The function simSC() generates simulated recurrent event data from either a Cox-type model, an accelerated mean model, an accelerated rate model, or a scale-change model.

simSC(
  n,
  a1 = a2,
  b1 = b2,
  a2 = a1,
  b2 = b1,
  type = "cox",
  zVar = 0.25,
  tau = 60,
  origin = 0,
  summary = FALSE
)

Arguments

n

number of observation.

a1, a2, b1, b2

are numeric vectors of length 2. These correspond to the \(\alpha\), \(\beta\), \(\eta\), and \(\theta\) in the joint model. See Details

type

is a character string specifying the underlying model. The rate function type and the hazard function type are separated by a vertical bar "|", with the rate function on the left. For example, type = "cox|am" generates the recurrent process from a Cox model and the terminal event from an accelerated mean model. Setting type = "cox" gives type = "cox|cox".

zVar

a numeric variable specifying the variance of the fraility variable,\(Z\), when zVar > 0. When zVar = 0, \(Z\) is set to a fixed constant 1. The default value is 0.25.

tau

a numeric value specifying the maximum observation time.

origin

a numeric value specifying the time origin.

summary

a logical value indicating whether a brief data summary will be printed.

Details

The function simSC() generates simulated recurrent event data over the interval \((0, \tau)\) based on the specification of the recurrent process and the terminal events. Specifically, the rate function, \(\lambda(t)\), of the recurrent process can be specified as one of the following model: $$\lambda(t) = Z \lambda_0(te^{X^\top\alpha}) e^{X^\top\beta}, h(t) = Z h_0(te^{X^\top\eta})e^{X^\top\theta}, $$ where \(\lambda_0(t)\) is the baseline rate function, \(h_0(t)\) is the baseline hazard function, \(X\) is a \(n\) by \(p\) covariate matrix and \(\alpha\), \(Z\) is an unobserved shared frailty variable, and \((\alpha, \eta)\) and \((\beta, \theta)\) correspond to the shape and size parameters of the rate function and the hazard function, respectively.

For all scenarios, two covariates are considered; \(X = (X_1, X_2)\), where \(X_1\) follows a Bernoulli distribution with probability 0.5 and \(X_2\) follows a standard normal distribution. The censoring time could be either independent (given covariates) or informative. The simulated data is used for illustration. An informative censoring time, \(C\), is generated separately from an exponential distribution with a rate parameter of 1 / 60 if \(X_1\) is 1, or \(Z^2 / 30\) if \(X_1\) is 0. The observed recurrent events is then observed up to the minimum of \(C\), terminal event, and \(\tau\). Lastly, we assume the baseline functions $$\lambda_0(t) = \frac{2}{1 + t}, h_0(t) = \frac{1}{8(1 + t)}.$$

