Class Bio::ContingencyTable
In: lib/bio/util/contingency_table.rb
Parent: Object

bio/util/contingency_table.rb - Statistical contingency table analysis for aligned sequences

Author:Trevor Wennblom <trevor@corevx.com>
Copyright:Copyright (c) 2005-2007 Midwinter Laboratories, LLC (midwinterlabs.com)
License:The Ruby License

Description

The Bio::ContingencyTable class provides basic statistical contingency table analysis for two positions within aligned sequences.

When ContingencyTable is instantiated the set of characters in the aligned sequences may be passed to it as an array. This is important since it uses these characters to create the table‘s rows and columns. If this array is not passed it will use it‘s default of an amino acid and nucleotide alphabet in lowercase along with the clustal spacer ’-’.

To get data from the table the most used functions will be chi_square and contingency_coefficient:

  ctable = Bio::ContingencyTable.new()
  ctable['a']['t'] += 1
  # .. put more values into the table
  puts ctable.chi_square
  puts ctable.contingency_coefficient  # between 0.0 and 1.0

The contingency_coefficient represents the degree of correlation of change between two sequence positions in a multiple-sequence alignment. 0.0 indicates no correlation, 1.0 is the maximum correlation.

Further Reading

Usage

What follows is an example of ContingencyTable in typical usage analyzing results from a clustal alignment.

  require 'bio'

  seqs = {}
  max_length = 0
  Bio::ClustalW::Report.new( IO.read('sample.aln') ).to_a.each do |entry|
    data = entry.data.strip
    seqs[entry.definition] = data.downcase
    max_length = data.size if max_length == 0
    raise "Aligned sequences must be the same length!" unless data.size == max_length
  end

  VERBOSE = true
  puts "i\tj\tchi_square\tcontingency_coefficient" if VERBOSE
  correlations = {}

  0.upto(max_length - 1) do |i|
    (i+1).upto(max_length - 1) do |j|
      ctable = Bio::ContingencyTable.new()
      seqs.each_value { |seq| ctable.table[ seq[i].chr ][ seq[j].chr ] += 1 }

      chi_square = ctable.chi_square
      contingency_coefficient = ctable.contingency_coefficient
      puts [(i+1), (j+1), chi_square, contingency_coefficient].join("\t") if VERBOSE

      correlations["#{i+1},#{j+1}"] = contingency_coefficient
      correlations["#{j+1},#{i+1}"] = contingency_coefficient  # Both ways are accurate
    end
  end

  require 'yaml'
  File.new('results.yml', 'a+') { |f| f.puts correlations.to_yaml }

Tutorial

ContingencyTable returns the statistical significance of change between two positions in an alignment. If you would like to see how every possible combination of positions in your alignment compares to one another you must set this up yourself. Hopefully the provided examples will help you get started without too much trouble.

  def lite_example(sequences, max_length, characters)

    %w{i j chi_square contingency_coefficient}.each { |x| print x.ljust(12) }
    puts

    0.upto(max_length - 1) do |i|
      (i+1).upto(max_length - 1) do |j|
        ctable = Bio::ContingencyTable.new( characters )
        sequences.each do |seq|
          i_char = seq[i].chr
          j_char = seq[j].chr
          ctable.table[i_char][j_char] += 1
        end
        chi_square = ctable.chi_square
        contingency_coefficient = ctable.contingency_coefficient
        [(i+1), (j+1), chi_square, contingency_coefficient].each { |x| print x.to_s.ljust(12) }
        puts
      end
    end

  end

  allowed_letters = Array.new
  allowed_letters = 'abcdefghijk'.split('')

  seqs = Array.new
  seqs << 'abcde'
  seqs << 'abcde'
  seqs << 'aacje'
  seqs << 'aacae'

  length_of_every_sequence = seqs[0].size  # 5 letters long

  lite_example(seqs, length_of_every_sequence, allowed_letters)

Producing the following results:

  i           j           chi_square  contingency_coefficient
  1           2           0.0         0.0
  1           3           0.0         0.0
  1           4           0.0         0.0
  1           5           0.0         0.0
  2           3           0.0         0.0
  2           4           4.0         0.707106781186548
  2           5           0.0         0.0
  3           4           0.0         0.0
  3           5           0.0         0.0
  4           5           0.0         0.0

The position i=2 and j=4 has a high contingency coefficient indicating that the changes at these positions are related. Note that i and j are arbitrary, this could be represented as i=4 and j=2 since they both refer to position two and position four in the alignment. Here are some more examples:

  seqs = Array.new
  seqs << 'abcde'
  seqs << 'abcde'
  seqs << 'aacje'
  seqs << 'aacae'
  seqs << 'akcfe'
  seqs << 'akcfe'

  length_of_every_sequence = seqs[0].size  # 5 letters long

  lite_example(seqs, length_of_every_sequence, allowed_letters)

Results:

  i           j           chi_square  contingency_coefficient
  1           2           0.0         0.0
  1           3           0.0         0.0
  1           4           0.0         0.0
  1           5           0.0         0.0
  2           3           0.0         0.0
  2           4           12.0        0.816496580927726
  2           5           0.0         0.0
  3           4           0.0         0.0
  3           5           0.0         0.0
  4           5           0.0         0.0

Here we can see that the strength of the correlation of change has increased when more data is added with correlated changes at the same positions.

