Statistics Tools in GeneSpring

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Statistics Tools in GeneSpring

• The Center for Bioinformatics
• UNC at Chapel Hill
• Jianping Jin Ph.D.
• Bioinformatics Scientist
• Phone [phone]
• E-mail jjin_at_email.unc.edu
• Fax [phone]

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What GeneSpring Can do?

• Works with both Affymetrix and two-color data.
• Views data graphically (classification, graph,
  tree, scatter plot, Vann Diagram )
• Performs statistical analyses.
• Annotates genes (updating from GenBank,
  LocusLink, Unigene biochemical pathways).

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What statistical analyses does GS do?

• Clustering
• k-means (non-hierarchical)
• Self-organizing map
• Gene trees (hierarchical dendrograms).
• principal component analysis
• T-Test analyses ( p-values)
• Like a known gene or average of genes
• Like a pattern drawn with the mouse
• Genes with high confidence
• Genes with relative expression in certain ranges
  
• Pathway analysis finding genes that fit in a
  certain place in a pathway.
• Sequence analysis to automatically find
  regulatory sequences.
• Automatic functional annotation of sub-trees in
  dendrograms.

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Tree Clustering

• Standard correlation
• Smooth correlation
• Change correlation
• Upregulated correlation
• Pearson correlation
• Spearman correlation
• Spearman confidence
• Two-sided Spearman confidence
• Distance

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Notations to the Formulas

•  Result the result of the calculation for genes
  A and B.
•  n the numbers of samples being correlated
  over.
• a the vector (a 1 , a 2 , a 3 ... a n) of
  expression values for gene A.
•  b the vector (b 1 , b 2 , b 3 ... b n) of
  expression values for gene B.
•  a.b a 1 b 1 a 2 b 2 ...a n b n.
•  asquare root(a.a)

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Standard Correlation

• Equation a.b/(ab)
• also called Pearson correlation around zero.
• Measure the angular separation of expression
  vectors for genes A B.
• Answer the question do the peaks match up?

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Pearson Correlation

• Equation A.B / ( A B )
• Very similar to the Std correlation, except it
  measures the angle of expression vector for genes
  A B around the mean of the expression vectors.
• A the mean of all element in vector a - the
  value from each element in a.
• Do the same for b to make a vector B

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Spearman Confidence

• r the value of the Spearman correlation,
• SC 1-(probability you would get a value of r
  or higher by chance)
• A measure of similarity, not a correlation
• High SC value if a high Spearman corr, a low
  p-value.
• Takes account of the number of sub-experiment in
  your experiment set.

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Two-sided Spearman Confidence

• A measure of similarity, very similar to the
  Spearman conf.
• Two-sided test of whether the Spearman corr. is
  either significantly gt/lt zero.
• what genes behave similarly/opposite to a
  specific gene?
• Probably not good for k-means/tree clustering.
• 1-(probability you would get a Spearman
  correlation of r or higher, or -r or lower,
  by chance).

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Distance

• A measurement of dissimilarity, not a correlation
  at all.
• Euclidian dist. b/w expression Profiles ( values
  for each point in N-dimensional space) of genes A
  B.
• Distance a-b/square root of N (expt. points)

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Special Case Correlations

• Smooth correlation, Change correlation and
  Upregulated correlation.
• All three modified version of the Std.
  correlation.
• Only make sense when data in a sequence, such as
  before/after, a time series, or a drug series.

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Smooth Correlation

• Make a new vector A from a by interpolating the
  avg. of each consecutive pair of elements of a.
• Insert this new value b/w the old values
• Do this for each pair of elements that would
  connected by a line in the graph screen
• Do the same to make a vector B from b.

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Change Correlation

• The opposite of what the Smooth corr. looks for.
  Only the chg. in expression level of adjacent
  points.
• Similar to the Std corr., but use an arc tangent
  transformation of ratio b/w adjacent pairs of
  points to create the expr. vector. Less sensitive
  to outliers than using the ratio directly.
• The value created b/w two values a i and a i1 is
  atan(a i1 /a i )- ? /4

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Upregulated Correlation

• Very similar to the Chg. Corr., but it only
  considers positive changes. All negative values
  for the arc tangent are set to zero.
• Make a new vector A from a by looking at the
  change b/w each pair of elements of a.
• The value created b/w two values a i and a i1
  is max(atan(a i1 /a i )- ? /4.0).

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Algorithm to Build Gene Tree

• Determine if there is only one gene or subtree
  left. If yes, go to step five.
• Find the two closest genes/subtrees.
• Merge these two into one subtree.
• Return to step one.
• Merge together branches where the distance
  between sub-branches is less than the separation
  ratio, subject to considering genes with less
  than the minimum distance apart.

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Algorithm to Build Tree

• The minimum distance how far down the tree
  discrete branches are depicted. Higher number,
  more genes in a group, less specific.
• The separate ratio the correlation diff. b/w
  groups of clustered genes. B/w 0 and 1.
  Increasing separation increases the branchiness
  of the tree.

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Principal Components Analysis

• Not a clustering method.
• PCA, the most abundant building blocks, a set of
  expression patterns.
• 1st PC is obtained by finding the linear
  combination of expr. Patterns for the most of
  variability in the data. And so on.

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k-Means Clustering

• Divides genes into a user-defined (k) of
  equal-sized groups, based on their expression
  patterns.
• Creates centroids at the avg. location of each
  group of genes
• With each iteration, genes are reassigned to the
  group with closest centroid
• After all of the genes have been reassigned, the
  location of the centroids is recalculated.

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Self-Organizing Maps

• Similar to k-means clustering.
• Relationship b/w groups in a 2-D map.
• Best represents the variability of the data,
  while still maintaining similarity b/w adjacent
  nodes, e.g. point 1,2 is one unit away from 1,3.

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What does t-test mean in GS

• Replicates one-sample Students t-test
• Comparisons for 2 groups Students two-sample
  t-test.
• Comparisons for multiple groups one-way analysis
  of variance (ANOVA).
• Filtering genes based on a one-sample t-test of
  the mean expression level across replicates vs. a
  reference value (Expression Percentage
  Restriction)

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Filter Genes Analysis Tools

• Global Error Model filters out genes with large
  std deviations or error values.
• Raw data filtering gets rid of genes too close
  to the background.
• Sample to sample comparison fold cmp. Among
  different samples.
• Statistical Group cmp. filters out genes not
  vary significantly across different groups.
• Data File Restriction based on other field ( P/S
  call, /- pairs).

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Statistical Group Comparison

• Genes statistically significant difference in the
  mean expression levels across all group.
• For two groups Studentss two-sample t-test.
• For multiple groups ANOVA
• Non-parametric cmp. for each gene, the rank
  order is used for analysis. Wilcoxon two-sample
  test (Mann-Whitney U test), the Kruskal-Wallis
  test for multiple groups.

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Data Normalization

• In two-color experiments, normalizing vs. the
  control channel (green) for each gene.
• Normalize each sample to itself or to a positive
  control. Make diff. samples comparable to one
  another.
• Normalizing each gene to itself remove the
  differing intensity scales from multiple expt
  readings (highly recommended if not using a
  two-color experiment.

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NCI-60 cell lines
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DrugActivity_AT