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parTimeROC: Parametric Time-dependent Receiver Operating Characteristic

The goal of parTimeROC is to store methods and procedures needed to run the time-dependent ROC analysis parametrically. This package adopts two different theoretical framework to produce the ROC curve which are from the proportional hazard model and copula function. Currently, this package only able to run analysis for single covariate/biomarker with survival time. The future direction for this work is to be able to include analysis for multiple biomarkers with longitudinal measurements.

Installation

You can install the development version of parTimeROC from GitHub with:

# The easiest way to get parTimeROC is to install:
install.packages("parTimeROC")

# Alternatively, install the development version from GitHub:
devtools::install_github("FaizAzhar/parTimeROC")

Since this package also include the bayesian estimation procedure (rstan), please ensure to follow the correct installation setup such as demonstrated in this article.

Theoretical Framework

A receiver operating characteristics (ROC) curve is a curve that measures a model’s accuracy to correctly classify a population into a binary status (eg: dead/alive). The curve acts as a tool for analysts to compare which model is suitable to be used as a classifiers. However, in survival analysis, it is noted that the status of population fluctuate across time. Thus, a standard ROC analysis might underestimates the true accuracy measurement that the classification model have. In a situation where the population might enter or exit any of the two status over time, including the time component into the ROC analysis is shown to be superior and can help analysts to assess the performance of the model’s accuracy over time. In addition, a time-dependent ROC can also show at which specific time point a model will have a similar performance measurement with other model.

For the time being, two methods are frequently used when producing the time-dependent ROC curve. The first method employs the Cox proportional hazard model (PH) to estimate the joint distribution of the covariates and time-to-event. The second method employs a copula function which link the marginal distributions of covariates and time-to-event to estimate its joint distribution. After obtaining estimates for the joint distribution, two metrics can be computed which is the time-dependent sensitivity and specificity. Plotting these two informations will generate the desired time-dependent ROC curve.

Example

Explanations below are showing the functions that can be found within parTimeROC package and its implementation.

timeroc_obj

Following an OOP approaches, a TimeROC object can be initialized by using the parTimeROC::timeroc_obj() method.

test <- parTimeROC::timeroc_obj("normal-gompertz-PH")
print(test)
#> Model Assumptions: Proportional Hazard (PH)
#> X                : Gaussian
#> Time-to-Event    : Gompertz
test <- parTimeROC::timeroc_obj("normal-gompertz-copula", copula = "gumbel90")
print(test)
#> Model Assumptions: 90 Degrees Rotated Gumbel Copula
#> X                : Gaussian
#> Time-to-Event    : Gompertz

Notice that we included the print method to generate the summary for the test object which has a TimeROC class.

A list of distributions and copula have been stored within this package. It is accessible via the get.distributions or get.copula script.

names(parTimeROC::get.distributions)
#> [1] "exponential" "weibull"     "gaussian"    "normal"      "lognormal"  
#> [6] "gompertz"    "skewnormal"  "pch"         "llogis"
names(parTimeROC::get.copula)
#> [1] "gaussian"  "clayton90" "gumbel90"  "gumbel"    "joe90"

rtimeroc

Common tasks in mathematical modelling are prepared. For simulation purposes, procedure to generate random data from PH or copula function is created. The random data can be obtained using the parTimeROC::rtimeroc(). The parTimeROC::rtimeroc() returns a dataframe of 3 columns (t, x, status).

library(parTimeROC)
## PH model
test <- timeroc_obj(dist = 'weibull-gompertz-PH')
set.seed(23456)
rr <- rtimeroc(obj = test, censor.rate = 0.5, n=500,
               params.t = c(shape=2, rate=1),
               params.x = c(shape=2, scale=1),
               params.ph=0.5)
plot(t~x, rr)

timeroc_fit

We can also fit datasets that have time-to-event, covariates and status columns with the PH or copula model using the parTimeROC::timeroc_fit().

For PH model, two fitting processes are done. One is to fit the biomarker distribution alone. Another is to fit the time-to-event that is assumed to follow a proportional hazard model.

Meanwhile, for copula method, the IFM technique is used due to its light computational requirement. Three fitting processes are conducted. One is to fit the marginal distribution for biomarker, another is to fit the marginal time-to-event. And lastly is to fit the copula function.

User can choose to conduct the model fitting procedure based on the frequentist or bayesian approach by specifying the method = 'mle' or method = 'bayes' within the parTimeROC::timeroc_fit() function.

By default, the frequentist approach is used to estimate the model’s parameters.

library(parTimeROC)
## fitting copula model
test <- timeroc_obj(dist = 'gompertz-gompertz-copula', copula = "gumbel90")
set.seed(23456)
rr <- rtimeroc(obj = test, censor.rate = 0, n=500,
               params.t = c(shape=3,rate=1),
               params.x = c(shape=1,rate=2),
               params.copula=-5) # name of parameter must follow standard

cc <- timeroc_fit(rr$x, rr$t, rr$event, obj = test)
print(cc)
#> Model:  gompertz-gompertz-copula 
#> ------
#> X (95% CI) :
#> AIC =  -65.51402 
#>             est       low    upper        se
#> shape 0.9342836 0.6216374 1.246930 0.1595163
#> rate  2.0930839 1.7975025 2.388665 0.1508096
#> ------
#> Time-to-Event (95% CI) :
#> AIC =  -141.7148 
#>             est       low    upper         se
#> shape 3.0894231 2.7066350 3.472211 0.19530364
#> rate  0.9160331 0.7546502 1.077416 0.08233974
#> ------
#> Copula (95% CI) :
#> AIC =  -1432.074 
#>           est     low   upper     se
#> theta -5.1126 -5.4868 -4.7384 0.1909

Notice that the print method also can be used to print the results obtained from the fitting process.

timeroc_gof

After fitting the model with either PH or copula model, its goodness-of-fit can be examined through the function parTimeROC::timeroc_gof(). This will return a list of test statistic and p-values denoting misspecification of model or not. Kolmogorov-Smirnov testing is performed for model checking. If p-value < 0.05, we reject the null hypothesis that the data (biomarker or time-to-event) are following the assumed distribution.

For copula model, additional testing is needed to check whether the copula used is able to model the data or not. After using the Rosenblatt transformation, we conduct an independent testing to check whether the empirical conditional and cumulative distribution are independent. If the p-value < 0.05, we reject the null hypothesis which stated that the conditional and cumulative are independent. Thus, for p-value < 0.05, the copula failed to provide a good estimation for the joint distribution.

library(parTimeROC)
# Copula model
rt <- timeroc_obj("normal-weibull-copula",copula="clayton90")
set.seed(1)
rr <- rtimeroc(rt, n=300, censor.rate = 0,
               params.x = c(mean=5, sd=1),
               params.t = c(shape=1, scale=5),
               params.copula = -2.5)
test <- timeroc_obj("normal-weibull-copula",copula="gumbel90")
jj <- timeroc_fit(test, rr$x, rr$t, rr$event)

timeroc_gof(jj)
#> $ks_x
#> 
#>  Asymptotic two-sample Kolmogorov-Smirnov test
#> 
#> data:  df$x and theo.q
#> D = 0.04, p-value = 0.97
#> alternative hypothesis: two-sided
#> 
#> 
#> $ks_t
#> 
#>  Asymptotic two-sample Kolmogorov-Smirnov test
#> 
#> data:  df$t and theo.q
#> D = 0.036667, p-value = 0.9877
#> alternative hypothesis: two-sided
#> 
#> 
#> $ind_u
#> $ind_u$statistic
#> [1] 1.875196
#> 
#> $ind_u$p.value
#> [1] 0.06076572
#> 
#> 
#> $ind_v
#> $ind_v$statistic
#> [1] 2.674574
#> 
#> $ind_v$p.value
#> [1] 0.007482435
test <- timeroc_obj("normal-weibull-copula",copula="clayton90")
jj <- timeroc_fit(test, rr$x, rr$t, rr$event)

