Control of the mean number of false discoveries, Bonferroni and stability of multiple testing

The Bonferroni multiple testing procedure is commonly perceived as being overly conservative in large-scale simultaneous testing situations such as those that arise in microarray data analysis. The objective of the present study is to show that this popular belief is due to overly stringent requirements that are typically imposed on the procedure rather than to its conservative nature. To get over its notorious conservatism, we advocate using the Bonferroni selection rule as a procedure that controls the per family error rate (PFER). The present paper reports the first study of stability properties of the Bonferroni and Benjamini--Hochberg procedures. The Bonferroni procedure shows a superior stability in terms of the variance of both the number of true discoveries and the total number of discoveries, a property that is especially important in the presence of correlations between individual $p$-values. Its stability and the ability to provide strong control of the PFER make the Bonferroni procedure an attractive choice in microarray studies.Comment: Published at http://dx.doi.org/10.1214/07-AOAS102 in the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

On the link between the Bonferroni index and the measurement of inclusive growth.

In a recent paper Ali and Son (2007) suggested measuring the concept of "inclusive growth" via the use of what they called a "social opportunity function". The latter was assumed to depend on the average opportunities available in the population and to give greater weight to the opportunities enjoyed by the poor. On the basis of this approach Ali and Son (2007) then defined an "opportunity index" and an "opportunity curve". The present paper derives the link which exists between these concepts of "opportunity index" and "opportunity curve" and what is known in the literature as the Bonferroni index and the Bonferroni curve. It also defines what could be called a Bonferroni concentration index, a Bonferroni concentration curve, a Generalized Bonferroni curve and a Generalized Bonferroni concentration curve.Bonferroni index – concentration curve - concentration index – generalized Lorenz curve – human opportunity – opportunity index – opportunity curve

A randomized trial to determine the impact on compliance of a psychophysical peripheral cue based on the Elaboration Likelihood Model

Objective: Non-compliance in clinical studies is a significant issue, but causes remain unclear. Utilizing the Elaboration Likelihood Model of persuasion, this study assessed the psychophysical peripheral cue ‘Interactive Voice Response System (IVRS) call frequency’ on compliance. Methods: 71 participants were randomized to once daily (OD), twice daily (BID) or three times daily (TID) call schedules over two weeks. Participants completed 30-item cognitive function tests at each call. Compliance was defined as proportion of expected calls within a narrow window (± 30 min around scheduled time), and within a relaxed window (− 30 min to + 4 h). Data were analyzed by ANOVA and pairwise comparisons adjusted by the Bonferroni correction. Results: There was a relationship between call frequency and compliance. Bonferroni adjusted pairwise comparisons showed significantly higher compliance (p = 0.03) for the BID (51.0%) than TID (30.3%) for the narrow window; for the extended window, compliance was higher (p = 0.04) with OD (59.5%), than TID (38.4%). Conclusion: The IVRS psychophysical peripheral cue call frequency supported the ELM as a route to persuasion. The results also support OD strategy for optimal compliance. Models suggest specific indicators to enhance compliance with medication dosing and electronic patient diaries to improve health outcomes and data integrity respectively