simmulti.msm: Simulate multiple trajectories from a multi-state Markov...
In msm: Multi-State Markov and Hidden Markov Models in Continuous Time
Description
Usage
Arguments
Details
Value
Author(s)
See Also
Examples
Description
Simulate a number of individual realisations from a
continuous-time Markov process. Observations of the process are made at
specified arbitrary times for each individual, giving panel-observed data.
Usage
1
2
3
Arguments
data
A data frame with a mandatory column named time,
representing observation times. The optional column named subject,
corresponds to subject identification numbers. If not given, all
observations are assumed to be on the same individual. Observation
times should be sorted within individuals. The optional column
named cens indicates the times at which simulated states
should be censored. If cens==0 then the state is not
censored, and if cens==k, say, then all simulated states at that
time which are in the set censor.states are replaced by
k.
Other named columns of the data frame represent any covariates,
which may be time-constant or time-dependent. Time-dependent
covariates are assumed to be constant between the observation
times.
qmatrix
The transition intensity matrix of the
Markov process, with any covariates set to zero. The diagonal of
qmatrix is ignored,
and computed as appropriate so that the rows sum to zero. For
example, a possible qmatrix for a three state illness-death
model with recovery is:
rbind(
c( 0, 0.1, 0.02 ),
c( 0.1, 0, 0.01 ),
c( 0, 0, 0 )
)
covariates
List of linear covariate effects on log transition
intensities. Each element is a vector of the effects of one
covariate on all the transition intensities. The intensities are ordered
by reading across rows of the intensity matrix, starting with the
first, counting the positive off-diagonal elements of the matrix.
For example, for a multi-state model with three transition
intensities, and two covariates x and y on each
intensity,
covariates=list(x = c(-0.3,-0.3,-0.3), y=c(0.1, 0.1, 0.1))
death
Vector of indices of the death states. A death state is
an absorbing state whose time of entry is known exactly, but the
individual is assumed to be in an unknown transient state ("alive")
at the previous instant. This is the usual situation for times of death in
chronic disease monitoring data. For example, if you specify
death = c(4, 5) then states 4 and 5 are assumed to be death
states.
death = TRUE indicates that the
final state is a death state, and death = FALSE (the default)
indicates that there is no death state.
start
A vector with the same number of elements as there are
distinct subjects in the data, giving the states in which each
corresponding individual begins. Or a single number, if all of these
are the same. Defaults to state 1 for each subject.
ematrix
An optional misclassification matrix for generating observed states
conditionally on the simulated true states. As defined in
msm.
misccovariates
Covariate effects on misclassification
probabilities via multinomial logistic regression. Linear effects
operate on the log of each probability relative to the probability of
classification in the correct state. In same format as
covariates.
hmodel
An optional hidden Markov model for generating observed
outcomes conditionally on the simulated true states. As defined in
msm.
hcovariates
List of the same length as hmodel, defining any covariates
governing the hidden Markov outcome models. Unlike in the
msm function, this should also define the values of the
covariate effects. Each element of the list is a named vector of the
initial values for each set of covariates for that state. For
example, for a three-state hidden Markov model with two, one and no
covariates on the state 1, 2 and 3 outcome models respectively,
hcovariates = list (c(acute=-8, age=0), c(acute=-8), NULL)
censor.states
Set of simulated states which should be replaced by a
censoring indicator at censoring times. By default this is all
transient states (representing alive, with unknown state).
drop.absorb
Drop repeated observations in the absorbing state,
retaining only one.
Details
sim.msm is called repeatedly to produce a simulated
trajectory for each individual. The state at each specified
observation time is then taken to produce a new column state.
The effect of time-dependent covariates on the transition intensity
matrix for an individual is determined by assuming that the covariate is a step function
which remains constant in between the individual's observation times.
If the subject enters an absorbing state, then only the first
observation in that state is kept in the data frame. Rows corresponding to future
observations are deleted. The entry times into states given in
death are assumed to be known exactly.
Value
A data frame with columns,
subject
Subject identification indicators
time
Observation times
state
Simulated (true) state at the corresponding time
obs
Observed outcome at the corresponding time, if
ematrix or hmodel was supplied
keep
Row numbers of the original data. Useful when
drop.absorb=TRUE, to show which rows were not dropped
plus any supplied covariates.