timeroc_gof(jj)
#> $ks_x
#> 
#>  Asymptotic two-sample Kolmogorov-Smirnov test
#> 
#> data:  df$x and theo.q
#> D = 0.04, p-value = 0.97
#> alternative hypothesis: two-sided
#> 
#> 
#> $ks_t
#> 
#>  Asymptotic two-sample Kolmogorov-Smirnov test
#> 
#> data:  df$t and theo.q
#> D = 0.036667, p-value = 0.9877
#> alternative hypothesis: two-sided
#> 
#> 
#> $ind_u
#> $ind_u$statistic
#> [1] 1.385664
#> 
#> $ind_u$p.value
#> [1] 0.1658495
#> 
#> 
#> $ind_v
#> $ind_v$statistic
#> [1] 0.07947699
#> 
#> $ind_v$p.value
#> [1] 0.9366532
library(parTimeROC)
# PH model
rt <- timeroc_obj("normal-weibull-PH")
set.seed(1)
rr <- rtimeroc(rt, n=300, censor.rate = 0,
              params.x = c(mean=5, sd=1),
              params.t = c(shape=1, scale=5),
              params.ph = 1.2)
test <- timeroc_obj("lognormal-lognormal-PH")
jj <- timeroc_fit(test, rr$x, rr$t, rr$event)
timeroc_gof(jj)
#> $ks_x
#> 
#>  Asymptotic two-sample Kolmogorov-Smirnov test
#> 
#> data:  df$x and theo.q
#> D = 0.056667, p-value = 0.7212
#> alternative hypothesis: two-sided
#> 
#> 
#> $ks_t
#>       A p-value   F(ym)      ym 
#>   0.673   0.756   0.996   4.960 
#> 
#> $df
#>            x            t event     coxsnell       mresid sgn     devresid
#> 180 6.207908 1.584490e-06     1 2.131038e-05  0.999978690   1  4.417315332
#> 280 5.919804 3.856797e-05     1 2.895444e-03  0.997104556   1  3.113683487
#> 174 4.922847 5.297660e-05     1 1.589046e-03  0.998410954   1  3.300366838
#> 203 6.586588 5.434546e-05     1 9.734000e-03  0.990266000   1  2.698838419
#> 283 6.324259 9.838639e-05     1 1.703462e-02  0.982965384   1  2.485776487
#> 11  6.511781 1.362743e-04     1 3.250970e-02  0.967490303   1  2.217533118
#> 239 6.096777 1.485618e-04     1 2.345591e-02  0.976544085   1  2.356305793
#> 272 5.394379 2.055676e-04     1 1.706850e-02  0.982931497   1  2.484990516
#> 5   5.329508 2.056777e-04     1 1.593797e-02  0.984062028   1  2.511966883
#> 206 7.497662 2.412804e-04     1 1.985675e-01  0.801432458   1  1.276866098
#> 50  5.881108 2.569037e-04     1 3.836344e-02  0.961636556   1  2.144301142
#> 178 7.075245 2.909709e-04     1 1.610414e-01  0.838958564   1  1.405087198
#> 9   5.575781 3.123474e-04     1 3.558197e-02  0.964418029   1  2.177842126
#> 254 4.752336 3.308331e-04     1 1.589561e-02  0.984104390   1  2.513009312
#> 208 5.541327 3.523408e-04     1 3.995380e-02  0.960046204   1  2.126022288
#> 70  7.172612 3.641114e-04     1 2.374854e-01  0.762514566   1  1.162010690
#> 31  6.358680 3.731538e-04     1 1.027467e-01  0.897253341   1  1.660262387
#> 43  5.696963 3.735145e-04     1 5.076778e-02  0.949232218   1  2.015569953
#> 241 5.707311 4.171255e-04     1 5.893075e-02  0.941069251   1  1.944388345
#> 109 5.384185 4.611596e-04     1 4.727337e-02  0.952726631   1  2.048941934
#> 30  5.417942 4.789896e-04     1 5.135475e-02  0.948645251   1  2.010150549
#> 163 6.058483 4.974118e-04     1 1.065678e-01  0.893432185   1  1.640452102
#> 4   6.595281 5.261248e-04     1 2.024376e-01  0.797562396   1  1.264722241
#> 110 6.682176 5.587205e-04     1 2.390025e-01  0.760997508   1  1.157828825
#> 171 7.307978 5.743735e-04     1 4.819979e-01  0.518002066   1  0.650866170
#> 251 5.136222 5.780635e-04     1 4.784186e-02  0.952158143   1  2.043377698
#> 93  6.160403 6.104503e-04     1 1.524681e-01  0.847531905   1  1.437545140
#> 21  5.918977 6.605556e-04     1 1.295785e-01  0.870421494   1  1.531696354
#> 61  7.401618 6.870186e-04     1 6.609741e-01  0.339025946   1  0.387336408
#> 48  5.768533 7.316284e-04     1 1.246976e-01  0.875302357   1  1.553422655
#> 2   5.183643 7.346172e-04     1 6.712258e-02  0.932877423   1  1.880615541
#> 90  5.267099 7.565577e-04     1 7.598775e-02  0.924012252   1  1.818334906
#> 147 7.087167 7.590941e-04     1 5.321981e-01  0.467801939   1  0.570854842
#> 274 7.649167 7.724052e-04     1 9.897290e-01  0.010271029   1  0.010306405
#> 6   4.179532 8.469456e-04     1 2.720088e-02  0.972799120   1  2.294213075
#> 126 5.712666 8.497752e-04     1 1.402481e-01  0.859751873   1  1.486331200
#> 185 5.521023 9.809825e-04     1 1.352010e-01  0.864798955   1  1.507443817
#> 187 6.464587 1.020379e-03     1 3.874071e-01  0.612592866   1  0.819373232
#> 160 6.869291 1.054860e-03     1 6.200787e-01  0.379921277   1  0.442690771
#> 15  6.124931 1.079218e-03     1 2.876596e-01  0.712340410   1  1.033089606
#> 73  5.610726 1.123521e-03     1 1.740439e-01  0.825956094   1  1.358301573
#> 282 4.592471 1.147806e-03     1 6.016727e-02  0.939832728   1  1.934318483
#> 201 5.409402 1.155275e-03     1 1.449571e-01  0.855042885   1  1.467156744
#> 216 6.519745 1.209462e-03     1 4.996520e-01  0.500347997   1  0.622085878
#> 102 5.042116 1.229168e-03     1 1.051468e-01  0.894853152   1  1.647752532
#> 39  6.100025 1.231089e-03     1 3.257711e-01  0.674228898   1  0.945866150
#> 122 6.343039 1.248639e-03     1 4.290984e-01  0.570901616   1  0.741845587
#> 55  6.433024 1.257002e-03     1 4.759558e-01  0.524044242   1  0.660887482
#> 182 5.983896 1.290249e-03     1 3.035914e-01  0.696408574   1  0.995654459
#> 152 4.981440 1.303752e-03     1 1.053863e-01  0.894613737   1  1.646517080
#> 217 4.691259 1.393261e-03     1 8.335384e-02  0.916646162   1  1.770883655
#> 41  4.835476 1.514742e-03     1 1.068080e-01  0.893191958   1  1.639225484
#> 288 5.945185 1.550642e-03     1 3.583808e-01  0.641619199   1  0.876972028
#> 234 5.570508 1.564560e-03     1 2.426722e-01  0.757327756   1  1.147794215
#> 166 7.206102 1.582535e-03     1 1.408195e+00 -0.408194560  -1 -0.363004490
#> 95  6.586833 1.583196e-03     1 7.274998e-01  0.272500198   1  0.302130283
#> 123 4.785421 1.590259e-03     1 1.069137e-01  0.893086310   1  1.638686726
#> 295 6.778429 1.600860e-03     1 9.036812e-01  0.096318810   1  0.099597558
#> 99  3.775387 1.616006e-03     1 3.703913e-02  0.962960868   1  2.160009001
#> 199 5.411975 1.625319e-03     1 2.137973e-01  0.786202688   1  1.230060295
#> 193 4.268252 1.705735e-03     1 6.655795e-02  0.933442050   1  1.884802501
#> 59  5.569720 1.787185e-03     1 2.810998e-01  0.718900152   1  1.048947272
#> 71  5.475510 1.847682e-03     1 2.637217e-01  0.736278310   1  1.092321039
#> 142 6.176583 1.847913e-03     1 5.573840e-01  0.442616032   1  0.532700468
#> 133 5.531496 1.873528e-03     1 2.842750e-01  0.715725041   1  1.041238016
#> 161 5.425100 1.876214e-03     1 2.541607e-01  0.745839252   1  1.117093634
#> 101 4.379633 1.900729e-03     1 8.447587e-02  0.915524133   1  1.763953090
#> 169 4.855600 1.952600e-03     1 1.446040e-01  0.855395959   1  1.468577586
#> 92  6.207868 1.973661e-03     1 6.195337e-01  0.380466273   1  0.443445293
#> 40  5.763176 2.000774e-03     1 3.912341e-01  0.608765855   1  0.812013802
#> 258 5.572740 2.044065e-03     1 3.268376e-01  0.673162446   1  0.943535438
#> 60  4.864945 2.075975e-03     1 1.561746e-01  0.843825421   1  1.423344918
#> 19  5.821221 2.162081e-03     1 4.529615e-01  0.547038533   1  0.699870968
#> 172 5.105802 2.162565e-03     1 2.111395e-01  0.788860544   1  1.238043529
#> 148 5.017396 2.181191e-03     1 1.939273e-01  0.806072739   1  1.291665124
#> 252 5.407168 2.257563e-03     1 3.051441e-01  0.694855920   1  0.992083970
#> 245 6.162965 2.291417e-03     1 6.947238e-01  0.305276158   1  0.343408515
#> 34  4.946195 2.486713e-03     1 2.070655e-01  0.792934507   1  1.250428436
#> 297 5.765599 2.579352e-03     1 5.163304e-01  0.483669648   1  0.595548241
