Median Dissimilarity Ratio New Scale Measure of Heritability in Binomial Trait Using Median Odds Ratio @˜- GSPH, SNU October 24, 2014 @˜- (GSPH, SNU) Median Dissimilarity Ratio October 24, 2014 1 / 33
Median Dissimilarity RatioNew Scale Measure of Heritability in Binomial Trait Using Median
Odds Ratio
김진섭
GSPH, SNU
October 24, 2014
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개요
1 Binomial Trait에서 heritabily를 가늠할 수 있는 새로운 scale의 지표를소개
2 Heritability + λsib + Median Odds Ratio(MOR)
3 Median Dissimilairty Ratio between Sibling pair and Unrelated pair(MDRSU)
4 HyperTG trait(Healthy Twin Study, Korea)에 적용
5 새로운 역학지표로서의 의의.
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Previous Measure of Heritability
Contents
1 Previous Measure of HeritabilityHeritabilityλsib
2 Median Odds RatioIntroduction of MORMOR formula
3 New measure of HeritabilityIdeaMDRSU formula
4 Example of hyperTG(≥200): Healthy Twin Study, Korea
5 Discussion
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Previous Measure of Heritability Heritability
Heritability
The portion of phenotypic variance in a population attributable toadditive genetic factors
Intraclass correlation coefficient(ICC) scale
Mixed model로 계산 - Covariate 보정가능.
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Previous Measure of Heritability Heritability
문제점
Binomial trait: Logit scale VS probability Scale
해석 어렵다.
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Previous Measure of Heritability Heritability
Different scale: ICC??
Var(Yi ) = pi (1− pi ) (1)
logit(pi ) = Xiβ + Groupi (2)
Proportional scale VS Logistic scale[1]
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Previous Measure of Heritability Heritability
Example: binomial case
glmer(formula = hyperTG ~ age + sex + BMI + (1 | FID), data = a,
family = binomial)
Estimate Std. Error z value Pr(>|z|)
(Intercept) -6.65451749 1.48227814 -4.4893852 7.142904e-06
age 0.01052907 0.01206682 0.8725635 3.829010e-01
sex -1.48506920 0.60773433 -2.4436158 1.454090e-02
BMI 0.19131619 0.05022612 3.8090977 1.394749e-04
Groups Name Std.Dev.
FID (Intercept) 1.1163
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Previous Measure of Heritability Heritability
Solution
1 Linearization : logit → proportion
2 Simulation : proportion → logit
3 Latent variable
Approximation of ICC, calculation issue[1, 5]
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Previous Measure of Heritability λsib
λsib
1 Recurrence risk ratio
2 Sibling recurrence risk ratio(λsib)
3 일반 인구집단의 prevalence에 비해 affected people의 sibling집단에서의 prevalence가 몇배나 더 높은지를 나타내어 유전적인정도를 측정한다.
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Previous Measure of Heritability λsib
문제
1 일반 인구 집단에서의 prevalence를 정확히 측정해야 한다는 부담
2 Ascertainment bias에 민감
3 Polygenic effect 없이 common environmental factor의 영향에의해서도 증가할 수 있다.
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Median Odds Ratio
Contents
1 Previous Measure of HeritabilityHeritabilityλsib
2 Median Odds RatioIntroduction of MORMOR formula
3 New measure of HeritabilityIdeaMDRSU formula
4 Example of hyperTG(≥200): Healthy Twin Study, Korea
5 Discussion
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Median Odds Ratio Introduction of MOR
Median Odds Ratio(MOR)
Larsen et al.(2000, 2005)임의의 두 group을 골랐을 때 (Odds가 큰 그룹: 작은 그룹) 의 OR이대충(median) 얼마나 되는가?[3, 2, 4]
MOR = exp (√
2VGroup × Φ−1(0.75)) ' exp (0.95√VGroup) (3)
1 1 ∼ inf : Group효과 없다, 엄청 크다.
2 VGroup만 있으면 계산가능: mixed model
3 OR scale로 해석: age, sex 해석하듯이 하면 된다.
4 Covariate 보정가능!!
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Median Odds Ratio Introduction of MOR
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Median Odds Ratio Introduction of MOR
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Median Odds Ratio Introduction of MOR
Example: binomial case
glmer(formula = hyperTG ~ age + sex + BMI + (1 | FID), data = a,
family = binomial)
Groups Name Std.Dev.