Author(s)
C. H. Jackson chris.jackson@mrc-bsu.cam.ac.uk
See Also
Examples
1
2
3
4
5
6
Example output
subject time state keep
1 1 0 1 1
2 1 2 2 2
3 1 4 3 3
4 1 6 2 4
5 1 8 2 5
6 1 10 1 6
7 1 12 1 7
8 1 14 3 8
9 1 16 3 9
10 1 18 3 10
11 1 20 2 11
12 1 22 3 12
13 1 24 2 13
14 2 0 1 14
15 2 2 3 15
16 2 4 3 16
17 2 6 3 17
18 2 8 3 18
19 2 10 3 19
20 2 12 3 20
21 2 14 3 21
22 2 16 3 22
23 2 18 3 23
24 2 20 3 24
25 2 22 3 25
26 2 24 3 26
27 3 0 1 27
28 3 2 1 28
29 3 4 1 29
30 3 6 1 30
31 3 8 2 31
32 3 10 3 32
33 3 12 2 33
34 3 14 2 34
35 3 16 1 35
36 3 18 1 36
37 3 20 1 37
38 3 22 1 38
39 3 24 1 39
40 4 0 1 40
41 4 2 1 41
42 4 4 1 42
43 4 6 1 43
44 4 8 1 44
45 4 10 1 45
46 4 12 3 46
47 4 14 3 47
48 4 16 1 48
49 4 18 3 49
50 4 20 3 50
51 4 22 3 51
52 4 24 3 52
53 5 0 1 53
54 5 2 1 54
55 5 4 1 55
56 5 6 1 56
57 5 8 1 57
58 5 10 1 58
59 5 12 1 59
60 5 14 1 60
61 5 16 2 61
62 5 18 2 62
63 5 20 2 63
64 5 22 3 64
65 5 24 3 65
66 6 0 1 66
67 6 2 1 67
68 6 4 1 68
69 6 6 1 69
70 6 8 1 70
71 6 10 1 71
72 6 12 1 72
73 6 14 1 73
74 6 16 1 74
75 6 18 1 75
76 6 20 2 76
77 6 22 2 77
78 6 24 2 78
79 7 0 1 79
80 7 2 1 80
81 7 4 1 81
82 7 6 1 82
83 7 8 1 83
84 7 10 1 84
85 7 12 3 85
86 7 14 3 86
87 7 16 3 87
88 7 18 3 88
89 7 20 3 89
90 7 22 3 90
91 7 24 2 91
92 8 0 1 92
93 8 2 1 93
94 8 4 1 94
95 8 6 1 95
96 8 8 1 96
97 8 10 1 97
98 8 12 1 98
99 8 14 1 99
100 8 16 1 100
101 8 18 1 101
102 8 20 1 102
103 8 22 1 103
104 8 24 1 104
105 9 0 1 105
106 9 2 1 106
107 9 4 1 107
108 9 6 1 108
109 9 8 1 109
110 9 10 1 110
111 9 12 2 111
112 9 14 2 112
113 9 16 2 113
114 9 18 1 114
115 9 20 1 115
116 9 22 1 116
117 9 24 1 117
118 10 0 1 118
119 10 2 1 119
120 10 4 2 120
121 10 6 2 121
122 10 8 2 122
123 10 10 2 123
124 10 12 2 124
125 10 14 2 125
126 10 16 2 126
127 10 18 2 127
128 10 20 2 128
129 10 22 2 129
130 10 24 2 130
131 11 0 1 131
132 11 2 1 132
133 11 4 1 133
134 11 6 1 134
135 11 8 1 135
136 11 10 1 136
137 11 12 1 137
138 11 14 1 138
139 11 16 1 139
140 11 18 1 140
141 11 20 1 141
142 11 22 1 142
143 11 24 1 143
144 12 0 1 144
145 12 2 1 145
146 12 4 1 146
147 12 6 1 147
148 12 8 1 148
149 12 10 2 149
150 12 12 2 150
151 12 14 2 151
152 12 16 2 152
153 12 18 2 153
154 12 20 2 154
155 12 22 2 155
156 12 24 2 156
157 13 0 1 157
158 13 2 1 158
159 13 4 2 159
160 13 6 2 160
161 13 8 2 161
162 13 10 2 162
163 13 12 3 163
164 13 14 3 164
165 13 16 3 165
166 13 18 3 166
167 13 20 3 167
168 13 22 3 168
169 13 24 3 169
170 14 0 1 170
171 14 2 1 171
172 14 4 2 172
173 14 6 2 173
174 14 8 1 174
175 14 10 3 175
176 14 12 3 176
177 14 14 3 177
178 14 16 3 178
179 14 18 3 179
180 14 20 3 180
181 14 22 3 181
182 14 24 3 182
183 15 0 1 183
184 15 2 1 184
185 15 4 2 185
186 15 6 3 186
187 15 8 3 187
188 15 10 3 188
189 15 12 3 189
190 15 14 3 190
191 15 16 3 191
192 15 18 3 192
193 15 20 3 193
194 15 22 3 194
195 15 24 3 195
196 16 0 1 196
197 16 2 1 197
198 16 4 1 198
199 16 6 1 199
200 16 8 2 200
201 16 10 2 201
202 16 12 2 202
203 16 14 3 203
204 16 16 3 204
205 16 18 2 205
206 16 20 2 206
207 16 22 2 207
208 16 24 2 208
209 17 0 1 209
210 17 2 1 210
211 17 4 2 211
212 17 6 2 212
213 17 8 2 213
214 17 10 1 214
215 17 12 1 215
216 17 14 1 216
217 17 16 1 217
218 17 18 3 218
219 17 20 3 219
220 17 22 3 220
221 17 24 3 221
222 18 0 1 222
223 18 2 1 223
224 18 4 1 224
225 18 6 1 225
226 18 8 1 226
227 18 10 1 227
228 18 12 1 228
229 18 14 1 229
230 18 16 1 230
231 18 18 2 231
232 18 20 2 232
233 18 22 2 233
234 18 24 2 234
235 19 0 1 235
