- Not really a talk (too long)
- Like an R package vignette (as long as necessary)
May, 2016
bit.ly/1UiTZvQ
About this talk
About lme4qtl
lme4qtl \(=\) an extension of the lme4 R package
lme4qtl \(=\)
linear
mixed
effects models for
4
quantitative
trait
loci mapping
About lme4qtl user
Implementation
2-column Layout
- Bullet 1
- Bullet 2
- Bullet 3
Results
QTL mapping examples using lme4qtl
Examples / Models
- Polygenic (quantitative trait)
- Polygenic (binary trait)
- Polygenic (counts)
- Association (quantitative trait)
- Linkage (quantitative trait)
- GxE (sex-especificity)
- GxE (ageing)
Data preparation
- Write the formula of your model
- Write your data table into a data frame
- Compute the relation matrix across your grouping IDs
relmatLmer( myTrait ~ myCovariate + (1|myID), # 1 myData, # 2 relmat = list(myID = myMatrix) # 3 )
Description of the GAIT data
| R objects | Description |
|---|---|
| phen/phen2 | A data frame with phenotypes and IDs (GAIT1/GAIT2) |
| dkin/dkin2 | The double kinship matrix with IDs in row/columns names (GAIT1/GAIT2) |
Description of the GAIT data (variables)
| Variables in phen | Type | Project | Description |
|---|---|---|---|
| ID | character | The individual's ID (must be unique) | |
| HHID | character | The individual's house-hold ID | |
| SEXf | factor | The gender (Male/Female) | |
| AGE/AGEc/AGEsc | numeric | The age (raw/centered/scaled) | |
| AGEc2/AGEsc2 | numeric | The age squared (centered/scaled) | |
| APTT | numeric | GAIT1 | Activated Partial Thromboplastin Time (units, sec) |
| Throm | factor | GAIT2 | The thrombosis disease status (control/affected) |
Models (1/7)
- Polygenic (quantitative trait)
- Polygenic (binary trait)
- Polygenic (counts)
- Association (quantitative trait)
- Linkage (quantitative trait)
- GxE (sex-especificity)
- GxE (ageing)
APTT phenotype
Activated partial thromboplastin time (APTT) is a clinical test used to screen for coagulation-factor deficiencies.
Associations with KNG1, HRG, F11, F12, and ABO were confirmed in a meta-anaysis of 9,240 individuals (European ancestry) (Tang et al. 2012)
Polygenic model for APTT
m <- relmatLmer(APTT ~ AGEsc + (1|ID), phen, relmat = list(ID = dkin)) m
## Linear mixed model fit by REML ['lmerMod'] ## Formula: APTT ~ AGEsc + (1 | ID) ## Data: phen ## REML criterion at convergence: -805.8705 ## Random effects: ## Groups Name Std.Dev. ## ID (Intercept) 0.0873 ## Residual 0.0423 ## Number of obs: 392, groups: ID, 392 ## Fixed Effects: ## (Intercept) AGEsc ## 0.96260 -0.03125
Residuals
r <- residuals(m)
qqnorm(r); qqline(r)
hist(r, breaks = 30)
Drop fixed effects
m <- relmatLmer(APTT ~ AGEsc + I(AGEsc^2) + SEXf + (1|HHID) + (1|ID), phen, relmat = list(ID = dkin), REML = FALSE)
drop1(m, test = "Chisq")
## Single term deletions ## ## Model: ## APTT ~ AGEsc + I(AGEsc^2) + SEXf + (1 | HHID) + (1 | ID) ## Df AIC LRT Pr(Chi) ## <none> -815.93 ## AGEsc 1 -748.67 69.254 < 2e-16 *** ## I(AGEsc^2) 1 -812.45 5.476 0.01928 * ## SEXf 1 -816.87 1.059 0.30346 ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Anova
m <- relmatLmer(APTT ~ AGEsc + I(AGEsc^2) + SEXf + (1|HHID) + (1|ID), phen, relmat = list(ID = dkin))
m0 <- update(m, . ~ . - (1|HHID)) anova(m, m0)
