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Methods for Lowering the Type I Error (a), the Group Sequential Method with Adaptive Designs

So far decisions were limited to stopping or continuing a trial. Other decisions may be useful as well, e.g., change in sample size, in primary outcome parameter, in population, in treatments, in allocation rules. As long as blinding is maintained, many changes are allowed (using protocol-amendments), either without spending alphas or with, although such amendments may impact the power of the trial. We are talking of adaptive designs, if data are unblinded for the purpose. This subject is also discussed and reviewed in the Chap. 3. It should always be in the protocol, and never applied on an ad-hoc basis. Examples of adaptive designs are the

- seamless phase II/phase III trials.

They are combined-phase studies, that, instead of a single phase II and a single phase III study, consist of both of them with an interim analysis in between. For statistical analysis separate p-values are combined, using some sort of combination test, e.g., Fisher’s combination test which look a bit like a chi-square test 2k degrees of freedom (Fisher, Statistical methods for research workers, Oliver & Boyd, Edinburgh UK, 1932):

where X² has two degrees of freedom, and p_i is the p-value for the ith hypothesis test.

The above trial recently published by the Ceftriaxone Study Investigators (Cudkowicz et al., Lancet Neurol 2014; 13: 1083-91) is an example of a seamless phase II/phase III trial. A Fisher’s combination test was performed, and the combined analysis was, virtually, statistically significant with a p-value of 0.055, while one of the separate phase studies was not statistically significant:

- phase II: p-value=0.0416
- phase III: p-value=0.2370
- X² = -2*(log (0.0416) + log (0.2370)) = 9.2387, where * is sign of multiplication with degrees of freedom 2 k=2*2=4, the combined p-value=0.0554.

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Methods for Lowering the Type I Error (a), the Group Sequential Method with a-Spending Function Approach
The alpha spending function approach does not, necessarily, use the same significance level at each analysis. As an example, O’Brien & Fleming in the GroupSeq program of the R statistical software package can be used here. It calculates maximal sample sizes for various settings, such that the overall...
(Understanding Clinical Data Analysis: Learning Statistical Principles from Published Clinical Research)
Methods for Lowering the Type I Error (a), the Armitage/Pocock Group Sequential Method
Interim analyses can be classified as follows: (1) group sequential design • Armitage et al/Pocock method for lowering the type I error • alpha spending function method for lowering the type I error (2) continuous sequential design. We will, first, addres the Armitage/Pocock group sequential method...
(Understanding Clinical Data Analysis: Learning Statistical Principles from Published Clinical Research)
Type I and type II errors
Whenever working with statistical tests there is a chance that the conclusion from the test could be wrong. We could accept a false null hypothesis and we could reject a correct null hypothesis. Hence, in order for decision rules or tests of hypothesis to be good, they must be designed so as to minimize...
(Econometrics)
Increased Risk of Type I Error
Each look at the data increases the type-I error rate and may introduce bias, particularly, the bias associated with random high outcomes. Suppose, your null hypothesis of no effect is correct, and k analyses will be performed, with a=0.05 for each analysis. Then, the true significance level after...
(Understanding Clinical Data Analysis: Learning Statistical Principles from Published Clinical Research)
Type III Error
The extant literature on the Type III (y) error originated in statistics. Frederick Mosteller [1916-2006], one of the most eminent statisticians of the twentieth century, reported: In other words it is possible for the null hypothesis to be false. It is also possible to reject the null hypothesis because...
(Systemic Decision Making: Fundamentals for Addressing Problems and Messes)
Type IV Error
A review of the extant literature on Type IV (8) errors shows that this type of error has been discussed principally in the psychology and the educational sciences. To the authors’ knowledge, the first mention of the Type IV error in the literature was by Marascuilo and Levin (1970). They define the...
(Systemic Decision Making: Fundamentals for Addressing Problems and Messes)
Type V Error
The Type V Error, like the Type IV Error, concerns actions taken in support of problem resolution. The field of cybernetics and the systems principles of homeostasis (Cannon, 1929) and homeorhesis (Waddington, 1957) inform individuals that systems have the ability to self-regulate to maintain...
(Systemic Decision Making: Fundamentals for Addressing Problems and Messes)
Type VIII Error
The Type VIII error refers to the phenomena where the correctly decided action has been incorrectly implemented. While it is coined in this text by the authors, it has its roots in the study of human error by psychologist and human factors researcher James Reason. In his seminal text on the subject,...
(Systemic Decision Making: Fundamentals for Addressing Problems and Messes)
Type I and Type II Errors
The extant literature on the Type I and Type II errors is founded in the mathematics (i.e., statistics) field of science, originating with Neyman and Pearson (1928a, b, 1933). The Type I and Type II errors have been explored extensively in the literature associated with these fields. They are driven...
(Systemic Decision Making: Fundamentals for Addressing Problems and Messes)