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## Optimal Sample Size for Multiple Testing: the Case of Gene Expression Microarrays (2004)

Venue: | Journal of the American Statistical Association |

Citations: | 75 - 5 self |

### Citations

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Significance analysis of microarrays applied to the ionizing radiation response
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Citation Context ...nes, the FDR is the fraction of truly unaltered genes among the genes classified as differentially expressed. Commonly used microarray software uses the FDR to guide gene selection (see, for example, =-=Tusher et al., 2001-=-). Applications of FDRs to microarray analysis are discussed by Storey and Tibshirani (2003). Extensions are discussed by Genovese and Wasserman (2002), who also introduce the definition of the poster... |

1880 |
Statistical Decision Theory and Bayesian Analysis, 2nd ed
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Citation Context ...zation is subject to the bound on FD. The sequence of alternating between the expectation and the optimization is characteristic for sequential decision problems. (See, for example DeGroot, 1970, and =-=Berger, 1985-=-, for a discussion of sequential decision problems in general.) The expectation is determined with respect to the prior probability model on the data yJ under a given sample size J . The only argument... |

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Quantitative monitoring of gene expression patterns with a complementary DNA microarray
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Citation Context ...umber of replications in microarray experiments. Gene expression microarrays are technologies for simultaneously quantifying the level of transcription of a large portion of the genes in an organism (=-=Schena et al., 1995-=-; Duggan et al., 1999). (For a recent review of microarray technology and related statistical methods see, for example, Kohane et al., 2002.) The range of applications is broad. Here we focus on contr... |

1342 | Reversible jump Markov chain Monte Carlo computation and Bayesian model determination
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Citation Context ...odel. This is done once, before starting the optimal design. Posterior simulation in mixture models like (8) is a standard problem. We include reversible jump moves to allow for random size mixtures (=-=Green, 1995-=-). We then fix the mixture model at the posterior modes K̂ and L̂, and the posterior means (w̄, m̄, w̄g, m̄g) = E(w,m,wg,mg | Xo, K̂, L̂). We proceed with the optimal sample size approach, using model... |

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Citation Context ...using the available control data as a pilot data set Xo. Estimation of (8) is implemented as a Markov chain Monte Carlo posterior simulation with reversible jump (RJ) moves. We use split-merge moves (=-=Richardson and Green, 1997-=-) for both mixtures defined in (8). Recall that the mixtures are defined with respect to the discrete mixing measures p(rij | w,m) and p(gj | wg,mg). The third mixture, with respect to sij, does not a... |

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Applied Statistical Decision Theory
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Citation Context ...size selection assume that the investigator is a rational decision maker choosing an action that minimizes the loss of the possible consequences – averaging with respect to all the relevant unknowns (=-=Raiffa and Schlaifer, 1961-=-; DeGroot, 1970). At the time of the sample size decision the relevant unknowns are the data y, the indicators z = (z1, . . . , zn) and the model parameters ω. The relevant probability model with resp... |

491 | A Bayesian framework for the analysis of microarray expression data: Regularized t-test and statistical inferences of gene changes - Baldi, Long - 2001 |

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147 | Issues in cDNA microarray analysis: quality filtering, channel normalization, models of variations and assessment of gene effects
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Citation Context ...wing discussion we thus assume that the data are appropriately standardized and normalized and that the noise distribution implicitly includes the consideration of those processes. (See, for example, =-=Tseng et al., 2001-=-; Baggerly et al., 2001; or Yang et al., 2002, for a discussion of the process of normalization.) For the implementation in the example we choose a variation of the model introduced in Newton et al. (... |

142 |
Expression profiling using cDNA microarrays. Nat Genet,
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(Show Context)
Citation Context ... in microarray experiments. Gene expression microarrays are technologies for simultaneously quantifying the level of transcription of a large portion of the genes in an organism (Schena et al., 1995; =-=Duggan et al., 1999-=-). (For a recent review of microarray technology and related statistical methods see, for example, Kohane et al., 2002.) The range of applications is broad. Here we focus on controlled experiments tha... |

132 |
An application oriented guide to Lagrangian relaxation.
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Citation Context ...need an additional argument. To minimize FNR subject to 24 http://biostats.bepress.com/jhubiostat/paper31 FDR ≤ α we write the Lagrangian function fλ(d) = FNR− λ(α− FDR). Using Lagrangian relaxation (=-=Fisher, 1985-=-) we find a weight λ∗ ≥ 0 such that the minimization of fλ∗(d) provides an approximate solution to the original constrained optimization problem. (The solution is only approximate because of the discr... |

121 | Genome-wide expression profiling in Escherichia coli K-12. Nucleic Acids Res - Richmond, Glasner, et al. - 1999 |

105 |
Making Decisions,
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(Show Context)
Citation Context ...llowing posterior expected losses: LN(d, y) = cFD + FN, and LR(d, y) = cFDR + FNR. The loss function LN is a natural extension of (0, 1, c) loss functions for traditional hypothesis testing problems (=-=Lindley, 1971-=-). From this perspective the combination of error rates in LR seems less attractive. The loss for a false discovery and false negative depends on the total number of discoveries or negatives, respecti... |

76 | How many replicates of arrays are required to detect gene expression changes in microarray experiments? A mixture model approach. Genome Biology 3 - Pan, Lin, et al. - 2002 |

49 | SAM thresholding and false discovery rates for detecting differential gene expression in DNA microarrays. In - Storey, Tibshirani - 2003 |

47 | A statistical framework for expression-based molecular classification in cancer,” - Parmigiani, Garrett, et al. - 2002 |

