Transcript CS 6293 Advanced Topics: Translational Bioinformatics

CS 6293 Advanced Topics:
Translational Bioinformatics
Intro & Ch2 - Data-Driven View of
Disease Biology
Jianhua Ruan
Road map
• What is translational bioinformatics
• Probability and statistics background
• Data-driven view of disease biology
– Bayesian Inference
– Network of functional related genes
– Evaluation of network
What is translational
bioinformatics?
– Advancement in biological technology (for high-throughput data
collection) and computing technology (for cheap and efficient largescale data storage, processing, and management) has shifted modern
biomedical research towards integrative and translational
– Translational medical research:
• the process of moving discoveries and innovations generated during
research in the laboratory, and in preclinical studies, to the development of
trials and studies in humans, leading to improved diagnosis, prognosis, and
treatment.
– Barriers to translating our molecular understanding into technologies
that impact patients:
• understanding health market size and forces, the regulatory milieu, how to
harden the technology for routine use, and how to navigate an increasingly
complex intellectual property landscape
• Connecting the stuff of molecular biology to the clinical world
– The book chapters in this PLoS Comput Bio collection deals mostly with
computational methodologies that likely to have an impact on clinical
research / practice
Topic 1: Network-based understanding of
disease mechanisms
• Chapter 2: Data-Driven View of Disease
Biology
• Chapter 4: Protein Interactions and
Disease
• Chapter 5: Network Biology Approach to
Complex Diseases
• Chapter 15: Disease Gene Prioritization
Topic 2: drug design / discovery using
computational / systems approaches
• Chapter 3: Small Molecules and Disease
• Chapter 7: Pharmacogenomics
• Chapter 17: Bioimage Informatics for
Systems Pharmacology
Topics 3: Genome sequencing and
disease
• Chapter 6: Structural Variation and
Medical Genomics
• Chapter 12: Human Microbiome Analysis
• Chapter 14: Cancer Genome Analysis
Topic 4: Automated knowledge
discovery and representation
• Chapter 8: Biological Knowledge
Assembly and Interpretation
• Chapter 9: Analyses Using Disease
Ontologies
• Chapter 13: Mining Electronic Health
Records in the Genomics Era
• Chapter 16: Text Mining for Translational
Bioinformatics
Ch2: Data-Driven View of Disease
Biology
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Diverse genome-scale datasets exist
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Genome sequences
Microarrays
genome-wide association studies
RNA interference screens
Proteomics databases
Databases of gene functions, pathways, chemicals, protein interactions, etc.
Promise to provide systems level understanding of disease mechanisms
– Modeling (understand)
– Inference (make prediction)
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Integration is the key challenge
– Experimental noise
– Biological heterogeneity: e.g. source of material – cells in culture or biopsied
tissues?
– Computational heterogeneity: e.g. data format – discrete or continuous?
Bayesian Inference
• Powerful tool used to make predictions
based on experimental evidence
• Simple yet elegant probabilistic theories
• Easy to understand and implement
• Data-driven modeling
– No explicit assumption about the underlying
biological mechanisms
Probability Basics
• Definition (informal)
– Probabilities are numbers assigned to events
that indicate “how likely” it is that the event
will occur when a random experiment is
performed
– A probability law for a random experiment is
a rule that assigns probabilities to the events
in the experiment
– The sample space S of a random experiment
is the set of all possible outcomes
Example
0  P(Ai)  1
P(S) = 1
Random variable
• A random variable is a function from a
sample to the space of possible values of
the variable
– When we toss a coin, the number of times
that we see heads is a random variable
– Can be discrete or continuous
• The resulting number after rolling a die
• The weight of an individual
Cumulative distribution function
(cdf)
• The cumulative distribution function FX(x)
of a random variable X is defined as the
probability of the event {X≤x}
F (x) = P(X ≤ x) for −∞ < x < +∞
Probability density function (pdf)
• The probability density function of a
continuous random variable X, if it
exists, is defined as the derivative of
FX(x)
• For discrete random variables, the
equivalent to the pdf is the probability
mass function (pmf):
Probability density function vs
probability
• What is the probability for
somebody weighting 200lb?
• The figure shows about 0.62
– What is the probability of
200.00001lb?
• The right question would be:
– What’s the probability for somebody
weighting 199-201lb.
