.BG
Fits proportional hazards regression model to exposure stratified
case-cohort data

.FN stcch

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

.IP 

.CS
stcch_function(formula, data=sys.parent(), subcoh, id, stratum,
               stratum.sizes, method="I")

.RA

.AG formula 
A formula object that must have a Surv object as the response on the left 
of the ~ operator and model terms separated by + operators on the right. 
The Surv object must be of type "right", Surv(time,event), or of type 
counting, Surv(tenter,texit,event).   

.AG subcoh 
Vector of indicators for subjects sampled as part of the sub-cohort         
0 = not a sub-cohort member, 1 = a sub-cohort member         

.AG id
Vector of unique identifiers

.AG stratum
Vector of (covariate) stratum indicators (1,2,...,J)

.AG stratum.sizes
J-vector containing sizes of J strata in original cohort

.OA

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


.AG method
Two procedures are available. The default method is "I" with 
option for "II" (Borgan I and II) 

.RT
list of estimated regression coefficients, two estimates of their 
asymptotic variance-covariance matrix and estimates of optimal subcohort
sampling fractions for each regression coefficient

.RC coef
regression coefficients

.RC naive.var
Naive variance estimator from weighted Cox regression fit -- ignores
sampling of controls

.RC var
Variance estimator that accounts for sampling of controls

.RC opt
p x J matrix of optimal sampling fractions (p = # coefficients)

.DT
Implements methods I and II for analysis of covariate (exposure) stratified 
case-cohort data described by Borgan et al.(2000). Only the versions with
time invariant weights are implemented. 

.IP
The output may be examined by the summary function, which returns the estimated 
coefficients and their standard errors in a tabular form
             
.SH REFERENCES

Borgan, Langholz, Samuelson, Goldstein and Pogoda (2000). Exposure
stratified case-cohort designs. Lifetime Data Analysis 6:39-58

Lin (2000) On fitting Cox's proportional hazards model to survey data.
Biometrika 87:37-47

.EX

options(contrasts=c("contr.treatment","contr.poly"))

# Read in the complete Wilms Tumor Data 
# (Breslow and Chatterjee, Applied Statistics, 1999)
#
# Read 4088 individual data records and place in data frame
#
nwtco_read.table("nwtco.asc",header=T)
nwtco_nwtco[!is.na(nwtco$edrel),] # Only 4028 subjects have positive observation time
attach(nwtco,pos=1)
#
# Tabulate main cohort stratum sizes
size2_table(instit)
#
# Select "balanced" sample for Phase II
#
set.seed(400)
id.subcoh_c(seqno[instit==2],sample(seqno[instit==1],size=262))
subcoh_as.numeric(!is.na(match(seqno,id.subcoh)))
bcoh.data_data.frame(nwtco[rel==1|subcoh==1,])
bcoh.data$subcoh_subcoh[rel==1|subcoh==1]
bcoh.data$hist0l_factor(bcoh.data$histol,labels=c("FH","UH"))  # Central histology 
bcoh.data$stage_factor(bcoh.data$stage,labels=c("I","II","III","IV")) # Stage
bcoh.data$age_bcoh.data$age/12 # Age in years
#
# Analyze incomplete data from BCOH sample using stratified case-cohort analyses
# in 2 strata
fit.cbBI2_stcch(Surv(edrel,rel)~stage+hist0l+age,data=bcoh.data,subcoh=bcoh.data$subcoh,
id=bcoh.data$seqno, stratum=bcoh.data$instit, stratum.sizes=size2)
#
# Output
summary(fit.cbBI2)
$call:
stcch(formula = Surv(edrel, rel) ~ stage + hist0l + age, data = bcoh.data, subcoh = bcoh.data$
	subcoh, id = bcoh.data$seqno, stratum = bcoh.data$instit, stratum.sizes = size2)

$method:
[1] "Borgan I"

$cohort.stratum.sizes:
    1   2 
 3622 406

$subcohort.stratum.sizes:
   1   2 
 656 406

$coefficients:
              Value         SE         Z             p 
 stageII 0.46908527 0.18609570  2.520667 1.171327e-002
stageIII 0.62880495 0.18265209  3.442638 5.760708e-004
 stageIV 1.10410380 0.21114869  5.229035 1.703974e-007
  hist0l 1.62465341 0.13798538 11.774099 0.000000e+000
     age 0.03598096 0.03423503  1.050998 2.932594e-001

attr(, "class"):
[1] "summary.stcch"