Distance-based estimator of survival predictive accuracy proposed by Schemper and Henderson

Schemper and Henderson's estimator of the absolute deviation between survival functions

schemper(train.fit, traindata, newdata)

Arguments

train.fit: A cph object containing the fit of a Cox proportional hazards model.
traindata: A data frame containing the set of training data.
newdata: A data frame containing the set of test data.

Value

schemper returns a list with the following components:

Model: The call to cph.
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.

Details

This code has been adapted from Lusa et al. (2007). Schemper and Henderson's estimator (as implemented by Lusa et al. 2007) assumes that predictions of the time-to-event outcome were obtained from a Cox proportional hazards model. The estimator is valid as long as the Cox model is specified correctly.

Technical details:

The Cox model has to be estimated via the cph function of the Design package.
The survival times and the censoring indicators have to be labelled “time” and “status”, respectively (see example below).
In contrast to the other estimators implemented in the survAUC package, schemper does not estimate the survival function of the censoring distribution from the training data but from the test data.

For details on the estimator and its implementation, we refer to Schemper and Henderson (2000) and Lusa et al. (2007).

References

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

Lusa, L., R. Miceli and L. Mariani (2007).
Estimation of predictive accuracy in survival analysis using R and S-PLUS.
Computer Methods and Programms in Biomedicine 87, 132–137.

Examples


data(cancer,package="survival")
ovarian$time <- ovarian$futime
ovarian$status <- ovarian$fustat
set.seed(2011)
trobs <- sample(1:26,16)
TR <- ovarian[trobs,]
TE <- ovarian[-trobs,]
train.fit  <- rms::cph(survival::Surv(time, status) ~ age,
                  x=TRUE, y=TRUE, method="breslow", data=TR)

schemper(train.fit, TR, TE)
#> $Model
#> rms::cph(formula = survival::Surv(time, status) ~ age, data = TR, 
#>     method = "breslow", x = TRUE, y = TRUE)
#> 
#> $D
#> [1] 0.3460937
#> 
#> $Dx
#> [1] 0.3169285
#> 
#> $V
#> [1] 0.0842697
#> 
#> $Mhat
#> [1] 0.4213731 0.3293749 0.2482184 0.2994786 0.2930806
#> 
#> $Mhat.0
#> [1] 0.1000 0.2375 0.4000 0.4500 0.5000
#> 
#> $timep
#> [1]  59 156 365 431 464
#>