See also

Examples

set.seed(123) simSC(100, c(-1, 1), c(-1, 1), summary = TRUE)
#> #> Summary results for number of recurrent event per subject: #> Min. 1st Qu. Median Mean 3rd Qu. Max. #> 0.00 1.00 2.00 4.29 6.00 34.00 #> #> Number of failures: 24 (24%); Number of censored events: 76 (76%) #> #> Number of x1 == 1: 41 (41%); Number of x1 == 0: 59 (59%) #> Summary results for x2: #> Min. 1st Qu. Median Mean 3rd Qu. Max. #> -3.31068 -0.82464 -0.03736 -0.01454 0.73703 2.70817 #> #>
#> id t.start t.stop event status x1 x2 #> 1 1 0.000000000 44.426167910 1 0 1 0.314152900 #> 2 1 44.426167910 60.000000000 0 0 1 0.314152900 #> 3 2 0.000000000 0.094921034 1 0 0 1.844838671 #> 4 2 0.094921034 0.125154110 1 0 0 1.844838671 #> 5 2 0.125154110 0.128363300 1 0 0 1.844838671 #> 6 2 0.128363300 0.128893639 1 0 0 1.844838671 #> 7 2 0.128893639 0.151798159 1 0 0 1.844838671 #> 8 2 0.151798159 0.156259693 1 0 0 1.844838671 #> 9 2 0.156259693 0.162467082 1 0 0 1.844838671 #> 10 2 0.162467082 0.192499996 1 0 0 1.844838671 #> 11 2 0.192499996 0.205361520 1 0 0 1.844838671 #> 12 2 0.205361520 0.212755086 0 1 0 1.844838671 #> 13 3 0.000000000 60.000000000 0 0 1 -0.981917149 #> 14 4 0.000000000 0.056292351 1 0 1 2.196003763 #> 15 4 0.056292351 0.072279983 1 0 1 2.196003763 #> 16 4 0.072279983 0.185730262 1 0 1 2.196003763 #> 17 4 0.185730262 0.289228289 1 0 1 2.196003763 #> 18 4 0.289228289 1.361980416 1 0 1 2.196003763 #> 19 4 1.361980416 1.874695287 1 0 1 2.196003763 #> 20 4 1.874695287 3.977850859 1 0 1 2.196003763 #> 21 4 3.977850859 4.480471395 1 0 1 2.196003763 #> 22 4 4.480471395 4.823564663 1 0 1 2.196003763 #> 23 4 4.823564663 4.982837852 1 0 1 2.196003763 #> 24 4 4.982837852 5.317014620 1 0 1 2.196003763 #> 25 4 5.317014620 5.340135942 1 0 1 2.196003763 #> 26 4 5.340135942 5.901524918 1 0 1 2.196003763 #> 27 4 5.901524918 5.956915706 1 0 1 2.196003763 #> 28 4 5.956915706 8.325919518 0 0 1 2.196003763 #> 29 5 0.000000000 0.129123255 1 0 0 -0.204667665 #> 30 5 0.129123255 0.693168398 1 0 0 -0.204667665 #> 31 5 0.693168398 1.332298107 1 0 0 -0.204667665 #> 32 5 1.332298107 1.858225226 1 0 0 -0.204667665 #> 33 5 1.858225226 3.180539355 0 0 0 -0.204667665 #> 34 6 0.000000000 0.216686503 1 0 0 0.975142936 #> 35 6 0.216686503 0.319404774 1 0 0 0.975142936 #> 36 6 0.319404774 0.588142311 1 0 0 0.975142936 #> 37 6 0.588142311 0.618091546 1 0 0 0.975142936 #> 38 6 0.618091546 1.085061481 1 0 0 0.975142936 #> 39 6 1.085061481 1.298248152 1 0 0 0.975142936 #> 40 6 1.298248152 1.354466114 1 0 0 0.975142936 #> 41 6 1.354466114 1.433272512 1 0 0 0.975142936 #> 42 6 1.433272512 1.479426384 1 0 0 0.975142936 #> 43 6 1.479426384 1.486390825 1 0 0 0.975142936 #> 44 6 1.486390825 1.603648039 1 0 0 0.975142936 #> 45 6 1.603648039 3.036196533 1 0 0 0.975142936 #> 46 6 3.036196533 4.378587285 1 0 0 0.975142936 #> 47 6 4.378587285 5.733083522 1 0 0 0.975142936 #> 48 6 5.733083522 7.070218220 1 0 0 0.975142936 #> 49 6 7.070218220 8.161021327 0 0 0 0.975142936 #> 50 7 0.000000000 12.204839610 0 0 0 -0.867566116 #> 51 8 0.000000000 0.480456759 1 0 0 -0.501187592 #> 52 8 0.480456759 9.182117175 0 0 0 -0.501187592 #> 53 9 0.000000000 0.004517227 1 0 0 0.785591163 #> 54 9 0.004517227 0.010845527 1 0 0 0.785591163 #> 55 9 0.010845527 0.231110693 1 0 0 0.785591163 #> 56 9 0.231110693 0.428345024 1 0 0 0.785591163 #> 57 9 0.428345024 0.481381589 1 0 0 0.785591163 #> 58 9 0.481381589 0.850984615 1 0 0 0.785591163 #> 59 9 0.850984615 0.957997791 1 0 0 0.785591163 #> 60 9 0.957997791 1.796847636 1 0 0 0.785591163 #> 61 9 1.796847636 2.040113204 1 0 0 0.785591163 #> 62 9 2.040113204 3.912920907 1 0 0 0.785591163 #> 63 9 3.912920907 4.187313729 0 1 0 0.785591163 #> 64 10 0.000000000 60.000000000 0 0 1 -2.102247324 #> 65 11 0.000000000 0.493291422 1 0 0 -0.042204930 #> 66 11 0.493291422 0.716490115 1 0 0 -0.042204930 #> 67 11 0.716490115 0.720544178 1 0 0 -0.042204930 #> 68 11 0.720544178 2.348637230 1 0 0 -0.042204930 #> 69 11 2.348637230 3.635269917 0 0 0 -0.042204930 #> 70 12 0.000000000 0.747892583 1 