#> 159 3.615573 2.589888e-03     1 5.227349e-02  0.947726505   1  2.001768882
#> 214 3.629792 2.621402e-03     1 5.376348e-02  0.946236518   1  1.988428674
#> 108 5.910174 2.633230e-03     1 6.159373e-01  0.384062664   1  0.448435913
#> 56  6.980400 2.707695e-03     1 1.988415e+00 -0.988414985  -1 -0.775986022
#> 94  5.700214 2.746805e-03     1 5.149560e-01  0.485043970   1  0.597711954
#> 230 5.263176 2.871097e-03     1 3.385427e-01  0.661457276   1  0.918311171
#> 135 5.306558 2.878444e-03     1 3.555474e-01  0.644452605   1  0.882773034
#> 62  4.960760 2.918194e-03     1 2.494177e-01  0.750582322   1  1.129640691
#> 183 5.219925 2.983556e-03     1 3.366834e-01  0.663316639   1  0.922275157
#> 51  5.398106 3.011408e-03     1 4.112154e-01  0.588784572   1  0.774407483
#> 284 4.298768 3.052306e-03     1 1.290339e-01  0.870966073   1  1.534088547
#> 157 6.000029 3.108070e-03     1 8.082057e-01  0.191794317   1  0.205642300
#> 85  5.593946 3.132134e-03     1 5.282332e-01  0.471766790   1  0.576975939
#> 197 6.441158 3.162805e-03     1 1.318130e+00 -0.318129773  -1 -0.289537147
#> 87  6.063100 3.293417e-03     1 9.186709e-01  0.081329149   1  0.083644865
#> 170 5.207538 3.330429e-03     1 3.729790e-01  0.627021042   1  0.847599236
#> 68  6.465555 3.442322e-03     1 1.478304e+00 -0.478303723  -1 -0.418111052
#> 215 5.987838 3.627942e-03     1 9.377089e-01  0.062291095   1  0.063633623
#> 131 5.060160 3.631898e-03     1 3.488022e-01  0.651197840   1  0.896719079
#> 82  4.864821 3.655713e-03     1 2.850911e-01  0.714908868   1  1.039266588
#> 96  5.558486 3.684344e-03     1 6.025747e-01  0.397425290   1  0.467158070
#> 224 4.659031 3.709862e-03     1 2.323901e-01  0.767609932   1  1.176204116
#> 250 6.020464 3.806544e-03     1 1.020473e+00 -0.020473094  -1 -0.020335023
#> 106 6.767287 3.885685e-03     1 2.313026e+00 -1.313025659  -1 -0.974134675
#> 289 5.433702 3.995757e-03     1 5.735310e-01  0.426468971   1  0.508869862
#> 104 5.158029 4.006017e-03     1 4.284770e-01  0.571523011   1  0.742960608
#> 278 5.741001 4.015517e-03     1 8.001913e-01  0.199808718   1  0.214922123
#> 120 4.822670 4.064548e-03     1 3.040620e-01  0.695937964   1  0.994570830
#> 290 6.005159 4.105513e-03     1 1.085223e+00 -0.085222751  -1 -0.082915435
#> 18  5.943836 4.305156e-03     1 1.067111e+00 -0.067111174  -1 -0.065666034
#> 220 4.955291 4.348745e-03     1 3.753921e-01  0.624607871   1  0.842824122
#> 138 4.471720 4.356570e-03     1 2.244638e-01  0.775536244   1  1.198753338
#> 265 6.719627 4.356954e-03     1 2.472257e+00 -1.472256627  -1 -1.065011999
#> 52  4.387974 4.408170e-03     1 2.077521e-01  0.792247885   1  1.248328306
#> 233 4.359518 4.482706e-03     1 2.050095e-01  0.794990454   1  1.256748409
#> 107 5.716707 4.505199e-03     1 8.770923e-01  0.122907662   1  0.128338160
#> 113 6.432282 4.706226e-03     1 1.967727e+00 -0.967726772  -1 -0.762689738
#> 226 6.803142 4.738835e-03     1 2.943720e+00 -1.943720178  -1 -1.314569154
#> 8   5.738325 4.760157e-03     1 9.491309e-01  0.050869148   1  0.051758242
#> 218 3.746710 4.840431e-03     1 1.152274e-01  0.884772614   1  1.597545127
#> 194 5.830373 4.899466e-03     1 1.078088e+00 -0.078088297  -1 -0.076143545
#> 151 5.450187 5.053122e-03     1 7.412365e-01  0.258763514   1  0.285208858
#> 249 4.833879 5.062990e-03     1 3.847246e-01  0.615275443   1  0.824563149
#> 66  5.188792 5.248453e-03     1 5.825742e-01  0.417425806   1  0.495727594
#> 181 3.768677 5.286819e-03     1 1.289132e-01  0.871086830   1  1.534620066
#> 124 4.820443 5.337817e-03     1 3.999172e-01  0.600082782   1  0.795506035
#> 49  4.887654 5.363530e-03     1 4.317297e-01  0.568270340   1  0.737136804
#> 1   4.373546 5.400864e-03     1 2.511521e-01  0.748847850   1  1.125031999
#> 204 4.669092 5.424176e-03     1 3.457752e-01  0.654224781   1  0.903041074
#> 202 6.688873 5.501575e-03     1 3.027711e+00 -2.027711151  -1 -1.356395380
#> 179 6.027392 5.660975e-03     1 1.537759e+00 -0.537758744  -1 -0.463535864
#> 64  5.028002 5.662658e-03     1 5.294170e-01  0.470582959   1  0.575144924
#> 86  5.332950 5.664599e-03     1 7.333142e-01  0.266685838   1  0.294941463
#> 83  6.178087 5.846703e-03     1 1.864996e+00 -0.864995614  -1 -0.695322821
#> 207 5.667066 5.876265e-03     1 1.086409e+00 -0.086409049  -1 -0.084038585
#> 119 5.494188 5.899703e-03     1 9.069424e-01  0.093057615   1  0.096111794
#> 269 4.668967 5.970098e-03     1 3.803613e-01  0.619638652   1  0.833060515
#> 287 4.331821 6.058580e-03     1 2.693125e-01  0.730687479   1  1.078142204
#> 26  4.943871 6.314466e-03     1 5.391229e-01  0.460877098   1  0.560240338
#> 81  4.431331 6.402171e-03     1 3.162470e-01  0.683752971   1  0.966931914
#> 263 4.715669 6.423455e-03     1 4.297703e-01  0.570229669   1  0.740641152
#> 45  4.311244 6.591379e-03     1 2.862872e-01  0.713712825   1  1.036385100
#> 114 4.349304 6.615928e-03     1 2.992452e-01  0.700754756   1  1.005720709
#> 25  5.619826 6.623362e-03     1 1.162505e+00 -0.162504838  -1 -0.154452697
#> 164 5.886423 6.755703e-03     1 1.575385e+00 -0.575384953  -1 -0.491701730
#> 225 3.843428 6.934491e-03     1 1.826221e-01  0.817377939   1  1.328878147
#> 238 3.813541 6.991735e-03     1 1.783151e-01  0.821684920   1  1.343516475
#> 23  5.074565 6.994508e-03     1 6.852397e-01  0.314760315   1  0.355601692
#> 273 4.148143 7.097236e-03     1 2.585961e-01  0.741403883   1  1.105517023
#> 212 5.420695 7.099505e-03     1 1.005974e+00 -0.005974452  -1 -0.005962596
#> 128 4.962366 7.101513e-03     1 6.169793e-01  0.383020688   1  0.446987914
#> 242 6.034108 7.188278e-03     1 1.959580e+00 -0.959580014  -1 -0.757429656
#> 7   5.487429 7.236927e-03     1 1.100596e+00 -0.100596274  -1 -0.097408149
#> 222 5.002132 7.294616e-03     1 6.607639e-01  0.339236086   1  0.387614710
#> 275 5.156012 7.337022e-03     1 7.830996e-01  0.216900406   1  0.234925476
#> 248 4.744329 7.403683e-03     1 5.091166e-01  0.490883380   1  0.606951057
#> 22  5.782136 7.505808e-03     1 1.561765e+00 -0.561764574  -1 -0.481556341
#> 76  5.291446 7.579080e-03     1 9.338333e-01  0.066166663   1  0.067685061
#> 236 4.901821 7.672389e-03     1 6.234807e-01  0.376519322   1  0.437991282
#> 223 4.369700 7.844831e-03     1 3.610064e-01  0.638993633   1  0.871626124
#> 219 5.642241 8.118891e-03     1 1.451164e+00 -0.451163617  -1 -0.396983345
#> 255 5.695551 8.198243e-03     1 1.550561e+00 -0.550561131  -1 -0.473168565
#> 12  5.389843 8.235466e-03     1 1.123788e+00 -0.123787742  -1 -0.119019746
#> 266 5.270055 8.264447e-03     1 9.922663e-01  0.007733713   1  0.007753741
#> 53  5.341120 8.365532e-03     1 1.083020e+00 -0.083020320  -1 -0.080828082
#> 175 4.665999 8.406353e-03     1 5.293532e-01  0.470646811   1  0.575243609
#> 281 5.398130 8.470306e-03     1 1.164784e+00 -0.164784009  -1 -0.156514148
#> 240 4.994656 8.508742e-03     1 7.605343e-01  0.239465737   1  0.261795256
#> 111 4.364264 8.565672e-03     1 3.905753e-01  0.609424684   1  0.813277041
#> 33  5.387672 9.010942e-03     1 1.222016e+00 -0.222016440  -1 -0.207432524
#> 167 4.744973 9.601335e-03     1 6.536791e-01  0.346320908   1  0.397033563
#> 67  3.195041 9.747181e-03     1 1.268132e-01  0.873186839   1  1.543925913
#> 286 3.998928 9.977149e-03     1 3.057256e-01  0.694274382   1  0.990750089
#> 44  5.556663 1.016483e-02     1 1.640487e+00 -0.640486779  -1 -0.539432600
#> 69  5.153253 1.027810e-02     1 1.077759e+00 -0.077758775  -1 -0.075830052