• The probability mass function is
true probability
– The chance to get any face is 1/6
Some common distributions
• Discrete:
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Binomial
Multinomial
Geometric
Hypergeometric
Possion
• Continuous
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Normal (Gaussian)
Uniform
EVD
Gamma
Beta
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Probabilistic Calculus
• If A, B are mutually exclusive:
– P(A U B) = P(A) + P(B)
• Thus: P(not(A)) = P(Ac) = 1 – P(A)
A
B
Probabilistic Calculus
• P(A U B) = P(A) + P(B) – P(A ∩ B)
Conditional probability
• The joint probability of two events A and B
P(A∩B), or simply P(A, B) is the probability that
event A and B occur at the same time.
• The conditional probability of P(B|A) is the
probability that B occurs given A occurred.
P(A | B) = P(A ∩ B) / P(B)
Example
• Roll a die
– If I tell you the number is less than 4
– What is the probability of an even number?
• P(d = even | d < 4) = P(d = even ∩ d < 4) / P(d < 4)
• P(d = 2) / P(d = 1, 2, or 3) = (1/6) / (3/6) = 1/3
Independence
• P(A | B) = P(A ∩ B) / P(B)
=> P(A ∩ B) = P(B) * P(A | B)
• A, B are independent iff
– P(A ∩ B) = P(A) * P(B)
– That is, P(A) = P(A | B)
• Also implies that P(B) = P(B | A)
– P(A ∩ B) = P(B) * P(A | B) = P(A) * P(B | A)
Examples
• Are P(d = even) and P(d < 4) independent?
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P(d = even and d < 4) = 1/6
P(d = even) = ½
P(d < 4) = ½
½ * ½ > 1/6
• If your die actually has 8 faces, will P(d = even)
and P(d < 5) be independent?
• Are P(even in first roll) and P(even in second
roll) independent?
• Playing card, are the suit and rank independent?
Bayes theorem
• P(A ∩ B) = P(B) * P(A | B) = P(A) * P(B | A)
Likelihood
=> P(B | A) =
Posterior probability of B
P ( A | B ) P (B )
Prior of B
P( A)
Normalizing constant
This is known as Bayes Theorem or Bayes Rule, and is (one of) the
most useful relations in probability and statistics
Bayes Theorem is definitely the fundamental relation in Statistical Pattern
Recognition
Example
• Prosecutor’s fallacy
– Some crime happened
– The suspect did not leave any evidence, except some
hair
– The police got his DNA from his hair
• Some expert matched the DNA with that of a
suspect
– Expert said that both the false-positive and false
negative rates are 10-6
• Can this be used as an evidence of guilty
against the suspect?
Prosecutor’s fallacy
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Prob (match | innocent) = 10-6
Prob (no match | guilty) = 10-6
Prob (match | guilty) = 1 - 10-6 ~ 1
Prob (no match | innocent) = 1 - 10-6 ~ 1
• Prob (guilty | match) = ?
Prosecutor’s fallacy
P (g | m) = P (m | g) * P(g) / P (m)
~ P(g) / P(m)
• P(g): the probability for someone to be
guilty with no other evidence
• P(m): the probability for a DNA match
• How to get these two numbers?
– We don’t really care P(m)
– We want to compare two models:
• P(g | m) and P(i | m)
Prosecutor’s fallacy
• P(i | m) = P(m | i) * P(i) / P(m)
= 10-6 * P(i) / P(m)
• Therefore
P(i | m) / P(g | m) = 10-6 * P(i) / P(g)
• P(i) + P(g) = 1
• It is clear, therefore, that whether we can conclude the
suspect is guilty depends on the prior probability P(i)
• How do you get P(i)?
Prosecutor’s fallacy
• How do you get P(i)?
• Depending on what other information you have on the
suspect
• Say if the suspect has no other connection with the
crime, and the overall crime rate is 10-7
• That’s a reasonable prior for P(g)
• P(g) = 10-7, P(i) ~ 1
• P(i | m) / P(g | m) = 10-6 * P(i) / P(g) = 10-6/10-7 = 10
Prosecutor’s fallacy
• P(i | m) / P(g | m) = 10-6/10-7 = 10
• Therefore, we would say the suspect is
more likely to be innocent than guilty,
given only the DNA samples
• We can also explicitly calculate P(i | m):
P(m) = P(m|i)*P(i) + P(m|g)*P(g)
= 10-6 * 1 + 1 * 10-7
= 1.1 x 10-6
P(i | m) = P(m | i) * P(i) / P(m) = 1 / 1.1 = 0.91
Another example
• A test for a rare disease claims that it will
report a positive result for 99.5% of people
with the disease, and 99.9% of time of
those without.