0 1 -0.404809413 #> 71 12 0.747892583 1.156108466 1 0 1 -0.404809413 #> 72 12 1.156108466 18.031380046 0 0 1 -0.404809413 #> 73 13 0.000000000 18.452001885 0 0 1 -0.112765966 #> 74 14 0.000000000 0.113047048 1 0 1 1.797140441 #> 75 14 0.113047048 0.136108410 1 0 1 1.797140441 #> 76 14 0.136108410 0.365452359 1 0 1 1.797140441 #> 77 14 0.365452359 0.391098229 1 0 1 1.797140441 #> 78 14 0.391098229 0.527733393 1 0 1 1.797140441 #> 79 14 0.527733393 0.590708249 1 0 1 1.797140441 #> 80 14 0.590708249 0.902421315 1 0 1 1.797140441 #> 81 14 0.902421315 1.019193212 1 0 1 1.797140441 #> 82 14 1.019193212 1.787599159 1 0 1 1.797140441 #> 83 14 1.787599159 2.533196580 1 0 1 1.797140441 #> 84 14 2.533196580 2.703503861 1 0 1 1.797140441 #> 85 14 2.703503861 3.003116132 1 0 1 1.797140441 #> 86 14 3.003116132 3.533033566 1 0 1 1.797140441 #> 87 14 3.533033566 5.135138577 1 0 1 1.797140441 #> 88 14 5.135138577 6.001520455 1 0 1 1.797140441 #> 89 14 6.001520455 8.129608877 1 0 1 1.797140441 #> 90 14 8.129608877 8.147785928 1 0 1 1.797140441 #> 91 14 8.147785928 14.463682858 1 0 1 1.797140441 #> 92 14 14.463682858 15.714660929 1 0 1 1.797140441 #> 93 14 15.714660929 16.000543655 1 0 1 1.797140441 #> 94 14 16.000543655 16.698048789 1 0 1 1.797140441 #> 95 14 16.698048789 19.074894239 1 0 1 1.797140441 #> 96 14 19.074894239 20.816736023 1 0 1 1.797140441 #> 97 14 20.816736023 21.072708316 0 1 1 1.797140441 #> 98 15 0.000000000 1.995573195 1 0 0 -0.810326258 #> 99 15 1.995573195 4.124126960 1 0 0 -0.810326258 #> 100 15 4.124126960 10.801766722 1 0 0 -0.810326258 #> 101 15 10.801766722 11.024803256 0 0 0 -0.810326258 #> 102 16 0.000000000 0.234114367 1 0 1 1.900900074 #> 103 16 0.234114367 0.851754751 1 0 1 1.900900074 #> 104 16 0.851754751 1.606035952 1 0 1 1.900900074 #> 105 16 1.606035952 1.762289385 1 0 1 1.900900074 #> 106 16 1.762289385 1.826441917 1 0 1 1.900900074 #> 107 16 1.826441917 3.124673952 1 0 1 1.900900074 #> 108 16 3.124673952 3.243853424 1 0 1 1.900900074 #> 109 16 3.243853424 4.395090357 1 0 1 1.900900074 #> 110 16 4.395090357 4.992642076 1 0 1 1.900900074 #> 111 16 4.992642076 5.642810119 0 0 1 1.900900074 #> 112 17 0.000000000 1.327927087 1 0 0 0.708954440 #> 113 17 1.327927087 2.701109679 1 0 0 0.708954440 #> 114 17 2.701109679 20.995077410 1 0 0 0.708954440 #> 115 17 20.995077410 25.360391444 1 0 0 0.708954440 #> 116 17 25.360391444 25.797039543 0 0 0 0.708954440 #> 117 18 0.000000000 0.367863189 1 0 1 0.736194775 #> 118 18 0.367863189 1.671345267 1 0 1 0.736194775 #> 119 18 1.671345267 2.488031575 1 0 1 0.736194775 #> 120 18 2.488031575 10.495364042 0 0 1 0.736194775 #> 121 19 0.000000000 0.003664993 0 1 0 1.365776554 #> 122 20 0.000000000 1.659010263 1 0 0 -0.576263893 #> 123 20 1.659010263 8.270060779 1 0 0 -0.576263893 #> 124 20 8.270060779 57.861444747 0 0 0 -0.576263893 #> 125 21 0.000000000 5.085302762 1 0 0 -0.804732320 #> 126 21 5.085302762 8.368098177 1 0 0 -0.804732320 #> 127 21 8.368098177 60.000000000 0 0 0 -0.804732320 #> 128 22 0.000000000 1.229565771 1 0 0 -0.535065812 #> 129 22 1.229565771 4.557610284 1 0 0 -0.535065812 #> 130 22 4.557610284 8.449352122 1 0 0 -0.535065812 #> 131 22 8.449352122 23.274458489 0 0 0 -0.535065812 #> 132 23 0.000000000 6.281136752 1 0 0 0.791547909 #> 133 23 6.281136752 13.303086271 1 0 0 0.791547909 #> 134 23 13.303086271 35.697385624 1 0 0 0.791547909 #> 135 23 35.697385624 60.000000000 0 0 0 0.791547909 #> 136 24 0.000000000 2.452900450 0 1 0 -0.707607151 #> 137 25 0.000000000 6.293977611 0 0 1 -1.275543372 #> 138 26 0.000000000 0.045506337 1 0 0 2.375464461 #> 139 26 0.045506337 0.178439471 1 0 0 2.375464461 #> 140 26 0.178439471 0.229764689 1 0 0 2.375464461 #> 141 26 0.229764689 0.391617573 1 0 0 2.375464461 #> 142 26 0.391617573 0.433009312 1 0 0 2.375464461 #> 143 26 0.433009312 0.444372840 1 0 0 2.375464461 #> 144 26 0.444372840 0.494782288 1 0 0 2.375464461 #> 145 26 0.494782288 0.534103344 1 0 0 2.375464461 #> 146 26 0.534103344 0.709791714 1 0 0 2.375464461 #> 147 26 0.709791714 0.715533114 1 0 