R: Survey-weighted Cox models.

svycoxph {survey} | R Documentation

## Survey-weighted Cox models.

### Description

Fit a proportional hazards model to data from a complex survey design.

### Usage

    svycoxph(formula, design,subset=NULL, ...)
    ## S3 method for class 'svycoxph'
    predict(object, newdata, se=FALSE,
        type=c("lp", "risk", "expected", "terms","curve"),...)

### Arguments

`formula` | Model formula. Any `cluster()` terms will be ignored.
`design` | `survey.design` object. Must contain all variables in the formula
`subset` | Expression to select a subpopulation
`object` | A `svycoxph` object
`newdata` | New data for prediction
`se` | Compute standard errors? This takes a lot of memory for `type="curve"`
`type` | "curve" does predicted survival curves. The other values are passed to `predict.coxph()`
`...` | Other arguments passed to `coxph`.

### Details

The main difference between `svycoxph` function and the `robust=TRUE` option to `coxph` in the survival package is that this function accounts for the reduction in variance from stratified sampling and the increase in variance from having only a small number of clusters.

Note that `strata` terms in the model formula describe subsets that have a separate baseline hazard function and need not have anything to do with the stratification of the sampling.

The standard errors for predicted survival curves are available only by linearization, not by replicate weights (at the moment). Use `withReplicates` to get standard errors with replicate weights. Predicted survival curves are not available for stratified Cox models.

The standard errors use the delta-method approach of Williams (1995) for the Nelson-Aalen estimator, modified to handle the Cox model following Tsiatis (1981). The standard errors agree closely with `survfit.coxph` for independent sampling when the model fits well, but are larger when the model fits poorly. I believe the standard errors are equivalent to those of Lin (2000), but I don't know of any implementation that would allow a check.

### Value

An object of class `svycoxph` for `svycoxph`, an object of class `svykm` or `svykmlist` for `predict(,type="curve")`.

### Warning

The standard error calculation for survival curves uses memory proportional to the sample size times the square of the number of events.

### Author(s)

Thomas Lumley

### References

Binder DA. (1992) Fitting Cox's proportional hazards models from survey data. Biometrika 79: 139-147

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

Tsiatis AA (1981) A Large Sample Study of Cox's Regression Model. Annals of Statistics 9(1) 93-108

Williams RL (1995) "Product-Limit Survival Functions with Correlated Survival Times" Lifetime Data Analysis 1: 171–186

### See Also

`coxph`, `predict.coxph`

`svykm` for estimation of Kaplan-Meier survival curves and for methods that operate on survival curves.

`regTermTest` for Wald and (Rao-Scott) likelihood ratio tests for one or more parameters.

### Examples

    ## Somewhat unrealistic example of nonresponse bias.
    data(pbc, package="survival")

    pbc$randomized<-with(pbc, !is.na(trt) & trt>0)
    biasmodel<-glm(randomized~age*edema,data=pbc,family=binomial)
    pbc$randprob<-fitted(biasmodel)
    if (is.null(pbc$albumin)) pbc$albumin<-pbc$alb ##pre2.9.0

    dpbc<-svydesign(id=~1, prob=~randprob, strata=~edema, data=subset(pbc,randomized))
    rpbc<-as.svrepdesign(dpbc)

    (model<-svycoxph(Surv(time,status>0)~log(bili)+protime+albumin,design=dpbc))

    svycoxph(Surv(time,status>0)~log(bili)+protime+albumin,design=rpbc)

    s<-predict(model,se=TRUE, type="curve",
         newdata=data.frame(bili=c(3,9), protime=c(10,10), albumin=c(3.5,3.5)))
    plot(s[[1]],ci=TRUE,col="sienna")
    lines(s[[2]], ci=TRUE,col="royalblue")
    quantile(s[[1]], ci=TRUE)
    confint(s[[2]], parm=365*(1:5))

[Package survey version 3.32-1 Index]