Weighted partial likelihood for nested casecontrol data
Description
Fits Cox proportional hazards models for nested casecontrol data
with a weigthed partial likelihood. Matching between cases and
controls is broken which enables the controls to be reused for other endpoints. It
handles competing risks (with simple survival data with one endpoint being a
special case) and cases and controls from one endpoint are being used as
additional controls for another endpoint. There are four choices of weights;
Samuelsen (1997) KM
, estimated with logistic regression (glm
), logistic
genralized additive model (gam
) and local averaging (Chen, 2001)
(Chen)
. KM
, glm
and gam
handle additional matching,
while all of them handle lefttruncation.
Usage
1 2 3 
Arguments
x 
A formula object, with the response on the left of a ~ operator, and the terms on the right. The response must be a survival object as returned by the Surv function. The status variable going in to Surv is not actually used but should have 1 for cases and zero for controls and nonsampled subjetcs. All elements going into the formula should have lenght equal to the number of subjects in the cohort. Generally some of the covariates are not known for all subjects in the cohort (due to the NCCsampling). The covariate values for those subjects should just be given some value e.g. 0 (not NA). Which value choosen is not important as the values are never used. 
data 
data.frame in which to interpret the variables named in the formula. 
samplestat 
A vector containing sampling and status information: 0 represents nonsampled subjects in the cohort, 1: sampled controls, 2,3,... indicate different events. Cohort dimension. 
m 
Number of sampled controls. A scalar if equal number of controls for all cases. If unequal number of controls per case: A vector of length number of cases. The vector must be in the same order as the cases in the samplestatvector. 
weight.method 
Which weigths should be used, possibilities 
no.intervals 
Number of intervals for censoring times for Chenweights with only right censoring 
variance 
Default is robust variances, but model based variance (only for KMweights),

no.intervals.left 
Number of intervals for Chenweights with lefttruncation. A vector on the form [number of intervals for left truncated time, number of intervals for survival time]. 
match.var 
If the controls are matched to the cases (on other variables than time), match.var is the vector or matrix of matching variables. Cohort dimension. 
match.int 
A vector of length 2*number of matching variables. For caliper matching (matched on value pluss/minus epsilon) match.int should consist of c(epsilon,epsilon). For exact matching match.int should consist of c(0,0). 
... 
Other arguments 
Value
An object of class wpl representing the fit. Objects of this class have methods
for the functions print
and summary
.
The wplobject consists of the following elements which are repeated for each
endpoint. Unfortunately only the values for the first endpoint can be reached
by $operator(ex. fit$coefficients only return the coefficients for the first
endpoint)
coefficients 
The vector of coefficients. 
var 
Robust or estimated variance 
weighted.loglik 
A vector of length 2 containing the loglikelihood with the initial values and with the final values of the coefficients. 
iter 
Number of iterations used 
linear.predictors 
The vector of linear predictors, one per subject. Note that this vector has been centered, see predict.coxph for more details 
residuals 
The martingale residuals 
means 
Vector of column means of the X matrix 
method 
The computation method used 
n 
The number of observations used in the fit 
nevent 
The number of events (usually deaths) used in the fit 
naive.var 
naive.var 
rscore 
The robust logrank statistic 
wald.test 
The Wald test of whether the final coefficients differ from the initial values 
y 
Inclusion time and event/censoring time 
weights 
The vector of weights, which are inverse sampling probabilities 
est.var 
Estimated variance (T) or robust variance (F) 
.
.
.
Author(s)
Nathalie C. Stoer
References
Samuelsen SO. A pseudolikelihood approach to analysis of nested casecontrol studies.
Biometrika, 84(2):379394, 1997.
Stoer NC and Samuelsen SO (2013): Inverse probability weighting in nested casecontrol
studies with additional matching  a simulation study. Statistics in Medicine,
32(30), 53285339.
See Also
coxph
, Chenprob
, GLMprob
, GAMprob
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16  data(CVD_Accidents)
wpl(Surv(agestart,agestop,dead24)~factor(smoking3gr)+bmi+factor(sex),data=CVD_Accidents,
samplestat=CVD_Accidents$samplestat,weight.method="gam")
wpl(Surv(agestart,agestop,dead24)~factor(smoking3gr)+bmi+factor(sex),data=CVD_Accidents,
samplestat=CVD_Accidents$samplestat,m=1,match.var=cbind(CVD_Accidents$sex,
CVD_Accidents$bmi),match.int=c(0,0,2,2),weight.method="glm")
## The function is currently defined as
function (x, data, samplestat, m = 1, weight.method = "KM", no.intervals = 10,
variance = "robust", no.intervals.left = c(3, 4), match.var = 0,
match.int = 0)
{
UseMethod("wpl")
}