#> 256 6.146228 1.039499e-02     1 3.143288e+00 -2.143287697  -1 -1.412811670
#> 103 4.089078 1.059418e-02     1 3.561478e-01  0.643852233   1  0.881541066
#> 153 4.681932 1.081129e-02     1 6.833968e-01  0.316603202   1  0.357984421
#> 176 4.965274 1.095095e-02     1 9.358722e-01  0.064127763   1  0.065552235
#> 259 5.374724 1.102584e-02     1 1.458020e+00 -0.458020081  -1 -0.402344813
#> 229 5.197193 1.159346e-02     1 1.264136e+00 -0.264136318  -1 -0.243914663
#> 105 4.345415 1.179439e-02     1 5.175169e-01  0.482483087   1  0.593683393
#> 16  4.955066 1.179744e-02     1 9.922079e-01  0.007792079   1  0.007812411
#> 235 4.940277 1.217200e-02     1 1.005367e+00 -0.005367369  -1 -0.005357796
#> 298 5.955137 1.295442e-02     1 3.145332e+00 -2.145331705  -1 -1.413797970
#> 115 4.792619 1.311679e-02     1 9.200434e-01  0.079956611   1  0.082192908
#> 243 5.223480 1.357681e-02     1 1.503959e+00 -0.503959386  -1 -0.437854233
#> 97  3.723408 1.358351e-02     1 3.034915e-01  0.696508542   1  0.995884805
#> 209 4.986600 1.363832e-02     1 1.172838e+00 -0.172838127  -1 -0.163777691
#> 79  5.074341 1.371792e-02     1 1.294843e+00 -0.294843368  -1 -0.270013450
#> 32  4.897212 1.390672e-02     1 1.085278e+00 -0.085277858  -1 -0.082967626
#> 276 6.130207 1.430250e-02     1 4.150937e+00 -3.150936842  -1 -1.858818328
#> 231 4.014173 1.444489e-02     1 4.378003e-01  0.562199660   1  0.726350683
#> 271 4.741067 1.461142e-02     1 9.609866e-01  0.039013396   1  0.039532613
#> 267 4.577816 1.467212e-02     1 8.103740e-01  0.189626028   1  0.203142394
#> 127 4.926436 1.486152e-02     1 1.189394e+00 -0.189394126  -1 -0.178606195
#> 264 5.857410 1.489175e-02     1 3.218355e+00 -2.218355054  -1 -1.448782025
#> 132 4.411106 1.510442e-02     1 6.963852e-01  0.303614762   1  0.341284360
#> 88  4.695816 1.523078e-02     1 9.507970e-01  0.049203018   1  0.050033982
#> 261 5.951013 1.529210e-02     1 3.642935e+00 -2.642935234  -1 -1.643256215
#> 63  5.689739 1.539405e-02     1 2.773061e+00 -1.773061389  -1 -1.227281129
#> 211 4.835624 1.569447e-02     1 1.134106e+00 -0.134105652  -1 -0.128540137
#> 29  4.521850 1.588777e-02     1 8.203718e-01  0.179628190   1  0.191673810
#> 237 5.560821 1.626491e-02     1 2.539465e+00 -1.539464838  -1 -1.102280792
#> 112 4.538355 1.627771e-02     1 8.533653e-01  0.146634740   1  0.154485448
#> 189 4.569788 1.630243e-02     1 8.836826e-01  0.116317369   1  0.121160443
#> 100 4.526599 1.635253e-02     1 8.462043e-01  0.153795656   1  0.162473082
#> 13  4.378759 1.643230e-02     1 7.258535e-01  0.274146486   1  0.304172878
#> 116 4.607192 1.669169e-02     1 9.393543e-01  0.060645657   1  0.061916910
#> 177 5.787640 1.715414e-02     1 3.393063e+00 -2.393062799  -1 -1.530574928
#> 20  5.593901 1.736921e-02     1 2.790149e+00 -1.790149154  -1 -1.236166736
#> 285 4.419386 1.760827e-02     1 8.063687e-01  0.193631348   1  0.207763849
#> 279 3.683755 1.802936e-02     1 3.755833e-01  0.624416716   1  0.842446819
#> 125 4.899809 1.869249e-02     1 1.419954e+00 -0.419954152  -1 -0.372369624
#> 72  4.290054 1.887332e-02     1 7.470585e-01  0.252941461   1  0.278101674
#> 42  4.746638 2.012913e-02     1 1.287258e+00 -0.287258479  -1 -0.263604750
#> 27  4.844204 2.036010e-02     1 1.442921e+00 -0.442920569  -1 -0.390515906
#> 196 3.952016 2.046926e-02     1 5.594364e-01  0.440563577   1  0.529644810
#> 213 4.599753 2.063958e-02     1 1.124957e+00 -0.124957180  -1 -0.120101684
#> 200 4.618924 2.065233e-02     1 1.148833e+00 -0.148833038  -1 -0.142030704
#> 77  4.556708 2.141979e-02     1 1.109920e+00 -0.109920166  -1 -0.106132708
#> 292 5.376370 2.146851e-02     1 2.667279e+00 -1.667278793  -1 -1.171511860
#> 192 5.402012 2.179250e-02     1 2.777357e+00 -1.777357283  -1 -1.229518137
#> 168 3.575505 2.181733e-02     1 3.957989e-01  0.604201101   1  0.803303089
#> 137 4.699024 2.242039e-02     1 1.344436e+00 -0.344435630  -1 -0.311323982
#> 296 5.134448 2.242761e-02     1 2.140331e+00 -1.140331427  -1 -0.871057676
#> 293 5.244165 2.268948e-02     1 2.430619e+00 -1.430619293  -1 -1.041607618
#> 58  3.955865 2.303471e-02     1 6.227020e-01  0.377297951   1  0.439065315
#> 210 5.510108 2.319029e-02     1 3.290097e+00 -2.290096855  -1 -1.482686650
#> 36  4.585005 2.350073e-02     1 1.240006e+00 -0.240005945  -1 -0.223113295
#> 129 4.318340 2.352118e-02     1 9.335781e-01  0.066421879   1  0.067952254
#> 17  4.983810 2.374099e-02     1 1.914658e+00 -0.914658235  -1 -0.728174561
#> 268 3.810887 2.376964e-02     1 5.481412e-01  0.451858781   1  0.546559321
#> 74  4.065902 2.434690e-02     1 7.346658e-01  0.265334164   1  0.293275857
#> 244 4.121292 2.538012e-02     1 8.077814e-01  0.192218553   1  0.206131950
#> 78  5.001105 2.589449e-02     1 2.101658e+00 -1.101658403  -1 -0.847268144
#> 262 4.610763 2.628633e-02     1 1.403531e+00 -0.403530615  -1 -0.359276175
#> 191 4.822896 2.648582e-02     1 1.771551e+00 -0.771550879  -1 -0.631973913
#> 186 4.841245 2.697997e-02     1 1.835330e+00 -0.835329577  -1 -0.675433943
#> 198 3.984153 2.773864e-02     1 7.528528e-01  0.247147192   1  0.271065869
#> 47  5.364582 2.786027e-02     1 3.297290e+00 -2.297289999  -1 -1.486061291
#> 227 4.668868 2.791929e-02     1 1.572078e+00 -0.572077873  -1 -0.489243585
#> 144 4.536470 2.819286e-02     1 1.376275e+00 -0.376275082  -1 -0.337326098
#> 173 5.456999 2.934729e-02     1 3.803133e+00 -2.803132652  -1 -1.713071827
#> 146 4.249181 2.939380e-02     1 1.049295e+00 -0.049294947  -1 -0.048507472
#> 260 4.574732 2.990610e-02     1 1.507058e+00 -0.507058160  -1 -0.440224143
#> 162 4.761353 3.042858e-02     1 1.866257e+00 -0.866256640  -1 -0.696163791
#> 65  4.256727 3.117679e-02     1 1.111610e+00 -0.111610072  -1 -0.107708795
#> 57  4.632779 3.160045e-02     1 1.679481e+00 -0.679480818  -1 -0.567443582
#> 80  4.410479 3.230765e-02     1 1.349568e+00 -0.349568299  -1 -0.315542505
#> 300 4.694185 3.260501e-02     1 1.840865e+00 -0.840865362  -1 -0.679160652
#> 28  3.529248 3.288957e-02     1 5.348434e-01  0.465156576   1  0.566788610
#> 118 4.720887 3.326862e-02     1 1.926233e+00 -0.926232915  -1 -0.735753596
#> 195 3.791917 3.474907e-02     1 7.410942e-01  0.258905847   1  0.285383086
#> 150 3.359394 3.477969e-02     1 4.674296e-01  0.532570427   1  0.675183177
#> 89  5.370019 3.532239e-02     1 4.047849e+00 -3.047848749  -1 -1.816404791
#> 38  4.940687 3.639618e-02     1 2.624194e+00 -1.624194265  -1 -1.148407909
#> 232 2.111079 3.741333e-02     1 1.310235e-01  0.868976483   1  1.525386490
#> 188 4.233918 3.822148e-02     1 1.285076e+00 -0.285076132  -1 -0.261756256
#> 75  3.746367 3.847363e-02     1 7.678837e-01  0.232116345   1  0.252984993
#> 158 4.378733 3.894701e-02     1 1.523210e+00 -0.523209554  -1 -0.452526014
#> 10  4.694612 4.001841e-02     1 2.181864e+00 -1.181864416  -1 -0.896308728
#> 253 4.930345 4.015504e-02     1 2.813855e+00 -1.813854676  -1 -1.248438514
#> 140 4.943103 4.185950e-02     1 2.950870e+00 -1.950869643  -1 -1.318157595
#> 46  4.292505 4.325768e-02     1 1.513548e+00 -0.513548410  -1 -0.445177662
#> 98  4.426735 4.402701e-02     1 1.771817e+00 -0.771816547  -1 -0.632156988
#> 54  3.870637 4.496208e-02     1 9.955218e-01  0.004478158   1  0.004484860
#> 165 4.380757 4.498094e-02     1 1.716483e+00 -0.716482512  -1 -0.593641923
#> 143 3.335028 4.525564e-02     1 5.650388e-01  0.434961240   1  0.521343857
#> 37  4.605710 4.624488e-02     1 2.231599e+00 -1.231599363  -1 -0.926154233
