Cmeasures: Concordance measures in shared frailty and Cox proportional...

In frailtypack: Shared, Joint (Generalized) Frailty Models; Surrogate Endpoints

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 compared two by two. If a counting process formulation is used to performed the fit, with 't.start' and 't.stop', the gap-times (t.stop-t.start) are used in the concordance estimation.
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"' instead of "Beta'X + log z_i". Default is marginal=0.
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 done at the group level. If Cox model is used, resampling is done at individual level.
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 on the development population. In this case for conditional measures, the frailties are a posteriori predicted. The two datasets must have the same covariates with the same coding without missing data.

Value

call	The shared frailty model evaluated.
Frailty	Logical value. Was model with frailties fitted.
frequencies	Numbers of patients, events and groups used to fit the model.
Npairs	Number of pairs of subjects, between-groups, within-groups and over all the population. If cindex=1, number of comparable (useable) pairs also available.
Nboot	Number of bootstrap resamplings required.
ties	A binary, indicating if the tied pairs on prediction were used to compute the concordance.
CPEcond	Values 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).
Cunocond	Values 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).
marginal	A binary, indicating if the marginal values were computed.
CPEmarg	Values 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).
Cunomarg	Values 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).
cindex	A binary, indicating if the c-indexes were computed.
cindexcond	Values 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).
cindexmarg	Values 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.

See Also

print.Cmeasures,frailtyPenal

Examples

#-- 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

frailtypack documentation built on Oct. 20, 2024, 1:08 a.m.