class Bio::ContingencyTable
bio/util/contingency_table.rb  Statistical contingency table analysis for aligned sequences
 Author

Trevor Wennblom <trevor@corevx.com>
 Copyright

Copyright © 20052007 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 multiplesequence alignment. 0.0 indicates no correlation, 1.0 is the maximum correlation.
Further Reading¶ ↑

Numerical Recipes in C by Press, Flannery, Teukolsky, and Vetterling
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 fivestring 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.
Attributes
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
# File lib/bio/util/contingency_table.rb, line 256 def initialize(characters_in_sequences = nil) @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} ) tmp = Hash[*@characters.collect { v [v, 0] }.flatten] @table = Hash[*@characters.collect { v [v, tmp.dup] }.flatten] end
Public Instance Methods
Report the chi square of the entire table
Arguments

none
 Returns

Float
chi square value
# File lib/bio/util/contingency_table.rb, line 332 def chi_square total = 0 @characters.each do i # Loop through every row in the ContingencyTable @characters.each do j # Loop through every column in the ContingencyTable total += chi_square_element(i, j) end end total end
Report the chisquare relation of two elements in the table
Arguments

i
: row 
j
: column
 Returns

Float
chisquare of an intersection
# File lib/bio/util/contingency_table.rb, line 349 def chi_square_element(i, j) eij = expected(i, j) return 0 if eij == 0 ( @table[i][j]  eij )**2 / eij end
Report the sum of all values in a given column
Arguments

j
: Column to sum
 Returns

Integer
sum of column
# File lib/bio/util/contingency_table.rb, line 280 def column_sum(j) total = 0 @table.each { row_key, column total += column[j] } total 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
# File lib/bio/util/contingency_table.rb, line 294 def column_sum_all total = 0 @characters.each { j total += column_sum(j) } total end
Report the contingency coefficient of the table
Arguments

none
 Returns

Float
#contingency_coefficient of the table
# File lib/bio/util/contingency_table.rb, line 361 def contingency_coefficient c_s = chi_square Math.sqrt(c_s / (table_sum_all + c_s) ) end
Calculate e, the expected value.
Arguments

i
: row 
j
: column
 Returns

Float
e(sub:ij) = (r(sub:i)/N) * (c(sub:j))
# File lib/bio/util/contingency_table.rb, line 322 def expected(i, j) (row_sum(i).to_f / table_sum_all) * column_sum(j) end
Report the sum of all values in a given row
Arguments

i
: Row to sum
 Returns

Integer
sum of row
# File lib/bio/util/contingency_table.rb, line 268 def row_sum(i) total = 0 @table[i].each { k, v total += v } total 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
# File lib/bio/util/contingency_table.rb, line 308 def row_sum_all total = 0 @characters.each { i total += row_sum(i) } total end