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survAUC: Estimators of Prediction Accuracy for Time-to-Event Data

License GPL-2. Repository CRAN. NeedsCompilation yes. Date/Publication 2022-05-20 07:30:02 UTC. R topics documented: AUC.cd .



Package timeROC

18 déc. 2019 Title Time-Dependent ROC Curve and AUC for Censored Survival Data. Version 0.4 ... Multiple comparisons using R. Chapman & Hall/CRC.

Package 'survAUC"

March 21, 2023

Version1.2-0

TitleEstimators of Prediction Accuracy for Time-to-Event Data AuthorSergej Potapov, Werner Adler and Matthias Schmid. DescriptionProvides a variety of functions to estimate time-dependent true/false positive rates and AUC curves from a set of censored survival data. MaintainerFrederic Bertrand

DependsR (>= 2.6.0),

Importssurvival, rms

Date2023-03-21

LicenseGPL-2

RepositoryCRAN

NeedsCompilationyes

Date/Publication2023-03-21 18:20:02 UTC

Rtopics documented:

AUC.cd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 AUC.hc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 AUC.sh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 AUC.uno . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 BeggC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 GHCI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 IntAUC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 OXS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 plot.survAUC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 predErr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 schemper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 UnoC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Index21

1

2AUC.cdAUC.cdAUC estimator proposed by Chambless and DiaoDescription

Chambless and Diao"s estimator of cumulative/dynamic AUC for right-censored time-to-event data Usage AUC.cd(Surv.rsp, Surv.rsp.new = NULL, lp, lpnew, times)

Arguments

Surv.rspASurv(.,.)object containing to the outcome of the training data. Surv.rsp.newASurv(.,.)object containing the outcome of the test data. lpThe vector of predictors estimated from the training data. lpnewThe vector of predictors obtained from the test data. timesA vector of time points at which to evaluate AUC.

Details

This function implements the estimator of cumulative/dynamic AUC proposed in Section 3.3 of Chambless and Diao (2006). In contrast to the general form of Chambless and Diao"s estimator, AUC.cdis restricted to Cox regression. Specifically, it is assumed thatlpandlpneware the predic- tors of a Cox proportional hazards model. Estimates obtained fromAUC.cdare valid as long as the Cox model is specified correctly. Theiaucsummary measure is given by the integral of AUC on [0, max(times)] (weighted by the estimated probability density of the time-to-event outcome). Note that the recursive estimators proposed in Sections 3.1 and 3.2 of Chambless and Diao (2006) are not implemented in thesurvAUCpackage. Value AUC.cdreturns an object of classsurvAUC. Specifically,AUC.cdreturns a list with the following components: aucThe cumulative/dynamic AUC estimates (evaluated attimes). timesThe vector of time points at which AUC is evaluated. iaucThe summary measure of AUC.

References

Chambless, L. E. and G. Diao (2006).

Estimation of time-dependent area under the ROC curve for long-term risk prediction.

Statistics in Medicine25, 3474-3486.

AUC.hc3

See Also

AUC.uno,AUC.sh,AUC.hc,IntAUC

Examples

data(cancer,package="survival")

TR <- ovarian[1:16,]

TE <- ovarian[17:26,]

train.fit <- survival::coxph(survival::Surv(futime, fustat) ~ age, x=TRUE, y=TRUE, method="breslow", data=TR) lp <- predict(train.fit) lpnew <- predict(train.fit, newdata=TE)

Surv.rsp <- survival::Surv(TR$futime, TR$fustat)

Surv.rsp.new <- survival::Surv(TE$futime, TE$fustat) times <- seq(10, 1000, 10)

AUC_CD <- AUC.cd(Surv.rsp, Surv.rsp.new, lp, lpnew, times)AUC.hcAUC estimator proposed by Hung and ChiangDescription

Hung and Chiang"s estimator of cumulative/dynamic AUC for right-censored time-to-event data Usage

AUC.hc(Surv.rsp, Surv.rsp.new, lpnew, times)

Arguments

Surv.rspASurv(.,.)object containing to the outcome of the training data. Surv.rsp.newASurv(.,.)object containing the outcome of the test data. lpnewThe vector of predictors obtained from the test data. timesA vector of time points at which to evaluate AUC.

Details

This function implements the estimator of cumulative/dynamic AUC proposed by Hung and Chiang (2010). The estimator is based on inverse-probability-of-censoring weights and does not assume a specific working model for deriving the predictorlpnew. It is assumed, however, that there is a one- to-one relationship between the predictor and the expected survival times conditional on the predic- tor. Theiaucsummary measure is given by the integral of AUC on [0, max(times)] (weighted by the estimated probability density of the time-to-event outcome). Note that the estimator implemented inAUC.hcis restricted to situations where the random censor- ing assumption holds (formula (4) in Hung and Chiang 2010).