236 19 2 2 236
237 19 4 2 237
238 19 6 2 238
239 19 8 2 239
240 19 10 2 240
241 19 12 2 241
242 19 14 2 242
243 19 16 2 243
244 19 18 3 244
245 19 20 3 245
246 19 22 2 246
247 19 24 3 247
248 20 0 1 248
249 20 2 2 249
250 20 4 2 250
251 20 6 2 251
252 20 8 2 252
253 20 10 2 253
254 20 12 2 254
255 20 14 3 255
256 20 16 3 256
257 20 18 3 257
258 20 20 2 258
259 20 22 3 259
260 20 24 3 260
261 21 0 1 261
262 21 2 1 262
263 21 4 1 263
264 21 6 1 264
265 21 8 1 265
266 21 10 1 266
267 21 12 1 267
268 21 14 2 268
269 21 16 3 269
270 21 18 3 270
271 21 20 1 271
272 21 22 2 272
273 21 24 3 273
274 22 0 1 274
275 22 2 2 275
276 22 4 2 276
277 22 6 3 277
278 22 8 3 278
279 22 10 3 279
280 22 12 3 280
281 22 14 3 281
282 22 16 3 282
283 22 18 3 283
284 22 20 3 284
285 22 22 3 285
286 22 24 3 286
287 23 0 1 287
288 23 2 1 288
289 23 4 1 289
290 23 6 1 290
291 23 8 2 291
292 23 10 1 292
293 23 12 1 293
294 23 14 1 294
295 23 16 1 295
296 23 18 1 296
297 23 20 1 297
298 23 22 3 298
299 23 24 3 299
300 24 0 1 300
301 24 2 2 301
302 24 4 2 302
303 24 6 3 303
304 24 8 3 304
305 24 10 3 305
306 24 12 3 306
307 24 14 3 307
308 24 16 3 308
309 24 18 2 309
310 24 20 2 310
311 24 22 2 311
312 24 24 2 312
313 25 0 1 313
314 25 2 2 314
315 25 4 2 315
316 25 6 2 316
317 25 8 2 317
318 25 10 2 318
319 25 12 2 319
320 25 14 2 320
321 25 16 2 321
322 25 18 2 322
323 25 20 2 323
324 25 22 2 324
325 25 24 1 325
326 26 0 1 326
327 26 2 1 327
328 26 4 2 328
329 26 6 2 329
330 26 8 2 330
331 26 10 2 331
332 26 12 2 332
333 26 14 2 333
334 26 16 2 334
335 26 18 3 335
336 26 20 2 336
337 26 22 2 337
338 26 24 2 338
339 27 0 1 339
340 27 2 1 340
341 27 4 1 341
342 27 6 1 342
343 27 8 1 343
344 27 10 1 344
345 27 12 1 345
346 27 14 1 346
347 27 16 1 347
348 27 18 1 348
349 27 20 1 349
350 27 22 1 350
351 27 24 1 351
352 28 0 1 352
353 28 2 1 353
354 28 4 1 354
355 28 6 1 355
356 28 8 1 356
357 28 10 2 357
358 28 12 3 358
359 28 14 3 359
360 28 16 3 360
361 28 18 3 361
362 28 20 3 362
363 28 22 2 363
364 28 24 2 364
365 29 0 1 365
366 29 2 1 366
367 29 4 1 367
368 29 6 1 368
369 29 8 1 369
370 29 10 1 370
371 29 12 1 371
372 29 14 1 372
373 29 16 1 373
374 29 18 1 374
375 29 20 1 375
376 29 22 1 376
377 29 24 2 377
378 30 0 1 378
379 30 2 1 379
380 30 4 1 380
381 30 6 1 381
382 30 8 2 382
383 30 10 3 383
384 30 12 3 384
385 30 14 2 385
386 30 16 2 386
387 30 18 2 387
388 30 20 2 388
389 30 22 3 389
390 30 24 3 390
391 31 0 1 391
392 31 2 1 392
393 31 4 1 393
394 31 6 1 394
395 31 8 1 395
396 31 10 1 396
397 31 12 3 397
398 31 14 3 398
399 31 16 2 399
400 31 18 2 400
401 31 20 2 401
402 31 22 2 402
403 31 24 2 403
404 32 0 1 404
405 32 2 2 405
406 32 4 2 406
407 32 6 2 407
408 32 8 2 408
409 32 10 3 409
410 32 12 3 410
411 32 14 3 411
412 32 16 3 412
413 32 18 3 413
414 32 20 3 414
415 32 22 3 415
416 32 24 3 416
417 33 0 1 417
418 33 2 1 418
419 33 4 1 419
420 33 6 1 420
421 33 8 1 421
422 33 10 1 422
423 33 12 1 423
424 33 14 1 424
425 33 16 1 425
426 33 18 1 426
427 33 20 1 427
428 33 22 1 428
429 33 24 1 429
430 34 0 1 430
431 34 2 1 431
432 34 4 1 432
433 34 6 1 433
434 34 8 1 434
435 34 10 2 435
436 34 12 3 436
437 34 14 3 437
438 34 16 3 438
439 34 18 1 439
440 34 20 1 440
441 34 22 2 441
442 34 24 2 442
443 35 0 1 443
444 35 2 1 444
445 35 4 1 445
446 35 6 1 446
447 35 8 1 447
448 35 10 1 448
449 35 12 1 449
450 35 14 1 450
451 35 16 1 451
452 35 18 1 452
453 35 20 1 453
454 35 22 3 454
455 35 24 3 455
456 36 0 1 456
457 36 2 1 457
458 36 4 1 458