45 |
A.J.: Microarrays for an Integrative Genomics,
- Kohane, Kho, et al.
- 2003
(Show Context)
Citation Context ...ranscription of a large portion of the genes in an organism (Schena et al., 1995; Duggan et al., 1999). (For a recent review of microarray technology and related statistical methods see, for example, =-=Kohane et al., 2002-=-.) The range of applications is broad. Here we focus on controlled experiments that aim to search or screen for genes whose expressions are regulated by modifying the conditions of interest, either en... |

40 |
Identifying differentially expressed genes in cDNA microarray experiments
- BAGGERLY, COOMBES, et al.
- 2001
(Show Context)
Citation Context ...hus assume that the data are appropriately standardized and normalized and that the noise distribution implicitly includes the consideration of those processes. (See, for example, Tseng et al., 2001; =-=Baggerly et al., 2001-=-; or Yang et al., 2002, for a discussion of the process of normalization.) For the implementation in the example we choose a variation of the model introduced in Newton et al. (2001) and Newton and Ke... |

36 | Gene expression analysis with the parametric bootstrap - Laan, Bryan - 2001 |

35 | Bayesian models for gene expression with DNA microarray data. - Ibrahim, Chen, et al. - 2002 |

34 | Estimating Dataset Size Requirements for Classifying DNA Microarray Data - Mukherjee, Tamayo, et al. - 2003 |

26 | Sample size determination: A review. - Adcock - 1997 |

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19 |
The choice of sample size.
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Citation Context ... decision theoretics, including the multistage nature central to our discussion, was formalized within a Bayesian framework as early as 1961 through the work of Raiffa and Schlaifer (1961). (See also =-=Lindley, 1997-=- or Adcock, 1997 and references therein for discussions of sample size determination.) Following this paradigm, we present a general decision theoretic framework for the choice of sample size for geno... |

18 |
Bayesian and frequentist multiple testing
- Genovese, Wasserman
- 2002
(Show Context)
Citation Context ...ively. FDR(·) and FNR(·) are the percentage of wrong decisions, relative to the number of discoveries and negatives, respectively (the additional term avoids a zero denominator). (See, for example, =-=Genovese and Wasserman, 2002-=-, for a discussion of FNR and FDR.) Conditioning on y and marginalizing with respect to z, we obtain the posterior expected FDR and FNR FDR(d, y) = ∫ FDR(d, z) dp(z | y) = ∑ di(1− vi)/(D + ) 6 http:/... |

9 | On dierential Variability of Expression Ratios: Improving Statistical Inference about Gene Expression Changes from Microarray Data - Newton, Kendziorski, et al. - 2001 |

5 |
Sample Size Determination
- Adcock
- 1997
(Show Context)
Citation Context ...ics, including the multistage nature central to our discussion, was formalized within a Bayesian framework as early as 1961 through the work of Raiffa and Schlaifer (1961). (See also Lindley, 1997 or =-=Adcock, 1997-=- and references therein for discussions of sample size determination.) Following this paradigm, we present a general decision theoretic framework for the choice of sample size for genomic screening or... |

4 | Power and sample size for microarray studies - Lee, Whitmore - 2002 |

3 |
Hosted by The Berkeley Electronic Press
- Goldstein, Dudoit, et al.
- 2000
(Show Context)
Citation Context ...re appropriately standardized and normalized and that the noise distribution implicitly includes the consideration of those processes. (See, for example, Tseng et al., 2001; Baggerly et al., 2001; or =-=Yang et al., 2002-=-, for a discussion of the process of normalization.) For the implementation in the example we choose a variation of the model introduced in Newton et al. (2001) and Newton and Kendziorski (2003). We f... |

1 | Identifying dierentially expressed genes in cDNA microarray experiments - Baggerly, Coombes, et al. - 2001 |

1 | Expression pro using cDNA microarrays - Duggan, Bittner, et al. - 1999 |

1 |
Laplace expansions in MCMC algorithms for latent variable models
- Guihenneuc, Rousseau
- 2002
(Show Context)
Citation Context ...nder suitable regularity conditions this result is uniform in (θ0i, θ1i, η) over compact sets. In the non-compact case, some conditions on the tails of the priors need to be added. (See, for example, =-=Guihenneuc and Rousseau, 2002-=-.) Therefore, when |θ0i−θ1i| is large p(zi = 1|yi, η) goes to 1 at an exponential rate and thus P (zi = 1|yi) is very close to 1 (the error being essentially of the order n−1). We now use (11) to stud... |

1 | Parametric Empirical Bayes Methods for Micorarrays," in The analysis of gene expression data: methods and software - Newton, Kendziorski - 2003 |

1 | Genome-wide expression pro in Escherichia coli K-12 - Richmond, Glasner, et al. - 1999 |

1 | Selecting an optimal rejection region for multiple testing: A decisiontheoretic alternative to FDR control, with an application to microarrays - Bickel - 2003 |

1 |
Hosted by The Berkeley Electronic Press
- DeGroot
- 1970
(Show Context)
Citation Context ...he investigator is a rational decision maker choosing an action that minimizes the loss of the possible consequences – averaging with respect to all the relevant unknowns (Raiffa and Schlaifer, 1961; =-=DeGroot, 1970-=-). At the time of the sample size decision the relevant unknowns are the data y, the indicators z = (z1, . . . , zn) and the model parameters ω. The relevant probability model with respect to which we... |

1 | differential variability of expression ratios: Improving statistical inference about gene expression changes from microarray data - “On |