Cmeasures: Concordance measures in shared frailty and Cox models

Description

Compute concordance probability estimation for Cox models or shared frailty models in case of grouped data (Mauguen et al. 2012). Concordance is given at different levels of comparison, taking into account the cluster membership: between-groups, within-groups and an overall measure, being a weighted average of the previous two. Can also compute the c-index (Harrell et al. 1996) at these three levels. It is possible to exclude tied pairs from concordance estimation (otherwise, account for 1/2).

Usage

Cmeasures(fitc, ties = 1, marginal = 0, cindex = 0, Nboot = 0)

Arguments

fitc

A frailtyPenal object , for a shared frailty model. If the fit is a Cox model (Frailty=FALSE), no clustering membership is taken into account and only marginal concordance probability estimation is provided. Only an overall measure is given, where all pat

ties

Indicates if the tied pairs on prediction value must be included (ties=1) or excluded (ties=0) from the concordance estimation. Default is ties=1. When included, tied pairs account for 1/2 in the concordance.

marginal

Indicates if the concordance based on marginal predictions must be given (marginal=1) in addition to conditional ones or not (marginal=0). Marginal predictions do not include the frailty estimation in the linear predictor computation: uses "`Beta'X"' inst

cindex

Indicates if the c-index (Harrell et al. 1996) must be computed (cindex=1) in addition to the concordance probability estimation or not (cindex=0). C-index is also given at the three comparison levels (between, within and overall). Default is cindex=0.

Nboot

Number of bootstrap resamplings to compute standard-error of the concordances measures, as well as a percentile 95% confidence interval. Nboot=0 indicates no bootstrap procedure. Maximum admitted is 1000. Minimum admitted is 2. Default is 0. Resampling is

Value

callThe shared frailty model evaluated.
FrailtyLogical value. Was model with frailties fitted.
frequenciesNumbers of patients, events and groups used to fit the model.
NbootNumber of bootstrap resamplings required.
NbproblemNumber of bootstrap resamplings in which the model did not converge. Those are excluded when computing the standard-error and the percentile 95% confidence interval.
tiesA binary, indicating if the tied pairs on prediction were used to compute the concordance.
CPEcondValues of the Concordance Probability Estimations (conditional) and the number of pairs used. If Nboot>0, give SE, the standard-error of the parameters evaluated by bootstrap, IC.low and IC.high, the lower and upper bounds of the percentile confidence interval evaluated by bootstrap (2.5% and 97.5% percentiles).
marginalA binary, indicating if the marginal values were computed.
CPEmargValues of the Concordance Probability Estimations (marginal) and the number of pairs used, if marginal=1. If Nboot>0, give SE, the standard-error of the parameters evaluated by bootstrap, IC.low and IC.high, the lower and upper bounds of the percentile confidence interval evaluated by bootstrap (2.5% and 97.5% percentiles).
cindexA binary, indicating if the c-indexes were computed.
cindexcondValues of the C-index (conditional) and the number of pairs used. If Nboot>0, give SE, the standard-error of the parameters evaluated by bootstrap, IC.low and IC.high, the lower and upper bounds of the percentile confidence interval evaluated by bootstrap (2.5% and 97.5% percentiles).
cindexmargValues of the C-index (marginal) and the number of pairs used, if marginal=1. If Nboot>0, give SE, the standard-error of the parameters evaluated by bootstrap, IC.low and IC.high, the lower and upper bounds of the percentile confidence interval evaluated by bootstrap (2.5% and 97.5% percentiles).

References

Concordance measures in shared frailty models: application to multicenter data in cancer prognosis. Mauguen A, Collette S, Pignon JP, Collette L and Rondeau V. (submitted 2012). Harrell FE et al. Tutorial in biostatistics: multivariable prognostic models: issues in developing models, evaluating assumptions and adequacy, and measuring and reducing errors. Statistics in Medicine 1996; 15:361-387. Gonen M, Heller G. Concordance probability and discriminatory power in proportional hazards regression. Biometrika 2005; 92:965-970.

Examples

Run this code

## load data
data(readmission)

## a frailtypenal fit
fit.frailtypenal <- frailtyPenal(Surv(time,event)~cluster(id)+dukes+
                      charlson+chemo,data=readmission,Frailty=TRUE,
                      cross.validation=FALSE,n.knots=10,kappa1=1,
                      hazard="Splines")

## a Cmeasures call
fit.Cmeasures <- Cmeasures(fit.frailtypenal)
fit.Cmeasures.noties <- Cmeasures(fit.frailtypenal, ties=0)

## a short summary
fit.Cmeasures
fit.Cmeasures.noties