459 36 6 1 459
460 36 8 1 460
461 36 10 1 461
462 36 12 1 462
463 36 14 2 463
464 36 16 2 464
465 36 18 2 465
466 36 20 2 466
467 36 22 2 467
468 36 24 2 468
469 37 0 1 469
470 37 2 1 470
471 37 4 1 471
472 37 6 1 472
473 37 8 1 473
474 37 10 1 474
475 37 12 1 475
476 37 14 1 476
477 37 16 1 477
478 37 18 1 478
479 37 20 1 479
480 37 22 1 480
481 37 24 2 481
482 38 0 1 482
483 38 2 1 483
484 38 4 2 484
485 38 6 3 485
486 38 8 3 486
487 38 10 3 487
488 38 12 3 488
489 38 14 3 489
490 38 16 3 490
491 38 18 3 491
492 38 20 3 492
493 38 22 3 493
494 38 24 3 494
495 39 0 1 495
496 39 2 1 496
497 39 4 1 497
498 39 6 1 498
499 39 8 2 499
500 39 10 2 500
501 39 12 1 501
502 39 14 2 502
503 39 16 2 503
504 39 18 3 504
505 39 20 3 505
506 39 22 2 506
507 39 24 2 507
508 40 0 1 508
509 40 2 1 509
510 40 4 2 510
511 40 6 2 511
512 40 8 2 512
513 40 10 3 513
514 40 12 3 514
515 40 14 3 515
516 40 16 2 516
517 40 18 2 517
518 40 20 2 518
519 40 22 2 519
520 40 24 2 520
521 41 0 1 521
522 41 2 2 522
523 41 4 3 523
524 41 6 3 524
525 41 8 3 525
526 41 10 3 526
527 41 12 3 527
528 41 14 3 528
529 41 16 3 529
530 41 18 3 530
531 41 20 3 531
532 41 22 3 532
533 41 24 3 533
534 42 0 1 534
535 42 2 1 535
536 42 4 1 536
537 42 6 1 537
538 42 8 1 538
539 42 10 2 539
540 42 12 2 540
541 42 14 2 541
542 42 16 2 542
543 42 18 2 543
544 42 20 1 544
545 42 22 2 545
546 42 24 2 546
547 43 0 1 547
548 43 2 1 548
549 43 4 1 549
550 43 6 1 550
551 43 8 1 551
552 43 10 1 552
553 43 12 1 553
554 43 14 1 554
555 43 16 1 555
556 43 18 2 556
557 43 20 2 557
558 43 22 3 558
559 43 24 3 559
560 44 0 1 560
561 44 2 1 561
562 44 4 1 562
563 44 6 1 563
564 44 8 1 564
565 44 10 2 565
566 44 12 3 566
567 44 14 3 567
568 44 16 3 568
569 44 18 2 569
570 44 20 2 570
571 44 22 3 571
572 44 24 3 572
573 45 0 1 573
574 45 2 1 574
575 45 4 1 575
576 45 6 2 576
577 45 8 2 577
578 45 10 2 578
579 45 12 2 579
580 45 14 3 580
581 45 16 2 581
582 45 18 2 582
583 45 20 2 583
584 45 22 2 584
585 45 24 2 585
586 46 0 1 586
587 46 2 2 587
588 46 4 2 588
589 46 6 2 589
590 46 8 3 590
591 46 10 3 591
592 46 12 3 592
593 46 14 2 593
594 46 16 2 594
595 46 18 2 595
596 46 20 2 596
597 46 22 3 597
598 46 24 3 598
599 47 0 1 599
600 47 2 1 600
601 47 4 1 601
602 47 6 1 602
603 47 8 1 603
604 47 10 1 604
605 47 12 2 605
606 47 14 2 606
607 47 16 1 607
608 47 18 2 608
609 47 20 2 609
610 47 22 2 610
611 47 24 3 611
612 48 0 1 612
613 48 2 2 613
614 48 4 2 614
615 48 6 2 615
616 48 8 2 616
617 48 10 2 617
618 48 12 1 618
619 48 14 1 619
620 48 16 1 620
621 48 18 2 621
622 48 20 2 622
623 48 22 2 623
624 48 24 3 624
625 49 0 1 625
626 49 2 2 626
627 49 4 3 627
628 49 6 3 628
629 49 8 3 629
630 49 10 3 630
631 49 12 3 631
632 49 14 3 632
633 49 16 1 633
634 49 18 1 634
635 49 20 1 635
636 49 22 1 636
637 49 24 1 637
638 50 0 1 638
639 50 2 1 639
640 50 4 1 640
641 50 6 1 641
642 50 8 1 642
643 50 10 1 643
644 50 12 1 644
645 50 14 1 645
646 50 16 1 646
647 50 18 1 647
648 50 20 1 648
649 50 22 1 649
650 50 24 1 650
651 51 0 1 651
652 51 2 1 652
653 51 4 1 653
654 51 6 1 654
655 51 8 1 655
656 51 10 1 656
657 51 12 2 657
658 51 14 2 658
659 51 16 2 659
660 51 18 2 660
661 51 20 2 661
662 51 22 2 662
663 51 24 2 663
664 52 0 1 664
665 52 2 1 665
666 52 4 1 666
667 52 6 2 667
668 52 8 2 668
669 52 10 3 669
670 52 12 2 670
671 52 14 2 671
672 52 16 1 672
673 52 18 1 673
674 52 20 1 674
675 52 22 1 675
676 52 24 1 676
677 53 0 1 677
678 53 2 1 678
679 53 4 2 679
680 53 6 2 680
