The function simGSC() generates simulated recurrent event data from either
a Cox-type model, an accelerated mean model, an accelerated rate model, or a generalized scale-change model.
simGSC(
n,
summary = FALSE,
para,
xmat,
censoring,
frailty,
tau,
origin,
Lam0,
Haz0
)number of observation.
a logical value indicating whether a brief data summary will be printed.
a list of numerical vectors for the regression coefficients
in the joint scale-change model.
The names of the list elements are alpha, beta, eta, and
theta, correspond to \(\alpha\), \(\beta\), \(\eta\), and \(\theta\)
in the joint scale-change model, respectively.
See Details for reReg.
an optional matrix specifying the design matrix.
a numeric variable specifying the censoring times for each of the \(n\) observation.
a numeric variable specifying the frailty variable.
a numeric value specifying the maximum observation time.
a numeric value specifying the time origin.
is an optional function that specifies the baseline cumulative rate function. When left-unspecified, the recurrent events are generated using the baseline rate function of $$\lambda_0(t) = \frac{2}{1 + t},$$ or equivalently, the cumulative rate function of $$\Lambda_0(t) = 2\log(1 + t).$$
is an optional function that specifies the baseline hazard function. When left-unspecified, the recurrent events are generated using the baseline hazard function $$h_0(t) = \frac{1}{5(1 + t)},$$ or equivalently, the cumulative hazard function of $$H_0(t) = \log(1 + t) / 5.$$
The function simGSC() 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.
Under the default settings, the simGSC() function assumes \(p = 2\)
and the regression parameters to be \(\alpha = \eta = (0, 0)^\top\),
and \(\beta = \theta = (1, 1)^\top\).
When the xmat argument is not specified, the simGSC() function
assumes \(X_i\) is a two-dimensional vector \(X_i = (X_{i1}, X_{i2}), i = 1, \ldots, n\),
where \(X_{i1}\) is a Bernoulli variable with rate 0.5 and
\(X_{i2}\) is a standard normal variable.
With the default xmat, the censoring time $C$ is generated from
an exponential distribution with mean \(\tau X_{i1} + Z^2\tau(1 - X_{i1})\).
Thus, the censoring distribution is covariate dependent and
is informative when \(Z\) is not a constant.
When the frailty argument is not specified, the frailty variable \(Z\) is generated
from a gamma distribution with a unit mean and a variance of 0.25.
The default values for tau and origin are 60 and 0, respectively.
When arguments Lam0 and Haz0 are left unspecified,
the simGSC() function uses \(\Lambda_0(t) = 2\log(1 + t)\)
and \(H_0(t) = \log(1 + t) / 5\), respectively.
This is equivalent to setting
Lam0 = function(x) 2 * log(1 + x) and Haz0 = function(x) log(1 + x) / 5.
Overall, the default specifications generate the recurrent events and the terminal events
from the model:
$$\lambda(t) = \displaystyle \frac{2Z}{1 + te^{-X_{i1} - X_{i2}}},
h(t) = \displaystyle \frac{Z}{5(1 + te^{X_{i1} + X_{i2}})}, t\in[0, 60].$$
See online vignette
for more examples.
set.seed(123)
simGSC(100, summary = TRUE)
#> Call:
#> simGSC(n = 100, summary = TRUE)
#>
#> Summary:
#> Sample size: 100
#> Number of recurrent event observed: 343
#> Average number of recurrent event per subject: 3.43
