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Statistical Analysis in Case-Control studies. Summer International Workshop Aug, 09, Beijing. Liu Tian Genome Institute of Singapore Outline . Introduction Basic Statistical Methods of Case-control Study GWAS A Novel Epistasis-testing Procedure .

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Statistical analysis in case control studies l.jpg

Statistical Analysis in Case-Control studies

Summer International Workshop

Aug, 09, Beijing

Liu Tian

Genome Institute of Singapore

Outline l.jpg



Basic Statistical Methods of Case-control Study


A Novel Epistasis-testing Procedure

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Aim of Genetic Studies

Dramatic variation do exist within a same spice

Almost every biological phenomenon involves a genetic component

There is always a keen need for us to seek the genetic variation relates to complex traits.

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Different Design Strategies

Intervention studies

Clinic trials

Observational studies

Case-control studies

Cohort studies

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Disease +/-

Cohort Studies

A cohort study is a study where a group of individuals are followed.

Cohort studies can be either prospective or retrospective

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Case-Control Studies

Case-control studies are used to identify factors that may contribute to a medical condition by comparing subjects who have that condition (the ‘cases’) with patients who do not have the condition but are otherwise similar (the ‘controls’)

Case-control studies are retrospective and non-randomized

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Case-Control Studies

Disease -

Disease +

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Selection of Cases

Population-based cases: include all subjects or a random sample of all subjects with the disease at a single point or during a given period of time in the defined population.

Hospital-based cases:

All patients in a hospital department at a given time

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Selection of Controls

Principles of Control Selection:

Study base: Controls can be used to characterise the distribution of exposure

Comparable-accuracy: Equal reliability in the information obtained from cases and controls (to avoid systematic misclassification)

Overcome confounding: Elimination of confounding through control selection (matching or stratified sampling)

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Selection of Controls

General population controls:

registries, households, telephone sampling

costly and time consuming

recall bias

eventually high non-response rate

Hospitalised controls:

Patients at the same hospital as the cases

Easy to identify; less recall bias; higher response rate

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Case-Control Studies vs. Cohort Studies

Cohort study

  • Rare exposure

  • Examine multiple effects of a single exposure

  • Minimizes bias in the in exposure determination

  • Direct measurements of incidence of the disease

Case-control study

  • Quick, inexpensive

  • Well-suited to the evaluation of diseases with long latency period

  • Rare diseases

  • Examine multiple etiologic factors for a single disease

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Case-Control Studies vs. Cohort Studies

Case-control study

  • Not rare exposure

  • Incidence rates cannot be estimated unless the study is population based

  • retrospective, non-randomized nature limits the conclusions that can be drawn from them.

Cohort study

Not rare diseases

Prospective: Expensive and time consuming

Retrospective: in adequate records

Validity can be affected by losses to follow-up

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sample id



Data Structure of Case-control studies

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Basic Statistical Methods of Case-control Study


A Novel Epistasis-testing Procedure

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Population-Based Case-Control Study

Individuals are unrelated

To test if marker genotypes distribute differently between the cases and controls

By comparing within cases and controls, we identify those genetic factors correlated with a pre-defined phenotype

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Coding Genotypes

For one marker with two alleles, there can be three possible genotypes:

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Genetic Models and Underlining Hypotheses

Genotypic Model

Hypothesis: all 3 different genotypes have different effects

Genotypic value is the expected phenotypic value of a particular genotype

AA vs. Aa vs. aa

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Genetic Models and Underlining Hypotheses

  • Dominant Model

    Hypothesis: the genetic effects of AA and Aa are the same (assuming A is the minor allele)

AA and Aa vs. aa

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Genetic Models and Underlining Hypotheses

  • Recessive Model

  • Hypothesis: the genetic effects of Aa and aa are the same (A is the minor allele)

AA vs. Aa and aa

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Genetic Models and Underlining Hypotheses

Allelic Model

Hypothesis: the genetic effects of allele A and allele a are different

A vs. a

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Pearson’s Chi-squaredTest

  • Genotypic Model:

  • Null Hypothesis: Independence

df = 2

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Pearson’s Chi-squaredTest

  • Dominant Model:

  • Null Hypothesis: Independence

df = 1

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Pearson’s Chi-squaredTest

  • Recessive Model:

  • Null Hypothesis: Independence

df = 1

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Pearson’s Chi-squaredTest

  • Allelic Model:

  • Null Hypothesis: Independence

df = 1

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Test Statistic

  • Chi-squared Test Statistic:

  • O is the observed cell counts

  • E is the expected cell counts, under null hypothesis of independence

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  • The following table summarize the genotype counts of marker M :