0 2.375464461 #> 148 26 0.715533114 0.734933214 1 0 0 2.375464461 #> 149 26 0.734933214 0.780807122 1 0 0 2.375464461 #> 150 26 0.780807122 1.022881411 1 0 0 2.375464461 #> 151 26 1.022881411 1.099555227 1 0 0 2.375464461 #> 152 26 1.099555227 1.210136244 1 0 0 2.375464461 #> 153 26 1.210136244 1.416993677 1 0 0 2.375464461 #> 154 26 1.416993677 1.435961365 1 0 0 2.375464461 #> 155 26 1.435961365 1.730702372 1 0 0 2.375464461 #> 156 26 1.730702372 2.048041744 1 0 0 2.375464461 #> 157 26 2.048041744 2.124960370 1 0 0 2.375464461 #> 158 26 2.124960370 2.298323196 1 0 0 2.375464461 #> 159 26 2.298323196 2.591394978 1 0 0 2.375464461 #> 160 26 2.591394978 3.301813924 1 0 0 2.375464461 #> 161 26 3.301813924 3.947651924 1 0 0 2.375464461 #> 162 26 3.947651924 4.131293060 1 0 0 2.375464461 #> 163 26 4.131293060 4.251416452 1 0 0 2.375464461 #> 164 26 4.251416452 4.292132687 1 0 0 2.375464461 #> 165 26 4.292132687 4.427350682 1 0 0 2.375464461 #> 166 26 4.427350682 4.585815077 1 0 0 2.375464461 #> 167 26 4.585815077 4.987689301 1 0 0 2.375464461 #> 168 26 4.987689301 5.283218406 1 0 0 2.375464461 #> 169 26 5.283218406 5.305954276 1 0 0 2.375464461 #> 170 26 5.305954276 5.574535236 1 0 0 2.375464461 #> 171 26 5.574535236 5.827979402 1 0 0 2.375464461 #> 172 26 5.827979402 6.318148700 0 1 0 2.375464461 #> 173 27 0.000000000 2.527861668 0 0 1 -1.093589748 #> 174 28 0.000000000 0.051920460 1 0 0 0.192441582 #> 175 28 0.051920460 0.144681734 1 0 0 0.192441582 #> 176 28 0.144681734 0.247917295 1 0 0 0.192441582 #> 177 28 0.247917295 0.750263763 1 0 0 0.192441582 #> 178 28 0.750263763 1.221031857 0 0 0 0.192441582 #> 179 29 0.000000000 0.226611928 1 0 0 -0.126160381 #> 180 29 0.226611928 0.377627929 0 0 0 -0.126160381 #> 181 30 0.000000000 43.694549172 0 0 0 -1.388432140 #> 182 31 0.000000000 0.045878423 1 0 0 0.469902192 #> 183 31 0.045878423 0.512235913 1 0 0 0.469902192 #> 184 31 0.512235913 0.646405086 0 0 0 0.469902192 #> 185 32 0.000000000 1.760455139 1 0 1 0.960382357 #> 186 32 1.760455139 22.378842132 0 0 1 0.960382357 #> 187 33 0.000000000 0.951569404 1 0 1 -0.005141288 #> 188 33 0.951569404 7.505540052 1 0 1 -0.005141288 #> 189 33 7.505540052 60.000000000 0 0 1 -0.005141288 #> 190 34 0.000000000 0.515407932 1 0 0 -0.870464442 #> 191 34 0.515407932 0.896151084 1 0 0 -0.870464442 #> 192 34 0.896151084 0.931286070 0 1 0 -0.870464442 #> 193 35 0.000000000 0.944737736 1 0 0 -0.462879040 #> 194 35 0.944737736 6.428637348 1 0 0 -0.462879040 #> 195 35 6.428637348 7.544621338 1 0 0 -0.462879040 #> 196 35 7.544621338 19.917613942 0 0 0 -0.462879040 #> 197 36 0.000000000 60.000000000 0 0 0 -1.911151255 #> 198 37 0.000000000 0.367580507 1 0 1 0.369816044 #> 199 37 0.367580507 0.484168162 1 0 1 0.369816044 #> 200 37 0.484168162 3.400619282 1 0 1 0.369816044 #> 201 37 3.400619282 6.287594223 1 0 1 0.369816044 #> 202 37 6.287594223 9.211417503 1 0 1 0.369816044 #> 203 37 9.211417503 11.041441969 1 0 1 0.369816044 #> 204 37 11.041441969 60.000000000 0 0 1 0.369816044 #> 205 38 0.000000000 60.000000000 0 0 1 -0.462288057 #> 206 39 0.000000000 8.910640641 1 0 1 0.321955892 #> 207 39 8.910640641 9.839924491 1 0 1 0.321955892 #> 208 39 9.839924491 15.569450855 0 0 1 0.321955892 #> 209 40 0.000000000 0.389491429 1 0 0 -0.284001390 #> 210 40 0.389491429 1.121575864 1 0 0 -0.284001390 #> 211 40 1.121575864 3.341656791 1 0 0 -0.284001390 #> 212 40 3.341656791 6.553368190 1 0 0 -0.284001390 #> 213 40 6.553368190 7.197774398 1 0 0 -0.284001390 #> 214 40 7.197774398 29.655227938 1 0 0 -0.284001390 #> 215 40 29.655227938 31.327400120 1 0 0 -0.284001390 #> 216 40 31.327400120 60.000000000 0 0 0 -0.284001390 #> 217 41 0.000000000 0.380419607 1 0 1 1.091856443 #> 218 41 0.380419607 2.947484754 1 0 1 1.091856443 #> 219 41 2.947484754 3.485678620 1 0 1 1.091856443 #> 220 41 3.485678620 12.721763638 0 1 1 1.091856443 #> 221 42 0.000000000 2.647586860 1 0 0 0.160216363 #> 222 42 2.647586860 4.222113713 1 0 0 0.160216363 #> 223 42 4.222113713 11.930325739 0 0 0 0.160216363 #> 224 43 0.000000000 