#> Proportion of subjects with a terminal event: 0.53
#> Median time-to-terminal event: 11.202
#>
#>
#> id t.start t.stop event status x1 x2
#> 1 1 0.00000000 0.79162625 1 0 1 0.157076450
#> 2 1 0.79162625 1.26276390 1 0 1 0.157076450
#> 3 1 1.26276390 45.11318934 1 0 1 0.157076450
#> 4 1 45.11318934 60.00000000 0 0 1 0.157076450
#> 5 2 0.00000000 0.30227581 1 0 0 0.922419336
#> 6 2 0.30227581 0.90335773 1 0 0 0.922419336
#> 7 2 0.90335773 2.38441607 1 0 0 0.922419336
#> 8 2 2.38441607 2.60041466 1 0 0 0.922419336
#> 9 2 2.60041466 2.96855402 0 1 0 0.922419336
#> 10 3 0.00000000 60.00000000 0 0 1 -0.490958575
#> 11 4 0.00000000 1.43868491 0 1 1 1.098001882
#> 12 5 0.00000000 0.26107532 1 0 0 -0.102333833
#> 13 5 0.26107532 0.46163165 1 0 0 -0.102333833
#> 14 5 0.46163165 0.46192449 1 0 0 -0.102333833
#> 15 5 0.46192449 1.14105041 1 0 0 -0.102333833
#> 16 5 1.14105041 3.82760327 1 0 0 -0.102333833
#> 17 5 3.82760327 4.06105187 1 0 0 -0.102333833
#> 18 5 4.06105187 5.41661163 1 0 0 -0.102333833
#> 19 5 5.41661163 5.50413410 1 0 0 -0.102333833
#> 20 5 5.50413410 6.50628946 1 0 0 -0.102333833
#> 21 5 6.50628946 11.74388386 1 0 0 -0.102333833
#> 22 5 11.74388386 13.00832888 1 0 0 -0.102333833
#> 23 5 13.00832888 13.60817463 1 0 0 -0.102333833
#> 24 5 13.60817463 20.85935224 1 0 0 -0.102333833
#> 25 5 20.85935224 36.50247425 1 0 0 -0.102333833
#> 26 5 36.50247425 37.56205361 1 0 0 -0.102333833
#> 27 5 37.56205361 44.90413413 1 0 0 -0.102333833
#> 28 5 44.90413413 60.00000000 0 0 0 -0.102333833
#> 29 6 0.00000000 0.07968560 0 1 0 0.487571468
#> 30 7 0.00000000 0.52713723 0 0 0 -0.433783058
#> 31 8 0.00000000 0.07596889 0 0 0 -0.250593796
#> 32 9 0.00000000 0.15887552 1 0 0 0.392795581
#> 33 9 0.15887552 0.45145920 1 0 0 0.392795581
#> 34 9 0.45145920 0.95050460 1 0 0 0.392795581
#> 35 9 0.95050460 1.22943797 0 1 0 0.392795581
#> 36 10 0.00000000 0.58502638 1 0 1 -1.051123662
#> 37 10 0.58502638 1.88079670 1 0 1 -1.051123662
#> 38 10 1.88079670 2.25568405 1 0 1 -1.051123662
#> 39 10 2.25568405 3.30296307 1 0 1 -1.051123662
#> 40 10 3.30296307 4.97999693 1 0 1 -1.051123662
#> 41 10 4.97999693 6.98154161 1 0 1 -1.051123662
#> 42 10 6.98154161 31.61794063 0 1 1 -1.051123662
#> 43 11 0.00000000 4.33261659 1 0 0 -0.021102465
#> 44 11 4.33261659 6.77366561 1 0 0 -0.021102465
#> 45 11 6.77366561 8.22945935 1 0 0 -0.021102465
#> 46 11 8.22945935 9.61893919 0 0 0 -0.021102465
#> 47 12 0.00000000 18.03138005 0 0 1 -0.202404707
#> 48 13 0.00000000 9.04088247 1 0 1 -0.056382983
#> 49 13 9.04088247 11.20185483 0 1 1 -0.056382983
#> 50 14 0.00000000 0.44361488 0 1 1 0.898570220
#> 51 15 0.00000000 0.08839869 1 0 0 -0.405163129
#> 52 15 0.08839869 0.18584832 1 0 0 -0.405163129
#> 53 15 0.18584832 1.79615217 1 0 0 -0.405163129
#> 54 15 1.79615217 2.08960718 1 0 0 -0.405163129
#> 55 15 2.08960718 3.14205836 1 0 0 -0.405163129
#> 56 15 3.14205836 3.24554692 1 0 0 -0.405163129
#> 57 15 3.24554692 4.30789368 1 0 0 -0.405163129
#> 58 15 4.30789368 6.58344304 1 0 0 -0.405163129
#> 59 15 6.58344304 6.94031987 1 0 0 -0.405163129
#> 60 15 6.94031987 7.19481553 1 0 0 -0.405163129
#> 61 15 7.19481553 8.02533680 1 0 0 -0.405163129
#> 62 15 8.02533680 10.47299913 1 0 0 -0.405163129
#> 63 15 10.47299913 11.10968894 1 0 0 -0.405163129
