Association mapping for mendelian, and complex disorders January 16Bafna, BfB

UG Bioinformatics specialization at UCSD January 16Bafna, BfB

Abstraction of a causal mutation January 16Bafna, BfB

Looking for the mutation in populations January 16Bafna, BfB A possible strategy is to collect cases (affected) and control individuals, and look for a mutation that consistently separates the two classes. Next, identify the gene.

Looking for the causal mutation in populations January 16Bafna, BfB Case Control Problem 1: many unrelated common mutations, around one every 1000bp

Case Control January 16Bafna, BfB

Looking for the causal mutation in populations January 16Bafna, BfB Case Control Problem 2: We may not sample the causal mutation.

How to hunt for disease genes We are guided by two simple facts governing these mutations 1. Nearby mutations are correlated 2. Distal mutations are not January 16Bafna, BfB Case Control

This lecture 1. The bottom line: How do these facts help in finding disease genes? 2. The genetics: why should this happen? 3. The computation 4. Challenge of complex diseases. January 16Bafna, BfB Case Control 1. Nearby mutations are correlated 2. Distal mutations are not

The basics of association mapping Sample a population of individuals at variant locations across the genome. Typically, these variants are single nucleotide polymorphisms (SNPs). Create a new bi-allelic variant corresponding to cases and controls, and test for correlations. By our assumptions, only the proximal variants will be correlated. Investigate genes near the correlated variants. January 16Bafna, BfB Case Control

So, why should the proximal SNPs be correlated, and distal SNPs not? January 16Bafna, BfB

A bit of evolution Consider a fixed population (of chromosomes) evolving in time. Each individual arises from a unique, randomly chosen parent from the previous generation January 16Bafna, BfB Time

Genealogy of a chromosomal population Current (extant) population Time January 16Bafna, BfB

Adding mutations January 16Bafna, BfB Infinite sites assumption: A mutation occurs at most once at a site.

SNPs January 16Bafna, BfB The collection of acquired mutations in the extant population describe the SNPs

Fixation and elimination Not all mutations survive. Some mutations get fixed, and are no longer polymorphic January 16Bafna, BfB

Removing extinct genealogies January 16Bafna, BfB

Removing fixed mutations January 16Bafna, BfB

The coalescent January 16Bafna, BfB

Disease mutation January 16Bafna, BfB We drop the ancestral chromosomes, and place the mutations on the internal branches.

Disease mutation A causal mutation creates a clade of affected descendants. January 16Bafna, BfB

Disease mutation Note that the tree (genealogy) is hidden. However, the underlying tree topology introduces a correlation between each pair of SNPs January 16Bafna, BfB

What have we learnt? The underlying genealogy creates a correlation between SNPs. By itself, this is not sufficient, because distal SNPs might also be correlated. Fortunately, for us the correlation between distal SNPs is quickly destroyed. January 16Bafna, BfB

Recombination January 16Bafna, BfB

Recombination In our idealized model, we assume that each individual chromosome chooses two parental chromosomes from the previous generation January 16Bafna, BfB

Multiple recombination change the local genealogy January 16Bafna, BfB

A bit of evolution Proximal SNPs are correlated, distal SNPs are not. The correlation (Linkage disequilibirium) decays rapidly after 20-50kb January 16Bafna, BfB

BASIC STATISTICS January 16Bafna, BfB

Testing for correlation In the absence of correlation January 16Bafna, BfB

Testing for correlation When correlated January 16Bafna, BfB

Assigning confidence January 16Bafna, BfB X X X X Expected Observed

Assigning confidence January 16Bafna, BfB X X X X Expected Observed

Assigning confidence January 16Bafna, BfB X X Expected Observed X X

STATISTICAL TESTS OF ASSOCIATION January 16Bafna, BfB

Tests for association: Pearson Case-control phenotype: –Build a 3X2 contingency table –Pearson test (2df)= CasesControls mm Mm MM O1O1 O2O2 O3O3 O4O4 O6O6 O5O5 January 16Bafna, BfB

The χ 2 test CasesControls mm Mm MM O1O1 O5O5 O3O3 O4O4 O2O2 O6O6 The statistic behaves like a χ 2 distribution. A p-value can be computed directly January 16Bafna, BfB

