cch                 package:survival                 R Documentation

Fits proportional hazards regression model to case-cohort data

Description:

     Returns estimates and standard errors from relative risk
     regression fit to data from case-cohort studies. A choice is
     available among the Prentice, Self-Prentice and Lin-Ying methods
     for unstratified data. For stratified data the choice is between
     Borgan I, a generalization of the Self-Prentice estimator for
     unstratified case-cohort data, and Borgan II, a generalization of
     the Lin-Ying estimator.

Usage:

     cch(formula, data = sys.parent(), subcoh, id, stratum=NULL, cohort.size,
         method =c("Prentice","SelfPrentice","LinYing","I.Borgan","II.Borgan"),
         robust=FALSE)

Arguments:

 formula: A formula object that must have a 'Surv' object as the
          response.  The Surv object must be of type '"right"', or of
          type '"counting"'. 

  subcoh: Vector of indicatorsfor subjects sampled as part of the
          sub-cohort. Code '1' or 'TRUE' for members of the sub-cohort,
          '0' or 'FALSE' for others. If 'data' is a data frame then
          'subcoh' may be a one-sided formula. 

      id: Vector of unique identifiers, or formula specifying such a
          vector. 

 stratum: A vector of stratum indicators or a formula specifying such a
          vector

cohort.size: Vector with size of each stratum original cohort from
          which subcohort was sampled 

    data: An optional data frame in which to interpret the variables 
          occurring in the formula.  

  method: Three procedures are available. The default method is
          "Prentice", with  options for "SelfPrentice" or "LinYing". 

  robust: For '"LinYing"' only, if 'robust=TRUE', use design-based
          standard errors even for phase I

Details:

     Implements methods for case-cohort data analysis described by
     Therneau and Li (1999). The three methods differ in the choice of
     "risk sets" used to compare the covariate values of the failure
     with those of others at risk at the time of failure. "Prentice"
     uses the sub-cohort members "at risk" plus the failure if that
     occurs outside the sub-cohort and is score unbiased. "SelfPren"
     (Self-Prentice) uses just the sub-cohort members "at risk". These
     two have the same asymptotic variance-covariance matrix. "LinYing"
     (Lin-Ying) uses the all members of the sub-cohort and all failures
     outside the sub-cohort who are "at risk". The methods also differ
     in the weights given to different score contributions.

     The 'data' argument must not have missing values for any variables
     in the model.  There must not be any censored observations outside
     the subcohort.

Value:

     An object of class "cch"  incorporating a list of estimated
     regression coefficients and two estimates of their  asymptotic
     variance-covariance matrix. 

    coef: regression coefficients.

naive.var: Self-Prentice model based variance-covariance matrix.

     var: Lin-Ying empirical variance-covariance matrix. 

Author(s):

     Norman Breslow, modified by Thomas Lumley

References:

     Prentice, RL (1986). A case-cohort design for epidemiologic cohort
     studies and disease prevention trials. Biometrika 73: 1-11.

     Self, S and Prentice, RL (1988). Asymptotic distribution theory
     and efficiency results for case-cohort studies. Annals of
     Statistics 16: 64-81.

     Lin, DY and Ying, Z (1993). Cox regression with incomplete
     covariate measurements. Journal of the American Statistical
     Association 88: 1341-1349.

     Barlow, WE (1994). Robust variance estimation for the case-cohort
     design. Biometrics 50: 1064-1072

     Therneau, TM and Li, H (1999). Computing the Cox model for
     case-cohort designs. Lifetime Data Analysis 5: 99-112.

     Borgan, O, Langholz, B, Samuelsen, SO, Goldstein, L and Pogoda, J
     (2000) Exposure stratified case-cohort designs. Lifetime Data
     Analysis 6, 39-58.

See Also:

     'twophase' and 'svycoxph' in the "survey" package for more general
     two-phase designs. <URL:
     http://faculty.washington.edu/tlumley/survey/>

Examples:

     ## The complete Wilms Tumor Data 
     ## (Breslow and Chatterjee, Applied Statistics, 1999)
     ## subcohort selected by simple random sampling.
     ##

     subcoh <- nwtco$in.subcohort
     selccoh <- with(nwtco, rel==1|subcoh==1)
     ccoh.data <- nwtco[selccoh,]
     ccoh.data$subcohort <- subcoh[selccoh]
     ## central-lab histology 
     ccoh.data$histol <- factor(ccoh.data$histol,labels=c("FH","UH"))
     ## tumour stage
     ccoh.data$stage <- factor(ccoh.data$stage,labels=c("I","II","III","IV"))
     ccoh.data$age <- ccoh.data$age/12 # Age in years

     ##
     ## Standard case-cohort analysis: simple random subcohort 
     ##

     fit.ccP <- cch(Surv(edrel, rel) ~ stage + histol + age, data =ccoh.data,
        subcoh = ~subcohort, id=~seqno, cohort.size=4028)

     fit.ccP

     fit.ccSP <- cch(Surv(edrel, rel) ~ stage + histol + age, data =ccoh.data,
        subcoh = ~subcohort, id=~seqno, cohort.size=4028, method="SelfPren")

     summary(fit.ccSP)

     ##
     ## (post-)stratified on instit
     ##
     stratsizes<-table(nwtco$instit)
     fit.BI<- cch(Surv(edrel, rel) ~ stage + histol + age, data =ccoh.data,
        subcoh = ~subcohort, id=~seqno, stratum=~instit, cohort.size=stratsizes,
        method="I.Borgan")

     summary(fit.BI)

