Estimate non-parametric survival curves for each level of categorical variables with missing data.

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Description

The function nested.km gives non-parametric survival curve estimates (like Kaplan-Meier) for each level of categorical variables that have missing data on some cohort members. These variables must be factor variables. nested.km requires knowledge of the variables that missingness depends on, with missingness probability modeled through a glm sampling model. Often, the data is in the form of a case-control sample taken within a cohort. nested.km allows cases to have missing data, and can extract efficiency from auxiliary variables by including them in the sampling model. nested.km makes heavy use of the survfit function in the survival package.

Usage

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nested.km(survfitformula, samplingmod, data, outputsamplingmod=FALSE,
          outputriskdiff = FALSE, exposureofinterest = "",
          timeofinterest = Inf, glmlink = binomial(link = "logit"),
          glmcontrol = glm.control(epsilon = 1e-10, maxit = 10, trace = FALSE),
          missvarwarn = TRUE, ...)

Arguments

Required arguments:

survfitformula

Legal formula for a survfit object

samplingmod

Right side of the formula for the glm sampling model that models the probability of missingness

data

Data Frame that all variables are in

Optional arguments:

outputsamplingmod

Output the sampling model, default is false

outputriskdiff

Output risk differences, default is false

exposureofinterest

Exposure level to make risk differences with respect to

timeofinterest

Time at which to report risk differenes, default is end of followup

glmlink

Sampling model link function, default is logistic regression

glmcontrol

See glm.control

missvarwarn

Warn if there is missing data in the sampling variable. Default is TRUE

...

Any additional arguments to be passed on to survfit

Details

nested.km provides survival estimates that are not standardized for confounders nor account for competing risks.

If nested.km reports that the sampling model "failed to converge", the sampling model will be returned for your inspection. Note that if some sampling probabilities are estimated at 1, the model technically cannot converge, but you get very close to 1, and nested.km will not report non-convergence for this situation.

Note these issues. The data must be in a dataframe and specified in the data statement. No variable in the dataframe can be named 'o.b.s.e.r.v.e.d.' or 'p.i.h.a.t.'. Cases and controls cannot be finely matched on time, but matching on time within large strata is allowed. Everyone must enter the cohort at the same time on the vival time scale. All covariates in the survfitformula must be factor even if binary. Never use '*' to mean interaction in the survfitformula, instead use interaction.

Value

If outputpropmod=F, the output is the survival curves in the survfit model. Any method that works for survfit objects will work for this so long as the method only requires consistent estimates of the parameters and their standard errors. If outputpropmod=T, then the sampling model is also returned, and the output is a list with components:

survmod

The survfit model of class survfit

propmod

The sampling model of class glm

Note

Requires the MASS library from the VR bundle that is available from the CRAN website.

Author(s)

Hormuzd A. Katki

References

Katki HA, Mark SD. Survival Analysis for Cohorts with Missing Covariate Information. R-News, 8(1) 14-9, 2008. http://www.r-project.org/doc/Rnews/Rnews_2008-1.pdf

Mark, S.D. and Katki, H.A. Specifying and Implementing Nonparametric and Semiparametric Survival Estimators in Two-Stage (sampled) Cohort Studies with Missing Case Data. Journal of the American Statistical Association, 2006, 101, 460-471.

Mark SD, Katki H. Influence function based variance estimation and missing data issues in case-cohort studies. Lifetime Data Analysis, 2001; 7; 329-342

Christian C. Abnet, Barry Lai, You-Lin Qiao, Stefan Vogt, Xian-Mao Luo, Philip R. Taylor, Zhi-Wei Dong, Steven D. Mark, Sanford M. Dawsey. Zinc concentration in esophageal biopsies measured by X-ray fluorescence and cancer risk. To Appear in Journal of the National Cancer Institute.

See Also

See Also: nested.stdsurv, zinc, nested.coxph, coxph, glm

Examples

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## Simple analysis of zinc and esophageal cancer data:
## We sampled zinc (variable znquartiles) on a fraction of the subjects, with
## sampling fractions depending on cancer status and baseline histology.
## We observed the confounding variables on almost all subjects.
data(zinc)
mod <- nested.km(survfitformula="Surv(futime01,ec01==1)~znquartiles",
                 samplingmod="ec01*basehist",data=zinc)

# This is the output
#  Risk Differences vs. znquartiles=Q1 by time Inf 
#          Risk Difference StdErr 95% CI Left 95% CI Right
#  Q1 - Q2         -0.2262 0.1100     -0.4419     -0.01060
#  Q1 - Q3         -0.1749 0.1145     -0.3993      0.04945
#  Q1 - Q4         -0.2818 0.1042     -0.4859     -0.07760

plot(mod,ymin=.6,xlab="Time (Days)",ylab="Survival",main="Survival by Quartile of Zinc",lty=1:4,)
legend(2000,0.7,c("Q1","Q2","Q3","Q4"),lty=1:4)