# SurvAccuracyMeasures

## estimate accuracy measures for risk prediction markers with survival data

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This R package computes non-parametric and semi-parametric estimates of common accuracy measures for risk prediction markers from survival data. It consists of the function survAM.estimate which estimates the AUC, TPR( c ), FPR( c ), PPV( c ), and NPV( c ) for for a specific prediction time and marker cutoff value c.

## Time-dependent measures of accuracy

For a continuous marker measured at baseline, Y, a marker cutpoint c, failure time T, and a prediction time t, accuracy measures are defined as:

## Estimation

Nonparametric estimates are calculated using inverse probability weighting, while semiparametric estimates are based on a Cox proportional hazards model. For detailed information regarding estimation methods, see references below.

Standard errors for estimates can be obtained by bootstrapping. Asymptotic standard error calculations are also available for semi-parametric Cox estimates. Confidence intervals using a normal approximation are computed.

## Tutorial

# install the package from CRAN
install.packages("survAccuracyMeasures")

# Alternatively, install the package directly from github
if (!require("devtools")) install.packages("devtools")
devtools::install_github("survMarkerTwoPhase", "mdbrown")


library(survAccuracyMeasures)

## Loading required package: survival


# simulated data for illustration
data(SimData)


##   survTime status        Y
## 1   0.1197      1  1.49310
## 2   1.0231      0 -0.73260
## 3   0.8282      0 -0.50211
## 4   2.0875      1  0.65758
## 5   4.6827      1  1.57806
## 6   0.3001      1  0.02419


Estimate all measures, using the bootstrap to estimate standard errors. First we obtain non-parametric estimates using inverse probablity weighting:


# Estimate all the measures at prediction time 2, with a marker cutpoint at 0.

##non-parametric estimates with bootstrap standard errrors
##in practice 'bootstraps' should be set to a larger value
survAM.estimate(time =survTime,
event = status,
marker = Y,
data = SimData,
estimation.method = "IPW",
se.method = "bootstrap",
predict.time = 1,
marker.cutpoint = 0,
bootstraps = 50)


## Non-Parametric IPW estimates of accuracy measures:
##    (SE's calculated using the bootstrap)
##
##         estimate     se      lower 0.95  upper 0.95
## AUC        0.786     0.032         0.717       0.841
## TPR(c)     0.769     0.054         0.648       0.858
## FPR(c)     0.410     0.024         0.364       0.459
## PPV(c)     0.231     0.030         0.177       0.295
## NPV(c)     0.941     0.015         0.905       0.964
##
##  marker cutpoint: c = 0


Alternatively, we can calculate semi-parametric estimates based on a Cox proportional hazards model:

# semi-parametric estimates assuming a cox model
##in practice 'bootstraps' should be set to a larger value

survAM.estimate(time =survTime,
event = status,
marker = Y,
data = SimData,
estimation.method = "Cox",
se.method = "bootstrap",
predict.time = 1,
marker.cutpoint = 0,
bootstraps = 50)


##
## Semi-Parametric Cox estimates of accuracy measures:
##    (SE's calculated using the bootstrap)
##
##         estimate     se      lower 0.95  upper 0.95
## coef       1.010     0.092         0.829       1.191
## AUC        0.768     0.021         0.724       0.808
## TPR(c)     0.788     0.031         0.722       0.842
## FPR(c)     0.412     0.022         0.369       0.457
## PPV(c)     0.241     0.029         0.189       0.302
## NPV(c)     0.943     0.011         0.918       0.961
##
##  marker cutpoint: c = 0

## here we calculate the SE's based on the asymptotic properties of the Cox estimator.
survAM.estimate(time =survTime,
event = status,
marker = Y,
data = SimData,
estimation.method = "Cox",
se.method = "asymptotic",
predict.time = 1,
marker.cutpoint = 0)

##
## Semi-Parametric Cox estimates of accuracy measures:
##    (SE's calculated using asymptotic variance)
##
##         estimate     se      lower 0.95  upper 0.95
## coef       1.010     0.085         0.842       1.177
## AUC        0.768     0.020         0.727       0.805
## TPR(c)     0.788     0.027         0.731       0.836
## FPR(c)     0.412     0.023         0.368       0.459
## PPV(c)     0.241     0.028         0.191       0.300
## NPV(c)     0.943     0.009         0.924       0.958
##
##  marker cutpoint: c = 0

For more information see ?survAM.estimate.

### References

Liu D, Cai T, Zheng Y. Evaluating the predictive value of biomarkers with stratified case-cohort design. Biometrics 2012, 4: 1219-1227.

Pepe MS, Zheng Y, Jin Y. Evaluating the ROC performance of markers for future events. Lifetime Data Analysis. 2008, 14: 86-113.

Zheng Y, Cai T, Pepe MS, Levy, W. Time-dependent predictive values of prognostic biomarkers with failure time outcome. JASA 2008, 103: 362-368.