• The disease is present in the population at
1 in 100,000
• What is P(disease | positive test)?
• What is P(disease | negative test)?
Relation to multiple testing problem
• When searching a DNA sequence against a database,
you get a high score, with a significant p-value
• P(unrelated | high score) / P(related | high score) =
P(high score | unrelated) * P(unrelated)
P(high score | related) * P(related)
Likelihood ratio
• P(high score | unrelated) is much smaller than P(high
score | related)
• But your database is huge, and most sequences should
be unrelated, so P(unrelated) is much larger than
P(related)
Combining Diverse Data Using
Bayesian Inference
• Want to calculate the probability that a
gene of unknown function is involved in a
disease
• Collect positive and negative genes (gold
standard)
• Measure their activities under three
hypothetical conditions
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Figure 1. Potential distributions of experimental results obtained for datasets collected under three different conditions.
Greene CS, Troyanskaya OG (2012) Chapter 2: Data-Driven View of Disease Biology. PLoS Comput Biol 8(12): e1002816.
doi:10.1371/journal.pcbi.1002816
http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002816
Higher score in cond A and lower score in cond C => involved in disease
P (involved in disease | experimental data)?
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Table 1. A contingency table for the experimental results for Condition A.
Greene CS, Troyanskaya OG (2012) Chapter 2: Data-Driven View of Disease Biology. PLoS Comput Biol 8(12): e1002816.
doi:10.1371/journal.pcbi.1002816
http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002816
• Probability that a gene i is involved in
disease given the experimental results for
likelihood
gene i
Prior
Normalizing factor
Prior
Combining datasets using Naïve
Bayes
P(D | EB, EC)  P(EB, EC | D) P(D)
 P(EB | D) P(EC | D) P(D)
P(~D | EB, EC)  P(EB, EC | ~D) P(~D)
 P(EB | ~D) P(EC | ~D) P(~D)
P(D | EB, EC) + P(~D | EB, EC) = 1.
Define Gold Standard (training
samples) for gene-gene network
• Positive examples: genes within the same
biological process
– Rely on expert selected Gene Ontology terms
• biological regulation 
• response to stimulus 
• cell-matrix adhesion involved in tangential migration using
cell-cell interactions 
• response to DNA damage stimulus 
• ldehyde metabolism 
• Negative examples: random gene pairs
– Assuming most gene pairs are not related
Building a Network of Functionally
Related Genes
• P(FRij | Eij) = P(Eij | FRij) P(FRij)
• Eij: evidence (score) for a functional relationship
between gene i and gene j from a particular
dataset
• For some dataset, e.g., physical interaction data,
obtaining Sij is trivial
• In general, Sij can be calculated using gene-wise
correlation
Fisher's z-transformation
• Pearson correlation coefficient
Z-transformation
Purpose: stabilizing variance
Source: wikipedia
•
Figure 4. The highest and lowest contributing datasets for the pair of APOE and PLTP are shown
(http://hefalmp.princeton.edu/gene/one_specific_gene/18543?argument=21697&amp;context=0).
Greene CS, Troyanskaya OG (2012) Chapter 2: Data-Driven View of Disease Biology. PLoS Comput Biol 8(12): e1002816.
doi:10.1371/journal.pcbi.1002816
http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002816
•
Figure 5. The diseases that are significantly connected to APOE through the guilt by association strategy used in HEFalMp.
Used Fisher’s exact test
Greene CS, Troyanskaya OG (2012) Chapter 2: Data-Driven View of Disease Biology. PLoS Comput Biol 8(12): e1002816.
doi:10.1371/journal.pcbi.1002816
http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002816
•
Figure 6. The genes that are most significantly connected to Alzheimer disease genes using the HEFalMp network and OMIM
disease gene annotations (http://hefalmp.princeton.edu/disease/all_genes/55?context=0).
Greene CS, Troyanskaya OG (2012) Chapter 2: Data-Driven View of Disease Biology. PLoS Comput Biol 8(12): e1002816.
doi:10.1371/journal.pcbi.1002816
http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002816
Evaluating Functional Relationship
Networks
• TPR vs FPR plot (ROC curve) and AUC
• Separate gold standard into training and
testing
• Cross validation
• Literature evaluation
Summary
• We talked about
– Prob / stats background
– Bayes inference method to integrate multiple largescale, noisy datasets to predict
• gene-disease associations
• gene-gene associations
– Network useful for discovering novel gene functions
and directing experimental followups
• Advantage against curated literature or analysis based on
single dataset
• Limited by availability / quality of gold standard data