#> 84  3.476433 5.110284e-02     1 7.243647e-01  0.275635287   1  0.306022807
#> 35  3.622940 5.139426e-02     1 8.508073e-01  0.149192697   1  0.157333499
#> 184 3.532750 5.404778e-02     1 8.042562e-01  0.195743811   1  0.210207548
#> 130 4.675730 5.421549e-02     1 2.730441e+00 -1.730441387  -1 -1.204971461
#> 91  4.457480 6.019117e-02     1 2.348705e+00 -1.348705062  -1 -0.994827546
#> 155 3.512540 6.029946e-02     1 8.579429e-01  0.142057139   1  0.149403067
#> 299 4.949434 6.122222e-02     1 4.023643e+00 -3.023643374  -1 -1.806352994
#> 3   4.164371 6.466188e-02     1 1.816506e+00 -0.816505980  -1 -0.662708255
#> 117 4.680007 6.538887e-02     1 3.176903e+00 -2.176903155  -1 -1.428983053
#> 139 4.347905 6.637455e-02     1 2.254816e+00 -1.254815843  -1 -0.939944189
#> 156 3.924808 7.424849e-02     1 1.564880e+00 -0.564880024  -1 -0.483881938
#> 145 3.884080 7.488925e-02     1 1.508194e+00 -0.508193644  -1 -0.441091763
#> 247 4.455209 7.715725e-02     1 2.838330e+00 -1.838329520  -1 -1.261042297
#> 154 4.070638 7.754922e-02     1 1.890120e+00 -0.890119557  -1 -0.712010494
#> 228 3.394487 8.530838e-02     1 9.873124e-01  0.012687573   1  0.012741632
#> 136 3.463550 9.491171e-02     1 1.151214e+00 -0.151213737  -1 -0.144200747
#> 270 4.060171 9.827059e-02     1 2.233113e+00 -1.233113128  -1 -0.927056087
#> 221 3.266782 1.044329e-01     1 1.001592e+00 -0.001591895  -1 -0.001591051
#> 14  2.785300 1.093166e-01     1 6.195863e-01  0.380413684   1  0.443372466
#> 246 2.999835 1.137469e-01     1 8.019561e-01  0.198043922   1  0.212873278
#> 190 4.073891 1.162474e-01     1 2.563631e+00 -1.563630915  -1 -1.115532461
#> 121 4.494043 1.215979e-01     1 4.147420e+00 -3.147419742  -1 -1.857381679
#> 149 3.713699 1.223064e-01     1 1.810979e+00 -0.810979208  -1 -0.658956008
#> 141 3.085641 1.298620e-01     1 9.673277e-01  0.032672339   1  0.033035105
#> 291 4.609881 1.313113e-01     1 4.960460e+00 -3.960459651  -1 -2.172077919
#> 134 3.481606 2.284535e-01     1 2.186512e+00 -1.186511657  -1 -0.899115381
#> 205 2.714764 2.495848e-01     1 1.023410e+00 -0.023410062  -1 -0.023229840
#> 277 2.710876 2.614048e-01     1 1.050993e+00 -0.050992746  -1 -0.050150895
#> 24  3.010648 2.686244e-01     1 1.473576e+00 -0.473576330  -1 -0.414449047
#> 294 3.573743 2.974617e-01     1 2.873731e+00 -1.873731125  -1 -1.279155891
#> 257 2.596904 2.979228e-01     1 1.014189e+00 -0.014188826  -1 -0.014122269
#>       Hcoxsnell
#> 180 0.003333333
#> 280 0.010033520
#> 174 0.006677815
#> 203 0.013400523
#> 283 0.023570092
#> 11  0.037292421
#> 239 0.030407719
#> 272 0.026983062
#> 5   0.020168732
#> 206 0.194036953
#> 50  0.047709172
#> 178 0.174036313
#> 9   0.040752629
#> 254 0.016778901
#> 208 0.051205675
#> 70  0.231078173
#> 31  0.101485511
#> 43  0.061769143
#> 241 0.076029619
#> 109 0.054714447
#> 30  0.065315242
#> 163 0.112596723
#> 4   0.198085536
#> 110 0.235279853
#> 171 0.466349036
#> 251 0.058235574
#> 93  0.166146736
#> 21  0.142844740
#> 61  0.627152655
#> 48  0.127606369
#> 2   0.086860038
#> 90  0.090496401
#> 147 0.515271714
#> 274 0.956174562
#> 6   0.033844145
#> 126 0.154427867
#> 185 0.150551898
#> 187 0.394707313
#> 160 0.596475499
#> 15  0.287127237
#> 73  0.178004567
#> 282 0.079626741
#> 201 0.162225167
#> 216 0.471668185
#> 102 0.105175548
#> 39  0.323248484
#> 122 0.429886746
#> 55  0.461058031
#> 182 0.300520272
#> 152 0.108879251
#> 217 0.094146037
#> 41  0.116328067
#> 288 0.360723527
#> 234 0.239499263
#> 166 1.408155097
#> 95  0.671745880
#> 123 0.120073385
#> 295 0.841764850
#> 99  0.044224851
#> 199 0.218578028
#> 193 0.083236849
#> 59  0.269544395
#> 71  0.260867564
#> 142 0.537807820
#> 133 0.273911207
#> 161 0.252265374
#> 101 0.097809040
#> 169 0.158318917
#> 92  0.584463379
#> 40  0.404632932
#> 258 0.327856779
#> 60  0.170083744
#> 19  0.450559271
#> 172 0.214445796
#> 148 0.190004695
#> 252 0.309549664
#> 245 0.646021077
#> 34  0.206232209
#> 297 0.487797528
#> 159 0.068873961
#> 214 0.072445389
#> 108 0.572593838
#> 56  2.029120841
#> 94  0.482392122
#> 230 0.337137571
#> 135 0.351222285
#> 62  0.243736551
#> 183 0.332486409
#> 51  0.419708563
#> 284 0.139013323
#> 157 0.774575718
#> 85  0.498696791
#> 197 1.342342829
#> 87  0.857329288
#> 170 0.370315908
#> 68  1.493311473
#> 215 0.897334409
#> 131 0.346505304
#> 82  0.278297172
#> 96  0.566711485
#> 224 0.226894072
#> 250 1.027953762
#> 106 2.255418685
#> 289 0.555049579
#> 104 0.424784705
#> 278 0.739111157
#> 120 0.305024777
#> 290 1.105286363
#> 18  1.065872713
#> 220 0.375146826
#> 138 0.222727405
#> 265 2.355492841
#> 52  0.210330570
#> 233 0.202150577
#> 107 0.826438954
#> 113 2.004120841
#> 226 2.901934887
#> 8   0.913795593
#> 218 0.123832784
#> 194 1.085385373
#> 151 0.698149958
#> 249 0.389781204
#> 66  0.560863532
#> 181 0.135196529
#> 124 0.414658058
#> 49  0.440169590
#> 1   0.247991870
#> 204 0.341810469
#> 202 3.031101554
#> 179 1.586400025
#> 64  0.509716159
#> 86  0.678281828
#> 83  1.865976634
#> 207 1.125591454
#> 119 0.849516788
#> 269 0.384879244
#> 287 0.265196569
#> 26  0.526476284
#> 81  0.318661328
#> 263 0.435014951
#> 45  0.282702458
#> 114 0.291571682
#> 25  1.222440344
#> 164 1.671194526
#> 225 0.185988631
#> 238 0.181988631
#> 23  0.639691964
#> 273 0.256557220
#> 212 1.009520191
#> 128 0.578510998
#> 242 1.979730597
#> 7   1.135900733
#> 222 0.620941475
#> 275 0.732166712
#> 248 0.477015778
#> 22  1.619460134
#> 76  0.881139811
#> 236 0.608633666
#> 223 0.365508216
#> 219 1.449827123
#> 255 1.602793467
#> 12  1.167482013
#> 266 0.973642144
#> 53  1.095286363
#> 175 0.504191297
#> 281 1.233803980
#> 240 0.718420846
#> 111 0.399657808
#> 33  1.268690846
#> 167 0.614768636
#> 67  0.131394247
#> 286 0.314095118
#> 44  1.689051668
#> 69  1.075581451
#> 256 3.102530125
#> 103 0.355961622
#> 153 0.633402655
#> 176 0.889204328
#> 259 1.464112837
#> 229 1.292643800
#> 105 0.493232310
#> 16  0.964870214
#> 235 1.000429282
#> 298 3.179453202
#> 115 0.865203303
#> 243 1.508236846
#> 97  0.296035967
#> 209 1.245298233
#> 79  1.329684601
#> 32  1.115387373
#> 276 5.282663880
#> 231 0.445350937
#> 271 0.930532288
#> 267 0.781822094
#> 127 1.256926140
#> 264 3.353695626
#> 132 0.652390504
#> 88  0.922128926
#> 261 3.832663880
#> 63  2.591850630
#> 211 1.189104266
#> 29  0.789121365
#> 237 2.391207127
#> 112 0.811344400
#> 189 0.834072542
#> 100 0.796474306
#> 13  0.665252374
#> 116 0.905531130
#> 177 3.689806737
#> 20  2.684924223
#> 285 0.760238616
#> 279 0.380001195
#> 125 1.421853727
#> 72  0.704861368
#> 42  1.317184601
#> 27  1.435742616
#> 196 0.543522105
#> 213 1.178234701
#> 200 1.200093277
#> 77  1.146317399
#> 292 2.506705703
#> 192 2.637305176
#> 168 0.409632932
#> 137 1.355163342
#> 296 2.081077656
#> 293 2.321010083
#> 58  0.602536105
#> 210 3.453695626
#> 36  1.280595608
#> 129 0.873139811
#> 17  1.932665260
#> 268 0.532126002
#> 74  0.684860775
#> 244 0.767381473
#> 78  2.054761867
#> 262 1.394641583
#> 191 1.744619930
#> 186 1.823866705
#> 198 0.711618124
#> 47  3.564806737
#> 227 1.653650666
#> 144 1.381308250
#> 173 3.999330547
#> 146 1.046733519
#> 260 1.523388361
#> 162 1.887715765
#> 65  1.156843715
#> 57  1.707233487
#> 80  1.368150355
#> 300 1.844700039
#> 28  0.520858306
#> 118 1.955921074
#> 195 0.691483292
#> 150 0.455794873
#> 89  4.449330547
#> 38  2.466705703
#> 232 0.146690894
#> 188 1.304838922
#> 75  0.725270161
#> 158 1.570270992
#> 10  2.108104684
#> 253 2.734924223