## refitting model(s) with ML (instead of REML)
## Data: phen ## Models: ## m0: APTT ~ AGEsc + I(AGEsc^2) + SEXf + (1 | ID) ## m: APTT ~ AGEsc + I(AGEsc^2) + SEXf + (1 | HHID) + (1 | ID) ## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq) ## m0 6 -817.93 -794.10 414.96 -829.93 ## m 7 -815.93 -788.13 414.96 -829.93 0 1 1
Exact Restricted LRT (single effect)
m <- relmatLmer(APTT ~ AGEsc + I(AGEsc^2) + SEXf + (1|ID), phen, relmat = list(ID = dkin))
library(RLRsim) exactRLRT(m)
## ## simulated finite sample distribution of RLRT. ## ## (p-value based on 10000 simulated values) ## ## data: ## RLRT = 105.16, p-value < 2.2e-16
Exact Restricted LRT (many effects)
m <- relmatLmer(APTT ~ AGEsc + I(AGEsc^2) + SEXf + (1|ID), phen, relmat = list(ID = dkin)) m0 <- update(m, . ~ . + (1|HHID))
library(RLRsim) exactRLRT(m0, mA = m, m0 = m0)
## ## simulated finite sample distribution of RLRT. ## ## (p-value based on 10000 simulated values) ## ## data: ## RLRT = 0, p-value = 1
Models (2/7)
- Polygenic (quantitative trait)
- Polygenic (binary trait)
- Polygenic (counts)
- Association (quantitative trait)
- Linkage (quantitative trait)
- GxE (sex-especificity)
- GxE (ageing)
Thrombosis phenotype
Thrombosis is a common complex disease associated with substantial morbidity and mortality.
The major determinants of thrombosis include both environmental and genetic factors.
- Enironmental: age & gender
- Genetic: ABO blood group system (wikipedia)
- Group O is protector
The contribution of genetic risk factors is estimated around 60% (Souto et al. 2000).
Polygenic model for Throm
m <- relmatGlmer(Throm ~ (1|ID), phen2, relmat = list(ID = dkin2), family = binomial) m
## Generalized linear mixed model fit by maximum likelihood (Laplace ## Approximation) [glmerMod] ## Family: binomial ( logit ) ## Formula: Throm ~ (1 | ID) ## Data: phen2 ## AIC BIC logLik deviance df.resid ## 955.1614 965.1910 -475.5807 951.1614 1111 ## Random effects: ## Groups Name Std.Dev. ## ID (Intercept) 1.264 ## Number of obs: 1113, groups: ID, 1113 ## Fixed Effects: ## (Intercept) ## -2.321
Covariates
m <- relmatGlmer(Throm ~ AGEsc + SEXf + ABOf3num + (1|ID), phen2, relmat = list(ID = dkin2), family = binomial)
summaryCoef(m, signif.legend = TRUE)
## Estimate Std. Error z value Pr(>|z|) ## (Intercept) -2.7106 0.5375 -5.043 4.59e-07 *** ## AGEsc 1.3554 0.2117 6.401 1.54e-10 *** ## SEXf2 0.2792 0.2695 1.036 0.30023 ## ABOf3num -0.5584 0.2160 -2.585 0.00973 ** ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Disease prevalence 5%
K <- 0.05 dat <- mutate(phen2, offset = log(K/(1 - K))) m <- relmatGlmer(Throm ~ -1 + AGEsc + SEXfnum + ABOf3num + (1|ID), dat, offset = offset, relmat = list(ID = dkin2), family = binomial)
summaryCoef(m) # offset = log(K/(1 - K)) = -2.944439
## Estimate Std. Error z value Pr(>|z|) ## AGEsc 1.4220 0.1673 8.498 <2e-16 *** ## SEXfnum 0.3171 0.2643 1.200 0.2302 ## ABOf3num -0.5662 0.2384 -2.374 0.0176 *
Probit link function
K <- 0.02 dat <- mutate(phen2, offset = -qnorm(1 - K)) m <- relmatGlmer(Throm ~ -1 + AGEsc + SEXfnum + ABOf3num + (1|ID), dat, offset = offset, relmat = list(ID = dkin2), family = binomial(probit))
summaryCoef(m) # offset = -qnorm(1 - K) = -2.053749
## Estimate Std. Error z value Pr(>|z|) ## AGEsc 0.8898 0.1048 8.491 <2e-16 *** ## SEXfnum 0.2728 0.1671 1.632 0.1026 ## ABOf3num -0.3037 0.1603 -1.894 0.0582 .