681 53 8 2 681
682 53 10 1 682
683 53 12 1 683
684 53 14 1 684
685 53 16 1 685
686 53 18 1 686
687 53 20 2 687
688 53 22 2 688
689 53 24 1 689
690 54 0 1 690
691 54 2 1 691
692 54 4 1 692
693 54 6 1 693
694 54 8 1 694
695 54 10 1 695
696 54 12 1 696
697 54 14 1 697
698 54 16 1 698
699 54 18 1 699
700 54 20 1 700
701 54 22 2 701
702 54 24 2 702
703 55 0 1 703
704 55 2 2 704
705 55 4 2 705
706 55 6 2 706
707 55 8 2 707
708 55 10 2 708
709 55 12 3 709
710 55 14 3 710
711 55 16 3 711
712 55 18 3 712
713 55 20 3 713
714 55 22 2 714
715 55 24 2 715
716 56 0 1 716
717 56 2 2 717
718 56 4 1 718
719 56 6 2 719
720 56 8 3 720
721 56 10 3 721
722 56 12 3 722
723 56 14 3 723
724 56 16 3 724
725 56 18 3 725
726 56 20 3 726
727 56 22 3 727
728 56 24 3 728
729 57 0 1 729
730 57 2 2 730
731 57 4 2 731
732 57 6 3 732
733 57 8 3 733
734 57 10 3 734
735 57 12 2 735
736 57 14 3 736
737 57 16 3 737
738 57 18 3 738
739 57 20 3 739
740 57 22 3 740
741 57 24 3 741
742 58 0 1 742
743 58 2 1 743
744 58 4 1 744
745 58 6 1 745
746 58 8 1 746
747 58 10 1 747
748 58 12 1 748
749 58 14 2 749
750 58 16 2 750
751 58 18 2 751
752 58 20 2 752
753 58 22 2 753
754 58 24 2 754
755 59 0 1 755
756 59 2 1 756
757 59 4 1 757
758 59 6 1 758
759 59 8 1 759
760 59 10 1 760
761 59 12 1 761
762 59 14 1 762
763 59 16 1 763
764 59 18 3 764
765 59 20 3 765
766 59 22 3 766
767 59 24 3 767
768 60 0 1 768
769 60 2 1 769
770 60 4 1 770
771 60 6 1 771
772 60 8 1 772
773 60 10 1 773
774 60 12 1 774
775 60 14 1 775
776 60 16 1 776
777 60 18 1 777
778 60 20 1 778
779 60 22 1 779
780 60 24 1 780
781 61 0 1 781
782 61 2 1 782
783 61 4 3 783
784 61 6 2 784
785 61 8 2 785
786 61 10 2 786
787 61 12 2 787
788 61 14 2 788
789 61 16 2 789
790 61 18 1 790
791 61 20 1 791
792 61 22 1 792
793 61 24 1 793
794 62 0 1 794
795 62 2 3 795
796 62 4 3 796
797 62 6 3 797
798 62 8 3 798
799 62 10 3 799
800 62 12 2 800
801 62 14 2 801
802 62 16 2 802
803 62 18 3 803
804 62 20 3 804
805 62 22 3 805
806 62 24 3 806
807 63 0 1 807
808 63 2 1 808
809 63 4 1 809
810 63 6 1 810
811 63 8 1 811
812 63 10 3 812
813 63 12 2 813
814 63 14 1 814
815 63 16 2 815
816 63 18 2 816
817 63 20 2 817
818 63 22 2 818
819 63 24 2 819
820 64 0 1 820
821 64 2 3 821
822 64 4 3 822
823 64 6 3 823
824 64 8 3 824
825 64 10 3 825
826 64 12 3 826
827 64 14 3 827
828 64 16 3 828
829 64 18 3 829
830 64 20 3 830
831 64 22 2 831
832 64 24 2 832
833 65 0 1 833
834 65 2 2 834
835 65 4 2 835
836 65 6 1 836
837 65 8 1 837
838 65 10 1 838
839 65 12 1 839
840 65 14 1 840
841 65 16 1 841
842 65 18 2 842
843 65 20 3 843
844 65 22 3 844
845 65 24 3 845
846 66 0 1 846
847 66 2 3 847
848 66 4 3 848
849 66 6 3 849
850 66 8 3 850
851 66 10 3 851
852 66 12 3 852
853 66 14 3 853
854 66 16 3 854
855 66 18 3 855
856 66 20 2 856
857 66 22 1 857
858 66 24 1 858
859 67 0 1 859
860 67 2 1 860
861 67 4 3 861
862 67 6 3 862
863 67 8 3 863
864 67 10 3 864
865 67 12 3 865
866 67 14 3 866
867 67 16 3 867
868 67 18 3 868
869 67 20 3 869
870 67 22 3 870
871 67 24 3 871
872 68 0 1 872
873 68 2 2 873
874 68 4 2 874
875 68 6 2 875
876 68 8 3 876
877 68 10 3 877
878 68 12 3 878
879 68 14 1 879
880 68 16 1 880
881 68 18 1 881
882 68 20 1 882
883 68 22 1 883
884 68 24 1 884
885 69 0 1 885
886 69 2 2 886
887 69 4 2 887
888 69 6 2 888
889 69 8 2 889
890 69 10 2 890
891 69 12 2 891
892 69 14 2 892
893 69 16 2 893
894 69 18 2 894
895 69 20 2 895
896 69 22 2 896
897 69 24 2 897
898 70 0 1 898
899 70 2 1 899
900 70 4 2 900
901 70 6 2 901
902 70 8 2 902