#> 140 2.964434887
#> 46  1.554397977
#> 98  1.763850699
#> 54  0.982491702
#> 165 1.725752005
#> 143 0.549269232
#> 37  2.164453890
#> 84  0.658800761
#> 35  0.803881713
#> 184 0.753146417
#> 130 2.548372369
#> 91  2.287676749
#> 155 0.818863197
#> 299 4.199330547
#> 3   1.803458542
#> 117 3.262786535
#> 139 2.224168685
#> 156 1.636409287
#> 145 1.538772977
#> 247 2.787555802
#> 154 1.909937987
#> 228 0.947553872
#> 136 1.211204389
#> 270 2.193865655
#> 221 0.991420273
#> 14  0.590451403
#> 246 0.746104164
#> 190 2.428244164
#> 121 4.782663880
#> 149 1.783458542
#> 141 0.939006864
#> 291 6.282663880
#> 134 2.135882461
#> 205 1.037299557
#> 277 1.056257329
#> 24  1.478605591
#> 294 2.843111358
#> 257 1.018694503
test <- timeroc_obj("normal-weibull-PH")
jj <- timeroc_fit(test, rr$x, rr$t, rr$event)
timeroc_gof(jj)
#> $ks_x
#> 
#>  Asymptotic two-sample Kolmogorov-Smirnov test
#> 
#> data:  df$x and theo.q
#> D = 0.04, p-value = 0.97
#> alternative hypothesis: two-sided
#> 
#> 
#> $ks_t
#>       A p-value   F(ym)      ym 
#>   0.500   0.964   0.998   6.353 
#> 
#> $df
#>            x            t event     coxsnell       mresid sgn     devresid
#> 180 6.207908 1.584490e-06     1 0.0006242926  0.999375707   1  3.571978642
#> 280 5.919804 3.856797e-05     1 0.0100663998  0.989933600   1  2.686491598
#> 174 4.922847 5.297660e-05     1 0.0045542511  0.995445749   1  2.965214469
#> 203 6.586588 5.434546e-05     1 0.0293308021  0.970669198   1  2.262055637
#> 283 6.324259 9.838639e-05     1 0.0390563095  0.960943690   1  2.136261758
#> 11  6.511781 1.362743e-04     1 0.0659149313  0.934085069   1  1.889605895
#> 239 6.096777 1.485618e-04     1 0.0453196568  0.954680343   1  2.068494173
#> 272 5.394379 2.055676e-04     1 0.0285914110  0.971408589   1  2.272989368
#> 5   5.329508 2.056777e-04     1 0.0266281163  0.973371884   1  2.303221975
#> 206 7.497662 2.412804e-04     1 0.3410192506  0.658980749   1  0.913055968
#> 50  5.881108 2.569037e-04     1 0.0607733923  0.939226608   1  1.929443757
#> 178 7.075245 2.909709e-04     1 0.2564927259  0.743507274   1  1.110988478
#> 9   5.575781 3.123474e-04     1 0.0524346020  0.947565398   1  2.000311557
#> 254 4.752336 3.308331e-04     1 0.0223265966  0.977673403   1  2.376679715
#> 208 5.541327 3.523408e-04     1 0.0567388301  0.943261170   1  1.962669253
#> 70  7.172612 3.641114e-04     1 0.3550710578  0.644928942   1  0.883751554
#> 31  6.358680 3.731538e-04     1 0.1479741801  0.852025820   1  1.455123128
#> 43  5.696963 3.735145e-04     1 0.0713092457  0.928690754   1  1.850426184
#> 241 5.707311 4.171255e-04     1 0.0802903292  0.919709671   1  1.790193525
#> 109 5.384185 4.611596e-04     1 0.0619378497  0.938062150   1  1.920188360
#> 30  5.417942 4.789896e-04     1 0.0667024731  0.933297527   1  1.883728070
#> 163 6.058483 4.974118e-04     1 0.1403914855  0.859608514   1  1.485740165
#> 4   6.595281 5.261248e-04     1 0.2682371474  0.731762853   1  1.080852403
#> 110 6.682176 5.587205e-04     1 0.3130012559  0.686998744   1  0.974216949
#> 171 7.307978 5.743735e-04     1 0.6418188502  0.358181150   1  0.412960119
#> 251 5.136222 5.780635e-04     1 0.0586472529  0.941352747   1  1.946721242
#> 93  6.160403 6.104503e-04     1 0.1916735999  0.808326400   1  1.298949540
#> 21  5.918977 6.605556e-04     1 0.1584883504  0.841511650   1  1.414611281
#> 61  7.401618 6.870186e-04     1 0.8468933517  0.153106648   1  0.161702548
#> 48  5.768533 7.316284e-04     1 0.1482191456  0.851780854   1  1.454154416
#> 2   5.183643 7.346172e-04     1 0.0779887186  0.922011281   1  1.805092693
#> 90  5.267099 7.565577e-04     1 0.0879983414  0.912001659   1  1.742662132
#> 147 7.087167 7.590941e-04     1 0.6592240048  0.340775995   1  0.389655979
#> 274 7.649167 7.724052e-04     1 1.2473022318 -0.247302232  -1 -0.229430719
#> 6   4.179532 8.469456e-04     1 0.0295330797  0.970466920   1  2.259104857
#> 126 5.712666 8.497752e-04     1 0.1611428213  0.838857179   1  1.404711387
#> 185 5.521023 9.809825e-04     1 0.1499002754  0.850099725   1  1.447539507
#> 187 6.464587 1.020379e-03     1 0.4416325977  0.558367402   1  0.719596508
#> 160 6.869291 1.054860e-03     1 0.7132159412  0.286784059   1  0.319959319
#> 15  6.124931 1.079218e-03     1 0.3204427849  0.679557215   1  0.957595240
#> 73  5.610726 1.123521e-03     1 0.1888118368  0.811188163   1  1.308293674
#> 282 4.592471 1.147806e-03     1 0.0625969205  0.937403080   1  1.915012332
#> 201 5.409402 1.155275e-03     1 0.1553088320  0.844691168   1  1.426638365
#> 216 6.519745 1.209462e-03     1 0.5535903284  0.446409672   1  0.538369155
#> 102 5.042116 1.229168e-03     1 0.1099343513  0.890065649   1  1.623456959
#> 39  6.100025 1.231089e-03     1 0.3542472714  0.645752729   1  0.885446073
#> 122 6.343039 1.248639e-03     1 0.4697377044  0.530262296   1  0.671295047
#> 55  6.433024 1.257002e-03     1 0.5222016079  0.477798392   1  0.586349983
#> 182 5.983896 1.290249e-03     1 0.3261232861  0.673876714   1  0.945095844
#> 152 4.981440 1.303752e-03     1 0.1088576600  0.891142340   1  1.628847311
#> 217 4.691259 1.393261e-03     1 0.0842639892  0.915736011   1  1.765256167
#> 41  4.835476 1.514742e-03     1 0.1071691073  0.892830893   1  1.637385940
#> 288 5.945185 1.550642e-03     1 0.3735154255  0.626484574   1  0.846535765
#> 234 5.570508 1.564560e-03     1 0.2490750774  0.750924923   1  1.130553837
#> 166 7.206102 1.582535e-03     1 1.5338952361 -0.533895236  -1 -0.460618780
#> 95  6.586833 1.583196e-03     1 0.7742611608  0.225738839   1  0.245386251
#> 123 4.785421 1.590259e-03     1 0.1063079665  0.893692034   1  1.641781361
#> 295 6.778429 1.600860e-03     1 0.9671188328  0.032881167   1  0.033248632
#> 99  3.775387 1.616006e-03     1 0.0353825975  0.964617403   1  2.180329229
#> 199 5.411975 1.625319e-03     1 0.2169392175  0.783060782   1  1.220718875
#> 193 4.268252 1.705735e-03     1 0.0642708317  0.935729168   1  1.902062150
#> 59  5.569720 1.787185e-03     1 0.2831625415  0.716837458   1  1.043931737
#> 71  5.475510 1.847682e-03     1 0.2635567035  0.736443296   1  1.092742828
#> 142 6.176583 1.847913e-03     1 0.5718148707  0.428185129   1  0.511380217
#> 133 5.531496 1.873528e-03     1 0.2841769968  0.715823003   1  1.041474919
#> 161 5.425100 1.876214e-03     1 0.2530178205  0.746982180   1  1.120101046
#> 101 4.379633 1.900729e-03     1 0.0807380084  0.919261992   1  1.787335357
#> 169 4.855600 1.952600e-03     1 0.1402057394  0.859794261   1  1.486506043
#> 92  6.207868 1.973661e-03     1 0.6309815511  0.369018449   1  0.427691958
#> 40  5.763176 2.000774e-03     1 0.3912322903  0.608767710   1  0.812017355
#> 258 5.572740 2.044065e-03     1 0.3236683800  0.676331620   1  0.950477970
#> 60  4.864945 2.075975e-03     1 0.1503410982  0.849658902   1  1.445814426
#> 19  5.821221 2.162081e-03     1 0.4497464529  0.550253547   1  0.705432840
#> 172 5.105802 2.162565e-03     1 0.2041041588  0.795895841   1  1.259546737
#> 148 5.017396 2.181191e-03     1 0.1866618154  0.813338185   1  1.315384802
#> 252 5.407168 2.257563e-03     1 0.2968589339  0.703141066   1  1.011293387
#> 245 6.162965 2.291417e-03     1 0.6940746064  0.305925394   1  0.344239535
#> 34  4.946195 2.486713e-03     1 0.1959571649  0.804042835   1  1.285158632
#> 297 5.765599 2.579352e-03     1 0.5019681100  0.498031890   1  0.618363642
#> 159 3.615573 2.589888e-03     1 0.0468764921  0.953123508   1  2.052859204
