survivROC: Generates the ROC curve at a given time point given the...
In RCASPAR: A package for survival time prediction based on a piecewise baseline hazard Cox regression model.

Description Usage Arguments Details Value Note Author(s) References See Also Examples

The function generates the Receiver-Operator Curve (ROC) at the specified time point using predicted and observed data in the presence of censored subjects. It so plots (1 - specificity) against the (specificity) at the designated cut off points. It is based on Patrick Heagerty's survivalROC function in the survivalROC package.

1	survivROC(Stime, status, marker, entry = NULL, predict.time, cut.values = NULL, plot = TRUE)

`Stime`	The observed survival times of the patients.
`status`	The censoring status of the patient. 1 for a censored patient, and 0 for a patient who has an event.
`marker`	The predicted survival time of the patients.
`entry`	The time of entry of the patients, set to NULL by default.
`predict.time`	The time point for which the ROC curve is to be plotted.
`cut.values`	The cut off values for which the ROC curves are to be constructed.
`plot`	A logical argument that specifies whether a plot is to be generated (TRUE) or not (FALSE). The argument is set to TRUE by default.

This function is basically the survivROC function in Patrick Heagerty's survivROC package, with slight modifications to it to better suit our purpose. Unlike Heagerty's function it only performs the calculations using the KM estimator and does not provide any other methods as options.

`cut.values`	the cut off values for which the sensitivity and (1-specificity) were calculated
`Comp.Specificity`	(1 - Specificity) as was calculated for every cut off value.
`Sensitivity`	The Sensitivity as was calculated for every cut off value
`predict.time`	The time point for which the ROC curve is calculated
`Survival`	The value of the estimated survivor function (using the KM estimator) at "predict.time"
`AUC`	The value of the area under the estimated ROC curve

It is important to note that using the Kaplan-Meier estimator as the method for estimating the survival function results in non-monotonous curves in some instances.

Douaa Mugahid

Heagerty,P., Lumely T. & Pepe M.(2000). Time-dependent ROC curves for censored survival data & a diagnostic marker. Biometrics, 56(2), 337-344.

survivAURC

True_STs <- c(1.416667,2.75,2.416667,2.583333,2.166667,2.5,2.5,1.833333,1.25,0.6666667,1,6.583333,6.5,6.666667,2.75,1.666667,1.166667,2.833333,3.583333,6.166667,6.166667,
3.416667,6.083333,1.833333,5.583333,0.75,5.75,5.5,0.5833333,7.666667,5,2.833333,1.333333,5.083333,0.8333333,1.5,4.75,3.416667,4.666667,1.916667,4.666667,7.416667,0.9166667,
1.083333,3.75,3.25,3,2.416667,2.75,2.5,2.666667,4.5,4.416667,1.5,0.8333333,3.166667,3.833333,3.833333,0.4166667,3.333333,2.75,3.083333,0.3333333,0.25,0.6666667,1.833333,
2.333333,3.416667,3.416667,3,0.6666667,0.75,2.166667,1,1.416667,1.333333,1.166667,1.166667,0.4166667,1.25,1.166667,1.083333)
Predicted_STs <- c(6.030591,6.014457,3.545584,5.414229,6.41576,9.393992,5.542331,6.890859,8.090213,4.98545,2.77357,6.275699,9.163978,7.511511,9.531218,7.63715,10.08977,
11.12364,3.982502,5.441881,12.61404,12.21851,17.05850,12.78141,16.22795,21.48544,6.281354,13.83925,8.859929,6.104142,8.255909,2.335526,6.564962,2.335761,9.33772,12.62540,
10.97276,15.63089,8.01967,5.817267,5.59897,4.340784,32.40319,33.74123,27.45024,26.31024,26.88833,24.34707,32.06541,38.90473,17.37102,15.11059,8.772035,14.24816,7.852889,
7.79996,5.601459,2.802408,35.77047,24.34717,30.65796,25.93927,20.64544,22.04807,19.15037,23.83430,1.876557,3.937208,6.526354,5.886377,9.301074,12.4657,14.49783,15.41502,
2.860931,2.541947,4.543111,4.525553,4.148272,3.986912,6.246755,6.89523)
censored <- c(0,1,1,1,1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0,1,1,1,0,1,1,1,1,1,0,1,1,1,1,0,1,1,1,1,0,0,0,1,1,1,1,0,0,1,0,1,1,1,1,1,1,1,
1)
survivROC(Stime=True_STs,status=censored, marker=Predicted_STs,predict.time=5)