See also (Zaitlen et al. 2012)
Modeling prevalence?
GAIT2 (118 vs. 817)
GAIT1 (53 vs. 340)
Models (3/7)
- Polygenic (quantitative trait)
- Polygenic (binary trait)
- Polygenic (counts)
- Association (quantitative trait)
- Linkage (quantitative trait)
- GxE (sex-especificity)
- GxE (ageing)
Polygenic model of PTES
m <- relmatGlmer(PTES ~ AGEsc + AGEsc2 + SEXf + (1|ID), phen2, relmat = list(ID = dkin2), family = poisson)
m
## Generalized linear mixed model fit by maximum likelihood (Laplace ## Approximation) [glmerMod] ## Family: poisson ( log ) ## Formula: PTES ~ AGEsc + AGEsc2 + SEXf + (1 | ID) ## Data: phen2 ## AIC BIC logLik deviance df.resid ## 10154.429 10178.627 -5072.215 10144.429 929 ## Random effects: ## Groups Name Std.Dev. ## ID (Intercept) 0.2697 ## Number of obs: 934, groups: ID, 934 ## Fixed Effects: ## (Intercept) AGEsc AGEsc2 SEXf2 ## 5.37879 -0.07799 0.01845 0.12344
Drop fixed effects
m <- relmatGlmer(PTES ~ AGEsc + AGEsc2 + SEXf + (1|ID), phen2, relmat = list(ID = dkin2), family = poisson)
drop1(m, test = "Chisq")
## Single term deletions ## ## Model: ## PTES ~ AGEsc + AGEsc2 + SEXf + (1 | ID) ## Df AIC LRT Pr(Chi) ## <none> 10154 ## AGEsc 1 10291 138.532 < 2.2e-16 *** ## AGEsc2 1 10166 13.798 0.0002035 *** ## SEXf 1 10220 67.163 2.499e-16 *** ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Models (4/7)
- Polygenic (quantitative trait)
- Polygenic (binary trait)
- Polygenic (counts)
- Association (quantitative trait)
- Linkage (quantitative trait)
- GxE (sex-especificity)
- GxE (ageing)
Association between APTT and AB0
dat <- subset(phen, !is.na(ab0)) m0 <- relmatLmer(APTT ~ AGEsc + (1|ID), dat, relmat = list(ID = dkin))
m <- update(m0, . ~. + ab0) anova(m0, m)
## refitting model(s) with ML (instead of REML)
## Data: dat ## Models: ## m0: APTT ~ AGEsc + (1 | ID) ## m: APTT ~ AGEsc + (1 | ID) + ab0 ## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq) ## m0 4 -792.18 -776.38 400.09 -800.18 ## m 5 -801.47 -781.71 405.73 -811.47 11.286 1 0.0007808 *** ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
lme4qtl is flexible
AB0 influences both mean and variance of APTT
*Not the same as in (Chen and Abecasis 2007)
AB0 fixed and random effects
dat <- subset(phen, !is.na(ab0)) m0 <- relmatLmer(APTT ~ AGEsc + (1|ID), dat, relmat = list(ID = dkin))
m1 <- update(m0, . ~. + ab0) m2 <- update(m0, . ~. + ab0 + (1|ab0)) anova(m1, m2)
## refitting model(s) with ML (instead of REML)
## Data: dat ## Models: ## m1: APTT ~ AGEsc + (1 | ID) + ab0 ## m2: APTT ~ AGEsc + (1 | ID) + ab0 + (1 | ab0) ## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq) ## m1 5 -801.47 -781.71 405.73 -811.47 ## m2 6 -799.47 -775.76 405.73 -811.47 0 1 1
Contribution of AB0 random effect
Additional variance explained by ABO is small, while df \(=\) 2
m2