0.060869045 1 0 0 2.708168284 #> 225 43 0.060869045 0.141328881 1 0 0 2.708168284 #> 226 43 0.141328881 0.156319137 1 0 0 2.708168284 #> 227 43 0.156319137 0.283256048 1 0 0 2.708168284 #> 228 43 0.283256048 0.374894071 1 0 0 2.708168284 #> 229 43 0.374894071 0.632541474 1 0 0 2.708168284 #> 230 43 0.632541474 0.754572416 1 0 0 2.708168284 #> 231 43 0.754572416 0.787107817 1 0 0 2.708168284 #> 232 43 0.787107817 0.907544674 1 0 0 2.708168284 #> 233 43 0.907544674 0.927490095 1 0 0 2.708168284 #> 234 43 0.927490095 1.062092047 0 1 0 2.708168284 #> 235 44 0.000000000 9.902336551 1 0 0 0.286289929 #> 236 44 9.902336551 10.162711700 0 0 0 0.286289929 #> 237 45 0.000000000 1.130904205 1 0 0 -0.032510251 #> 238 45 1.130904205 1.184472075 1 0 0 -0.032510251 #> 239 45 1.184472075 1.555413216 1 0 0 -0.032510251 #> 240 45 1.555413216 60.000000000 0 0 0 -0.032510251 #> 241 46 0.000000000 7.260021570 1 0 0 -0.989678019 #> 242 46 7.260021570 7.935806037 1 0 0 -0.989678019 #> 243 46 7.935806037 10.324601177 1 0 0 -0.989678019 #> 244 46 10.324601177 37.580687785 0 0 0 -0.989678019 #> 245 47 0.000000000 4.021075863 1 0 1 0.211809928 #> 246 47 4.021075863 6.647520104 1 0 1 0.211809928 #> 247 47 6.647520104 60.000000000 0 0 1 0.211809928 #> 248 48 0.000000000 2.798082020 1 0 1 -0.972017534 #> 249 48 2.798082020 4.302783453 1 0 1 -0.972017534 #> 250 48 4.302783453 60.000000000 0 0 1 -0.972017534 #> 251 49 0.000000000 0.176975346 1 0 1 0.549224014 #> 252 49 0.176975346 0.743075179 1 0 1 0.549224014 #> 253 49 0.743075179 0.813259869 1 0 1 0.549224014 #> 254 49 0.813259869 1.153431976 1 0 1 0.549224014 #> 255 49 1.153431976 1.354066606 1 0 1 0.549224014 #> 256 49 1.354066606 2.304182033 1 0 1 0.549224014 #> 257 49 2.304182033 4.215737676 1 0 1 0.549224014 #> 258 49 4.215737676 9.764389491 1 0 1 0.549224014 #> 259 49 9.764389491 11.533429121 1 0 1 0.549224014 #> 260 49 11.533429121 12.113327177 1 0 1 0.549224014 #> 261 49 12.113327177 16.493736204 1 0 1 0.549224014 #> 262 49 16.493736204 19.744157497 1 0 1 0.549224014 #> 263 49 19.744157497 20.497090013 1 0 1 0.549224014 #> 264 49 20.497090013 30.745422361 1 0 1 0.549224014 #> 265 49 30.745422361 31.091008194 1 0 1 0.549224014 #> 266 49 31.091008194 34.601702514 0 1 1 0.549224014 #> 267 50 0.000000000 0.230084990 1 0 0 -1.049021530 #> 268 50 0.230084990 48.263490207 0 0 0 -1.049021530 #> 269 51 0.000000000 0.067797362 1 0 0 0.449133935 #> 270 51 0.067797362 0.264214934 1 0 0 0.449133935 #> 271 51 0.264214934 0.462465771 1 0 0 0.449133935 #> 272 51 0.462465771 0.806881110 1 0 0 0.449133935 #> 273 51 0.806881110 0.886435166 1 0 0 0.449133935 #> 274 51 0.886435166 5.881111896 1 0 0 0.449133935 #> 275 51 5.881111896 8.606163806 1 0 0 0.449133935 #> 276 51 8.606163806 8.942277607 1 0 0 0.449133935 #> 277 51 8.942277607 14.864964116 0 0 0 0.449133935 #> 278 52 0.000000000 13.784086765 1 0 1 -0.385855653 #> 279 52 13.784086765 27.970609279 1 0 1 -0.385855653 #> 280 52 27.970609279 41.380154919 0 0 1 -0.385855653 #> 281 53 0.000000000 45.917339621 0 0 1 -1.570135523 #> 282 54 0.000000000 0.132881709 1 0 0 1.226942601 #> 283 54 0.132881709 0.220699343 1 0 0 1.226942601 #> 284 54 0.220699343 0.428962098 1 0 0 1.226942601 #> 285 54 0.428962098 0.517601886 1 0 0 1.226942601 #> 286 54 0.517601886 0.638980442 1 0 0 1.226942601 #> 287 54 0.638980442 0.656049954 1 0 0 1.226942601 #> 288 54 0.656049954 1.253642173 1 0 0 1.226942601 #> 289 54 1.253642173 1.407435662 1 0 0 1.226942601 #> 290 54 1.407435662 1.694336288 1 0 0 1.226942601 #> 291 54 1.694336288 1.767217579 1 0 0 1.226942601 #> 292 54 1.767217579 2.159906265 1 0 0 1.226942601 #> 293 54 2.159906265 2.408250542 1 0 0 1.226942601 #> 294 54 2.408250542 2.417505832 1 0 0 1.226942601 #> 295 54 2.417505832 2.796181193 1 0 0 1.226942601 #> 296 54 2.796181193 2.863436992 1 0 0 1.226942601 #> 297 54 2.863436992 2.962453010 1 0 0 1.226942601 #> 298 54 2.962453010 3.324677789 1 0 0 1.226942601 #> 299 54 3.324677789 3.562060613 1 0 0 1.226942601 #> 300 54 3.562060613 3.913280487 1 0 0 1.226942601 #> 301 54 3.913280487 3.950248888 1 0 0 1.226942601 #> 302 54 3.950248888 4.455959171 1 0 0 1.226942601 #> 303 54 4.455959171 4.989831279 1 0 0 1.226942601 #> 304 54 4.989831279 5.192937332 1 0 0 1.226942601 #> 305 54 5.192937332 5.329145827 1 0 0 1.226942601 #> 306 54 5.329145827 5.378969353 1 0 0 1.226942601 #> 307 54 5.378969353 5.514449219 1 0 0 1.226942601 #> 308 54 5.514449219 9.091785237 1 0 0 1.226942601 #> 309 54 9.091785237 16.474294053 1 0 0 1.226942601 #> 310 54 16.474294053 19.403666424 1 0 0 1.226942601 #> 311 54 19.403666424 30.590409252 1 0 0 1.226942601 #> 312 54 30.590409252 30.962417132 0 0 0 1.226942601 #> 313 55 0.000000000 0.317940276 1 0 1 0.666694396 #> 314 55 0.317940276 1.168614638 1 0 1 0.666694396 #> 315 55 1.168614638 1.713942123 1 0 1 0.666694396 #> 316 55 1.713942123 2.607341604 1 0 1 0.666694396 #> 317 55 2.607341604 5.271562205 1 0 1 0.666694396 #> 318 55 5.271562205 5.639152530 1 0 1 0.666694396 #> 319 55 5.639152530 10.220013936 1 0 1 0.666694396 #> 320 55 10.220013936 19.553747046 1 0 1 0.666694396 #> 321 55 19.553747046 28.152110925 1 0 1 0.666694396 #> 322 55 28.152110925 38.274645992 0 0 1 0.666694396 #> 323 56 0.000000000 22.337666746 1 0 0 -1.151603163 #> 324 56 22.337666746 39.205379870 1 0 0 -1.151603163 #> 325 56 39.205379870 60.000000000 0 0 0 -1.151603163 #> 326 57 0.000000000 1.123956508 1 0 0 -0.160788483 #> 327 57 1.123956508 7.478829245 1 0 0 -0.160788483 #> 328 57 7.478829245 7.608661820 1 0 0 -0.160788483 #> 329 57 7.608661820 22.129391233 0 0 0 -0.160788483 #> 330 58 0.000000000 35.858826935 0 0 1 -0.972913776 #> 331 59 0.000000000 0.106334237 1 0 0 -0.610461659 #> 332 59 0.106334237 0.143066590 1 0 0 -0.610461659 #> 333 59 0.143066590 0.399736278 1 0 0 -0.610461659 #> 334 59 0.399736278 1.329412686 0 0 0 -0.610461659 #> 335 60 0.000000000 0.289244137 1 0 0 0.499276876 #> 336 60 0.289244137 1.119889409 1 0 0 0.499276876 #> 337 60 1.119889409 1.861822395 1 0 0 0.499276876 #> 338 60 1.861822395 1.921929449 1 0 0 0.499276876 #> 339 60 1.921929449 2.411083779 1 0 0 0.499276876 #> 340 60 2.411083779 2.546129412 1 0 0 0.499276876 #> 341 60 2.546129412 5.750243466 1 0 0 0.499276876 #> 342 60 5.750243466 6.923099549 1 0 0 0.499276876 #> 343 60 6.923099549 7.432479386 1 0 0 0.499276876 #> 344 60 7.432479386 9.919762625 0 0 0 0.499276876 #> 345 61 0.000000000 0.329834180 1 0 0 0.879364139 #> 346 61 0.329834180 1.287722228 1 0 0 0.879364139 #> 347 61 1.287722228 1.659425957 1 0 0 0.879364139 #> 348 61 1.659425957 1.756849354 1 0 0 0.879364139 #> 349 61 1.756849354 4.536289698 1 0 0 0.879364139 #> 350 61 4.536289698 7.866204392 1 0 0 0.879364139 #> 351 61 7.866204392 11.104906100 1 0 0 0.879364139 #> 352 61 11.104906100 15.570550002 1 0 0 0.879364139 #> 353 61 15.570550002 30.687902796 1 0 0 0.879364139 #> 354 61 30.687902796 58.924853849 1 0 0 0.879364139 #> 355 61 58.924853849 60.000000000 0 0 0 0.879364139 #> 356 62 0.000000000 0.423540384 1 0 1 0.923129239 #> 357 62 0.423540384 5.744994749 1 0 1 0.923129239 #> 358 62 5.744994749 7.426180952 1 0 1 0.923129239 #> 359 62 7.426180952 60.000000000 0 0 1 0.923129239 #> 360 63 0.000000000 0.233545879 1 0 0 0.693133972 #> 361 63 0.233545879 0.234017989 1 0 0 0.693133972 #> 362 63 0.234017989 0.538450199 1 0 0 0.693133972 #> 363 63 0.538450199 0.627526061 1 0 0 0.693133972 #> 364 63 0.627526061 0.861556521 1 0 0 0.693133972 #> 365 63 0.861556521 1.102409116 1 0 0 0.693133972 #> 366 63 1.102409116 3.258602170 1 0 0 0.693133972 #> 367 63 3.258602170 6.293075161 1 0 0 0.693133972 #> 368 63 6.293075161 14.284947113 1 0 0 0.693133972 #> 369 63 14.284947113 17.246547226 1 0 0 0.693133972 #> 370 63 17.246547226 30.399024532 1 0 0 0.693133972 #> 371 63 30.399024532 33.538318472 0 1 0 0.693133972 #> 372 64 0.000000000 0.150317201 1 0 1 -0.139500325 #> 373 64 0.150317201 4.096807626 1 0 1 -0.139500325 #> 374 64 4.096807626 13.747458877 0 0 1 -0.139500325 #> 375 65 0.000000000 30.085791836 0 0 0 -3.310678727 #> 376 66 0.000000000 5.254560647 1 0 1 0.538465799 #> 377 66 5.254560647 