#> 64 15 11.10968894 11.27363789 1 0 0 -0.405163129
#> 65 15 11.27363789 25.48988929 1 0 0 -0.405163129
#> 66 15 25.48988929 60.00000000 0 0 0 -0.405163129
#> 67 16 0.00000000 0.57676712 0 1 1 0.950450037
#> 68 17 0.00000000 0.54498747 1 0 0 0.354477220
#> 69 17 0.54498747 1.13209144 0 1 0 0.354477220
#> 70 18 0.00000000 3.02912424 0 1 1 0.368097387
#> 71 19 0.00000000 9.25047301 0 1 0 0.682888277
#> 72 20 0.00000000 0.05210728 0 1 0 -0.288131946
#> 73 21 0.00000000 0.77471756 1 0 0 -0.402366160
#> 74 21 0.77471756 1.60270233 1 0 0 -0.402366160
#> 75 21 1.60270233 1.78024184 1 0 0 -0.402366160
#> 76 21 1.78024184 1.88561006 1 0 0 -0.402366160
#> 77 21 1.88561006 3.19259507 1 0 0 -0.402366160
#> 78 21 3.19259507 11.79773426 1 0 0 -0.402366160
#> 79 21 11.79773426 15.21785161 0 0 0 -0.402366160
#> 80 22 0.00000000 1.37767984 0 0 0 -0.267532906
#> 81 23 0.00000000 1.50594395 1 0 0 0.395773955
#> 82 23 1.50594395 1.75861105 1 0 0 0.395773955
#> 83 23 1.75861105 1.80267914 1 0 0 0.395773955
#> 84 23 1.80267914 4.51812448 1 0 0 0.395773955
#> 85 23 4.51812448 5.28666642 1 0 0 0.395773955
#> 86 23 5.28666642 6.53089379 1 0 0 0.395773955
#> 87 23 6.53089379 13.53141563 0 0 0 0.395773955
#> 88 24 0.00000000 0.41991347 1 0 0 -0.353803575
#> 89 24 0.41991347 2.33241050 1 0 0 -0.353803575
#> 90 24 2.33241050 2.92127177 1 0 0 -0.353803575
#> 91 24 2.92127177 3.10026121 1 0 0 -0.353803575
#> 92 24 3.10026121 4.52826189 1 0 0 -0.353803575
#> 93 24 4.52826189 6.08884111 1 0 0 -0.353803575
#> 94 24 6.08884111 6.45393470 0 1 0 -0.353803575
#> 95 25 0.00000000 6.29397761 0 0 1 -0.637771686
#> 96 26 0.00000000 1.13027008 1 0 0 1.187732231
#> 97 26 1.13027008 1.98111944 1 0 0 1.187732231
#> 98 26 1.98111944 2.04596710 0 1 0 1.187732231
#> 99 27 0.00000000 0.05681231 0 1 1 -0.546794874
#> 100 28 0.00000000 0.20117010 0 1 0 0.096220791
#> 101 29 0.00000000 0.64909412 1 0 0 -0.063080191
#> 102 29 0.64909412 1.33593293 0 0 0 -0.063080191
#> 103 30 0.00000000 1.50659690 1 0 0 -0.694216070
#> 104 30 1.50659690 2.51742284 1 0 0 -0.694216070
#> 105 30 2.51742284 3.04602864 1 0 0 -0.694216070
#> 106 30 3.04602864 4.57322485 1 0 0 -0.694216070
#> 107 30 4.57322485 4.75602077 1 0 0 -0.694216070
#> 108 30 4.75602077 7.91947850 1 0 0 -0.694216070
#> 109 30 7.91947850 9.55289875 1 0 0 -0.694216070
#> 110 30 9.55289875 10.00277008 1 0 0 -0.694216070
#> 111 30 10.00277008 10.64665836 1 0 0 -0.694216070
#> 112 30 10.64665836 11.03089566 1 0 0 -0.694216070
#> 113 30 11.03089566 11.08933110 1 0 0 -0.694216070
#> 114 30 11.08933110 12.09100807 1 0 0 -0.694216070
#> 115 30 12.09100807 26.91632324 1 0 0 -0.694216070
#> 116 30 26.91632324 44.82494415 0 0 0 -0.694216070
#> 117 31 0.00000000 0.93724384 1 0 0 0.234951096
#> 118 31 0.93724384 1.36756560 0 0 0 0.234951096
#> 119 32 0.00000000 0.94782802 1 0 1 0.480191179
#> 120 32 0.94782802 12.52976869 0 1 1 0.480191179
#> 121 33 0.00000000 0.07466582 0 1 1 -0.002570644
#> 122 34 0.00000000 0.50137025 1 0 0 -0.435232221
#> 123 34 0.50137025 0.65878014 1 0 0 -0.435232221
#> 124 34 0.65878014 2.05024074 1 0 0 -0.435232221
#> 125 34 2.05024074 2.55702490 1 0 0 -0.435232221
#> 126 34 2.55702490 8.43139702 1 0 0 -0.435232221
#> 127 34 8.43139702 10.84759217 1 0 0 -0.435232221
