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This goal requires to minimize the Type II error of the test jointly for both hypotheses, i.e. maximize the power for both hypotheses.
We assessed the type II error of the likelihood ratio tests using PO as the primary (alternative) hypothesis and U, HS or FS as null hypotheses.
Briefly, we simulated alternative scenarios of allele frequencies and pairs of individuals of the relationship we sought to test, and assessed the type II error of the likelihood ratio tests.
This means that there may still be some misclassification during data collection, which may result in a bias towards the null hypothesis (Type II error) of the intervention study.
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With the bibliometric data of the applicants subsequent to application we were able to calculate the extent of over- and under-estimation (type 1 and type II errors) of the future success of the applicants.
Traditionally, phase 2 PoC trials are designed to have a type I error of 10% and a type II error of 20% (the power is 100% minus the type II error, thus 80% power in this case).
Measurement of type-II error was not preplanned in present study and this is of course a shortcoming of this study because assuming the percent difference of PFO frequency between the tension headache patients and the control group to be 7% (23 16%) with an α = 0.05, the post hoc type-II error of the study would be 0.82.
Using a significance level of 0.05 and a risk of type II error of 0.20, the statistical power of two different designs was compared: a single biopsy design comparing the responses in two groups after the treatment; and a paired biopsy design in which individual differences (posttreatment minus baseline) were calculated before the comparison of the two groups.
Given a type I error of 0.05 and a Type II error of 0.1, the required sample size was 22 patients per group; 25 patients were included in each group to take into account possible dropouts.
Assuming an overall incidence of viral respiratory tract infections of 0.15 for the population over the time of study and a laboratory measurement coefficient of variation of 10% for serum vitamin D called for an enrollment of at least168 participants to achieve a Type I error of 0.05 and a Type II error of 0.2 if the odds ratio between the two groups for an event was ≥0.5 [33].
Finally, we have to note that according to previously published data (Polish-Greek study) a patient number of between 175 280 would be necessary to detect the reported association with a type I error of 0.05 and a type II error of 0.10, thus the present study had enough statistical power to detect the above differences in NOD2/CARD15 polymorphisms if present.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com