WEE-package: Weighted Estimated Equation (WEE) Approaches in Genetic...

In WEE: Weighted Estimated Equation (WEE) Approaches in Genetic Case-Control Studies

Description

Secondary analysis of case-control studies using a weighted estimating equation (WEE) approach: logistic regression for binary secondary outcomes, linear regression and quantile regression for continuous secondary outcomes.

Author(s)

Xiaoyu Song, Iuliana Ionita-Laza, Mengling Liu, Joan Reitman, Ying Wei

Maintainer: Wodan Ling <[e-mail]>

References

[1] Ying Wei, Xiaoyu Song, Mengling Liu, Iuliana Ionita-Laza and Joan Reibman (2016). Quantile Regression in the Secondary Analysis of Case Control Data. Journal of the American Statistical Association, 111:513, 344-354; DOI: 10.1080/01621459.2015.1008101

[2] Xiaoyu Song, Iuliana Ionita-Laza, Mengling Liu, Joan Reibman, Ying Wei (2016). A General and Robust Framework for Secondary Traits Analysis. Genetics, vol. 202 no. 4 1329-1343; DOI: 10.1534/genetics.115.181073

Examples

#---------------------- WEE logistic regression ----------------------#
## Generate simulated data
# set population size as 500000
n = 500000 

# set parameters
beta = c(0.2, 0.1) # P(Y|X,Z)
gamma = c(0.3, log(2), log(2)) #P(D|X,Y,Z)

# generate the genetic variant X
x = rbinom(n,size=2,prob=0.3)

# generate the standardized continuous covariate Z correlated with X
z = rnorm(n, mean=0.5*x-0.3, sd=1)

# generate the binary secondary trait Y
py = exp(-1+beta[1]*x+beta[2]*z)/
        (1+exp(-1+beta[1]*x+beta[2]*z))
y = rbinom(n,1, py)

# generate the primary disease D 
# (alpha changes to make sure the disease prevalence = 0.1 )
alpha = -2.88
pd = exp(alpha+x*gamma[1]+y*log(2)+z*log(2))/
(1+exp(alpha+x*gamma[1]+y*log(2)+z*log(2)))
d = rbinom(n,size=1,prob=pd)

# form the population dataset
dat = as.data.frame(cbind(d, y, z, x))

# generate sample dataset with 200 cases and 200 controls
dat_cases = dat[which(dat$d==1),]
dat_controls= dat[which(dat$d==0),]
dat_cases_sample = dat_cases[sample(sum(dat$d==1),
                             200,replace=FALSE),]
dat_controls_sample = dat_controls[sample(sum(dat$d==0), 
                                   200,replace=FALSE),]

dat_logistic = rbind(dat_cases_sample,dat_controls_sample)	
colnames(dat_logistic) = c("D", "y", "z","x")
D = dat_logistic$D # Disease status
pD = sum(dat$d==1)/500000 # Population disease prevalence

## WEE logsitic regression
WEE.logistic(y ~ x + z, D, 
             data = dat_logistic, pD)	  

WEE.logistic(y ~ x + z, D, 
             data = dat_logistic, pD, boot = 500)	 



#---------------------- WEE linear regression ----------------------#
## Generate simulated data
# set population size as 500000
n = 500000

# set parameters
beta = c(0.2, 0.1) # P(Y|X,Z)
gamma = c(0.3, log(2), log(2)) #P(D|X,Y,Z)

# generate the genetic variant X
x = rbinom(n,size=2,prob=0.3)

# generate the standardized continuous covariate Z correlated with X
z = rnorm(n, mean=0.5*x-0.3, sd=1)

# generate the continuous secondary trait Y
y = 1+beta[1]*x+beta[2]*z+rnorm(n)

# generate the primary disease D
alpha = -3.62
pd = exp(alpha + x*gamma[1] + y*log(2) + z*log(2))/
(1 + exp(alpha + x*gamma[1] + y*log(2) + z*log(2)))
d = rbinom(n,size=1,prob=pd)

# form population data set
dat=as.data.frame(cbind(d, y, z, x))

# generate sample dataset with 200 cases and 200 controls
dat_cases = dat[which(dat$d==1),]
dat_controls= dat[which(dat$d==0),]
dat_cases_sample = dat_cases[sample(sum(dat$d==1),
                             200, replace=FALSE),]
dat_controls_sample = dat_controls[sample(sum(dat$d==0),
                                   200, replace=FALSE),]
  
dat_linear=rbind(dat_cases_sample,dat_controls_sample)
colnames(dat_linear)=c("D", "y", "z","x")
D = dat_linear$D # Disease status
pD = sum(dat$d == 1)/500000 # Population disease prevalence

## WEE linear regresssion
WEE.linear(y ~ x + z, D, 
           data = dat_linear, pD)   

WEE.linear(y ~ x + z, D, 
          data = dat_linear, pD, boot = 500) 



#---------------------- WEE quantile regression ----------------------#
## Generate simulated data
# set population size as 500000
n = 500000 

# set parameters
beta = c(0.12, 0.1) # P(Y|X,Z)
gamma = c(-4, log(1.5), log(1.5), log(2) ) #P(D|X,Y,Z)

# generate the genetic variant X
x = rbinom(n,size=2,prob=0.3)
  
# generate the continuous covariate Z
z = rnorm(n)
  
# generate the continuous secondary trait Y
y= 1 + beta[1]*x + beta[2]*z + (1+0.02*x)*rnorm(n)

# generate disease status D
p = exp(gamma[1]+x*gamma[2]+z*gamma[3]+y*gamma[4])/
(1+exp(gamma[1]+x*gamma[2]+z*gamma[3]+y*gamma[4]))
d = rbinom(n,size=1,prob=p)

# form population data dataset
dat = as.data.frame(cbind(x,y,z,d))
colnames(dat) = c("x","y","z","d")

# Generate sample dataset with 200 cases and 200 controls
dat_cases = dat[which(dat$d==1),]
dat_controls= dat[which(dat$d==0),]
dat_cases_sample = dat_cases[sample(sum(dat$d==1),
                            200, replace=FALSE),]
dat_controls_sample = dat_controls[sample(sum(dat$d==0),
                                   200, replace=FALSE),]

dat_quantile = as.data.frame(rbind(dat_cases_sample,
                                   dat_controls_sample))
colnames(dat_quantile) = c("x","y","z","D")
D = dat_quantile$D # Disease status
pd = sum(d==1)/n # population disease prevalence

# WEE quantile regressions:
WEE.quantile(y ~ x, D, tau = 0.5, 
             data = dat_quantile, pd_pop = pd)	  				

WEE.quantile(y ~ x + z, D, tau = 1:9/10, 
             data = dat_quantile, pd_pop = pd, boot = 500)

WEE documentation built on May 2, 2019, 6:43 a.m.