#> 128 34 10.84759217 23.15024896 0 0 0 -0.435232221
#> 129 35 0.00000000 0.22102875 1 0 0 -0.231439520
#> 130 35 0.22102875 0.51182518 1 0 0 -0.231439520
#> 131 35 0.51182518 0.62828817 1 0 0 -0.231439520
#> 132 35 0.62828817 0.63033587 1 0 0 -0.231439520
#> 133 35 0.63033587 1.32460875 1 0 0 -0.231439520
#> 134 35 1.32460875 2.16115727 1 0 0 -0.231439520
#> 135 35 2.16115727 2.37637214 1 0 0 -0.231439520
#> 136 35 2.37637214 2.46100310 1 0 0 -0.231439520
#> 137 35 2.46100310 4.25553284 1 0 0 -0.231439520
#> 138 35 4.25553284 7.63551503 1 0 0 -0.231439520
#> 139 35 7.63551503 9.49738975 1 0 0 -0.231439520
#> 140 35 9.49738975 9.89725753 1 0 0 -0.231439520
#> 141 35 9.89725753 12.91355879 0 1 0 -0.231439520
#> 142 36 0.00000000 0.34421769 1 0 0 -0.955575628
#> 143 36 0.34421769 0.52706635 1 0 0 -0.955575628
#> 144 36 0.52706635 1.68677164 1 0 0 -0.955575628
#> 145 36 1.68677164 2.24275156 1 0 0 -0.955575628
#> 146 36 2.24275156 7.11223899 0 0 0 -0.955575628
#> 147 37 0.00000000 0.65590477 1 0 1 0.184908022
#> 148 37 0.65590477 2.81058410 1 0 1 0.184908022
#> 149 37 2.81058410 9.74247339 0 1 1 0.184908022
#> 150 38 0.00000000 6.15402891 1 0 1 -0.231144029
#> 151 38 6.15402891 60.00000000 0 0 1 -0.231144029
#> 152 39 0.00000000 0.02654707 0 1 1 0.160977946
#> 153 40 0.00000000 0.07855291 1 0 0 -0.142000695
#> 154 40 0.07855291 0.29034769 1 0 0 -0.142000695
#> 155 40 0.29034769 1.26327474 1 0 0 -0.142000695
#> 156 40 1.26327474 2.27996544 1 0 0 -0.142000695
#> 157 40 2.27996544 2.65567126 1 0 0 -0.142000695
#> 158 40 2.65567126 7.18636429 1 0 0 -0.142000695
#> 159 40 7.18636429 11.14522228 1 0 0 -0.142000695
#> 160 40 11.14522228 21.42065920 1 0 0 -0.142000695
#> 161 40 21.42065920 23.85875892 1 0 0 -0.142000695
#> 162 40 23.85875892 42.40323869 1 0 0 -0.142000695
#> 163 40 42.40323869 60.00000000 0 0 0 -0.142000695
#> 164 41 0.00000000 0.95032158 1 0 1 0.545928222
#> 165 41 0.95032158 1.53798878 1 0 1 0.545928222
#> 166 41 1.53798878 4.93164904 0 1 1 0.545928222
#> 167 42 0.00000000 0.71398107 1 0 0 0.080108181
#> 168 42 0.71398107 0.72424859 0 1 0 0.080108181
#> 169 43 0.00000000 6.28047434 0 0 0 1.354084142
#> 170 44 0.00000000 0.16585079 0 0 0 0.143144965
#> 171 45 0.00000000 1.05565463 1 0 0 -0.016255125
#> 172 45 1.05565463 2.10469672 1 0 0 -0.016255125
#> 173 45 2.10469672 6.49277294 1 0 0 -0.016255125
#> 174 45 6.49277294 6.57651593 0 0 0 -0.016255125
#> 175 46 0.00000000 0.73564547 1 0 0 -0.494839010
#> 176 46 0.73564547 1.31027832 1 0 0 -0.494839010
#> 177 46 1.31027832 2.32866788 1 0 0 -0.494839010
#> 178 46 2.32866788 5.86168764 1 0 0 -0.494839010
#> 179 46 5.86168764 6.83580771 1 0 0 -0.494839010
#> 180 46 6.83580771 7.08830167 1 0 0 -0.494839010
#> 181 46 7.08830167 11.79661639 1 0 0 -0.494839010
#> 182 46 11.79661639 13.44688553 1 0 0 -0.494839010
#> 183 46 13.44688553 15.58755959 1 0 0 -0.494839010
#> 184 46 15.58755959 16.97441871 1 0 0 -0.494839010
#> 185 46 16.97441871 21.90748581 1 0 0 -0.494839010
#> 186 46 21.90748581 60.00000000 0 0 0 -0.494839010
#> 187 47 0.00000000 6.15409598 0 1 1 0.105904964
#> 188 48 0.00000000 4.57039521 1 0 1 -0.486008767
#> 189 48 4.57039521 9.78986723 1 0 1 -0.486008767
#> 190 48 9.78986723 28.18814054 1 0 1 -0.486008767