  seqs = Array.new
  seqs << 'abcde'
  seqs << 'abcde'
  seqs << 'kacje'  # changed first letter
  seqs << 'aacae'
  seqs << 'akcfa'  # changed last letter
  seqs << 'akcfe'

  length_of_every_sequence = seqs[0].size  # 5 letters long

  lite_example(seqs, length_of_every_sequence, allowed_letters)

Results:

  i           j           chi_square  contingency_coefficient
  1           2           2.4         0.534522483824849
  1           3           0.0         0.0
  1           4           6.0         0.707106781186548
  1           5           0.24        0.196116135138184
  2           3           0.0         0.0
  2           4           12.0        0.816496580927726
  2           5           2.4         0.534522483824849
  3           4           0.0         0.0
  3           5           0.0         0.0
  4           5           2.4         0.534522483824849

With random changes it becomes more difficult to identify correlated changes, yet positions two and four still have the highest correlation as indicated by the contingency coefficient. The best way to improve the accuracy of your results, as is often the case with statistics, is to increase the sample size.

A Note on Efficiency

ContingencyTable is slow. It involves many calculations for even a seemingly small five-string data set. Even worse, it‘s very dependent on matrix traversal, and this is done with two dimensional hashes which dashes any hope of decent speed.

Finally, half of the matrix is redundant and positions could be summed with their companion position to reduce calculations. For example the positions (5,2) and (2,5) could both have their values added together and just stored in (2,5) while (5,2) could be an illegal position. Also, positions (1,1), (2,2), (3,3), etc. will never be used.

The purpose of this package is flexibility and education. The code is short and to the point in aims of achieving that purpose. If the BioRuby project moves towards C extensions in the future a professional caliber version will likely be created.

Methods

Attributes

characters  [R] 
table  [RW]  Since we‘re making this math-notation friendly here is the layout of @table:
  • @table[row][column]
  • @table[i][j]
  • @table[y][x]

Public Class methods

Create a ContingencyTable that has characters_in_sequence.size rows and characters_in_sequence.size columns for each row


Arguments

  • characters_in_sequences: (optional) The allowable characters that will be present in the aligned sequences.
Returns:ContingencyTable object to be filled with values and calculated upon

[Source]

     # File lib/bio/util/contingency_table.rb, line 256
256:   def initialize(characters_in_sequences = nil)
257:     @characters = ( characters_in_sequences or %w{a c d e f g h i k l m n p q r s t v w y - x u} )
258:     tmp = Hash[*@characters.collect { |v| [v, 0] }.flatten]
259:     @table = Hash[*@characters.collect { |v| [v, tmp.dup] }.flatten]
260:   end

Public Instance methods

Report the chi square of the entire table


Arguments

  • none
Returns:Float chi square value

[Source]

     # File lib/bio/util/contingency_table.rb, line 332
332:   def chi_square
333:     total = 0
334:     c = @characters
335:     max = c.size - 1
336:     @characters.each do |i|    # Loop through every row in the ContingencyTable
337:       @characters.each do |j|  # Loop through every column in the ContingencyTable
338:         total += chi_square_element(i, j)
339:       end
340:     end
341:     total
342:   end

Report the chi-square relation of two elements in the table


Arguments

  • i: row
  • j: column
Returns:Float chi-square of an intersection

[Source]

     # File lib/bio/util/contingency_table.rb, line 351
351:   def chi_square_element(i, j)
352:     eij = expected(i, j)
353:     return 0 if eij == 0
354:     ( @table[i][j] - eij )**2 / eij
355:   end

Report the sum of all values in a given column


Arguments

  • j: Column to sum
Returns:Integer sum of column

[Source]

     # File lib/bio/util/contingency_table.rb, line 280
280:   def column_sum(j)
281:     total = 0
282:     @table.each { |row_key, column| total += column[j] }
283:     total
284:   end

Report the sum of all values in all columns.

  • This is the same thing as asking for the sum of all values in the table.

Arguments

  • none
Returns:Integer sum of all columns

[Source]

     # File lib/bio/util/contingency_table.rb, line 294
294:   def column_sum_all
295:     total = 0
296:     @characters.each { |j| total += column_sum(j) }
297:     total
298:   end

Report the contingency coefficient of the table


Arguments

  • none
Returns:Float contingency_coefficient of the table

[Source]

     # File lib/bio/util/contingency_table.rb, line 363
363:   def contingency_coefficient
364:     c_s = chi_square
365:     Math.sqrt(c_s / (table_sum_all + c_s) )
366:   end

Calculate e, the expected value.


Arguments

  • i: row
  • j: column
Returns:Float e(sub:ij) = (r(sub:i)/N) * (c(sub:j))

[Source]

     # File lib/bio/util/contingency_table.rb, line 322
322:   def expected(i, j)
323:     (row_sum(i).to_f / table_sum_all) * column_sum(j)
324:   end

Report the sum of all values in a given row


Arguments

  • i: Row to sum
Returns:Integer sum of row

[Source]

     # File lib/bio/util/contingency_table.rb, line 268
268:   def row_sum(i)
269:     total = 0
270:     @table[i].each { |k, v| total += v }
271:     total
272:   end

Report the sum of all values in all rows.

  • This is the same thing as asking for the sum of all values in the table.

Arguments

  • none
Returns:Integer sum of all rows

[Source]

     # File lib/bio/util/contingency_table.rb, line 308
308:   def row_sum_all
309:     total = 0
310:     @characters.each { |i| total += row_sum(i) }
311:     total
312:   end
table_sum_all()

Alias for row_sum_all

[Validate]