FID (Intercept) 1.1163
MOR = exp(√
2× 1.11632 × 0.6745) = 3.67 (4)
: 임의의 두 가족을 뽑으면 대충(median) OR이 3.67이다.
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Median Odds Ratio MOR formula
Multilevel logistic regression[3]
Logit[Pr(Yij = 1|Xij ,Gj)] = β0 + X ′ijβ1 + Gj (5)
(β0: intercept, β1: vector of fixed regression coefficients, Gj : randomintercept Gj ∼ N(0,Vg ))
Odds[Pr(Yij = 1|Xij ,Gj)] = exp (β0) exp (X ′ijβ1) exp (Gj) (6)
Odds[Pr(Yij = 1|X ,Gj)]
Odds[Pr(Yik = 1|X ,Gk)]= exp (Gj − Gk) (7)
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Median Odds Ratio MOR formula
Odds가 큰그룹을 Odds가 작은 그룹과 비교!
OR = exp |Gj − Gk | (8)
(Gj − Gk) ∼ N(0, 2Vg ) (9)
결국 임의로 두 그룹을 뽑았을 때 Odds가 큰 그룹과 Odds가 작은 그룹을비교하여 OR의 median값을 계산하였을 때 그 결과는
MOR = exp (√
2Vg × Φ−1(0.75)) ' exp (0.95√
Vg) (10)
(Φ: probability density function(PDF) of standard normal distribution)
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New measure of Heritability
Contents
1 Previous Measure of HeritabilityHeritabilityλsib
2 Median Odds RatioIntroduction of MORMOR formula
3 New measure of HeritabilityIdeaMDRSU formula
4 Example of hyperTG(≥200): Healthy Twin Study, Korea
5 Discussion
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New measure of Heritability Idea
장점만 빼내자
Heritability : Covariate보정
λsib : 직관적인 해석(sib VS unrelated)
MOR의 비율로 만듦.
MDRSU : Ratio of MOR(sib VS unrelated)
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New measure of Heritability Idea
단점은 극복
Heritability: 해석어려움.
λsib : 유병률 알아야.. Bias.. Covariate보정안됨.
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New measure of Heritability MDRSU formula
MDRSU
Yi : ith individual의 health status(case: 1, control: 0, 1 ≤ i ≤ n)
Xi : vector of covariates
Gi : ith individual의 polygenic effect.
Logit[Pr(Yi = 1|Xi ,Gi )] = β0 + X ′i β1 + Gi (11)
(β0: intercept, β1: vector of fixed regression coefficients, Gi : polygeniceffect of ith individual
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New measure of Heritability MDRSU formula
Gi들의 vector: G = (G1,G2, · · · ,Gn)′
G ∼ N(0,Vp∑
). (∑
: genetic relationship matrix, Vp: variance ofpolygenic effect).
Odds[Pr(Yi = 1|Xi ,Gi )] = exp (β0) exp (X ′i β1) exp (Gi ) (12)
로 표현할 수 있으며 임의로 뽑은 ith individual과 jth individual의 Oddsratio는
Odds[Pr(Yi = 1|X ,Gi )]
Odds[Pr(Yj = 1|X ,Gj)]= exp (Gi − Gj) (13)
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New measure of Heritability MDRSU formula
unrelated individuals
i와 j를 unrelated individuals에서 뽑았을 경우
(Gi − Gj) ∼ N(0, 2Vg )
MORunrelated = exp (√
2Vg × Φ−1(0.75)) ' exp (0.95√
Vg ) (14)
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New measure of Heritability MDRSU formula
i ,j를 sibling pair에서 뽑았다면
i와 j가 항상 sibling이라면 Cov(Gi ,Gj) = 12Vg
(Gi − Gj) ∼ N(0,Vg )
MORsibling = exp (√
Vg × Φ−1(0.75)) ' exp (0.67√Vg ) (15)
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New measure of Heritability MDRSU formula
MOR은 대략적인 pair의 polygenic dissimilarity를 의미
Unrelated pair, sibling pair에서의 MOR의 비인 Median dissimilarityratio(MDR)를 정의.