## Linear mixed model fit by REML ['lmerMod'] ## Formula: APTT ~ AGEsc + (1 | ID) + ab0 + (1 | ab0) ## Data: dat ## REML criterion at convergence: -786.5521 ## Random effects: ## Groups Name Std.Dev. ## ID (Intercept) 0.085365 ## ab0 (Intercept) 0.004455 ## Residual 0.043433 ## Number of obs: 384, groups: ID, 384; ab0, 3 ## Fixed Effects: ## (Intercept) AGEsc ab0 ## 0.95564 -0.03065 0.02563
lme4qtl is efficient
CPU time on GWAS
| Model | SOLAR (days) | lme4qtl (days) |
|---|---|---|
APTT ~ 1 + (1|ID) |
1.2 | 1.6 |
APTT ~ AGE + SEX + (1|ID) |
1.6 | 1.6 |
APTT ~ 1 + (1|HHID) + (1|ID) |
5.6 | 1.7 |
APTT ~ AGE+ SEX + (1|HHID) + (1|ID) |
8.2 | 1.7 |
- Server with RAM 128G, 64 CPU \(\times\) 2.3G
- SOLAR 7.6.6 (stable on March, 2015)
- GAIT2: N = 934 individuals, M = 10M markers
Models (5/7)
- Polygenic (quantitative trait)
- Polygenic (binary trait)
- Polygenic (counts)
- Association (quantitative trait)
- Linkage (quantitative trait)
- GxE (sex-especificity)
- GxE (ageing)
FXII phenotype
(Soria et al. 2002) showed that a locus in the F12 gene influences both
- Coagulation Factor XII (FXII) activity
- Susceptibility to thrombosis
Results of (a) linkage and (b) association mappings on Chromosome 5 for Factor FXII in the GAIT1 sample. The identified locus is the F12 gene. Figure source: (Ziyatdinov et al. 2015).
Locus F12 and related MIBD matrix
f <- system.file("extdata/gait1/mibd.5.200.gz", package = "gait")
library(solarius)
mf <- read_mibd_csv_gz(f)
mibd <- Matrix(mf2mat(mf))
mibd[1:7, 1:7] # a sub-matrix of 449 x 449
## 7 x 7 sparse Matrix of class "dsCMatrix" ## 01101 01102 01202 01203 01204 01205 01208 ## 01101 1.0 . 0.5000 0.5000 . 0.5000 0.5000 ## 01102 . 1.0 0.5000 0.5000 . 0.5000 0.5000 ## 01202 0.5 0.5 1.0000 0.9965 . 0.9963 0.0091 ## 01203 0.5 0.5 0.9965 1.0000 . 0.9972 0.0079 ## 01204 . . . . 1 . . ## 01205 0.5 0.5 0.9963 0.9972 . 1.0000 0.0084 ## 01208 0.5 0.5 0.0091 0.0079 . 0.0084 1.0000
Locus F12 linked to APTT
dat <- mutate(phen, IBDID = ID) m <- relmatLmer(APTT ~ AGEsc + (1|ID) + (1|IBDID), dat, relmat = list(ID = dkin, IBDID = mibd), REML = FALSE) m0 <- update(m, . ~ . - (1|IBDID)) # anova(m, m0) (LOD <- (logLikNum(m) - logLikNum(m0)) / log(10))
## [1] 1.271161
Locus F12 linked to FXII
m <- relmatLmer(FXII ~ (1|ID) + (1|IBDID), dat, relmat = list(ID = dkin, IBDID = mibd), REML = FALSE) m0 <- update(m, . ~ . - (1|IBDID)) # anova(m, m0) (LOD <- (logLikNum(m) - logLikNum(m0)) / log(10))
## [1] 9.326086
lme4qtl is flexible
Combined linkage-association model
*Aslmost the same model as in (Chen and Abecasis 2007)
Combined linkage-association model
dat <- mutate(subset(phen, !is.na(c46t)), IBDID = ID) m <- relmatLmer(FXII ~ c46t + (1|ID) + (1|IBDID), dat, relmat = list(ID = dkin, IBDID = mibd)) m0 <- update(m, . ~ . - c46t - (1|IBDID)) anova(m, m0)
## refitting model(s) with ML (instead of REML)
## Data: dat ## Models: ## m0: FXII ~ (1 | ID) ## m: FXII ~ c46t + (1 | ID) + (1 | IBDID) ## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq) ## m0 3 3739.8 3751.6 -1866.9 3733.8 ## m 5 3592.0 3611.8 -1791.0 3582.0 151.76 2 < 2.2e-16 *** ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Which of two genetic components?