19.785907300 0 0 1 0.538465799 #> 378 67 0.000000000 0.042599725 1 0 1 0.892485867 #> 379 67 0.042599725 0.460391154 1 0 1 0.892485867 #> 380 67 0.460391154 0.486884850 1 0 1 0.892485867 #> 381 67 0.486884850 0.623984366 1 0 1 0.892485867 #> 382 67 0.623984366 1.316361786 1 0 1 0.892485867 #> 383 67 1.316361786 16.813802408 0 1 1 0.892485867 #> 384 68 0.000000000 0.353305779 1 0 1 0.489462036 #> 385 68 0.353305779 1.326752035 1 0 1 0.489462036 #> 386 68 1.326752035 2.319360850 1 0 1 0.489462036 #> 387 68 2.319360850 2.344870833 0 0 1 0.489462036 #> 388 69 0.000000000 0.348996492 0 0 1 -1.196351747 #> 389 70 0.000000000 1.148963316 1 0 0 0.462737853 #> 390 70 1.148963316 1.312017315 1 0 0 0.462737853 #> 391 70 1.312017315 2.542578920 1 0 0 0.462737853 #> 392 70 2.542578920 5.151759989 1 0 0 0.462737853 #> 393 70 5.151759989 11.690276404 1 0 0 0.462737853 #> 394 70 11.690276404 60.000000000 0 0 0 0.462737853 #> 395 71 0.000000000 0.266150966 1 0 0 0.971703576 #> 396 71 0.266150966 0.349670849 0 1 0 0.971703576 #> 397 72 0.000000000 42.047029902 0 0 0 -1.472158964 #> 398 73 0.000000000 0.393912335 1 0 1 0.528964941 #> 399 73 0.393912335 50.322384926 1 0 1 0.528964941 #> 400 73 50.322384926 60.000000000 0 0 1 0.528964941 #> 401 74 0.000000000 0.226227290 0 1 0 2.454400353 #> 402 75 0.000000000 0.604137764 1 0 0 -1.649345480 #> 403 75 0.604137764 1.302897180 0 0 0 -1.649345480 #> 404 76 0.000000000 0.297104808 1 0 1 0.795805155 #> 405 76 0.297104808 1.442722956 1 0 1 0.795805155 #> 406 76 1.442722956 6.228937470 1 0 1 0.795805155 #> 407 76 6.228937470 33.654580313 1 0 1 0.795805155 #> 408 76 33.654580313 60.000000000 0 0 1 0.795805155 #> 409 77 0.000000000 0.247724744 1 0 0 -0.341293167 #> 410 77 0.247724744 0.883275948 1 0 0 -0.341293167 #> 411 77 0.883275948 0.965598205 1 0 0 -0.341293167 #> 412 77 0.965598205 1.267030058 1 0 0 -0.341293167 #> 413 77 1.267030058 2.136561426 1 0 0 -0.341293167 #> 414 77 2.136561426 11.737178714 1 0 0 -0.341293167 #> 415 77 11.737178714 19.006126729 1 0 0 -0.341293167 #> 416 77 19.006126729 19.508749921 1 0 0 -0.341293167 #> 417 77 19.508749921 33.068292801 1 0 0 -0.341293167 #> 418 77 33.068292801 37.221890340 0 0 0 -0.341293167 #> 419 78 0.000000000 1.634828342 1 0 0 -1.405253800 #> 420 78 1.634828342 2.166839239 0 0 0 -1.405253800 #> 421 79 0.000000000 18.849900991 0 1 1 -0.922960815 #> 422 80 0.000000000 0.057899323 1 0 0 0.009898130 #> 423 80 0.057899323 0.563149307 1 0 0 0.009898130 #> 424 80 0.563149307 1.729418601 1 0 0 0.009898130 #> 425 80 1.729418601 1.742868436 1 0 0 0.009898130 #> 426 80 1.742868436 2.184840182 1 0 0 0.009898130 #> 427 80 2.184840182 3.269702071 1 0 0 0.009898130 #> 428 80 3.269702071 6.823633670 0 0 0 0.009898130 #> 429 81 0.000000000 2.088983908 1 0 1 -0.408859774 #> 430 81 2.088983908 60.000000000 0 0 1 -0.408859774 #> 431 82 0.000000000 10.473374901 0 0 1 -1.388245289 #> 432 83 0.000000000 4.738025556 1 0 1 -0.264595238 #> 433 83 4.738025556 10.707105999 1 0 1 -0.264595238 #> 434 83 10.707105999 23.299277838 1 0 1 -0.264595238 #> 435 83 23.299277838 36.803331552 0 0 1 -0.264595238 #> 436 84 0.000000000 3.101080222 1 0 0 -0.947298279 #> 437 84 3.101080222 6.626583844 1 0 0 -0.947298279 #> 438 84 6.626583844 31.520187178 0 1 0 -0.947298279 #> 439 85 0.000000000 0.644340177 1 0 0 0.739521328 #> 440 85 0.644340177 0.710910608 1 0 0 0.739521328 #> 441 85 0.710910608 1.536251400 1 0 0 0.739521328 #> 442 85 1.536251400 1.816507927 1 0 0 0.739521328 #> 443 85 1.816507927 2.401143401 1 0 0 0.739521328 #> 444 85 2.401143401 2.613061991 1 0 0 0.739521328 #> 445 85 2.613061991 3.121227252 0 1 0 0.739521328 #> 446 86 0.000000000 0.016017404 1 0 0 0.896778709 #> 447 86 0.016017404 0.232698496 1 0 0 0.896778709 #> 448 86 0.232698496 0.577077685 1 0 0 0.896778709 #> 449 86 0.577077685 0.978526520 1 0 0 0.896778709 #> 450 86 0.978526520 1.057186346 1 0 0 0.896778709 #> 451 86 1.057186346 1.462097773 0 1 0 0.896778709 #> 452 87 0.000000000 0.895563396 1 0 0 -0.346000887 #> 453 87 0.895563396 33.465054977 0 0 