4AUC.sh

Value AUC.hcreturns an object of classsurvAUC. Specifically,AUC.hcreturns a list with the following components: aucThe cumulative/dynamic AUC estimates (evaluated attimes). timesThe vector of time points at which AUC is evaluated. iaucThe summary measure of AUC.

References

Hung, H. and C.-T. Chiang (2010).

Estimation methods for time-dependent AUC models with survival data.

Canadian Journal of Statistics38, 8-26.

See Also

AUC.uno,AUC.sh,AUC.cd,IntAUC

Examples

data(cancer,package="survival")

TR <- ovarian[1:16,]

TE <- ovarian[17:26,]

train.fit <- survival::coxph(survival::Surv(futime, fustat) ~ age, x=TRUE, y=TRUE, method="breslow", data=TR) lpnew <- predict(train.fit, newdata=TE)

Surv.rsp <- survival::Surv(TR$futime, TR$fustat)

Surv.rsp.new <- survival::Surv(TE$futime, TE$fustat) times <- seq(10, 1000, 10) AUC_hc <- AUC.hc(Surv.rsp, Surv.rsp.new, lpnew, times) AUC_hcAUC.shAUC estimator proposed by Song and ZhouDescription Song and Zhou"s estimators of AUC for right-censored time-to-event data Usage AUC.sh(Surv.rsp, Surv.rsp.new=NULL, lp, lpnew, times, type="incident", savesensspec=FALSE) sens.sh(Surv.rsp, lp, lpnew, times, type="incident") spec.sh(Surv.rsp, lp, lpnew, times)

AUC.sh5

Arguments

Surv.rspASurv(.,.)object containing to the outcome of the training data. Surv.rsp.newASurv(.,.)object containing the outcome of the test data. lpThe vector of predictors estimated from the training data. lpnewThe vector of predictors obtained from the test data. timesA vector of time points at which to evaluate AUC. typeA string defining the type of true positive rate (TPR):"incident"refers to incident TPR ,"cumulative"refers to cumulative TPR. savesensspecA logical specifying whether sensitivities and specificities should be saved.

Details

Thesens.shandspec.shfunctions implement the estimators of time-dependent true and false positive rates proposed by Song and Zhou (2008). TheAUC.shfunction implements the estimators of cumulative/dynamic and incident/dynamic AUC proposed by Song and Zhou (2008). These estimators are given by the areas under the time- dependent ROC curves estimated bysens.shandspec.sh. In case of cumulative/dynamic AUC, theiaucsummary measure is given by the integral of AUC on [0, max(times)] (weighted by the estimated probability density of the time-to-event outcome). In case of incident/dynamic AUC, iaucis given by the integral of AUC on [0, max(times)] (weighted by 2 times the product of the estimated probability density and the estimated survival function of the time-to-event outcome). The results obtained fromspec.sh,spec.shandAUC.share valid as long aslpandlpneware the predictors of a correctly specified Cox proportional hazards model. In this case, the estimators remain valid even if the censoring times depend on the values of the predictors. Value AUC.shreturns an object of classsurvAUC. Specifically,AUC.shreturns a list with the following components: timesThe vector of time points at which AUC is evaluated. iaucThe summary measure of AUC. sens.shandspec.shreturn matrices of dimensionstimesxlpnew + 1. The elements of these matrices are the sensitivity and specificity estimates for each threshold oflpnewand for each time point specified intimes.

References

Song, X. and X.-H. Zhou (2008).

A semiparametric approach for the covariate specific ROC curve with survival outcome.

Statistica Sinica18, 947-965.

6AUC.uno

See Also

AUC.uno,AUC.cd,AUC.hc,GHCI,IntAUC

Examples

data(cancer,package="survival")

TR <- ovarian[1:16,]

TE <- ovarian[17:26,]

train.fit <- survival::coxph(survival::Surv(futime, fustat) ~ age, x=TRUE, y=TRUE, method="breslow", data=TR) lp <- predict(train.fit) lpnew <- predict(train.fit, newdata=TE)

Surv.rsp <- survival::Surv(TR$futime, TR$fustat)

