical Hypotheses. Reading: Addison-Wesley.
Chernoff, Herman (1972). Sequential Analysis and Optimal Design. SIAM.
Siegmund, David (1985). Sequential Analysis. Springer Series in Statistics. New York: Springer-Verlag. ISBN 0-387-96134-8.
Bakeman, R., Gottman, J.M., (1997) Observing Interaction: An Introduction to Sequential Analysis, Cambridge: Cambridge University Press
Jennison, C. and Turnbull, B.W (2000) Group Sequential Methods With Applications to Clinical Trials. Chapman & Hall/CRC.
Whitehead, J. (1997). The Design and Analysis of Sequential Clinical Trials, 2nd Edition. John Wiley & Sons.

External links

R Package: Wald's Sequential Probability Ratio Test by OnlineMarketr.com
Sequential Analysis: Design Methods & Applications Journal
Course given by Rebecca Betensky at Harvard University, lecture note slides
Software for conducting sequential analysis and applications of sequential analysis in the study of group interaction in computer-mediated communication by Dr. Allan Jeong at Florida State University

Commercial

PASS Sample Size Software includes features for the setup of group sequential designs.

UpToDate Contents

全文を閲覧するには購読必要です。 To read the full text you will need to subscribe.

1. ヘリコバクターピロリ菌の治療レジメン treatment regimens for helicobacter pylori
2. 成人における単極性うつ病：継続療法および維持療法 unipolar depression in adults continuation and maintenance treatment
3. 限局期の小細胞肺癌：初期マネージメント limited stage small cell lung cancer initial management
4. システマティックレビューおよびメタアナリシス systematic review and meta analysis
5. 原発性（本態性）高血圧における薬物療法の選択 choice of drug therapy in primary essential hypertension

English Journal

Programmable strand displacement-based magnetic separation for simultaneous amplified detection of multiplex microRNAs by chemiluminescence imaging array.

Yue S1, Zhao T2, Bi S3, Zhang Z2.
Biosensors & bioelectronics.Biosens Bioelectron.2017 Dec 15;98:234-239. doi: 10.1016/j.bios.2017.06.060. Epub 2017 Jun 28.
PMID 28688309

Developing a new Bayesian Risk Index for risk evaluation of soil contamination.

Albuquerque MTD1, Gerassis S2, Sierra C3, Taboada J2, Martín JE2, Antunes IMHR4, Gallego JR5.
The Science of the total environment.Sci Total Environ.2017 Dec 15;603-604:167-177. doi: 10.1016/j.scitotenv.2017.06.068. Epub 2017 Jun 15.
PMID 28624637

The protective association of endogenous immunoglobulins against sepsis mortality is restricted to patients with moderate organ failure.

Martin-Loeches I1, Muriel-Bombín A2, Ferrer R3,4, Artigas A4,5,6, Sole-Violan J4,7, Lorente L4,8, Andaluz-Ojeda D9, Prina-Mello A10, Herrán-Monge R2, Suberviola B4,11, Rodriguez-Fernandez A12, Merino P2, Loza AM4,13, Garcia-Olivares P4,14, Anton E4,15, Tamayo E16, Trapiello W17, Blanco J2,6, Bermejo-Martin JF18; GRECIA group.
Annals of intensive care.Ann Intensive Care.2017 Dec;7(1):44. doi: 10.1186/s13613-017-0268-3. Epub 2017 Apr 20.
PMID 28429310

Japanese Journal

Real-time observations of lithium battery reactions-operando neutron diffraction analysis during practical operation.

Scientific reports 6, 2016-06-30
NAID 120005774688

Learning Experiences with Active Learning Method Applied during the Early Years of Undergraduate Nursing Students :Through Global Nursing Training Course in the Philippines