18%20Moderated-t%20Test%204_3_08

# 18%20Moderated-t%20Test%204_3_08 - Consider a CRD with Two...

This preview shows pages 1–4. Sign up to view the full content.

1 1 Introduction to Empirical Bayes Models and Moderated t-test Peng Liu 4/3/2008 2 Consider a CRD with Two Treatments 1 2 1 1 2 2 3 Measure Expression with Affy GeneChips 1 2 1 1 2 2 4 A Model for the Log Data from Gene j Treatment 1 observations i.i.d. Treatment 2 observations i.i.d. independent of Mean may be different for each combination of gene and treatment. Parameters: ( μ 1j , μ 2j , and σ j ) 2

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
2 5 A Model for the Log Data from Gene j Treatment 1 observations i.i.d. Treatment 2 observations i.i.d. independent of Variance is assumed to be the same for both treatments within each gene, but the variance is allowed to change from gene to gene. 6 Testing for Differential Expression We wish to test for each gene j =1,2,. .., J. 7 Consider a Two-Sample t -Test for Each Gene mean of treatment 1 observations for gene j mean of treatment 2 observations for gene j pooled variance estimate of variance of trt 1 observations for gene j variance of trt 2 observations for gene j 8 Distribution of the t -Statistics under Our Model Assumptions ± Whenever H 0j is true (i.e., whenever gene j is EE), t j will have a t -distribution with d=n 1 +n 2 -2 degrees of freedom. ± Whenever H 0j is false (i.e., whenever gene j is DE), t j will have a non-central t -distribution with d=n 1 +n 2 -2 degrees of freedom and non- centrality parameter
3 9 Distributions of test statistic under H 0 and H a H 0j is true μ 1j μ 2j = 0 σ j 2 =1 n 1 = n 2 =5 H 0j is false μ 1j μ 2j = 1 σ j 2 =1 n 1 = n 2 =5 t -statistic density 10 The above test uses “frequentist” idea ± The previous 2-sample t-test is based on the reasoning of “frequentist” approach. ± With this approach, the parameters ( μ 1j , μ 2j , and σ j ) are parameters that are unknown but fixed at some values. ± Inferences are done for those parameters based on our observed data. E.g., we either reject H 0 or accept H 0 based on the p-value that is calculated from our data under the assumed model. 2 11 Bayesian statistics ± Another branch of statistical inference uses the “Bayesian” idea. ± For the parameters such as σ j , instead of treating them as unknown fixed values, they are assumed to follow some kind of distribution. ± Then inferences are done based on both the data and the assumed distribution of the parameters. 2 12 Motivating vignette ± Suppose you are going to submit a manuscript to a journal whose acceptance rate is 10% for all submission. ± What would you expect of the result for your first

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 11

18%20Moderated-t%20Test%204_3_08 - Consider a CRD with Two...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online