Surv.rsp.new <- survival::Surv(TE$futime, TE$fustat) times <- seq(10, 1000, 10) AUC_sh <- AUC.sh(Surv.rsp, Surv.rsp.new, lp, lpnew, times) names(AUC_sh) AUC_sh$iaucAUC.unoAUC estimator proposed by Uno et al.Description Uno"s estimator of cumulative/dynamic AUC for right-censored time-to-event data Usage AUC.uno(Surv.rsp, Surv.rsp.new, lpnew, times, savesensspec=FALSE) sens.uno(Surv.rsp, Surv.rsp.new, lpnew, times) spec.uno(Surv.rsp.new, lpnew, times)

Arguments

Surv.rspASurv(.,.)object containing to the outcome of the training data. Surv.rsp.newASurv(.,.)object containing the outcome of the test data. lpnewThe vector of predictors obtained from the test data. timesA vector of time points at which to evaluate AUC. savesensspecA logical specifying whether sensitivities and specificities should be saved.

AUC.uno7

Details

Thesens.unoandspec.unofunctions implement the estimators of time-dependent true and false positive rates proposed in Section 5.1 of Uno et al. (2007). TheAUC.unofunction implements the estimator of cumulative/dynamic AUC that is based on the TPR and FPR estimators proposed by Uno et al. (2007). It is given by the area(s) under the time- dependent ROC curve(s) estimated bysens.shandspec.sh. Theiaucsummary measure is given by the integral of AUC on [0, max(times)] (weighted by the estimated probability density of the time-to-event outcome). working model for deriving the predictorlpnew. It is assumed, however, that there is a one-to-one relationshipbetweenthepredictorandtheexpectedsurvivaltimesconditionalonthepredictor. Note that the estimators implemented insens.uno,spec.unoandAUC.unoare restricted to situations where the random censoring assumption holds. Value AUC.unoreturns an object of classsurvAUC. Specifically,AUC.unoreturns a list with the following components: aucThe cumulative/dynamic AUC estimates (evaluated attimes). timesThe vector of time points at which AUC is evaluated. iaucThe summary measure of AUC. sens.unoandspec.unoreturn matrices of dimensionstimesx(lpnew + 1). The elements of these matrices are the sensitivity and specificity estimates for each threshold oflpnewand for each time point specified intimes.

References

Uno, H., T. Cai, L. Tian, and L. J. Wei (2007).

Evaluating prediction rules for t-year survivors with censored regression models. Journal of the American Statistical Association102, 527-537.

See Also

AUC.cd,AUC.sh,AUC.hc,IntAUC

Examples

data(cancer,package="survival")

TR <- ovarian[1:16,]

TE <- ovarian[17:26,]

train.fit <- survival::coxph(survival::Surv(futime, fustat) ~ age, x=TRUE, y=TRUE, method="breslow", data=TR) lpnew <- predict(train.fit, newdata=TE)

Surv.rsp <- survival::Surv(TR$futime, TR$fustat)

Surv.rsp.new <- survival::Surv(TE$futime, TE$fustat)

8BeggC

times <- seq(10, 1000, 10) AUC_Uno <- AUC.uno(Surv.rsp, Surv.rsp.new, lpnew, times) names(AUC_Uno) AUC_Uno$iaucBeggCC-statistic by Begg et al.Description

C-statistic by Begg et al.

Usage

BeggC(Surv.rsp, Surv.rsp.new, lp, lpnew)

Arguments

Surv.rspASurv(.,.)object containing to the outcome of the training data. Surv.rsp.newASurv(.,.)object containing the outcome of the test data. lpThe vector of predictors estimated from the training data. lpnewThe vector of predictors obtained from the test data.

Details

This function implements the C-statistic proposed by Begg et al. (2000). It has the same inter- pretation as Harrell"s C for survival data (implemented in thercorr.censfunction of theHmisc package).BeggCis restricted to Cox regression. Specifically, it is assumed thatlpandlpneware the predictors of a Cox proportional hazards model. Estimates obtained fromBeggCare valid as long as the Cox model is specified correctly. Value

The estimated C-statistic.

References

Begg, B. C., L. D. Craemer, E. S. Venkatraman and J. Rosai (2000). Comparing tumor staging and grading systems: a case study and a review of the issues, using thy- moma as a model.

Statistics in Medicine19, 1997-2014.