0 -0.346000887 #> 454 88 0.000000000 22.899505699 0 0 1 -1.782057068 #> 455 89 0.000000000 0.037101618 1 0 0 0.464941753 #> 456 89 0.037101618 0.102710022 1 0 0 0.464941753 #> 457 89 0.102710022 0.216567111 1 0 0 0.464941753 #> 458 89 0.216567111 0.796068242 1 0 0 0.464941753 #> 459 89 0.796068242 0.958993995 1 0 0 0.464941753 #> 460 89 0.958993995 1.028313254 1 0 0 0.464941753 #> 461 89 1.028313254 1.074377107 0 0 0 0.464941753 #> 462 90 0.000000000 60.000000000 0 0 0 -1.951030610 #> 463 91 0.000000000 0.078056200 0 1 0 -0.516113340 #> 464 92 0.000000000 0.176685484 1 0 0 0.489080318 #> 465 92 0.176685484 0.296731331 1 0 0 0.489080318 #> 466 92 0.296731331 0.538848097 1 0 0 0.489080318 #> 467 92 0.538848097 0.571099060 1 0 0 0.489080318 #> 468 92 0.571099060 0.998071193 1 0 0 0.489080318 #> 469 92 0.998071193 1.283195611 1 0 0 0.489080318 #> 470 92 1.283195611 2.193886966 1 0 0 0.489080318 #> 471 92 2.193886966 3.611732953 1 0 0 0.489080318 #> 472 92 3.611732953 7.750845917 0 0 0 0.489080318 #> 473 93 0.000000000 0.025896790 1 0 1 0.902024726 #> 474 93 0.025896790 2.654534720 1 0 1 0.902024726 #> 475 93 2.654534720 2.711107298 1 0 1 0.902024726 #> 476 93 2.711107298 3.396050813 1 0 1 0.902024726 #> 477 93 3.396050813 4.747309685 0 0 1 0.902024726 #> 478 94 0.000000000 3.672871226 1 0 1 0.640362995 #> 479 94 3.672871226 5.452322593 1 0 1 0.640362995 #> 480 94 5.452322593 16.537795976 1 0 1 0.640362995 #> 481 94 16.537795976 21.891690916 1 0 1 0.640362995 #> 482 94 21.891690916 25.337334766 1 0 1 0.640362995 #> 483 94 25.337334766 60.000000000 0 0 1 0.640362995 #> 484 95 0.000000000 0.070926623 1 0 0 0.951208879 #> 485 95 0.070926623 0.423656815 1 0 0 0.951208879 #> 486 95 0.423656815 0.487280034 1 0 0 0.951208879 #> 487 95 0.487280034 0.496622564 1 0 0 0.951208879 #> 488 95 0.496622564 0.553466751 1 0 0 0.951208879 #> 489 95 0.553466751 0.605335217 1 0 0 0.951208879 #> 490 95 0.605335217 0.803361018 1 0 0 0.951208879 #> 491 95 0.803361018 0.965024233 0 1 0 0.951208879 #> 492 96 0.000000000 3.769555449 0 1 1 -0.599123210 #> 493 97 0.000000000 1.274006209 0 1 0 -1.330694993 #> 494 98 0.000000000 11.432728756 1 0 0 -0.592209746 #> 495 98 11.432728756 11.998121025 1 0 0 -0.592209746 #> 496 98 11.998121025 14.377420871 1 0 0 -0.592209746 #> 497 98 14.377420871 22.412248553 1 0 0 -0.592209746 #> 498 98 22.412248553 23.615610800 1 0 0 -0.592209746 #> 499 98 23.615610800 45.509140172 1 0 0 -0.592209746 #> 500 98 45.509140172 59.117118140 0 1 0 -0.592209746 #> 501 99 0.000000000 0.024035847 1 0 0 1.801050856 #> 502 99 0.024035847 0.169182346 1 0 0 1.801050856 #> 503 99 0.169182346 0.204678212 1 0 0 1.801050856 #> 504 99 0.204678212 0.429791121 1 0 0 1.801050856 #> 505 99 0.429791121 0.564102773 1 0 0 1.801050856 #> 506 99 0.564102773 0.612301930 1 0 0 1.801050856 #> 507 99 0.612301930 0.920473254 1 0 0 1.801050856 #> 508 99 0.920473254 1.029332820 1 0 0 1.801050856 #> 509 99 1.029332820 1.351443755 1 0 0 1.801050856 #> 510 99 1.351443755 1.689399361 0 1 0 1.801050856 #> 511 100 0.000000000 0.062282158 1 0 1 1.055338591 #> 512 100 0.062282158 0.092470102 1 0 1 1.055338591 #> 513 100 0.092470102 0.099136473 1 0 1 1.055338591 #> 514 100 0.099136473 0.119418775 1 0 1 1.055338591 #> 515 100 0.119418775 0.494375485 1 0 1 1.055338591 #> 516 100 0.494375485 0.535604140 1 0 1 1.055338591 #> 517 100 0.535604140 0.928665456 1 0 1 1.055338591 #> 518 100 0.928665456 2.430407324 1 0 1 1.055338591 #> 519 100 2.430407324 2.924293729 1 0 1 1.055338591 #> 520 100 2.924293729 5.242506460 1 0 1 1.055338591 #> 521 100 5.242506460 5.727066391 1 0 1 1.055338591 #> 522 100 5.727066391 7.211164372 1 0 1 1.055338591 #> 523 100 7.211164372 8.749865224 1 0 1 1.055338591 #> 524 100 8.749865224 9.247636836 1 0 1 1.055338591 #> 525 100 9.247636836 10.889850475 1 0 1 1.055338591 #> 526 100 10.889850475 11.144609855 1 0 1 1.055338591 #> 527 100 11.144609855 11.155463685 1 0 1 1.055338591 #> 528 100 11.155463685 42.939965866 1 0 1 1.055338591 #> 529 100 42.939965866 44.020624512 0 0 1 1.055338591