# cch

##### 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 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.

- Keywords
- survival

##### 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 indicators for 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.

regression coefficients.

Self-Prentice model based variance-covariance matrix.

Lin-Ying empirical variance-covariance matrix.

##### 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. http://faculty.washington.edu/tlumley/survey/

##### Examples

```
# NOT RUN {
## 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)
# }
```

*Documentation reproduced from package survival, version 2.44-1.1, License: LGPL (>= 2)*