#> 191 48 28.18814054 60.00000000 0 0 1 -0.486008767
#> 192 49 0.00000000 0.61907998 0 1 1 0.274612007
#> 193 50 0.00000000 0.11987149 1 0 0 -0.524510765
#> 194 50 0.11987149 0.83112324 1 0 0 -0.524510765
#> 195 50 0.83112324 1.65675604 1 0 0 -0.524510765
#> 196 50 1.65675604 1.66117712 0 0 0 -0.524510765
#> 197 51 0.00000000 0.12832105 1 0 0 0.224566967
#> 198 51 0.12832105 0.25821327 0 1 0 0.224566967
#> 199 52 0.00000000 0.94766476 1 0 1 -0.192927826
#> 200 52 0.94766476 3.88605892 1 0 1 -0.192927826
#> 201 52 3.88605892 23.27870623 1 0 1 -0.192927826
#> 202 52 23.27870623 26.92918303 1 0 1 -0.192927826
#> 203 52 26.92918303 41.38015492 0 0 1 -0.192927826
#> 204 53 0.00000000 0.35141989 1 0 1 -0.785067761
#> 205 53 0.35141989 1.59501429 1 0 1 -0.785067761
#> 206 53 1.59501429 6.25901255 1 0 1 -0.785067761
#> 207 53 6.25901255 45.91733962 0 0 1 -0.785067761
#> 208 54 0.00000000 0.54384052 1 0 0 0.613471301
#> 209 54 0.54384052 1.03401351 1 0 0 0.613471301
#> 210 54 1.03401351 1.23009416 1 0 0 0.613471301
#> 211 54 1.23009416 2.01223306 1 0 0 0.613471301
#> 212 54 2.01223306 3.24446113 1 0 0 0.613471301
#> 213 54 3.24446113 8.71315010 1 0 0 0.613471301
#> 214 54 8.71315010 16.24555194 1 0 0 0.613471301
#> 215 54 16.24555194 17.00400999 1 0 0 0.613471301
#> 216 54 17.00400999 28.59499664 1 0 0 0.613471301
#> 217 54 28.59499664 45.44767103 1 0 0 0.613471301
#> 218 54 45.44767103 60.00000000 0 0 0 0.613471301
#> 219 55 0.00000000 0.14591559 1 0 1 0.333347198
#> 220 55 0.14591559 0.43850607 1 0 1 0.333347198
#> 221 55 0.43850607 0.81476877 1 0 1 0.333347198
#> 222 55 0.81476877 3.09244733 0 1 1 0.333347198
#> 223 56 0.00000000 0.19336449 1 0 0 -0.575801582
#> 224 56 0.19336449 0.33180288 1 0 0 -0.575801582
#> 225 56 0.33180288 2.30109340 1 0 0 -0.575801582
#> 226 56 2.30109340 2.51210750 1 0 0 -0.575801582
#> 227 56 2.51210750 4.84482959 1 0 0 -0.575801582
#> 228 56 4.84482959 12.95972589 1 0 0 -0.575801582
#> 229 56 12.95972589 18.41915516 1 0 0 -0.575801582
#> 230 56 18.41915516 35.70057106 0 0 0 -0.575801582
#> 231 57 0.00000000 1.15811178 1 0 0 -0.080394242
#> 232 57 1.15811178 2.86500299 0 0 0 -0.080394242
#> 233 58 0.00000000 0.24401303 1 0 1 -0.486456888
#> 234 58 0.24401303 1.35890638 1 0 1 -0.486456888
#> 235 58 1.35890638 3.26246296 0 1 1 -0.486456888
#> 236 59 0.00000000 0.08723446 1 0 0 -0.305230830
#> 237 59 0.08723446 5.30702960 0 0 0 -0.305230830
#> 238 60 0.00000000 0.30145862 1 0 0 0.249638438
#> 239 60 0.30145862 0.39423451 1 0 0 0.249638438
#> 240 60 0.39423451 2.48048620 1 0 0 0.249638438
#> 241 60 2.48048620 4.32144450 1 0 0 0.249638438
#> 242 60 4.32144450 6.06868874 1 0 0 0.249638438
#> 243 60 6.06868874 7.12077742 1 0 0 0.249638438
#> 244 60 7.12077742 11.47633594 0 0 0 0.249638438
#> 245 61 0.00000000 4.65032702 0 0 0 0.439682070
#> 246 62 0.00000000 0.17498146 0 1 1 0.461564620
#> 247 63 0.00000000 0.42106093 1 0 0 0.346566986
#> 248 63 0.42106093 1.57534657 1 0 0 0.346566986
#> 249 63 1.57534657 2.91813256 0 1 0 0.346566986
#> 250 64 0.00000000 0.16921676 0 1 1 -0.069750162
#> 251 65 0.00000000 0.17859176 1 0 0 -1.655339363
#> 252 65 0.17859176 0.27838475 1 0 0 -1.655339363
#> 253 65 0.27838475 0.66610227 1 0 0 -1.655339363
#> 254 65 0.66610227 0.72066250 1 0 0 -1.655339363
