- Sequential Methods And Their Applications By Nitis Mukhopadhyay 12222
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- An Overview of Sequential Methods and Their Application in Clinical Trials
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Sequential Methods And Their Applications By Nitis Mukhopadhyay 12222
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Sequential Methods and Their Applications - PDF Free Download
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In statistics , sequential analysis or sequential hypothesis testing is statistical analysis where the sample size is not fixed in advance. Instead data are evaluated as they are collected, and further sampling is stopped in accordance with a pre-defined stopping rule as soon as significant results are observed.
Its value to the war effort was immediately recognised, and led to its receiving a "restricted" classification. Another early contribution to the method was made by K. Arrow with D.
Blackwell and M. A similar approach was independently developed from first principles at about 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 s. Peter Armitage introduced the use of sequential analysis in medical research, especially in the area of clinical trials.
An Overview of Sequential Methods and Their Application in Clinical Trials
Sequential methods became increasingly popular in medicine following Stuart Pocock 's work that provided clear recommendations on how to control Type 1 error rates in sequential designs. When researchers repeatedly analyze data as more observations are added, the probability of a Type 1 error increases.
Therefore, it is important to adjust the alpha level at each interim analysis, such that the overall Type 1 error rate remains at the desired level. This is conceptually similar to using the Bonferroni correction , but because the repeated looks at the data are dependent, more efficient corrections for the alpha level can be used. Among the earliest proposals is the Pocock boundary.
A limitation of corrections such as the Pocock boundary is that the number of looks at the data must be determined before the data is collected, and that the looks at the data should be equally spaced e. 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 are available an interim analysis is conducted. A statistical test is performed to compare the two groups and if the null hypothesis is rejected the trial is terminated; otherwise, the trial continues, another n subjects per group are recruited, and the statistical test is performed again, including all subjects.
If the null is rejected, the trial is terminated, and otherwise it continues with periodic evaluations until a maximum number of interim analyses have been performed, at which point the last statistical test is conducted and the trial is discontinued. Sequential analysis also has a connection to the problem of gambler's ruin that has been studied by, among others, Huygens in 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. 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.
Trials that are terminated early because they reject the null hypothesis typically overestimate the true effect size.