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CHOOSING THE LESSER EVIL: TRADEOFF BETWEEN FALSE DISCOVERY RATE AND NONDISCOVERY RATE
"... Abstract: The problem of multiple comparisons has become increasingly important in light of the significant surge in volume of data available to statisticians. The seminal work of Benjamini and Hochberg (1995) on the control of the false discovery rate (FDR) has brought forth an alternative way of m ..."
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Abstract: The problem of multiple comparisons has become increasingly important in light of the significant surge in volume of data available to statisticians. The seminal work of Benjamini and Hochberg (1995) on the control of the false discovery rate (FDR) has brought forth an alternative way of measuring type I error rate that is often more relevant than the one based on the familywise error rate. In this paper, we emphasize the importance of considering type II error rates in the context of multiple hypothesis testing. We propose a suitable quantity, the expected proportion of false negatives among the true alternative hypotheses, which we call nondiscovery rate (NDR). We argue that NDR is a natural extension of the type II error rate of single hypothesis to multiple comparisons. The utility of NDR is emphasized through the tradeoff between FDR and NDR, which is demonstrated using a few real and simulated examples. We also show analytically the equivalence between the FDRadjusted pvalue approach of Yekutieli and Benjamini (1999) and the qvalue method of Storey (2002). This equivalence dissolves the dilemma encountered by many practitioners of choosing the “right ” FDR controlling procedure. Key words and phrases: False discovery rate, genomescans, microarray data, multiple comparisons, multiple hypothesis testing, nondiscovery rate, power, type I error, type II error. 1.
PERSPECTIVE
"... Background: Bioassays are routinely used to evaluate the toxicity of test agents. Experimental designs for bioassays are largely encompassed by fixed effects linear models. In toxicogenomics studies where DNA arrays measure mRNA levels, the tissue samples are typically generated in a bioassay. These ..."
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Background: Bioassays are routinely used to evaluate the toxicity of test agents. Experimental designs for bioassays are largely encompassed by fixed effects linear models. In toxicogenomics studies where DNA arrays measure mRNA levels, the tissue samples are typically generated in a bioassay. These measurements introduce additional sources of variation, which must be properly managed to obtain valid tests of treatment effects. Results: An analysis of covariance model is developed which combines a fixedeffects linear model for the bioassay with important variance components associated with DNA array measurements. These models can accommodate the dominant characteristics of measurements from DNA arrays, and they account for technical variation associated with normalization, spots, dyes, and batches as well as the biological variation associated with the bioassay. An example illustrates how the model is used to identify valid designs and to compare competing designs. Conclusions: Many toxicogenomics studies are bioassays which measure gene expression using DNA arrays. These studies can be designed and analyzed using standard methods with a few modifications to account for characteristics of array measurements, such as multiple endpoints and normalization. As much as possible, technical variation associated with probes, dyes, and batches are managed by blocking treatments within these sources of variation. An example shows how some practical constraints can be accommodated by this modelling and how it allows one to objectively compare competing
doi:10.1093/bioinformatics/bti699BIOINFORMATICS ORIGINAL PAPER Gene
, 2005
"... Motivation: There is not a widely applicable method to determine the sample size for experiments basing statistical significance on the false discovery rate (FDR). Results: We propose and develop the anticipated FDR (aFDR) as a conceptual tool for determining sample size. We derive mathematical expr ..."
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Motivation: There is not a widely applicable method to determine the sample size for experiments basing statistical significance on the false discovery rate (FDR). Results: We propose and develop the anticipated FDR (aFDR) as a conceptual tool for determining sample size. We derive mathematical expressions for the aFDR and anticipated average statistical power. These expressions are used to develop a general algorithm to determine sample size. We provide specific details on how to implement the algorithm for a kgroup (k5 2) comparisons. The algorithm performs well for kgroup comparisons in a series of traditional simulations and in a realdata simulation conducted by resampling from a large, publicly available dataset. Availability: Documented Splus and R code libraries are freely available from www.stjuderesearch.org/depts/biostats
Original Papers A Neural Network Model for Constructing Endophenotypes of Common Complex DiseasesAn Application to Male Youngonset Hypertension Microarray Data
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BIOINFORMATICS Sample Size Determination for the False Discovery Rate
"... Motivation There is not a widely applicable method to determine the sample size for experiments basing statistical significance on the false discovery rate (FDR). Results We propose and develop the anticipated false discovery ratio (aFDR) as a conceptual tool for determining sample size. We derive m ..."
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Motivation There is not a widely applicable method to determine the sample size for experiments basing statistical significance on the false discovery rate (FDR). Results We propose and develop the anticipated false discovery ratio (aFDR) as a conceptual tool for determining sample size. We derive mathematical expressions for the aFDR and anticipated average statistical power. These expressions are used to develop a general algorithm to determine sample size. We provide specific details on how to implement the algorithm for a kgroup (k ≥ 2) comparisons. The algorithm performs well for kgroup comparisons in a series of traditional simulations and in a real data simulation conducted by resampling from a large, publicly available data set. Availability Documented Splus and R code libraries are freely available from www.stjuderesearch.org/depts/biostats. Contact: Stan Pounds,