dat <- mutate(subset(phen, !is.na(c46t)), IBDID = ID) m <- relmatLmer(FXII ~ c46t + (1|ID) + (1|IBDID), dat, relmat = list(ID = dkin, IBDID = mibd)) m0 <- update(m, . ~ . - c46t - (1|IBDID)) m1 <- update(m, . ~ . - c46t) m2 <- update(m, . ~ . - (1|IBDID))
c46t (fixed effect) is the key player
anova(m, m0, m1, m2)
## refitting model(s) with ML (instead of REML)
## Data: dat ## Models: ## m0: FXII ~ (1 | ID) ## m1: FXII ~ (1 | ID) + (1 | IBDID) ## m2: FXII ~ c46t + (1 | ID) ## m: FXII ~ c46t + (1 | ID) + (1 | IBDID) ## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq) ## m0 3 3739.8 3751.6 -1866.9 3733.8 ## m1 4 3698.8 3714.6 -1845.4 3690.8 42.9508 1 5.614e-11 *** ## m2 4 3592.7 3608.5 -1792.4 3584.7 106.0915 0 < 2.2e-16 *** ## m 5 3592.0 3611.8 -1791.0 3582.0 2.7186 1 0.09918 . ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Models (6/7)
- Polygenic (quantitative trait)
- Polygenic (binary trait)
- Polygenic (counts)
- Association (quantitative trait)
- Linkage (quantitative trait)
- GxE (sex-especificity)
- GxE (ageing)
Sex-specificity for BMI (GAIT1)
# Common polygenic model m0 <- relmatLmer( BMI ~ AGEsc + AGEsc2 + SEXf + (1|HHID) + (1|ID), phen, relmat = list(ID = dkin)) # Sex-specificity only in the residual variance m1 <- relmatLmer( BMI ~ AGEsc + AGEsc2 + SEXf + (1|ID) + (0 + SEXf|RID) + (1|HHID), phen, relmat = list(ID = dkin), weights = rep(1e10, nrow(phen)), vcControl = list(rho0 = list(rid = 3))) # Sex-specificity in both polygenic and residual variances m2 <- relmatLmer( BMI ~ AGEsc + AGEsc2 + SEXf + (0 + SEXf|ID) + (0 + SEXf|RID) + (1|HHID), phen, relmat = list(ID = dkin), weights = rep(1e10, nrow(phen)), vcControl = list(rho0 = list(rid = 5)))
Examine the models' parameters
VarCorr(m1)
## Groups Name Std.Dev. Corr ## ID (Intercept) 0.089062 ## RID SEXf1 0.095182 ## SEXf2 0.135234 0.000 ## HHID (Intercept) 0.052327 ## Residual 0.093239
VarCorr(m2)
## Groups Name Std.Dev. Corr ## ID SEXf1 0.101001 ## SEXf2 0.105480 0.421 ## RID SEXf1 0.081500 ## SEXf2 0.123478 0.000 ## HHID (Intercept) 0.051211 ## Residual 0.108221
Test the sex-specificity hypothesis
anova(m0, m1, m2)
## refitting model(s) with ML (instead of REML)
## Data: phen ## Models: ## m0: BMI ~ AGEsc + AGEsc2 + SEXf + (1 | HHID) + (1 | ID) ## m1: BMI ~ AGEsc + AGEsc2 + SEXf + (1 | ID) + (0 + SEXf | RID) + (1 | ## m1: HHID) ## m2: BMI ~ AGEsc + AGEsc2 + SEXf + (0 + SEXf | ID) + (0 + SEXf | RID) + ## m2: (1 | HHID) ## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq) ## m0 7 -359.40 -331.64 186.70 -373.40 ## m1 10 -362.06 -322.39 191.03 -382.06 8.6533 3 0.03427 * ## m2 12 -362.91 -315.32 193.46 -386.91 4.8551 2 0.08825 . ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Models (7/7)
- Polygenic (quantitative trait)
- Polygenic (binary trait)
- Polygenic (counts)
- Association (quantitative trait)
- Linkage (quantitative trait)
- GxE (sex-especificity)
- GxE (ageing)
Ageing model in SOLAR
\(y_i = \mu + x_i \beta + g_i + e_i\)
\(\Omega_{i,j} = G_{i,j} \sigma_g^2 + I_{i,j} \sigma_e^2\)
\(\sigma_g^2 = [exp(\alpha_g + \gamma_g \delta_i)]^{0.5} \times \\ \mbox{ } \mbox{ } \mbox{ } [exp(\alpha_g + \gamma_g \delta_j)]^{0.5} \times \\ \mbox{ } \mbox{ } \mbox{ } exp(-\lambda |\delta_i - \delta_j|)\)
\(\sigma_e^2 = [exp(\alpha_e + \gamma_e \delta_i)]\)
(J. Blangero 2009)
Ageing for BMI (GAIT1)