$cut.values
 [1]      -Inf  2.106041  2.335644  2.438854  2.657758  2.787989  2.831669
 [8]  3.203257  3.741396  3.959855  3.984707  4.067592  4.244528  4.433169
[15]  4.534332  4.764280  5.199839  5.428055  5.492106  5.570650  5.600214
[22]  5.709363  5.851822  5.950417  6.022524  6.067367  6.175448  6.261227
[29]  6.278526  6.348557  6.471057  6.545658  6.727911  6.893045  7.203371
[36]  7.574331  7.718555  7.826424  7.936279  8.054941  8.173061  8.513972
[43]  8.815982  9.011954  9.232526  9.319397  9.365856  9.462605  9.810494
[50] 10.531265 11.048200 11.671075 12.342105 12.539870 12.619720 12.703405
[57] 13.310330 14.043705 14.372995 14.804210 15.262805 15.522955 15.929420
[64] 16.643225 17.214760 18.260695 19.897905 21.065440 21.766755 22.941185
[71] 24.090685 24.347120 25.143220 26.124755 26.599285 27.169285 29.054100
[78] 31.361685 32.234300 33.072210 34.755850 37.337600 39.404730

$Comp.Specificity
 [1] 1.0000000 0.9821748 0.9924764 0.9682785 0.9527760 0.9535285 0.9292419
 [8] 0.9135443 0.8948918 0.8730116 0.8957963 0.8802806 0.8675175 0.8444934
[15] 0.8294908 0.8144851 0.8013226 0.7816220 0.7589534 0.7392861 0.7165404
[22] 0.6936453 0.6953055 0.6745942 0.6550623 0.6562666 0.6333187 0.6187269
[29] 0.5957905 0.5726522 0.5550577 0.5318487 0.5327762 0.5153474 0.5015889
[36] 0.4785633 0.4791497 0.4590372 0.4465276 0.4235972 0.4238493 0.4006179
[43] 0.3770068 0.3772680 0.3531610 0.3534337 0.3537224 0.3548333 0.3373101
[50] 0.3376398 0.3132349 0.3207219 0.2959151 0.2962930 0.2702836 0.2706840
[57] 0.2711178 0.2431833 0.2436438 0.2278717 0.1976449 0.1981402 0.2428441
[64] 0.2214508 0.1999978 0.1784730 0.1792697 0.1673184 0.1673184 0.1673184
[71] 0.1673184 0.1673184 0.1464036 0.1254888 0.1045740 0.0836592 0.0627444
[78] 0.0418296 0.0209148 0.0209148 0.0209148 0.0209148 0.0000000

$Sensitivity
 [1] 1.00000000 0.99567900 0.95202045 0.95661209 0.94904260 0.91873928
 [7] 0.92345506 0.91615838 0.91299434 0.91434460 0.85322748 0.84567650
[13] 0.83427573 0.83722579 0.82895716 0.82069276 0.80985066 0.80815245
[19] 0.81060533 0.80886050 0.81142122 0.81419075 0.78261800 0.78233331
[25] 0.78039929 0.74946407 0.75230752 0.74346439 0.74629171 0.74940137
[31] 0.74475780 0.74796636 0.71741829 0.71254277 0.70253417 0.70548638
[37] 0.67541528 0.67429323 0.66253784 0.66535687 0.63575331 0.63899328
[43] 0.64276434 0.61314802 0.61761264 0.58798032 0.55832556 0.52752102
[49] 0.52277761 0.49306555 0.49794680 0.45822476 0.46366802 0.43388855
[55] 0.44101378 0.41120284 0.38134524 0.39116284 0.36126778 0.35407535
[61] 0.36709897 0.33715527 0.24538266 0.24605180 0.24680458 0.24765774
[67] 0.21729250 0.20475640 0.17550548 0.14625457 0.11700365 0.08775274
[73] 0.08775274 0.08775274 0.08775274 0.08775274 0.08775274 0.08775274
[79] 0.08775274 0.05850183 0.02925091 0.00000000 0.00000000

$predict.time
[1] 5

$Survival
[1] 0.5830858

$AUC
[1] 0.4102913