##-----------------------------------------------------------------## 
##  R code for obtaining the maximum composite partial likelihood  ##
##  estimator for the CSHA data. See the paper " Composite Partial ##
##  Likelihood Estimation Under Length-Biased Sampling, With       ##
##  Application to a Prevalent Cohort Study of Dementia"           ## 
##  by Huang and Qin.                                              ##  
##-----------------------------------------------------------------## 
 
#  A: time from onset to study enrollment
#  Y: time from onset to death or loss to follow-up
#  D: event indicator (= 1 if died; = 0 if censored)
#  X1: indocator for probable Alzheimer
#  X2: indocator for vascular dementia

# Cox regression with partial likelihood method
  fit <- coxph( Surv( time = A, time2 = Y, event = D) ~ X1 + X2,  
         method = "breslow")  
  
# Cox regression with composite partial likelihood method
  cpdata <- data.frame( cbind( 
                        A = c(A, (Y-A)[D == 1]),  
                        Y = c(Y,  Y[D == 1]),
                        D = c(D,  D[D == 1]),  
                       X1 = c(X1, X1[D == 1]),
                       X2 = c(X2, X2[D == 1])   ))    
 
  cpfit <- coxph( Surv( time = A, time2 = Y, event = D ) ~ X1 + X2, 
                        data = cpdata, method = "breslow" )