#> 255 65 0.72066250 1.47180157 1 0 0 -1.655339363
#> 256 65 1.47180157 2.73261150 1 0 0 -1.655339363
#> 257 65 2.73261150 3.18454415 1 0 0 -1.655339363
#> 258 65 3.18454415 6.51805133 0 1 0 -1.655339363
#> 259 66 0.00000000 6.71670423 0 1 1 0.269232900
#> 260 67 0.00000000 0.22311224 0 1 1 0.446242933
#> 261 68 0.00000000 1.51687570 0 1 1 0.244731018
#> 262 69 0.00000000 0.18673390 1 0 1 -0.598175873
#> 263 69 0.18673390 0.34899649 0 0 1 -0.598175873
#> 264 70 0.00000000 1.15854727 0 1 0 0.231368927
#> 265 71 0.00000000 0.46071326 1 0 0 0.485851788
#> 266 71 0.46071326 1.51947842 1 0 0 0.485851788
#> 267 71 1.51947842 1.56495641 1 0 0 0.485851788
#> 268 71 1.56495641 1.87183690 1 0 0 0.485851788
#> 269 71 1.87183690 39.35334799 0 0 0 0.485851788
#> 270 72 0.00000000 0.02094241 1 0 0 -0.736079482
#> 271 72 0.02094241 0.08672262 1 0 0 -0.736079482
#> 272 72 0.08672262 1.98382511 1 0 0 -0.736079482
#> 273 72 1.98382511 4.24543687 1 0 0 -0.736079482
#> 274 72 4.24543687 5.07665333 1 0 0 -0.736079482
#> 275 72 5.07665333 12.13539233 1 0 0 -0.736079482
#> 276 72 12.13539233 13.34700252 1 0 0 -0.736079482
#> 277 72 13.34700252 13.66708844 1 0 0 -0.736079482
#> 278 72 13.66708844 16.07956783 0 0 0 -0.736079482
#> 279 73 0.00000000 0.90083523 0 1 1 0.264482470
#> 280 74 0.00000000 0.30203451 0 1 0 1.227200176
#> 281 75 0.00000000 0.13850024 1 0 0 -0.824672740
#> 282 75 0.13850024 0.35575232 1 0 0 -0.824672740
#> 283 75 0.35575232 0.78882687 1 0 0 -0.824672740
#> 284 75 0.78882687 0.89604837 1 0 0 -0.824672740
#> 285 75 0.89604837 0.92914305 1 0 0 -0.824672740
#> 286 75 0.92914305 1.15403070 1 0 0 -0.824672740
#> 287 75 1.15403070 1.29915312 1 0 0 -0.824672740
#> 288 75 1.29915312 1.33072868 1 0 0 -0.824672740
#> 289 75 1.33072868 1.70559707 1 0 0 -0.824672740
#> 290 75 1.70559707 1.71682778 1 0 0 -0.824672740
#> 291 75 1.71682778 1.96496754 1 0 0 -0.824672740
#> 292 75 1.96496754 1.98660726 1 0 0 -0.824672740
#> 293 75 1.98660726 2.94479200 1 0 0 -0.824672740
#> 294 75 2.94479200 3.06126113 1 0 0 -0.824672740
#> 295 75 3.06126113 3.37712395 1 0 0 -0.824672740
#> 296 75 3.37712395 3.66929411 1 0 0 -0.824672740
#> 297 75 3.66929411 4.12850098 1 0 0 -0.824672740
#> 298 75 4.12850098 4.22745938 1 0 0 -0.824672740
#> 299 75 4.22745938 4.89096688 0 1 0 -0.824672740
#> 300 76 0.00000000 0.39385840 1 0 1 0.397902578
#> 301 76 0.39385840 6.15053166 0 1 1 0.397902578
#> 302 77 0.00000000 0.09365299 1 0 0 -0.170646583
#> 303 77 0.09365299 1.09119578 1 0 0 -0.170646583
#> 304 77 1.09119578 2.40993384 1 0 0 -0.170646583
#> 305 77 2.40993384 3.51427673 1 0 0 -0.170646583
#> 306 77 3.51427673 4.33947793 1 0 0 -0.170646583
#> 307 77 4.33947793 6.60910482 1 0 0 -0.170646583
#> 308 77 6.60910482 7.71178029 1 0 0 -0.170646583
#> 309 77 7.71178029 9.35732662 1 0 0 -0.170646583
#> 310 77 9.35732662 9.60146405 1 0 0 -0.170646583
#> 311 77 9.60146405 20.19636516 1 0 0 -0.170646583
#> 312 77 20.19636516 23.58836390 1 0 0 -0.170646583
#> 313 77 23.58836390 30.67249041 1 0 0 -0.170646583
#> 314 77 30.67249041 32.63159612 1 0 0 -0.170646583
#> 315 77 32.63159612 44.32515460 1 0 0 -0.170646583
#> 316 77 44.32515460 52.73087987 1 0 0 -0.170646583
#> 317 77 52.73087987 53.05953510 1 0 0 -0.170646583
