MAEBAYES procedure

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

Options

PRINT = strings

What to print (estimates); default esti

PLOT = strings

What to plot (phistograms, thistograms, pvalues, tvalues); default * i.e. nothing

DATATYPE = string

Type of data specified by the DATA parameter when it is a variate (means, tvalues); default tval

METHOD = string

Type of test to use to form probability values (twosided, greaterthan, lessthan); default twos

DEVICE = scalar

Device number on which to plot the graphs

GRAPHICSFILE = text

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

SD = variates

Supplies standard deviations of the data when DATA is a variate of means or t-values

DF = variates

or scalars Supplies degrees of freedom when DATA is a variate of means or t-values

SD0 = scalars

Saves the estimated prior standard deviation

DF0 = scalars

Saves the estimated number of degrees of freedom assigned to the prior standard deviation

TMODIFIED = variates

Saves the modified t-values

SDMODIFIED = variates

Saves the shrunken SD values

PMODIFIED = variates

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, s_p², of each probe is distributed as a multiple of a chi-square distribution with d₀ degrees of

freedom, i.e. 1/s_p² 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 s_p of the probe (in this case its degrees of freedom d_p). The modified standard deviation s^~_p is then given by:

s^~_p = √((d₀² × s₀² + d_p² × s_p²) / (d₀ + d_p))

A modified t-test can then be performed using the modified standard deviation with d₀ + d_p 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;

thistograms

two histograms showing the modified and raw t-values plotted on the same scale;

pvalues

a scatter plot of modified versus raw probabilities; and

tvalues

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.

http://www.bepress.com/sagmb/vol3/iss1/art3