Description Usage Arguments Details Value Note Author(s) See Also Examples

This function assesses the significance of intensity-dependent bias by an one-sided random permutation test. The observed average values of logged fold-changes within an intensity neighbourhood are compared to an empirical distribution generated by random permutation. The significance is given by the false discovery rate.

1 | ```
fdr.int(A,M,delta=50,N=100,av="median")
``` |

`A` |
vector of average logged spot intensity |

`M` |
vector of logged fold changes |

`delta` |
integer determining the size of the neighbourhood. The actual window size is
( |

`N` |
number of random permutations performed for generation of empirical distribution |

`av` |
averaging of |

The function `fdr.int`

assesses significance of intensity-dependent bias using a one-sided random permutation test.
The null hypothesis states the independence of A and M. To test if `M`

depends on `A`

,
spots are ordered with respect to A. This defines a neighbourhood of spots with similar A for each spot.
Next, a test statistic is defined by calculating the *median* or *mean* of `M`

within
a symmetrical spot's intensity neighbourhood of chosen size (`2 *delta+1`

). An empirical distribution of the
test statistic is produced by calculating for `N`

random intensity orders of spots.
Comparing this empirical distribution of *median/mean of \code{M}*
with the observed distribution of *median/mean of \code{M}*,
the independence of `M`

and `A`

is assessed. If `M`

is independent of `A`

, the empirical distribution
of *median/mean of \code{M}* can be expected to be
distributed around its mean value. The false discovery rate (*FDR*) is used to
assess the significance of observing positive deviations of *median/mean of \code{M}*.
It indicates the expected proportion of false positives
among rejected null hypotheses. It is defined as *FDR=q*T/s*,
where *q* is the fraction of *median/mean of \code{M}* larger than chosen threshold *c*
for the empirical distribution, `s`

is the number of neighbourhoods with
*(median/mean of \code{M})> c*
for the distribution derived from the original data and `T`

is the total number of neighbourhoods in the original data.
Varying threshold *c* determines the FDR for each spot neighbourhood. FDRs equal zero are set to
*FDR=1/T*N* for computational reasons, as `log10(FDR)`

is plotted by `sigint.plot`

.
Correspondingly, the significance
of observing negative deviations of *median/mean of \code{M}* can be determined. If the neighbourhood
window extends over the limits of the intensity scale, the significance is set to `NA`

.

A list of vector containing the false discovery rates for positive (`FDRp`

) and negative (`FDRn`

) deviations of
*median/mean of \code{M}* (of the spot's neighbourhood) is produced.

The same functionality but with our input and output formats is offered by `fdr.int`

Matthias E. Futschik (http://itb.biologie.hu-berlin.de/~futschik)

`fdr.int2`

,`p.int`

, `fdr.spatial`

, `sigint.plot`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 | ```
# To run these examples, delete the comment signs (#) in front of the commands.
#
# LOADING DATA NOT-NORMALISED
# data(sw)
# CALCULATION OF SIGNIFICANCE OF SPOT NEIGHBOURHOODS
# For this example, N was chosen rather small. For "real" analysis, it should be larger.
# FDR <- fdr.int(maA(sw)[,1],maM(sw)[,1],delta=50,N=10,av="median")
# VISUALISATION OF RESULTS
# sigint.plot(maA(sw)[,1],maM(sw)[,1],FDR$FDRp,FDR$FDRn,c(-5,-5))
# LOADING NORMALISED DATA
# data(sw.olin)
# CALCULATION OF SIGNIFICANCE OF SPOT NEIGHBOURHOODS
# FDR <- fdr.int(maA(sw.olin)[,1],maM(sw.olin)[,1],delta=50,N=10,av="median")
# VISUALISATION OF RESULTS
# sigint.plot(maA(sw.olin)[,1],maM(sw.olin)[,1],FDR$FDRp,FDR$FDRn,c(-5,-5))
``` |

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