#> 318 77 53.05953510 60.00000000 0 0 0 -0.170646583
#> 319 78 0.00000000 0.07858750 1 0 0 -0.702626900
#> 320 78 0.07858750 0.40095783 1 0 0 -0.702626900
#> 321 78 0.40095783 0.64362627 1 0 0 -0.702626900
#> 322 78 0.64362627 1.05161616 1 0 0 -0.702626900
#> 323 78 1.05161616 1.09811038 1 0 0 -0.702626900
#> 324 78 1.09811038 1.50948731 0 0 0 -0.702626900
#> 325 79 0.00000000 0.31669278 1 0 1 -0.461480408
#> 326 79 0.31669278 0.57557313 1 0 1 -0.461480408
#> 327 79 0.57557313 0.68087304 1 0 1 -0.461480408
#> 328 79 0.68087304 0.99911935 1 0 1 -0.461480408
#> 329 79 0.99911935 12.78250323 0 1 1 -0.461480408
#> 330 80 0.00000000 0.46109438 1 0 0 0.004949065
#> 331 80 0.46109438 3.25756385 1 0 0 0.004949065
#> 332 80 3.25756385 7.35074220 1 0 0 0.004949065
#> 333 80 7.35074220 9.39342785 1 0 0 0.004949065
#> 334 80 9.39342785 14.42394606 1 0 0 0.004949065
#> 335 80 14.42394606 17.42522135 1 0 0 0.004949065
#> 336 80 17.42522135 22.08724074 1 0 0 0.004949065
#> 337 80 22.08724074 34.78937953 1 0 0 0.004949065
#> 338 80 34.78937953 36.44221633 1 0 0 0.004949065
#> 339 80 36.44221633 55.75291106 1 0 0 0.004949065
#> 340 80 55.75291106 60.00000000 0 0 0 0.004949065
#> 341 81 0.00000000 9.02577005 1 0 1 -0.204429887
#> 342 81 9.02577005 13.21497289 0 1 1 -0.204429887
#> 343 82 0.00000000 0.18149717 1 0 1 -0.694122644
#> 344 82 0.18149717 0.57995248 1 0 1 -0.694122644
#> 345 82 0.57995248 0.73895334 0 1 1 -0.694122644
#> 346 83 0.00000000 0.04422852 0 1 1 -0.132297619
#> 347 84 0.00000000 0.04871240 1 0 0 -0.473649139
#> 348 84 0.04871240 0.06495945 1 0 0 -0.473649139
#> 349 84 0.06495945 0.17149636 1 0 0 -0.473649139
#> 350 84 0.17149636 0.78337725 1 0 0 -0.473649139
#> 351 84 0.78337725 1.32719705 1 0 0 -0.473649139
#> 352 84 1.32719705 2.91829623 1 0 0 -0.473649139
#> 353 84 2.91829623 4.36579096 1 0 0 -0.473649139
#> 354 84 4.36579096 4.48391501 1 0 0 -0.473649139
#> 355 84 4.48391501 5.44933433 1 0 0 -0.473649139
#> 356 84 5.44933433 5.71707436 1 0 0 -0.473649139
#> 357 84 5.71707436 12.18437166 1 0 0 -0.473649139
#> 358 84 12.18437166 14.59368263 1 0 0 -0.473649139
#> 359 84 14.59368263 15.64552977 1 0 0 -0.473649139
#> 360 84 15.64552977 22.47543056 1 0 0 -0.473649139
#> 361 84 22.47543056 27.64150557 1 0 0 -0.473649139
#> 362 84 27.64150557 40.82102725 1 0 0 -0.473649139
#> 363 84 40.82102725 45.45347103 1 0 0 -0.473649139
#> 364 84 45.45347103 46.63442545 1 0 0 -0.473649139
#> 365 84 46.63442545 60.00000000 0 0 0 -0.473649139
#> 366 85 0.00000000 0.48047661 1 0 0 0.369760664
#> 367 85 0.48047661 1.19914847 1 0 0 0.369760664
#> 368 85 1.19914847 3.97802258 1 0 0 0.369760664
#> 369 85 3.97802258 10.11107753 1 0 0 0.369760664
#> 370 85 10.11107753 12.45774093 1 0 0 0.369760664
#> 371 85 12.45774093 15.99120428 0 1 0 0.369760664
#> 372 86 0.00000000 0.16771877 1 0 0 0.448389354
#> 373 86 0.16771877 8.94393114 1 0 0 0.448389354
#> 374 86 8.94393114 15.50336528 1 0 0 0.448389354
#> 375 86 15.50336528 15.51861450 1 0 0 0.448389354
#> 376 86 15.51861450 27.12591882 1 0 0 0.448389354
#> 377 86 27.12591882 31.21858855 1 0 0 0.448389354
#> 378 86 31.21858855 33.41878360 0 0 0 0.448389354
#> 379 87 0.00000000 2.86679606 1 0 0 -0.173000444
#> 380 87 2.86679606 9.83961336 1 0 0 -0.173000444