m0 <- relmatLmer( BMI ~ AGEsc + AGEsc2 + SEXf + (1|HHID) + (1|ID), phen, relmat = list(ID = dkin)) m1 <- relmatLmer( BMI ~ AGEsc + AGEsc2 + SEXf + (1|ID) + (1 + AGEsc|RID) + (1|HHID), phen, relmat = list(ID = dkin), weights = rep(1e10, nrow(phen)), vcControl = list(rho0 = list(rid = 3))) m2 <- relmatLmer( BMI ~ AGEsc + AGEsc2 + SEXf + (1 + AGEsc|ID) + (1 + AGEsc|RID) + (1|HHID), phen, relmat = list(ID = dkin), weights = rep(1e10, nrow(phen)), vcControl = list(rho0 = list(rid = 5)))
Examine the models' parameters
VarCorr(m1)
## Groups Name Std.Dev. Corr ## ID (Intercept) 0.085639 ## RID (Intercept) 0.112998 ## AGEsc 0.037605 0.000 ## HHID (Intercept) 0.057153 ## Residual 0.078124
VarCorr(m2)
## Groups Name Std.Dev. Corr ## ID (Intercept) 0.088349 ## AGEsc 0.057975 -0.011 ## RID (Intercept) 0.100757 ## AGEsc 0.011939 0.000 ## HHID (Intercept) 0.062106 ## Residual 0.068442
Test the ageing hypothesis
anova(m0, m1, m2)
## refitting model(s) with ML (instead of REML)
## Data: phen ## Models: ## m0: BMI ~ AGEsc + AGEsc2 + SEXf + (1 | HHID) + (1 | ID) ## m1: BMI ~ AGEsc + AGEsc2 + SEXf + (1 | ID) + (1 + AGEsc | RID) + ## m1: (1 | HHID) ## m2: BMI ~ AGEsc + AGEsc2 + SEXf + (1 + AGEsc | ID) + (1 + AGEsc | ## m2: RID) + (1 | HHID) ## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq) ## m0 7 -359.40 -331.64 186.70 -373.40 ## m1 10 -354.91 -315.25 187.45 -374.91 1.5054 3 0.68102 ## m2 12 -357.87 -310.28 190.94 -381.87 6.9658 2 0.03072 * ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Dichotomized ageing model
# Common polygenic model m0 <- relmatLmer( BMI ~ AGEsc + AGEsc2 + SEXf + (1|HHID) + (1|ID), phen, relmat = list(ID = dkin)) m1 <- relmatLmer( BMI ~ AGEsc + AGEsc2 + SEXf + (1|ID) + (0 + AGEf2|RID) + (1|HHID), phen, relmat = list(ID = dkin), weights = rep(1e10, nrow(phen)), vcControl = list(rho0 = list(rid = 3))) m2 <- relmatLmer( BMI ~ AGEsc + AGEsc2 + SEXf + (0 + SEXf|ID) + (0 + AGEf2|RID) + (1|HHID), phen, relmat = list(ID = dkin), weights = rep(1e10, nrow(phen)), vcControl = list(rho0 = list(rid = 5)))
Examine the models' parameters
VarCorr(m1)
## Groups Name Std.Dev. Corr ## ID (Intercept) 0.087055 ## RID AGEf20 0.116760 ## AGEf21 0.123646 0.000 ## HHID (Intercept) 0.057289 ## Residual 0.098676
VarCorr(m2)
## Groups Name Std.Dev. Corr ## ID SEXf1 0.079366 ## SEXf2 0.123532 0.417 ## RID AGEf20 0.101516 ## AGEf21 0.110564 0.000 ## HHID (Intercept) 0.056166 ## Residual 0.085696
Test the hypothesis
anova(m0, m1, m2)
## refitting model(s) with ML (instead of REML)
## Data: phen ## Models: ## m0: BMI ~ AGEsc + AGEsc2 + SEXf + (1 | HHID) + (1 | ID) ## m1: BMI ~ AGEsc + AGEsc2 + SEXf + (1 | ID) + (0 + AGEf2 | RID) + ## m1: (1 | HHID) ## m2: BMI ~ AGEsc + AGEsc2 + SEXf + (0 + SEXf | ID) + (0 + AGEf2 | ## m2: RID) + (1 | HHID) ## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq) ## m0 7 -359.40 -331.64 186.70 -373.40 ## m1 10 -353.53 -313.87 186.76 -373.53 0.1284 3 0.988221 ## m2 12 -359.43 -311.84 191.72 -383.43 9.9002 2 0.007083 ** ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Thank you
- The official repository at github.com/variani/lme4qtl
- This presentation lives here bit.ly/1UiTZvQ
More examples
Examples
- ABO covariate effect on Thrombosis
- comparision of two tests, t-test vs. anova
- Categorical age effect on Thrombosis
- increasing disease risk with age (non-linearly?)