MDRSU =MORunrelated
MORsibling' exp(0.28
√Vp) (16)
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New measure of Heritability MDRSU formula
Sibling pair의 Dissimilarity vs Unrelated의 Dissimilarity
MDRSU 크다.→ unrelated에서 sibling pair보다 dissimilarity가 크다.→ 유전적인 부분이 크다.
Polygenic effect의 variance만 이용하여 계산 → 간단히 계산GLMM이용 → covariate 보정가능!!
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Example of hyperTG(≥200): Healthy Twin Study, Korea
Contents
1 Previous Measure of HeritabilityHeritabilityλsib
2 Median Odds RatioIntroduction of MORMOR formula
3 New measure of HeritabilityIdeaMDRSU formula
4 Example of hyperTG(≥200): Healthy Twin Study, Korea
5 Discussion
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Example of hyperTG(≥200): Healthy Twin Study, Korea
R의 hglm 패키지 이용
Variable: Mean (SD) or N (%) Male Female P-value P-value:NP*Age 44.6 (13.6) 43.94 (12.73) 0.2 0.285
Smoking status < 0.001 < 0.0011 278 (26.18) 1505 (90.28)2 290 (27.31) 53 (3.18)3 494 (46.52) 109 (6.54)
TG 140.34 (92.34) 98.8 (62.82) < 0.001 < 0.001HyperTG* < 0.001 < 0.001
Control 862 (81.02) 1550 (92.65)Case 202 (18.98) 123 (7.35)
Table: Descriptive statistics of study population
(NP: non parametric: Wilcox rank sum test or Fisher exact test, HyperTG: I(TG≥200))
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Example of hyperTG(≥200): Healthy Twin Study, Korea
Parameter(95% CI) Model 1 Model 2 Model 3
Vp 0.92(0.76˜1.11) 0.96(0.79˜1.16) 0.94(0.78˜1.14)MORunrelated 2.49(2.29˜2.72) 2.54(2.33˜2.78) 2.51(2.31˜2.76)
MORsibling 1.9(1.8˜2.03) 1.93(1.82˜2.06) 1.92(1.8˜2.05)MDRsu 1.31(1.28˜1.34) 1.32(1.28˜1.35) 1.31(1.28˜1.35)
Table: Variance parameter and MOR related measures of Polygenic effects
(Model 1: no covariate, Model 2: age & sex as covariates, Model 3: age,sex and smoking status as covariates)
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Discussion
Contents
1 Previous Measure of HeritabilityHeritabilityλsib
2 Median Odds RatioIntroduction of MORMOR formula
3 New measure of HeritabilityIdeaMDRSU formula
4 Example of hyperTG(≥200): Healthy Twin Study, Korea
5 Discussion
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Discussion
1 New measure of Heritability
2 h2, λsib의 장점만 취하고 단점은 버린다.
3 본 지표가 binomial trait의 polygenic effect를 직관적으로 설명하는간단한 지표가 될 것이라 생각한다.
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Discussion
Reference I
[1] Browne, W. J., Subramanian, S. V., Jones, K., and Goldstein, H. (2005). Variance partitioning in multilevel logistic modelsthat exhibit overdispersion. Journal of the Royal Statistical Society: Series A (Statistics in Society), 168(3):599–613.
[2] Larsen, K. and Merlo, J. (2005). Appropriate assessment of neighborhood effects on individual health: integrating randomand fixed effects in multilevel logistic regression. American journal of epidemiology, 161(1):81–88.
[3] Larsen, K., Petersen, J. H., Budtz-Jørgensen, E., and Endahl, L. (2000). Interpreting parameters in the logistic regressionmodel with random effects. Biometrics, 56(3):909–914.
[4] Merlo, J., Chaix, B., Ohlsson, H., Beckman, A., Johnell, K., Hjerpe, P., Rastam, L., and Larsen, K. (2006). A briefconceptual tutorial of multilevel analysis in social epidemiology: using measures of clustering in multilevel logistic regressionto investigate contextual phenomena. Journal of Epidemiology and Community Health, 60(4):290–297.
[5] Vigre, H., Dohoo, I., Stryhn, H., and Busch, M. (2004). Intra-unit correlations in seroconversion to actinobacilluspleuropneumoniae and mycoplasma hyopneumoniae at different levels in danish multi-site pig production facilities. Preventiveveterinary medicine, 63(1-2):9–28.
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Discussion
END
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