Cmeasures: Concordance measures in shared frailty and Cox proportional hazard models

Description

Compute concordance probability estimation for Cox proportional hazard 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,
          tau = 0, data.val)

Arguments

fitc

A frailtyPenal object, for a shared frailty model. If the fit is a Cox model, no clustering membership is taken into account and only marginal concordance probability estimation is provided. Only an overall measure is given, where all patients are compare

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

tau

Time used to limit the interval on which the concordance is estimated. Note that the survival function for the underlying censoring time distribution needs to be positive at tau. If tau=0, the maximum of the observed event times is used. Default is tau=0.

data.val

A dataframe. It is possible to specify a different dataset than the one used in the model input in the argument 'fitc'. This new dataset will be a validation population and the function will compute new concordance measures from the parameters estimated o

Value

callThe shared frailty model evaluated.
FrailtyLogical value. Was model with frailties fitted.
frequenciesNumbers of patients, events and groups used to fit the model.
NpairsNumber of pairs of subjects, between-groups, within-groups and over all the population. If cindex=1, number of comparable (useable) pairs also available.
NbootNumber of bootstrap resamplings required.
tiesA binary, indicating if the tied pairs on prediction were used to compute the concordance.
CPEcondValues of Gonen & Heller's measure (conditional). 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).
CunocondValues of Uno's measure (conditional). 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 Gonen & Heller's measure (marginal), 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).
CunomargValues of Uno's measure (marginal), 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 of Harrell (conditional). 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 of Harrell (marginal), 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

Mauguen, A., Collette, S., Pignon, J. P. and Rondeau, V. (2013). Concordance measures in shared frailty models: application to clustered data in cancer prognosis. Statistics in Medicine 32, 27, 4803-4820 Harrell, F.E. et al. (1996). Tutorial in biostatistics: multivariable prognostic models: issues in developing models, evaluating assumptions and adequacy, and measuring and reducing errors. Statistics in Medicine 15, 361-387. Gonen, M., Heller, G. (2005). Concordance probability and discriminatory power in proportional hazards regression. Biometrika 92, 965-970.

Examples

Run this code

#-- load data
data(readmission)

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

#-- a Cmeasures call
fit.Cmeasures <- Cmeasures(fit)
fit.Cmeasures.noties <- Cmeasures(fit, ties=0)
fit.Cmeasures.marginal <- Cmeasures(fit, marginal=1)
fit.Cmeasures.cindex <- Cmeasures(fit, cindex=1)

#-- a short summary
fit.Cmeasures
fit.Cmeasures.noties
fit.Cmeasures.marginal
fit.Cmeasures.cindex