Χ 2 distribution properties A related distribution is the F-distribution January 16Bafna, BfB

Likelihood ratio Another way to check the extremeness of the distribution is by computing a (log) likelihood ratio. We have two competing hypothesis. Let N be the total number of observations January 16Bafna, BfB

LLR An LLR value close to 0, implies that the null hypothesis is true. Asymptotically, the LLR statistic also follows the chi-square distribution. January 16Bafna, BfB

Exact test The chi-square test does not work so well when the numbers are small. How can we compute an exact probability of seeing a specific distribution of values in the cells? Remember: we know the marginals (# cases, # controls, January 16Bafna, BfB

Fischer exact test CasesControls mm Mm MM a e cd b f Num: #ways of getting configuration (a,b,c,d,e,f) Den: #ways of ensuring that the row sums and column sums are fixed January 16Bafna, BfB

Fischer exact test Remember that the probability of seeing any specific values in the cells is going to be small. To get a p-value, we must sum over all similarly extreme values. How? January 16Bafna, BfB

Test for association: Fisher exact test Here P is the probability of seeing the exact count. The actual significance is computed by summing over all such tables that are at least this extreme. CasesControls mm Mm MM a e cd b f January 16Bafna, BfB

Test for association: Fisher exact test CasesControls mm Mm MM a e cd b f January 16Bafna, BfB

Continuous outcomes Instead of discrete (Case/control) data, we have real-valued phenotypes –Ex: Diastolic Blood Pressure In this case, how do we test for association January 16Bafna, BfB

Continuous outcome ANOVA Often, the phenotypes are not offered as case- controls but like a continuous variable –Ex: blood-pressure measurements Question: Are the mean values of the two groups significantly different? MMmm January 16Bafna, BfB

Two-sided t-test For two categories, ANOVA is also known as the t-test Assume that the variables from the two sets are drawn from Normal distributions –Different means, equal variances Null hypothesis is that they are both from the same distribution January 16Bafna, BfB

t-test continued January 16Bafna, BfB

Two-sample t-test As the variance is not known, we use an estimate S, defined by The T-statistic is given by Significant deviations from 0 are used to reject the Null hypothesis January 16Bafna, BfB

Two-sample t-test (unequal variances) If the variances cannot be assumed to be equal, we use The T-statistic is given by Significant deviations from 0 are used to reject the Null hypothesis January 16Bafna, BfB

CONFOUNDING ASSOCIATION January 16Bafna, BfB

Confounding association Association tests can be confounded in many ways. We will explore a few of these, at a high level, and point to a few algorithmic problems. January 16Bafna, BfB

Confounding association with population substructure January 16Bafna, BfB If the cases and controls are from different subpopulations, then sites with differing allele frequencies will confound association

The algorithmic problem Given a collection of individual genotypes, separate them into sub-populations. Idea: take markers that are very far apart so that no LD is possible. LD indicates structure. Problem: Partition individuals into sub-populations so that all correlation across pairs of distant markers is minimized. Penalty for increasing sub-populations? January 16Bafna, BfB

Confounding associations with genotypes January 16Bafna, BfB A recombination event Distinct haplotypes can create identical genotypes confounding association

Confounding association with interactions Individually, the markers do not correlate. Together, they perfectly predict genes. Find interacting partners that associate with genes January 16Bafna, BfB

Confounding association with rare variants Not only can we have multiple interacting SNPs, each SNP individually occurs with very low frequency (< 1%). Can you detect associations with rare variants? January 16Bafna, BfB

Other problems January 16Bafna, BfB Can we reconstruct the phylogeny? Useful for computing recombination bounds.

Conclusion As individual genomes are sequenced, the association of variations with phenotypes presents many confounding challenges. Some of these challenges can be modeled as algorithmic problems. Population genetics should be part of a bioinformatics undergraduate curriculum. January 16Bafna, BfB

Thank you Homework (due Monday, March 15) –Describe an algorithm to detect associations of interacting, rare-variants with a complex disease phenotype, in the presence of population substructure in the case-control population. January 16Bafna, BfB