#> 214 3.629792 2.621402e-03     1 0.0481809121  0.951819088   1  2.040084931
#> 108 5.910174 2.633230e-03     1 0.6008259372  0.399174063   1  0.469629525
#> 56  6.980400 2.707695e-03     1 2.0133894792 -1.013389479  -1 -0.791921548
#> 94  5.700214 2.746805e-03     1 0.4963923105  0.503607689   1  0.627345243
#> 230 5.263176 2.871097e-03     1 0.3197568905  0.680243110   1  0.959115405
#> 135 5.306558 2.878444e-03     1 0.3362863597  0.663713640   1  0.923123589
#> 62  4.960760 2.918194e-03     1 0.2325948314  0.767405169   1  1.175629271
#> 183 5.219925 2.983556e-03     1 0.3164231046  0.683576895   1  0.966538284
#> 51  5.398106 3.011408e-03     1 0.3887449204  0.611255080   1  0.816794714
#> 284 4.298768 3.052306e-03     1 0.1169398170  0.883060183   1  1.589361934
#> 157 6.000029 3.108070e-03     1 0.7793748618  0.220625138   1  0.239324055
#> 85  5.593946 3.132134e-03     1 0.5014022264  0.498597774   1  0.619271959
#> 197 6.441158 3.162805e-03     1 1.2904169829 -0.290416983  -1 -0.266276451
#> 87  6.063100 3.293417e-03     1 0.8839389127  0.116061087   1  0.120882048
#> 170 5.207538 3.330429e-03     1 0.3472896195  0.652710380   1  0.899873134
#> 68  6.465555 3.442322e-03     1 1.4392465195 -0.439246519  -1 -0.387625575
#> 215 5.987838 3.627942e-03     1 0.8935085817  0.106491418   1  0.110525305
#> 131 5.060160 3.631898e-03     1 0.3210110602  0.678988940   1  0.956337557
#> 82  4.864821 3.655713e-03     1 0.2603541740  0.739645826   1  1.100969156
#> 96  5.558486 3.684344e-03     1 0.5644529715  0.435547029   1  0.522209116
#> 224 4.659031 3.709862e-03     1 0.2103965773  0.789603423   1  1.240288388
#> 250 6.020464 3.806544e-03     1 0.9705303261  0.029469674   1  0.029764242
#> 106 6.767287 3.885685e-03     1 2.2592284777 -1.259228478  -1 -0.942555149
#> 289 5.433702 3.995757e-03     1 0.5320720140  0.467927986   1  0.571048944
#> 104 5.158029 4.006017e-03     1 0.3933705155  0.606629485   1  0.807928016
#> 278 5.741001 4.015517e-03     1 0.7507091108  0.249290889   1  0.273664572
#> 120 4.822670 4.064548e-03     1 0.2754441100  0.724555890   1  1.062840203
#> 290 6.005159 4.105513e-03     1 1.0269302934 -0.026930293  -1 -0.026692275
#> 18  5.943836 4.305156e-03     1 1.0049380354 -0.004938035  -1 -0.004929931
#> 220 4.955291 4.348745e-03     1 0.3405239993  0.659476001   1  0.914104669
#> 138 4.471720 4.356570e-03     1 0.1999495575  0.800050443   1  1.272509108
#> 265 6.719627 4.356954e-03     1 2.3952676792 -1.395267679  -1 -1.021540688
#> 52  4.387974 4.408170e-03     1 0.1843776172  0.815622383   1  1.322986753
#> 233 4.359518 4.482706e-03     1 0.1816041257  0.818395874   1  1.332313942
#> 107 5.716707 4.505199e-03     1 0.8171935105  0.182806489   1  0.195309333
#> 113 6.432282 4.706226e-03     1 1.8793735323 -0.879373532  -1 -0.704890117
#> 226 6.803142 4.738835e-03     1 2.8499541154 -1.849954115  -1 -1.267005305
#> 8   5.738325 4.760157e-03     1 0.8828803601  0.117119640   1  0.122032292
#> 218 3.746710 4.840431e-03     1 0.0994277219  0.900572278   1  1.677946384
#> 194 5.830373 4.899466e-03     1 1.0051268100 -0.005126810  -1 -0.005118075
#> 151 5.450187 5.053122e-03     1 0.6805354761  0.319464524   1  0.361692693
#> 249 4.833879 5.062990e-03     1 0.3451513381  0.654848662   1  0.904349087
#> 66  5.188792 5.248453e-03     1 0.5289804093  0.471019591   1  0.575819921
#> 181 3.768677 5.286819e-03     1 0.1109769683  0.889023032   1  1.618276590
#> 124 4.820443 5.337817e-03     1 0.3579709032  0.642029097   1  0.877809176
#> 49  4.887654 5.363530e-03     1 0.3873616781  0.612638322   1  0.819460959
#> 1   4.373546 5.400864e-03     1 0.2210070731  0.778992927   1  1.208774293
#> 204 4.669092 5.424176e-03     1 0.3076134161  0.692386584   1  0.986432809
#> 202 6.688873 5.501575e-03     1 2.9035870749 -1.903587075  -1 -1.294326218
#> 179 6.027392 5.660975e-03     1 1.4376095405 -0.437609541  -1 -0.386336246
#> 64  5.028002 5.662658e-03     1 0.4767878918  0.523212108   1  0.659502009
#> 86  5.332950 5.664599e-03     1 0.6679801483  0.332019852   1  0.378092508
#> 83  6.178087 5.846703e-03     1 1.7520358614 -0.752035861  -1 -0.618477809
#> 207 5.667066 5.876265e-03     1 1.0011872619 -0.001187262  -1 -0.001186792
#> 119 5.494188 5.899703e-03     1 0.8303440452  0.169655955   1  0.180328572
#> 269 4.668967 5.970098e-03     1 0.3375763942  0.662423606   1  0.920369312
#> 287 4.331821 6.058580e-03     1 0.2359576648  0.764042335   1  1.166242291
#> 26  4.943871 6.314466e-03     1 0.4829409855  0.517059015   1  0.649310098
#> 81  4.431331 6.402171e-03     1 0.2778602943  0.722139706   1  1.056879486
#> 263 4.715669 6.423455e-03     1 0.3816209096  0.618379090   1  0.830600332
#> 45  4.311244 6.591379e-03     1 0.2503196760  0.749680324   1  1.127241012
#> 114 4.349304 6.615928e-03     1 0.2620115742  0.737988426   1  1.096702489
#> 25  5.619826 6.623362e-03     1 1.0673478272 -0.067347827  -1 -0.065892668
#> 164 5.886423 6.755703e-03     1 1.4606348198 -0.460634820  -1 -0.404385139
#> 225 3.843428 6.934491e-03     1 0.1568411180  0.843158882   1  1.420818842
#> 238 3.813541 6.991735e-03     1 0.1529636414  0.847036359   1  1.435631335
#> 23  5.074565 6.994508e-03     1 0.6161844112  0.383815589   1  0.448092407
#> 273 4.148143 7.097236e-03     1 0.2246060163  0.775393984   1  1.198343412
#> 212 5.420695 7.099505e-03     1 0.9163088936  0.083691106   1  0.086146906
#> 128 4.962366 7.101513e-03     1 0.5524403764  0.447559624   1  0.540092851
#> 242 6.034108 7.188278e-03     1 1.8262295890 -0.826229589  -1 -0.669292285
#> 7   5.487429 7.236927e-03     1 1.0049366567 -0.004936657  -1 -0.004928556
#> 222 5.002132 7.294616e-03     1 0.5924784089  0.407521591   1  0.481496119
#> 275 5.156012 7.337022e-03     1 0.7062158336  0.293784166   1  0.328786279
#> 248 4.744329 7.403683e-03     1 0.4521186687  0.547881331   1  0.701326259
#> 22  5.782136 7.505808e-03     1 1.4417783198 -0.441778320  -1 -0.389617823
#> 76  5.291446 7.579080e-03     1 0.8464345578  0.153565442   1  0.162215581
#> 236 4.901821 7.672389e-03     1 0.5569748299  0.443025170   1  0.533310526
#> 223 4.369700 7.844831e-03     1 0.3161760766  0.683823923   1  0.967090578
#> 219 5.642241 8.118891e-03     1 1.3331711142 -0.333171114  -1 -0.302028851
#> 255 5.695551 8.198243e-03     1 1.4274486906 -0.427448691  -1 -0.378311967
#> 12  5.389843 8.235466e-03     1 1.0228502731 -0.022850273  -1 -0.022678512
#> 266 5.270055 8.264447e-03     1 0.8991382152  0.100861785   1  0.104467490
#> 53  5.341120 8.365532e-03     1 0.9841099139  0.015890086   1  0.015975040
#> 175 4.665999 8.406353e-03     1 0.4690484679  0.530951532   1  0.672454669
#> 281 5.398130 8.470306e-03     1 1.0608171362 -0.060817136  -1 -0.059626200
#> 240 4.994656 8.508742e-03     1 0.6823214925  0.317678507   1  0.359376761
#> 111 4.364264 8.565672e-03     1 0.3422786960  0.657721304   1  0.910394057
#> 33  5.387672 9.010942e-03     1 1.1135420556 -0.113542056  -1 -0.109508719
#> 167 4.744973 9.601335e-03     1 0.5822856220  0.417714378   1  0.496144765
#> 67  3.195041 9.747181e-03     1 0.1066442252  0.893355775   1  1.640061711
#> 286 3.998928 9.977149e-03     1 0.2651058002  0.734894200   1  1.088790234
#> 44  5.556663 1.016483e-02     1 1.5085973482 -0.508597348  -1 -0.441400130
#> 69  5.153253 1.027810e-02     1 0.9765986891  0.023401311   1  0.023586384
#> 256 6.146228 1.039499e-02     1 2.9569695086 -1.956969509  -1 -1.321215031
