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 : GompertzNotice 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$event, obj = test)
print(cc)
#> Model: gompertz-gompertz-copula
#> ------
#> X (95% CI) :
#> AIC = -65.51402
#> est low upper se
#> shape 0.9342836 0.6216374 1.246930 0.1595163
#> rate 2.0930839 1.7975025 2.388665 0.1508096
#> ------
#> Time-to-Event (95% CI) :
#> AIC = -141.7148
#> est low upper se
#> shape 3.0894231 2.7066350 3.472211 0.19530364
#> rate 0.9160331 0.7546502 1.077416 0.08233974
#> ------
#> Copula (95% CI) :
#> AIC = -1432.074
#> est low upper se
#> theta -5.1126 -5.4868 -4.7384 0.1909Notice that the print method also can be used to print the results obtained from the fitting process.
timeroc_gof
After fitting the model with either PH or copula model, its
goodness-of-fit can be examined through the function
parTimeROC::timeroc_gof(). This will return a list of test statistic
and p-values denoting misspecification of model or not.
Kolmogorov-Smirnov testing is performed for model checking. If
p-value < 0.05, we reject the null hypothesis that the data (biomarker
or time-to-event) are following the assumed distribution.
For copula model, additional testing is needed to check whether the
copula used is able to model the data or not. After using the Rosenblatt
transformation, we conduct an independent testing to check whether the
empirical conditional and cumulative distribution are independent. If
the p-value < 0.05, we reject the null hypothesis which stated that
the conditional and cumulative are independent. Thus, for
p-value < 0.05, the copula failed to provide a good estimation for the
joint distribution.
library(parTimeROC)
# Copula model
rt <- timeroc_obj("normal-weibull-copula",copula="clayton90")
set.seed(1)
rr <- rtimeroc(rt, n=300, censor.rate = 0,
params.x = c(mean=5, sd=1),
params.t = c(shape=1, scale=5),
params.copula = -2.5)
test <- timeroc_obj("normal-weibull-copula",copula="gumbel90")
jj <- timeroc_fit(test, rr$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] 0.007482435test <- 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] 0.9366532library(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 1.018694503test <- 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.