Evaluation and integration of multiple datasets

using Bayes theorem

John van Dam

How can we integrate multiple datasets?Proteomics data

Genetic dataPublished data

Expression data Evolutionary data

?

How can we integrate multiple datasets?Proteomics data

Genetic dataPublished data

Expression data Evolutionary data

Thomas Bayes (1701 – 1761)• Presbyterian minister• Fellow of the Royal Society

• Published two works:• A religious essay• An essay defending the work of Sir Isaac Newton

• His work on the “Bayes’ theorem” was published by Richard Price in 1763

• Mathematics of probabilities• A hot topic in science in early 18th century• A lot of people at the time were interested in mathematics,

statistics and probabilities because of gambling!

Bayes’ theorem

• P(A|B) = Probability of A given observation B

• P(B|A) = Probability of observation of B given A

• P(A) = The a priori probability of A

• P(B) = The probability that B is observed

• Bayes’ theorem deals with “inverse probabilities”

Example:• A friend tells you he had a nice conversation with someone in the train to

Nijmegen• What is the chance that this other person is a woman?• Your friend only tells you that this person has long hair.

• Does this change the previous probability?

• Say:• 75% of women have long hair• 15% of men have long hair

Bayes’ theorem• What if your friend told you that this person was also wearing high heels?• We can use P(W|L) as the new prior!

• This is called Bayesian updating• You adjust your ‘belief’ with each new piece of information!

• Bayesian updating assumes no relationship between L and H other than via W!

Bayesian odds• For convenience we can rewrite Bayes’ equation into odds (or Bayes factor)

Bayesian odds• If we now perform Bayesian updating we can simply write

Beware of ‘extreme’ cases (or priors)

• “A Bayesian is one who, vaguely expecting a horse, and catching a glimpse of a donkey, strongly believes he has seen a mule.”• http://www2.isye.gatech.edu/~brani/isyebayes/jokes.html

• What did we just “probabilistically” describe if the person was actually a man?

How can we integrate multiple datasets?Proteomics data

Genetic dataPublished data

Expression data Evolutionary data

Ciliary biology; a relatively young field

Ciliated tissues (some examples)Inner ear:Cilia function in hearing and balance

Cerebral cavities, Bronchia &Fallopian tubes

Retina:Cones and Rods

Sperm cells

Bayesian integration on SysCilia data

• Tandem Affinity Purifications & SILAC

• Yeast 2 Hybrid screens

• Ciliary evolutionary co-occurrence

• Gene presence/absence profiles matching ciliary presence/absence

• System co-expression

• Genes with XBOX transcription factor binding sites

• What is the probability that gene X is ciliary given that

it is reported by experiments 1, 2, 3, …, and n?

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Bayesian integration of multiple observations

• n is the number of datasets considered• fi = dataset i

• P(fi|T) = probability that a gene is reported by dataset i given it is a known ciliary gene

• We take log odds because deviations, caused by rounding and measurement errors, are not enlarged with each multiplication

Can we say something about genes that were not reported?

• In case of yes/no experiments, “No” can also have meaning.

• In case we have a result which has a value, we can use categories.For instance:

• Each gene falls into one category for each experiment.

Evaluating True and False per experiment• We need a list of known ciliary genes (a Gold Standard)• We need a list of known non-ciliary genes (a Negative Set)

• Then simply becomes

Fraction of GS reported by experiment iFraction of NS reported by experiment i

Gold Standard & Negative set

System co-expression

Distinguishing between ciliary vs. non-ciliary genes

Ranking based on Bayesian integration

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The Bayesian integration enriches for more known ciliary genes, than the individual datasets. We can control for False Discovery Rate.

CiliaryPredictedNon-ciliary

ROC-curve and performance of individual datasets

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AUC: 0.86

Application of the Bayesian integration• Predicting causative genes in ciliopathy disease loci or exome data• Predict which genes are likely involved in ciliary function, and which are not• Example BBS5 locus (182 genes):

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Ensembl GeneID Gene Symbol Rank Score

ENSG00000123607 TTC21B 65 5.580545431

ENSG00000163093 BBS5 99 4.863543816

ENSG00000154479 CCDC173 157 3.916022407

ENSG00000081479 LRP2 503 0.756945148

Conclusion• Bayesian integration is a powerful way to predict novel ciliary genes by

objective evaluation and integration of experimental datasets• New datasets can easily be incorporated

• You can use such a Bayesian integration to• Predict novel ciliary genes• Rank target genes from new experiments• Predict causative genes in patient exome data

Acknowledgements• Huynen Lab, Radboud UMC

• Roepman lab, Radboud UMC

• Oliver Blacque, UCD Dublin

Ueffing lab, Tübingen