#> 381 87 9.83961336 23.60365448 0 0 0 -0.173000444
#> 382 88 0.00000000 4.45045302 1 0 1 -0.891028534
#> 383 88 4.45045302 22.89950570 0 0 1 -0.891028534
#> 384 89 0.00000000 0.40282541 0 1 0 0.232470877
#> 385 90 0.00000000 0.12338417 1 0 0 -0.975515305
#> 386 90 0.12338417 0.54509689 1 0 0 -0.975515305
#> 387 90 0.54509689 0.99259467 1 0 0 -0.975515305
#> 388 90 0.99259467 1.03162337 1 0 0 -0.975515305
#> 389 90 1.03162337 1.37625495 1 0 0 -0.975515305
#> 390 90 1.37625495 1.39620311 1 0 0 -0.975515305
#> 391 90 1.39620311 1.49651550 1 0 0 -0.975515305
#> 392 90 1.49651550 1.94472561 1 0 0 -0.975515305
#> 393 90 1.94472561 7.33259398 1 0 0 -0.975515305
#> 394 90 7.33259398 8.51453793 1 0 0 -0.975515305
#> 395 90 8.51453793 11.06627566 1 0 0 -0.975515305
#> 396 90 11.06627566 13.10017134 1 0 0 -0.975515305
#> 397 90 13.10017134 13.59857468 1 0 0 -0.975515305
#> 398 90 13.59857468 14.79794355 1 0 0 -0.975515305
#> 399 90 14.79794355 23.58773471 1 0 0 -0.975515305
#> 400 90 23.58773471 24.64989354 1 0 0 -0.975515305
#> 401 90 24.64989354 31.82882907 1 0 0 -0.975515305
#> 402 90 31.82882907 44.17050896 1 0 0 -0.975515305
#> 403 90 44.17050896 59.93686882 0 0 0 -0.975515305
#> 404 91 0.00000000 0.51218749 1 0 0 -0.258056670
#> 405 91 0.51218749 1.42096228 1 0 0 -0.258056670
#> 406 91 1.42096228 3.65033169 1 0 0 -0.258056670
#> 407 91 3.65033169 4.34800730 1 0 0 -0.258056670
#> 408 91 4.34800730 23.39744948 1 0 0 -0.258056670
#> 409 91 23.39744948 27.55704919 1 0 0 -0.258056670
#> 410 91 27.55704919 55.68663066 0 0 0 -0.258056670
#> 411 92 0.00000000 2.01208192 0 1 0 0.244540159
#> 412 93 0.00000000 0.43448769 0 1 1 0.451012363
#> 413 94 0.00000000 13.01693201 0 1 1 0.320181497
#> 414 95 0.00000000 0.37479471 1 0 0 0.475604439
#> 415 95 0.37479471 1.48531088 1 0 0 0.475604439
#> 416 95 1.48531088 1.64303900 1 0 0 0.475604439
#> 417 95 1.64303900 2.24502438 1 0 0 0.475604439
#> 418 95 2.24502438 4.17605499 1 0 0 0.475604439
#> 419 95 4.17605499 37.84312660 1 0 0 0.475604439
#> 420 95 37.84312660 60.00000000 0 0 0 0.475604439
#> 421 96 0.00000000 0.12223435 0 1 1 -0.299561605
#> 422 97 0.00000000 0.09063569 1 0 0 -0.665347496
#> 423 97 0.09063569 0.32890187 1 0 0 -0.665347496
#> 424 97 0.32890187 0.78996199 1 0 0 -0.665347496
#> 425 97 0.78996199 0.88446804 1 0 0 -0.665347496
#> 426 97 0.88446804 1.69266784 1 0 0 -0.665347496
#> 427 97 1.69266784 3.48190466 1 0 0 -0.665347496
#> 428 97 3.48190466 3.50208921 1 0 0 -0.665347496
#> 429 97 3.50208921 4.16088755 1 0 0 -0.665347496
#> 430 97 4.16088755 5.74684092 1 0 0 -0.665347496
#> 431 97 5.74684092 16.75506562 1 0 0 -0.665347496
#> 432 97 16.75506562 18.95771882 1 0 0 -0.665347496
#> 433 97 18.95771882 46.43449909 1 0 0 -0.665347496
#> 434 97 46.43449909 55.70267324 1 0 0 -0.665347496
#> 435 97 55.70267324 60.00000000 0 0 0 -0.665347496
#> 436 98 0.00000000 0.09775081 1 0 0 -0.296104873
#> 437 98 0.09775081 0.71956989 1 0 0 -0.296104873
#> 438 98 0.71956989 1.40108895 1 0 0 -0.296104873
#> 439 98 1.40108895 1.78064510 1 0 0 -0.296104873
#> 440 98 1.78064510 2.98046872 1 0 0 -0.296104873
#> 441 98 2.98046872 4.18897652 0 1 0 -0.296104873
#> 442 99 0.00000000 0.37126084 0 1 0 0.900525428
#> 443 100 0.00000000 0.30475566 0 1 1 0.527669296