903 70 10 2 903
904 70 12 2 904
905 70 14 2 905
906 70 16 2 906
907 70 18 2 907
908 70 20 2 908
909 70 22 1 909
910 70 24 2 910
911 71 0 1 911
912 71 2 1 912
913 71 4 1 913
914 71 6 1 914
915 71 8 1 915
916 71 10 1 916
917 71 12 1 917
918 71 14 1 918
919 71 16 1 919
920 71 18 1 920
921 71 20 1 921
922 71 22 1 922
923 71 24 1 923
924 72 0 1 924
925 72 2 1 925
926 72 4 1 926
927 72 6 1 927
928 72 8 1 928
929 72 10 1 929
930 72 12 1 930
931 72 14 1 931
932 72 16 1 932
933 72 18 2 933
934 72 20 2 934
935 72 22 2 935
936 72 24 1 936
937 73 0 1 937
938 73 2 2 938
939 73 4 1 939
940 73 6 1 940
941 73 8 1 941
942 73 10 1 942
943 73 12 1 943
944 73 14 2 944
945 73 16 2 945
946 73 18 2 946
947 73 20 2 947
948 73 22 2 948
949 73 24 3 949
950 74 0 1 950
951 74 2 1 951
952 74 4 1 952
953 74 6 1 953
954 74 8 1 954
955 74 10 1 955
956 74 12 1 956
957 74 14 1 957
958 74 16 1 958
959 74 18 1 959
960 74 20 1 960
961 74 22 1 961
962 74 24 1 962
963 75 0 1 963
964 75 2 1 964
965 75 4 1 965
966 75 6 1 966
967 75 8 1 967
968 75 10 1 968
969 75 12 1 969
970 75 14 2 970
971 75 16 1 971
972 75 18 1 972
973 75 20 1 973
974 75 22 3 974
975 75 24 3 975
976 76 0 1 976
977 76 2 1 977
978 76 4 1 978
979 76 6 2 979
980 76 8 2 980
981 76 10 2 981
982 76 12 2 982
983 76 14 2 983
984 76 16 2 984
985 76 18 2 985
986 76 20 2 986
987 76 22 2 987
988 76 24 2 988
989 77 0 1 989
990 77 2 1 990
991 77 4 1 991
992 77 6 1 992
993 77 8 1 993
994 77 10 2 994
995 77 12 2 995
996 77 14 3 996
997 77 16 3 997
998 77 18 3 998
999 77 20 3 999
1000 77 22 2 1000
1001 77 24 2 1001
1002 78 0 1 1002
1003 78 2 2 1003
1004 78 4 2 1004
1005 78 6 2 1005
1006 78 8 2 1006
1007 78 10 2 1007
1008 78 12 3 1008
1009 78 14 3 1009
1010 78 16 2 1010
1011 78 18 2 1011
1012 78 20 2 1012
1013 78 22 2 1013
1014 78 24 1 1014
1015 79 0 1 1015
1016 79 2 1 1016
1017 79 4 1 1017
1018 79 6 1 1018
1019 79 8 1 1019
1020 79 10 1 1020
1021 79 12 2 1021
1022 79 14 2 1022
1023 79 16 2 1023
1024 79 18 2 1024
1025 79 20 2 1025
1026 79 22 2 1026
1027 79 24 2 1027
1028 80 0 1 1028
1029 80 2 1 1029
1030 80 4 1 1030
1031 80 6 1 1031
1032 80 8 2 1032
1033 80 10 2 1033
1034 80 12 2 1034
1035 80 14 2 1035
1036 80 16 2 1036
1037 80 18 2 1037
1038 80 20 2 1038
1039 80 22 2 1039
1040 80 24 1 1040
1041 81 0 1 1041
1042 81 2 1 1042
1043 81 4 1 1043
1044 81 6 1 1044
1045 81 8 1 1045
1046 81 10 1 1046
1047 81 12 2 1047
1048 81 14 2 1048
1049 81 16 2 1049
1050 81 18 2 1050
1051 81 20 2 1051
1052 81 22 2 1052
1053 81 24 2 1053
1054 82 0 1 1054
1055 82 2 1 1055
1056 82 4 2 1056
1057 82 6 3 1057
1058 82 8 3 1058
1059 82 10 3 1059
1060 82 12 3 1060
1061 82 14 3 1061
1062 82 16 3 1062
1063 82 18 3 1063
1064 82 20 3 1064
1065 82 22 3 1065
1066 82 24 3 1066
1067 83 0 1 1067
1068 83 2 1 1068
1069 83 4 1 1069
1070 83 6 1 1070
1071 83 8 1 1071
1072 83 10 1 1072
1073 83 12 1 1073
1074 83 14 1 1074
1075 83 16 2 1075
1076 83 18 1 1076
1077 83 20 1 1077
1078 83 22 1 1078
1079 83 24 1 1079
1080 84 0 1 1080
1081 84 2 1 1081
1082 84 4 1 1082
1083 84 6 1 1083
1084 84 8 2 1084
1085 84 10 2 1085
1086 84 12 3 1086
1087 84 14 3 1087
1088 84 16 3 1088
1089 84 18 2 1089
1090 84 20 1 1090
1091 84 22 1 1091
1092 84 24 1 1092
1093 85 0 1 1093
1094 85 2 1 1094
1095 85 4 1 1095
1096 85 6 1 1096
1097 85 8 2 1097
1098 85 10 1 1098
1099 85 12 2 1099
1100 85 14 2 1100
1101 85 16 2 1101
1102 85 18 2 1102
1103 85 20 2 1103
1104 85 22 2 1104
1105 85 24 2 1105
1106 86 0 1 1106
1107 86 2 1 1107
1108 86 4 1 1108
1109 86 6 1 1109
1110 86 8 2 1110
