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# MAEBAYES procedure

Modifies t-values by an empirical Bayes method (D.B. Baird).

### Options

`PRINT` = string tokens What to print (`estimates`); default `esti` What to plot (`phistograms`, `thistograms`, `pvalues`, `tvalues`); default `*` i.e. nothing Type of data specified by the `DATA` parameter when it is a variate (`means`, `tvalues`); default `tval` Type of test to use to form probability values (`twosided`, `greaterthan`, `lessthan`); default `twos` Device number on which to plot the graphs What graphics filename template to use to save the graphs; default `*`

### Parameters

`DATA` = pointers or variates Pointers of variates or variates of means or t-values to be summarized Supplies standard deviations of the data when `DATA` is a variate of means or t-values Supplies degrees of freedom when `DATA` is a variate of means or t-values Saves the estimated prior standard deviation Saves the estimated number of degrees of freedom assigned to the prior standard deviation Saves the modified t-values Saves the shrunken `SD` values Saves the modified probability values

### Description

In a microarray experiment, as hundreds and often thousands of probes are being processed in parallel, there is a loss of power if you consider the variation of each probe in isolation. If this parallelism is used between the genes to gain extra information on the variation of an individual probe, then more powerful tests of the level of differential expression of a probe can be obtained. To do this, a prior distribution of the standard deviations (or equivalently the variances) over the probes is assumed. In particular, it is assumed that the reciprocal of the variance, sp2, of each probe is distributed as a multiple of a chi-square distribution with d0 degrees of

freedom, i.e. 1/sp2 is distributed as 1/(d0 × s02) × Chisquare(d0).

If the parameters of this distribution, the prior degrees of freedom d0 and standard deviation s0 are estimated, more information can be gained on an individual probe, by shrinking it towards the prior by an amount that depends on the amount of information in the standard deviation sp of the probe (in this case its degrees of freedom dp). The modified standard deviation s~p is then given by:

s~p = √((d02 × s02 + dp2 × sp2) / (d0 + dp))

A modified t-test can then be performed using the modified standard deviation with d0 + dp degrees of freedom. The method can also produce the probability values for tests that the differential expression differs from zero. The `METHOD` option selects the type of test i.e. two-sided, or for values greater than or less than zero (the default is two-sided).

The `DATA` parameter can supply a pointer containing one variate per slide, with the probes in the same position within each variate. The means and standard deviations are then be calculated from the raw data. Alternatively, `DATA` can supply a variate containing means or t-values for each probe. The `DATATYPE` option should then indicate which of these has been given, the `SD` parameter should supply a variate containing the standard deviations for each probe, and the `DF` parameter should supply a variate with the numbers of degrees of freedom.

The estimated prior number of degrees of freedom d0 and standard deviation s0 can be saved, in scalars, by the `D0` and `S0` parameters. The `TMODIFIED` parameter can supply a variate to save the modified t-values, the `SDMODIFIED` parameter can save the shrunken `SD` values, and the `PMODIFIED` parameter can save the modified probability values.

By default, the estimates are printed, but this can be suppressed by setting option `PRINT=*`. The `PLOT` option controls what plots are produced, with settings:

    `phistograms` two histograms showing the modified and raw probabilities plotted on the same scale; two histograms showing the modified and raw t-values plotted on the same scale; a scatter plot of modified versus raw probabilities; and a scatter plot of modified versus t-values.

By default, nothing is plotted. You can use the `DEVICE` option to plot to a device other than the screen. The `GRAPHICSFILE` specifies then supplies a template for the file names.

Options: `PRINT`, `PLOT`, `DATATYPE`, `METHOD`, `DEVICE`, `GRAPHICSFILE`.

Parameters: `DATA`, `SD`, `DF`, `SD0`, `DF0`, `TMODIFIED`, `SDMODIFIED`, `PMODIFIED`.

### Reference

Smyth, G.K. (2004). Linear models and empirical Bayes methods for assessing differential expression in microarray experiments. Statistical Applications in Genetics and Molecular Biology, 3, No. 1, Article 3.

Procedures: `AFFYMETRIX`, `FDRBONFERRONI`, `FDRMIXTURE`, `MAANOVA`, `MABGCORRECT`, `MAREGRESSION`, `MARMA`, `MAROBUSTMEANS`, `MAVDIFFERENCE`, `MAVOLCANO`, `QNORMALIZE`.

Commands for: Microarray data.

### Example

```CAPTION    'MAEBAYES example'; STYLE=meta
ENQUIRE    CHANNEL=-1; EXIST=check; NAME=\
'%GENDIR%/Data/Microarrays/ApoAIKnockOutEffects.GSH'
IF check