#> 103 4.089078 1.059418e-02     1 0.3104306294  0.689569371   1  0.980025967
#> 153 4.681932 1.081129e-02     1 0.6094358206  0.390564179   1  0.457509464
#> 176 4.965274 1.095095e-02     1 0.8438544164  0.156145584   1  0.165104258
#> 259 5.374724 1.102584e-02     1 1.3352660852 -0.335266085  -1 -0.303761414
#> 229 5.197193 1.159346e-02     1 1.1522921992 -0.152292199  -1 -0.145182809
#> 105 4.345415 1.179439e-02     1 0.4572775006  0.542722499   1  0.692448338
#> 16  4.955066 1.179744e-02     1 0.8969302251  0.103069775   1  0.106840367
#> 235 4.940277 1.217200e-02     1 0.9095780182  0.090421982   1  0.093300820
#> 298 5.955137 1.295442e-02     1 2.9645945397 -1.964594540  -1 -1.325031521
#> 115 4.792619 1.311679e-02     1 0.8308403803  0.169159620   1  0.179766317
#> 243 5.223480 1.357681e-02     1 1.3827623041 -0.382762304  -1 -0.342575936
#> 97  3.723408 1.358351e-02     1 0.2638277854  0.736172215   1  1.092049909
#> 209 4.986600 1.363832e-02     1 1.0690892318 -0.069089232  -1 -0.067559322
#> 79  5.074341 1.371792e-02     1 1.1845666541 -0.184566654  -1 -0.174296524
#> 32  4.897212 1.390672e-02     1 0.9870684245  0.012931576   1  0.012987742
#> 276 6.130207 1.430250e-02     1 3.9599171043 -2.959917104  -1 -1.779715715
#> 231 4.014173 1.444489e-02     1 0.3861267957  0.613873204   1  0.821847033
#> 271 4.741067 1.461142e-02     1 0.8715204423  0.128479558   1  0.134435115
#> 267 4.577816 1.467212e-02     1 0.7306481594  0.269351841   1  0.298232824
#> 127 4.926436 1.486152e-02     1 1.0873256860 -0.087325686  -1 -0.084905873
#> 264 5.857410 1.489175e-02     1 3.0467432373 -2.046743237  -1 -1.365774512
#> 132 4.411106 1.510442e-02     1 0.6251339554  0.374866045   1  0.435713849
#> 88  4.695816 1.523078e-02     1 0.8631184335  0.136881567   1  0.143678782
#> 261 5.951013 1.529210e-02     1 3.4667622787 -2.466762279  -1 -1.564315301
#> 63  5.689739 1.539405e-02     1 2.6144698231 -1.614469823  -1 -1.143160960
#> 211 4.835624 1.569447e-02     1 1.0370114812 -0.037011481  -1 -0.036564476
#> 29  4.521850 1.588777e-02     1 0.7420210255  0.257978974   1  0.284248924
#> 237 5.560821 1.626491e-02     1 2.3918576234 -1.391857623  -1 -1.019595323
#> 112 4.538355 1.627771e-02     1 0.7736703743  0.226329626   1  0.246088372
#> 189 4.569788 1.630243e-02     1 0.8021860531  0.197813947   1  0.212606513
#> 100 4.526599 1.635253e-02     1 0.7670955014  0.232904499   1  0.253927052
#> 13  4.378759 1.643230e-02     1 0.6546017180  0.345398282   1  0.395803008
#> 116 4.607192 1.669169e-02     1 0.8553948326  0.144605167   1  0.152229805
#> 177 5.787640 1.715414e-02     1 3.2358444974 -2.235844497  -1 -1.457089258
#> 20  5.593901 1.736921e-02     1 2.6442183421 -1.644218342  -1 -1.159174571
#> 285 4.419386 1.760827e-02     1 0.7321589003  0.267841100   1  0.296366705
#> 279 3.683755 1.802936e-02     1 0.3324001705  0.667599830   1  0.931467523
#> 125 4.899809 1.869249e-02     1 1.3190775218 -0.319077522  -1 -0.290326976
#> 72  4.290054 1.887332e-02     1 0.6789045216  0.321095478   1  0.363811212
#> 42  4.746638 2.012913e-02     1 1.1967528133 -0.196752813  -1 -0.185153521
#> 27  4.844204 2.036010e-02     1 1.3477824545 -0.347782455  -1 -0.314075911
#> 196 3.952016 2.046926e-02     1 0.5056628339  0.494337166   1  0.612450817
#> 213 4.599753 2.063958e-02     1 1.0425473640 -0.042547364  -1 -0.041958485
#> 200 4.618924 2.065233e-02     1 1.0654989012 -0.065498901  -1 -0.064121134
#> 77  4.556708 2.141979e-02     1 1.0305937618 -0.030593762  -1 -0.030287221
#> 292 5.376370 2.146851e-02     1 2.5542576925 -1.554257693  -1 -1.110401767
#> 192 5.402012 2.179250e-02     1 2.6661241826 -1.666124183  -1 -1.170895710
#> 168 3.575505 2.181733e-02     1 0.3549146542  0.645085346   1  0.884073055
#> 137 4.699024 2.242039e-02     1 1.2606891155 -0.260689116  -1 -0.240959030
#> 296 5.134448 2.242761e-02     1 2.0400037009 -1.040003701  -1 -0.808767060
#> 293 5.244165 2.268948e-02     1 2.3289481576 -1.328948158  -1 -0.983393539
#> 58  3.955865 2.303471e-02     1 0.5694889572  0.430511043   1  0.514790916
#> 210 5.510108 2.319029e-02     1 3.1911376480 -2.191137648  -1 -1.435799544
#> 36  4.585005 2.350073e-02     1 1.1634522633 -0.163452263  -1 -0.155309941
#> 129 4.318340 2.352118e-02     1 0.8673346470  0.132665353   1  0.139032665
#> 17  4.983810 2.374099e-02     1 1.8253928431 -0.825392843  -1 -0.668726585
#> 268 3.810887 2.376964e-02     1 0.5002351298  0.499764870   1  0.621147585
#> 74  4.065902 2.434690e-02     1 0.6786243340  0.321375666   1  0.364175513
#> 244 4.121292 2.538012e-02     1 0.7511430331  0.248856967   1  0.273138139
#> 78  5.001105 2.589449e-02     1 2.0242158473 -1.024215847  -1 -0.798790908
#> 262 4.610763 2.628633e-02     1 1.3345284675 -0.334528467  -1 -0.303151599
#> 191 4.822896 2.648582e-02     1 1.6993484850 -0.699348485  -1 -0.581555761
#> 186 4.841245 2.697997e-02     1 1.7655415691 -0.765541569  -1 -0.627828142
#> 198 3.984153 2.773864e-02     1 0.7037078264  0.296292174   1  0.331963416
#> 47  5.364582 2.786027e-02     1 3.2469465426 -2.246946543  -1 -1.462348463
#> 227 4.668868 2.791929e-02     1 1.5087244839 -0.508724484  -1 -0.441497231
#> 144 4.536470 2.819286e-02     1 1.3158447263 -0.315844726  -1 -0.287631325
#> 173 5.456999 2.934729e-02     1 3.7820856320 -2.782085632  -1 -1.704001185
#> 146 4.249181 2.939380e-02     1 0.9976268257  0.002373174   1  0.002375054
#> 260 4.574732 2.990610e-02     1 1.4535504608 -0.453550461  -1 -0.398851611
#> 162 4.761353 3.042858e-02     1 1.8166015702 -0.816601570  -1 -0.662773089
#> 65  4.256727 3.117679e-02     1 1.0651582529 -0.065158253  -1 -0.063794522
#> 57  4.632779 3.160045e-02     1 1.6349661711 -0.634966171  -1 -0.535432643
#> 80  4.410479 3.230765e-02     1 1.3067564790 -0.306756479  -1 -0.280029935
#> 300 4.694185 3.260501e-02     1 1.8036821618 -0.803682162  -1 -0.653990735
#> 28  3.529248 3.288957e-02     1 0.5023007977  0.497699202   1  0.617829973
#> 118 4.720887 3.326862e-02     1 1.8943658685 -0.894365868  -1 -0.714817068
#> 195 3.791917 3.474907e-02     1 0.7082069674  0.291793033   1  0.326269424
#> 150 3.359394 3.477969e-02     1 0.4395778693  0.560422131   1  0.723212652
#> 89  5.370019 3.532239e-02     1 4.1126998898 -3.112699890  -1 -1.843160421
#> 38  4.940687 3.639618e-02     1 2.6350354645 -1.635035465  -1 -1.154243322
#> 232 2.111079 3.741333e-02     1 0.1188361379  0.881163862   1  1.580408723
#> 188 4.233918 3.822148e-02     1 1.2657694586 -0.265769459  -1 -0.245313080
#> 75  3.746367 3.847363e-02     1 0.7434157155  0.256584284   1  0.282544145
#> 158 4.378733 3.894701e-02     1 1.5127059858 -0.512705986  -1 -0.444535477
#> 10  4.694612 4.001841e-02     1 2.2015683686 -1.201568369  -1 -0.908183206
#> 253 4.930345 4.015504e-02     1 2.

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Install

install.packages('parTimeROC')

Monthly Downloads

190

Version

0.2.0

License

MIT + file LICENSE

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Maintainer

Faiz Azhar

Last Published

July 11th, 2025

Functions in parTimeROC (0.2.0)

timeroc_gof

timeroc_gof
timeroc_auc

timeroc_auc
print.TimeROC

print.TimeROC
parTimeROC-package

The 'parTimeROC' package.
rtimeroc

rtimeroc
get.distributions

get.distributions
timeroc_fit

timeroc_fit
print.fitTROC

print.fitTROC
timeroc_predict

timeroc_predict
timeroc_obj

timeroc_obj
rate_change

rate_change
get.copula

get.copula