survPerformance {ems}

Survival models performance analysis

Description

Colection of functions for survival models performance analysis.

R2sh estimates a distance-based estimator of survival predictive accuracy proposed by Schemper and Henderson. It was inspirated in survAUC::schemper function, but receives the predicted values directly. Besides that, R2sh does bootstrap resampling and returns its confidence interval estimate.

R2pm calculates a estimator of survival predictive accuracy proposed by Kent & O'Quigley and its bootstrap confidence interval.

cal.Slope returns the calibration slope of a survival model and its bootstrap confidence interval.

Usage

R2sh(time, status, lin.pred, data, R)

R2pm(lin.pred, R)

cal.Slope(time, status, lin.pred, R)

Arguments

time

A vector of event times.

status

A indicator vector of event occurrence.

lin.pred

A vector of linear predictors of a survival model for each observation. (prognostic index)

data

A data.frame where to find column vectors.

R

The number of bootstrap replicates. Usually this will be a single positive integer. For importance resampling, some resamples may use one set of weights and others use a different set of weights. In this case R would be a vector of integers where each component gives the number of resamples from each of the rows of weights. To be passed to boot.

Value

R2sh returns a list with the following components:

• D: The estimator of predictive accuracy obtained from the covariate-free null model.

• Dx: The estimator of predictive accuracy obtained from the Cox model.

• V: The estimator of relative gains in predictive accuracy.

• Mhat: The absolute distance estimator obtained from the Cox model (evaluated at the event times of the test data).

• Mhat.0: The absolute distance estimator obtained from the covariate-free null model (evaluated at the event times of the test data).

• timep: The event times of the test data.

• lower: V lower confidence limit.

• upper: V upper confidence limit.

• boot: An object of class "boot".

• bootCI: Boot confidence intervals resampling.

R2pm returns a list with the following components:

• r2: The estimator of predictive accuracy obtained from the Cox model.

• lower: r2 lower confidence limit.

• upper: r2 upper confidence limit.

• boot: An object of class "boot".

• bootCI: Boot confidence intervals resampling.

cal.Slope returns a list with the following components:

• slope: The calibration slope measure of a survival model.

• lower: slope lower confidence limit.

• upper: slope upper confidence limit.

• boot: An object of class "boot".

• bootCI: Boot confidence intervals resampling.

Author(s)

Lunna Borges <[e-mail]>

References

Schemper, M. and R. Henderson (2000). Predictive accuracy and explained variation in Cox regression. Biometrics 56, 249-255.

Davison, A.C. and Hinkley, D.V. (1997) Bootstrap Methods and Their Application, Chapter 5. Cambridge University Press.

DiCiccio, T.J. and Efron B. (1996) Bootstrap confidence intervals (with Discussion). Statistical Science, 11, 189-228.

Efron, B. (1987) Better bootstrap confidence intervals (with Discussion). Journal of the American Statistical Association, 82, 171-200.

Kent, John T., and J. O. H. N. O'QUIGLEY. "Measures of dependence for censored survival data." Biometrika 75.3 (1988): 525-534.

van Houwelingen, Hans C. "Validation, calibration, revision and combination of prognostic survival models." Statistics in medicine 19.24 (2000): 3401-3415.

Rahman, M. Shafiqur, et al. "Review and evaluation of performance measures for survival prediction models in external validation settings." BMC medical research methodology 17.1 (2017): 60.

Examples

#### Survival model ####

data(breastCancer)
class(breastCancer$gradd1) <- "character"
class(breastCancer$gradd2) <- "character"

traindata <- breastCancer[sample(nrow(breastCancer), nrow(breastCancer)*2/3),]
newdata <- breastCancer[-sample(nrow(breastCancer), nrow(breastCancer)*2/3),]
model <- rms::cph(survival::Surv(rectime, censrec) ~ rms::rcs(age,6) +
 rms::rcs(nodes,3) + rms::rcs(pgr,3) + gradd1 + gradd2 +
 hormon, data = traindata)

lp <- predict(model, newdata = newdata)

#### R2sh  example ####

R2sh(newdata$rectime, newdata$censrec, lp, data = newdata, R = 50)

#### R2pm example ####

R2pm(lp, R = 50)

#### cal.slope example ####

cal.Slope(newdata$rectime, newdata$censrec, lp, R = 50)