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Regression-Based Models
Published in Nusrat Rabbee, Biomarker Analysis in Clinical Trials with R, 2020
Since we assume that the number of comparisons will be small in the context of the number of biomarkers in a typical clinical biomarkers, relative to genomics data where there are hundreds or thousands of biomarkers, we will use FWER (family-wise error rate) to control the type I error rate of 0.05. The Holm–Bonferroni correction takes the original alpha level and divides it by the total number of comparisons subtracted by the rank of the p-value plus one. This is more powerful than Bonferroni, which is equally punitive to each comparison.
Multiplicity
Published in Shein-Chung Chow, Innovative Statistics in Regulatory Science, 2019
Holm’s method is a sequentially rejective procedure, which sequentially contrasts ordered unadjusted p-values with a set of critical values and rejects a null hypothesis if the p-values and each of the smaller p-values are less than their corresponding critical values. Holm’s method not only improves the sensitivity of Bonferroni’s correction method to detect real differences, but also increases in power and provides a strong control of the FWER.
Multiple Comparisons, Multiple Primary Endpoints and Subpopulation Analysis
Published in Susan Halabi, Stefan Michiels, Textbook of Clinical Trials in Oncology, 2019
Ekkehard Glimm, Dong Xi, Paul Gallo
The Holm procedure is a stepwise extension of the Bonferroni test. It applies the Bonferroni test in each step [10]. Assume that the raw p-values are denoted by p1, …, pm, respectively. The procedure first orders the p-values from the smallest to the largest: p(1) ≤ p(2) ≤ · · · ≤ p(m). Then it tests hypothesis H(1) and rejects it if p(1) ≤ α/m. If H(1) is rejected, the procedure tests H(2) and rejects it if p(2) ≤ α/(m − 1); otherwise, testing stops. If H(2) is also rejected, the procedure tests H(3) and rejects it if p(3) ≤ α/(m − 2); otherwise, testing stops. In general, given that H(1), …, H(i) are rejected, the procedure tests H(i+1) and rejects it if p(i+1) ≤ α/(m − i); otherwise, testing stops and no further hypothesis can be rejected. If the procedure proceeds to H(m), it will be tested at level α. It can be shown that the Holm procedure is a closed testing procedure which applies the Bonferroni test to each intersection hypothesis. As a result, the Holm procedure controls the FWER strongly [10].
Risk Model Development and Validation in Clinical Oncology: Lessons Learned
Published in Cancer Investigation, 2023
Gary H. Lyman, Pavlos Msaouel, Nicole M. Kuderer
In highly exploratory settings and large-scale searches, such as genome-wide association studies (GWAS) (32), formal multiplicity adjustment is essential to inform decisions on which of the potential prognostic variables to further purse (30). Multiplicity adjustments have been most commonly associated with the frequentist paradigm in biostatistics to control the overall type I error probability, also known as the familywise error rate (33). The familywise error rate is the probability of making an assertion of a prognostic effect when all such assertions are wrong. Of these methods, the Bonferroni tests can be applied to all multiplicity scenarios but is generally inefficient because it overcorrects thus increasing the risk of mistakenly discounting a meaningful effect (34). Other methods such as the Hochberg (35) and Hommel (36) multiplicity adjustments are considered more efficient than Bonferroni (33,34). Another approach is to focus on the false discovery rate (FDR) which corresponds to the proportion of assertions of a prognostic effect that are falsely made among all assertions of a prognostic effect made (37). This is in contrast to the familywise error probability which controls for the assertion of at least one or more false assertions. Thus, the FDR is less likely to overcorrect than the methods controlling for the familywise error rate, but is more likely to increase the numbers of type I errors (37). FDR approaches are often used in high-dimensional situations, such as GWAS, involving multiple candidate variables (38).
The effects of spinal stabilization exercises in patients with myasthenia gravis: a randomized crossover study
Published in Disability and Rehabilitation, 2022
Ali Naim Ceren, Yeliz Salcı, Ayla Fil Balkan, Ebru Çalık Kütükçü, Kadriye Armutlu, Sevim Erdem Özdamar
Mann-Whitney U Test and Chi-square test were used to compare the clinical and demographic characteristics of the patients. Due to the small sample size, non-parametric tests were used. The washout effect was evaluated with the Wilcoxon Test between the first (pre-first program) and third (pre-second program) evaluations. The data of the groups were combined, as it was seen that there was a washout effect in all data, and new groups were created according to the exercise programs. Wilcoxon Test was used again to evaluate the changes of exercise groups over time. The Mann-Whitney U Test was used to see the difference between exercises. The significance value was accepted as p < .05. In this study, although fatigue was determined as the primary outcome measure, muscle strength, respiratory functions, and functional capacity assessments were also important outcome measures. When examining the effects of an intervention on more than one outcome, false positive significant results can be found. This error probability is named as the familywise error rate (FWER). A multiple correction method is required to control the FWER [29]. In this study, the Bonferroni correction was used for controlling the FWER. The significance level (α) was split as the number of important outcome measures (k) and each outcome measure was tested at level α/k (.05/4) =0.0125. Statistical analyses were performed using IBM SPSS 20.0 for Mac software (SPSS Inc., Chicago, IL, USA).
The Implications of Self-Definitions of Child Sexual Abuse for Understanding Socioemotional Adaptation in Young Adulthood
Published in Journal of Child Sexual Abuse, 2021
Linnea B. Linde-Krieger, Cynthia M. Moon, Tuppett M. Yates
Planned contrast p-values were adjusted to control for the false discovery rate (FDR), which is the expected proportion of type I errors. The FDR approach is an alternative to family-wise error rate corrections, such as the Bonferroni correction. The FDR controls for the expected proportion of false positives, rather than guarding against making any false-positive conclusions, which allows for both increased statistical power and fewer type I errors (Benjamini & Hochberg, 1995). Following contrast analyses, effect sizes and confidence intervals quantified the magnitude of mean differences between the concordant CSA and nonmaltreated groups, and between the discordant CSA and nonmaltreated groups across measures of psychopathology, self-system functioning, and risk behaviors. Cohen’s (1988) d values were calculated to evaluate the degree of CSA impact as a function of concordant versus discordant abuse self-definition with small, medium, and large effects indicated by values of .2, .5, and .8, respectively.