  • Different tests can be performed:

    - Allelic test

    - Dominant gene action

    - Recessive gene action

    - Genotypic test

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Example (Dominant Gene Action)

  • Using R:

  • dominant_table <- matrix(c(80,90,20,10), ncol = 2)

  • print(dominant_table )

  • chisq.test(dominant_table ,correct=FALSE)

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Example (Recessive Gene Action)

  • Using R:

  • recessive_table <- matrix(c(36,18,164,182), ncol = 2)

  • print(recessive_table)

  • chisq.test(recessive_table,correct=FALSE)

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Example (Genotypic Test)

  • Using R:

  • genotypic_table <- matrix(c(36,18,100,84,64,98), ncol = 3)

  • print(genotypic_table)

  • chisq.test(genotypic_table,correct=FALSE)

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Example (Allelic Test)

  • Using R:

  • allelic_table <- matrix(c(172,120,228,280), ncol = 2)

  • print(allelic _table)

  • chisq.test(allelic_table,correct=FALSE)

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Logistic Regression Analysis

A General Model:


pdisease is the probability that an individual has a particular disease.

β0 is the intercept

β1, β2 …βJ are the effects of genetic factors

X1, X2 …XJ are the dummy variables of genetic factors

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Logistic Regression Analysis

Logistic regression describes the relationship between a dichotomousresponse variable and a set of explanatory variables.

Logit model is the only model under which β, the effect parameter, can be estimated in retrospective studies as same as in prospective studies.

If the sampling rate for cases is 10 times that for controls, the intercept estimated is log(10) =2.3 than the one estimated with a prospective study.

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Inference and Interpretation

Significant test focus on:

Estimator is the estimated odds ratio for genetic factor i.

The sign of determines whether is increasing or decreasing when the effect of genetic factor i exists.

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Other Options

Fisher’s Exact Test:

When sample size is small, the asymptotic approximation of null distribution is no longer valid. By performing Fisher’s exact test, exact significance of the deviation from a null hypothesis can be calculated.

For a 2 by 2 table, the exact p-value can be calculated as:

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Other Options

  • Cochram-Armitage Trend Test

    -- An advantage of the Cochran-Armitage test is that it does not assume Hardy-Weinberg equilibrium

    -- Typically used to test a 2 × k contingency table, when the effects of AA, Aa, and aa are thought to be ordered.

    -- In genome-wide association studies, the additive (or codominant) version of the test is often used.

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  • Introduction

  • Basic Statistical Methods of Case-control Study

  • GWAS

  • A Novel Epistasis-testing Procedure

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Genome-wide Association Study

  • In genetic epidemiology, a genome-wide association study (GWAS) - also known as whole genome association study (WGA study) - is an examination of genetic variation across a given genome, designed to identify genetic associations with observable traits. In human studies, this might include traits such as blood pressure or weight, or why some people get a disease or condition.


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Genome-wide Association Study

  • Technology makes it feasible

    -- Affymetrix: 500K; 1M chip arrives in early 2007.

    (Randomly distributed)

    -- Illumina: 550K chip costs (gene-based)

  • Requires little on sample, Case-control data, case-parents trio data are enough.

  • Good for moderate effect sizes ( odds ratio < 1.5).

  • Particularly useful in finding genetic variations that contribute to common, complex diseases.

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What Is A SNP?


Chromosome 1



Chromosome 2


Single Nucleotide Polymorphism

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Handling GWAS

  • Storing and converting large amounts of genotype data

  • Quality control

  • Generating initial association analysis

  • Specialized analysis

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Quality Control Of SNPs

  • Exclude SNPs that failure the Hardy-Weinberg test

    -- Expected proportions of genotypes are not consistent with observed allele frequency

    -- HWE p-value < 10-4 to 10-6

  • Genotyping success rate < 95%

  • Differential missingness in cases and controls

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Quality Control Of Samples

  • Poor quality samples

    -- Sample genotype success rate < 95 to 97.5%

    -- Greater proportion of heterozygous genotypes than expected

  • Related individuals (if independent samples)

    -- Based on pair-wise comparisons of similarity of genotypes

  • Samples with miss specified gender

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Genetic Stratification

  • Assess population structure

  • Adjust both phenotypes and genotypes for possible stratification using

    --principal component analysis (Price’s method)

    -- cluster analyses (Plink)

  • Genomic Control

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Software Demonstration

  • Plink

    -- Case/control, TDT, quantitative traits

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-- Develop by Shaun Purcell

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Software Demonstration

  • Haploview:

    -- LD and haplotype block analysis

    -- tag SNP selection algorithm

    -- visualization and plotting GWAS results from PLINK