See Also

UnoC,GHCI,AUC.sh,IntAUC

GHCI9

Examples

data(cancer,package="survival")

TR <- ovarian[1:16,]

TE <- ovarian[17:26,]

train.fit <- survival::coxph(survival::Surv(futime, fustat) ~ age, x=TRUE, y=TRUE, method="breslow", data=TR) lp <- predict(train.fit) lpnew <- predict(train.fit, newdata=TE)

Surv.rsp <- survival::Surv(TR$futime, TR$fustat)

Surv.rsp.new <- survival::Surv(TE$futime, TE$fustat)

Cstat <- BeggC(Surv.rsp, Surv.rsp.new, lp, lpnew)

CstatGHCIGonen and Heller"s Concordance Index for Cox modelsDescription Gonen and Heller"s Concordance Index for Cox proportional hazards models Usage

GHCI(lpnew)

Arguments

lpnewThe vector of predictors obtained from the test data.

Details

This function implements the concordance probability estimator proposed by Gonen and Heller (2005). IthasthesameinterpretationasHarrell"sCforsurvivaldata(implementedinthercorr.cens function of theHmiscpackage). The results obtained fromGHCIare valid as long aslpnewis the predictor of a correctly specified Cox proportional hazards model. In this case, the estimator remains valid even if the censoring times depend on the values of the predictor. Note that the smoothed version ofGHCI, which is proposed in Section 3 of Gonen and Heller (2005), is not implemented in R packagesurvAUC. Value A length-one numeric vector containing the concordance probability estimate.

10IntAUC

References

Harrell, F. E., R. M. Califf, D. B. Pryor, K. L. Lee and R. A. Rosati (1982).

Evaluating the yield of medical tests.

Journal of the American Medical Association247, 2543-2546. Harrell, F. E., K. L. Lee, R. M. Califf, D. B. Pryor and R. A. Rosati (1984). Regression modeling strategies for improved prognostic prediction.

Statistics in Medicine3, 143-152.

Gonen, M. and G. Heller (2005).

Concordance probability and discriminatory power in proportional hazards regression.

Biometrika92, 965-970.

See Also

AUC.sh,IntAUC

Examples

data(cancer,package="survival")

TR <- ovarian[1:16,]

TE <- ovarian[17:26,]

train.fit <- survival::coxph(survival::Surv(futime, fustat) ~ age, x=TRUE, y=TRUE, method="breslow", data=TR) lpnew <- predict(train.fit, newdata=TE) GHCI(lpnew)IntAUCIntegration of time-dependent AUC curvesDescription Compute summary measures of a time-dependent AUC curve Usage IntAUC(AUC, times, S, tmax, auc.type="cumulative")

IntAUC11

Arguments

AUCA vector of AUCs.

timesThe vector of time points corresponding toAUC. SA vector of survival probabilities corresponding totimes. tmaxA number specifying the upper limit of the time range for which to compute the summary measure. auc.typeA string defining the type of AUC. "cumulative" refers to cumulative/dynamic

AUC, "incident" refers to incident/dynamic AUC.

Details

This function calculates the integral under a time-dependent AUC curve ("IAUC" measure) using the integration limits [0,tmax]. The values of the AUC curve are specified via theAUCargument. In caseauc.type = "cumulative"(cumulative/dynamic IAUC), the values ofAUCare weighted by the estimated probability density of the time-to-event outcome. In caseauc.type = "incident" (incident/dynamic IAUC), the values ofAUCare weighted by 2 times the product of the estimated probability density and the (estimated) survival function of the time-to-event outcome. The survival function has to be specified via theSargument. As shown by Heagerty and Zheng (2005), the incident/dynamic version of IAUC can be interpreted as a global concordance index measuring the probability that observations with a large predic- tor value have a shorter survival time than observations with a small predictor value. The inci- dent/dynamic version of IAUC has the same interpretation as Harrell"s C for survival data. Value A scalar number corresponding to the summary measure of interest.

References

Harrell, F. E., R. M. Califf, D. B. Pryor, K. L. Lee and R. A. Rosati (1982).

Evaluating the yield of medical tests.

Journal of the American Medical Association247, 2543-2546. Harrell, F. E., K. L. Lee, R. M. Califf, D. B. Pryor and R. A. Rosati (1984). Regression modeling strategies for improved prognostic prediction.

Statistics in Medicine3, 143-152.

Heagerty, P. J. and Y. Zheng (2005).

Survival model predictive accuracy and ROC curves.

Biometrics61, 92-105.

See Also

AUC.cd,AUC.sh,AUC.uno,AUC.hc

12OXS

Examples

data(cancer,package="survival")

TR <- ovarian[1:16,]

TE <- ovarian[17:26,]

train.fit <- survival::coxph(survival::Surv(futime, fustat) ~ age, x=TRUE, y=TRUE, method="breslow", data=TR) lp <- predict(train.fit) lpnew <- predict(train.fit, newdata=TE)

Surv.rsp <- survival::Surv(TR$futime, TR$fustat)

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