- Sex-specificity for BMI (GAIT2)
- The effect is more pronounced that in GAIT1
ABO covariate effect (t-test)
K <- 0.05 dat <- mutate(subset(phen2, !is.na(ABOf3num)), offset = log(K/(1 - K))) m <- relmatGlmer(Throm ~ -1 + AGEsc + SEXfnum + ABOf3num + (1|ID), dat, offset = offset, relmat = list(ID = dkin2), family = binomial)
summaryCoef(m, signif.legend = TRUE)
## Estimate Std. Error z value Pr(>|z|) ## AGEsc 1.4220 0.1673 8.498 <2e-16 *** ## SEXfnum 0.3171 0.2643 1.200 0.2302 ## ABOf3num -0.5662 0.2384 -2.374 0.0176 * ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ABO covariate effect (anova)
K <- 0.05 dat <- mutate(subset(phen2, !is.na(ABOf3num)), offset = log(K/(1 - K))) m <- relmatGlmer(Throm ~ -1 + AGEsc + SEXfnum + ABOf3num + (1|ID), dat, offset = offset, relmat = list(ID = dkin2), family = binomial) m0 <- update(m, . ~ . - ABOf3num)
anova(m, m0)
## Data: dat ## Models: ## m0: Throm ~ AGEsc + SEXfnum + (1 | ID) - 1 ## m: Throm ~ -1 + AGEsc + SEXfnum + ABOf3num + (1 | ID) ## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq) ## m0 3 584.09 598.54 -289.04 578.09 ## m 4 577.82 597.08 -284.91 569.82 8.2699 1 0.004031 ** ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ABO covariate effect (summary)
| Model | Estimate | Std. Error | z-value |
|---|---|---|---|
| Intercept-free | -0.5584 | 0.2160 | -2.585 |
| Intercept (prevalence) | -0.5662 | 0.2384 | -2.374 |
| Model | p-value (t-test) | p-value (anova) |
|---|---|---|
| Intercept-free | 0.00973 (**) |
0.005092 (**) |
| Intercept (prevalence) | 0.0176 (*) |
0.004031 (**) |
Categorical age effect
| Factor level of AGEf | Range of AGE | Number of ind. |
|---|---|---|
| 0 | [ 2.6 - 54.8 ] | 715 |
| 1 | [ 55.2 - 64 ] | 79 |
| 2 | [ 64.1 - 73.8 ] | 81 |
| 3 | [ 74.1 - 83.9 ] | 43 |
| 4 | [ 84.2 - 101.1 ] | 17 |
Categorical age effect
K <- 0.05 dat <- mutate(phen2, offset = -qnorm(1 - K)) m <- relmatGlmer(Throm ~ AGEf + SEXf + ABOf3num + (1|ID), dat, offset = offset, relmat = list(ID = dkin2), family = binomial(probit))
summaryCoef(m)
## Estimate Std. Error z value Pr(>|z|) ## (Intercept) 0.05822 0.22775 0.256 0.79824 ## AGEf1 0.85723 0.21692 3.952 7.75e-05 *** ## AGEf2 1.19339 0.21552 5.537 3.07e-08 *** ## AGEf3 1.43971 0.27434 5.248 1.54e-07 *** ## AGEf4 1.70217 0.40137 4.241 2.23e-05 *** ## SEXf2 0.18430 0.13522 1.363 0.17288 ## ABOf3num -0.28707 0.10718 -2.679 0.00739 **
Sex-specificity for BMI (GAIT2)
m0 <- relmatLmer(BMI ~ AGEsc + AGEsc2 + SEXf + (1|HHID) + (1|ID),
phen2, relmat = list(ID = dkin2))
