cch {survival}R Documentation

Fits proportional hazards regression model to case-cohort data


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 estimation of regression coefficients and standard errors.


cch(formula, data = sys.parent(), subcoh, id, cohort.size,
    method = c("Prentice", "SelfPrentice", "LinYing"))


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. If data is a data frame then subcoh may be a one-sided formula.
cohort.size Scalar with size of 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".


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.


A whole bunch of stuff including 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.


Norman Breslow, modified by Thomas Lumley


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 Wei, LJ (1989). The robust inference for the Cox proportional hazards model. Journal of the American Statistical Association 84: 1074–1078.

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 et al. (1999). Exposure stratified case-cohort designs. Lifetime Data Analysis


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


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

## Standard case-cohort analysis: simple random subcohort 

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


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


[Package survival version 2.20 Index]