1111 86 10 1 1111
1112 86 12 1 1112
1113 86 14 1 1113
1114 86 16 1 1114
1115 86 18 1 1115
1116 86 20 2 1116
1117 86 22 2 1117
1118 86 24 2 1118
1119 87 0 1 1119
1120 87 2 1 1120
1121 87 4 1 1121
1122 87 6 2 1122
1123 87 8 2 1123
1124 87 10 2 1124
1125 87 12 2 1125
1126 87 14 2 1126
1127 87 16 3 1127
1128 87 18 3 1128
1129 87 20 3 1129
1130 87 22 3 1130
1131 87 24 3 1131
1132 88 0 1 1132
1133 88 2 1 1133
1134 88 4 1 1134
1135 88 6 2 1135
1136 88 8 2 1136
1137 88 10 2 1137
1138 88 12 2 1138
1139 88 14 1 1139
1140 88 16 1 1140
1141 88 18 2 1141
1142 88 20 2 1142
1143 88 22 2 1143
1144 88 24 2 1144
1145 89 0 1 1145
1146 89 2 1 1146
1147 89 4 2 1147
1148 89 6 2 1148
1149 89 8 2 1149
1150 89 10 1 1150
1151 89 12 2 1151
1152 89 14 2 1152
1153 89 16 2 1153
1154 89 18 2 1154
1155 89 20 2 1155
1156 89 22 2 1156
1157 89 24 2 1157
1158 90 0 1 1158
1159 90 2 1 1159
1160 90 4 1 1160
1161 90 6 1 1161
1162 90 8 1 1162
1163 90 10 1 1163
1164 90 12 1 1164
1165 90 14 1 1165
1166 90 16 1 1166
1167 90 18 1 1167
1168 90 20 1 1168
1169 90 22 3 1169
1170 90 24 2 1170
1171 91 0 1 1171
1172 91 2 1 1172
1173 91 4 1 1173
1174 91 6 1 1174
1175 91 8 1 1175
1176 91 10 1 1176
1177 91 12 1 1177
1178 91 14 1 1178
1179 91 16 2 1179
1180 91 18 1 1180
1181 91 20 1 1181
1182 91 22 1 1182
1183 91 24 1 1183
1184 92 0 1 1184
1185 92 2 1 1185
1186 92 4 1 1186
1187 92 6 1 1187
1188 92 8 1 1188
1189 92 10 1 1189
1190 92 12 1 1190
1191 92 14 1 1191
1192 92 16 1 1192
1193 92 18 1 1193
1194 92 20 1 1194
1195 92 22 1 1195
1196 92 24 2 1196
1197 93 0 1 1197
1198 93 2 1 1198
1199 93 4 1 1199
1200 93 6 1 1200
1201 93 8 1 1201
1202 93 10 1 1202
1203 93 12 1 1203
1204 93 14 1 1204
1205 93 16 1 1205
1206 93 18 1 1206
1207 93 20 1 1207
1208 93 22 2 1208
1209 93 24 3 1209
1210 94 0 1 1210
1211 94 2 1 1211
1212 94 4 1 1212
1213 94 6 2 1213
1214 94 8 2 1214
1215 94 10 2 1215
1216 94 12 2 1216
1217 94 14 2 1217
1218 94 16 2 1218
1219 94 18 2 1219
1220 94 20 2 1220
1221 94 22 2 1221
1222 94 24 2 1222
1223 95 0 1 1223
1224 95 2 1 1224
1225 95 4 1 1225
1226 95 6 1 1226
1227 95 8 1 1227
1228 95 10 1 1228
1229 95 12 1 1229
1230 95 14 1 1230
1231 95 16 1 1231
1232 95 18 1 1232
1233 95 20 3 1233
1234 95 22 3 1234
1235 95 24 2 1235
1236 96 0 1 1236
1237 96 2 1 1237
1238 96 4 1 1238
1239 96 6 1 1239
1240 96 8 1 1240
1241 96 10 1 1241
1242 96 12 1 1242
1243 96 14 1 1243
1244 96 16 1 1244
1245 96 18 1 1245
1246 96 20 1 1246
1247 96 22 1 1247
1248 96 24 2 1248
1249 97 0 1 1249
1250 97 2 2 1250
1251 97 4 2 1251
1252 97 6 2 1252
1253 97 8 2 1253
1254 97 10 1 1254
1255 97 12 2 1255
1256 97 14 2 1256
1257 97 16 2 1257
1258 97 18 1 1258
1259 97 20 1 1259
1260 97 22 1 1260
1261 97 24 1 1261
1262 98 0 1 1262
1263 98 2 1 1263
1264 98 4 1 1264
1265 98 6 1 1265
1266 98 8 1 1266
1267 98 10 1 1267
1268 98 12 1 1268
1269 98 14 1 1269
1270 98 16 1 1270
1271 98 18 1 1271
1272 98 20 1 1272
1273 98 22 1 1273
1274 98 24 1 1274
1275 99 0 1 1275
1276 99 2 1 1276
1277 99 4 3 1277
1278 99 6 3 1278
1279 99 8 3 1279
1280 99 10 3 1280
1281 99 12 3 1281
1282 99 14 1 1282
1283 99 16 1 1283
1284 99 18 1 1284
1285 99 20 1 1285
1286 99 22 1 1286
1287 99 24 1 1287
1288 100 0 1 1288
1289 100 2 1 1289
1290 100 4 1 1290
1291 100 6 1 1291
1292 100 8 2 1292
1293 100 10 2 1293
1294 100 12 1 1294
1295 100 14 1 1295
1296 100 16 1 1296
1297 100 18 1 1297
1298 100 20 1 1298
1299 100 22 1 1299
1300 100 24 3 1300
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msm documentation built on May 2, 2019, 6:51 p.m.
