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https://github.com/jokergoo/statistics-multtest

Control false discovery rate in multiple test
https://github.com/jokergoo/statistics-multtest

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Control false discovery rate in multiple test

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README 

        
## Control false discovery rate in multiple test



### install



```

cpan -i Statistics::Multtest

```



### usage



```perl

use Statistics::Multtest qw(bonferroni holm hommel hochberg BH BY qvalue);

use Statistics::Multtest qw(:all);

use strict;

 

my $p;

# p-values can be stored in an array by reference

$p = [0.01, 0.02, 0.05,0.41,0.16,0.51];

# @$res has the same order as @$p

my $res = BH($p);

print join "\n", @$res;

 

# p-values can also be stored in a hash by reference

$p = {"a" => 0.01,

      "b" => 0.02,

      "c" => 0.05,

      "d" => 0.41,

      "e" => 0.16,

      "f" => 0.51 };

# $res is also a hash reference which is the same as $p

$res = holm($p);

foreach (sort {$res->{a} <=> $res->{$b}} keys %$res) {

    print "$_ => $res->{$_}\n";

}

 

# since qvalue does not always run successfully,

# it should be embeded in 'eval'

$res = eval 'qvalue($p)';

if($@) {

    print $@;

}

else {

    print join "\n", @$res;

}

```



### description



For statistical test, p-value is the probability of false positives. While there are many hypothesis for testing simultaneously, the probability of getting at least one false positive would be large. Therefore the origin p-values should be adjusted to decrease the false discovery rate.



Seven procedures to controlling false positive rates is provided. The names of the methods are derived from `p.adjust` in `stat` package and `qvalue` in `qvalue` package (http://www.bioconductor.org/packages/release/bioc/html/qvalue.html) in R. Code is translated directly from R to Perl using `List::Vectorize` module.



All seven subroutines receive one argument which can either be an array reference or a hash reference, and return the adjusted p-values in corresponding data structure. The order of items in the array does not change after the adjustment.



### subroutines



- `bonferroni($pvalue)`



  Bonferroni single-step process.



- `hommel($pvalue)`



  Hommel singlewise process.



  Hommel, G. (1988). A stagewise rejective multiple test procedure based on a modified Bonferroni test. Biometrika, 75, 383¨C386.



- `holm($pvalue)`



  Holm step-down process.



  Holm, S. (1979). A simple sequentially rejective multiple test procedure. Scandinavian Journal of Statistics, 6, 65¨C70.



- `hochberg($pvalue)`

  

  Hochberg step-up process.



  Hochberg, Y. (1988). A sharper Bonferroni procedure for multiple tests of significance. Biometrika, 75, 800¨C803.



- `BH($pvalue)`

  

  Benjamini and Hochberg, controlling the FDR.



  Benjamini, Y., and Hochberg, Y. (1995). Controlling the false discovery rate: a practical and powerful approach to multiple testing. Journal of the Royal Statistical Society Series B, 57, 289¨C300.



- `BY($pvalue)`

  

  Use Benjamini and Yekutieli.



  Benjamini, Y., and Yekutieli, D. (2001). The control of the false discovery rate in multiple testing under dependency. Annals of Statistics 29, 1165¨C1188.



- `qvalue($pvalue, %setup)`



  Storey and Tibshirani.



  Storey JD and Tibshirani R. (2003) Statistical significance for genome-wide experiments. Proceedings of the National Academy of Sciences, 100: 9440-9445.



The default method for estimating `pi0` in the origin `qvalue` package is to utilize cubic spline interpolation. However, there is no suitable perl module to do such work (external libraries should be installed if using `Math::GSL::Spline` and there seems to be some mistakes when I using `Math::Spline`). Therefore, in this module, we only provide 'bootstrap' method to estimate `pi0`, which is also the second `pi0` method in `qvalue` package. Some arguments which are the same in `qvalue` package can be set in `%setup` as follows.



```perl

lambda => multiply(seq(0, 90, 5), # The value of the tuning parameter

                   0.01),         # to estimate pi_0. Must be in [0,1).

                                  # It should be an array reference

robust => 0, # An indicator of whether it is desired to make the estimate 

             # more robust for small p-values and a direct finite sample

             # estimate of pFDR

```



For details, please see the Storey (2003) and the qvalue document in R.



NOTE: The results of this subroutine are not always exactly consistent to the `qvalue` package due to the floating point number calculation.



In some circumstance, the estimated `pi0 <= 0`, and the subroutine would throw an error. (try p-value list: `[0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1]`). So you should embeded this subroutine in 'eval' such as:



```perl

my $qvalue;

eval '$qvalue = qvalue($pvalue, %setup)';

if($@) {

  # do something

}

else {

    print join ", ", @$qvalue;

}

```