m1 <- relmatLmer(BMI ~ AGEsc + AGEsc2 + SEXf +
(1|ID) + (0 + SEXf|RID) + (1|HHID),
phen2, relmat = list(ID = dkin2),
weights = rep(1e10, nrow(phen2)), vcControl = list(rho0 = list(rid = 3)))
m2 <- relmatLmer(BMI ~ AGEsc + AGEsc2 + SEXf +
(0 + SEXf|ID) + (0 + SEXf|RID) + (1|HHID),
phen2, relmat = list(ID = dkin2),
weights = rep(1e10, nrow(phen2)), vcControl = list(rho0 = list(rid = 5)))
Sex-specificity for BMI (GAIT2)
VarCorr(m1)
## Groups Name Std.Dev. Corr ## ID (Intercept) 0.103256 ## RID SEXf1 0.089512 ## SEXf2 0.136570 0.000 ## HHID (Intercept) 0.033367 ## Residual 0.101783
VarCorr(m2)
## Groups Name Std.Dev. Corr ## ID SEXf1 0.085383 ## SEXf2 0.132376 0.804 ## RID SEXf1 0.099653 ## SEXf2 0.113160 0.000 ## HHID (Intercept) 0.036435 ## Residual 0.094210
Sex-specificity for BMI (GAIT2)
anova(m0, m1, m2)
## refitting model(s) with ML (instead of REML)
## Data: phen2 ## Models: ## m0: BMI ~ AGEsc + AGEsc2 + SEXf + (1 | HHID) + (1 | ID) ## m1: BMI ~ AGEsc + AGEsc2 + SEXf + (1 | ID) + (0 + SEXf | RID) + (1 | ## m1: HHID) ## m2: BMI ~ AGEsc + AGEsc2 + SEXf + (0 + SEXf | ID) + (0 + SEXf | RID) + ## m2: (1 | HHID) ## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq) ## m0 7 -858.56 -824.68 436.28 -872.56 ## m1 10 -879.32 -830.91 449.66 -899.32 26.755 3 6.626e-06 *** ## m2 12 -885.72 -827.63 454.86 -909.72 10.405 2 0.005504 ** ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Caveats
Caveats
- Disease prevalence 1%
Disease prevalence 1%
K <- 0.01 dat <- mutate(phen2, offset = log(K/(1 - K))) m1 <- relmatGlmer(Throm ~ -1 + AGEsc + SEXfnum + ABOf3num + (1|ID), dat, offset = offset, relmat = list(ID = dkin2), family = binomial)
summaryCoef(m1) # offset = log(K/(1 - K)) = -4.59512
## Estimate Std. Error z value Pr(>|z|) ## AGEsc 4.710 1.231 3.825 0.000131 *** ## SEXfnum -3.170 1.917 -1.653 0.098321 . ## ABOf3num -5.971 1.873 -3.188 0.001434 **
Disease prevalence 1% (nloptwrap)
m2 <- relmatGlmer(Throm ~ -1 + AGEsc + SEXfnum + ABOf3num + (1|ID), dat, offset = offset, relmat = list(ID = dkin2), family = binomial, control = glmerControl(optimizer = "nloptwrap"))
## Warning in lme4:::checkConv(attr(opt, "derivs"), opt$par, ctrl = control ## $checkConv, : Model failed to converge with max|grad| = 0.00650688 (tol = ## 0.001, component 1)
summaryCoef(m2) # offset = log(K/(1 - K)) = -4.59512
## Estimate Std. Error z value Pr(>|z|) ## AGEsc 4.709 1.231 3.824 0.000131 *** ## SEXfnum -3.159 1.912 -1.652 0.098482 . ## ABOf3num -5.962 1.870 -3.188 0.001435 **
References
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