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Description Usage Arguments Details Value Author(s) See Also Examples
Description
Simulate a number of individual realisations from a continuous-time Markov process. Observations of the process are made at specified arbitrary times for each individual, giving panel-observed data.
Usage
1 2 3 |
Arguments
data |
A data frame with a mandatory column named |
qmatrix |
The transition intensity matrix of the
Markov process, with any covariates set to zero. The diagonal of
|
covariates |
List of linear covariate effects on log transition intensities. Each element is a vector of the effects of one covariate on all the transition intensities. The intensities are ordered by reading across rows of the intensity matrix, starting with the first, counting the positive off-diagonal elements of the matrix. For example, for a multi-state model with three transition
intensities, and two covariates
|
death |
Vector of indices of the death states. A death state is
an absorbing state whose time of entry is known exactly, but the
individual is assumed to be in an unknown transient state ("alive")
at the previous instant. This is the usual situation for times of death in
chronic disease monitoring data. For example, if you specify
|
start |
A vector with the same number of elements as there are distinct subjects in the data, giving the states in which each corresponding individual begins. Or a single number, if all of these are the same. Defaults to state 1 for each subject. |
ematrix |
An optional misclassification matrix for generating observed states
conditionally on the simulated true states. As defined in
|
misccovariates |
Covariate effects on misclassification
probabilities via multinomial logistic regression. Linear effects
operate on the log of each probability relative to the probability of
classification in the correct state. In same format as
|
hmodel |
An optional hidden Markov model for generating observed
outcomes conditionally on the simulated true states. As defined in
|
hcovariates |
List of the same length as
|
censor.states |
Set of simulated states which should be replaced by a censoring indicator at censoring times. By default this is all transient states (representing alive, with unknown state). |
drop.absorb |
Drop repeated observations in the absorbing state, retaining only one. |
Details
sim.msm is called repeatedly to produce a simulated
trajectory for each individual. The state at each specified
observation time is then taken to produce a new column state.
The effect of time-dependent covariates on the transition intensity
matrix for an individual is determined by assuming that the covariate is a step function
which remains constant in between the individual's observation times.
If the subject enters an absorbing state, then only the first
observation in that state is kept in the data frame. Rows corresponding to future
observations are deleted. The entry times into states given in
death are assumed to be known exactly.
Value
A data frame with columns,
subject |
Subject identification indicators |
time |
Observation times |
state |
Simulated (true) state at the corresponding time |
obs |
Observed outcome at the corresponding time, if
|
keep |
Row numbers of the original data. Useful when
|
plus any supplied covariates.
Author(s)
C. H. Jackson chris.jackson@mrc-bsu.cam.ac.uk
See Also
Examples
1 2 3 4 5 6 |
Example output
subject time state keep
1 1 0 1 1
2 1 2 2 2
3 1 4 3 3
4 1 6 2 4
5 1 8 2 5
6 1 10 1 6
7 1 12 1 7
8 1 14 3 8
9 1 16 3 9
10 1 18 3 10
11 1 20 2 11
12 1 22 3 12
13 1 24 2 13
14 2 0 1 14
15 2 2 3 15
16 2 4 3 16
17 2 6 3 17
18 2 8 3 18
19 2 10 3 19
20 2 12 3 20
21 2 14 3 21
22 2 16 3 22
23 2 18 3 23
24 2 20 3 24
25 2 22 3 25
26 2 24 3 26
27 3 0 1 27
28 3 2 1 28
29 3 4 1 29
30 3 6 1 30
31 3 8 2 31
32 3 10 3 32
33 3 12 2 33
34 3 14 2 34
35 3 16 1 35
36 3 18 1 36
37 3 20 1 37
38 3 22 1 38
39 3 24 1 39
40 4 0 1 40
41 4 2 1 41
42 4 4 1 42
43 4 6 1 43
44 4 8 1 44
45 4 10 1 45
46 4 12 3 46
47 4 14 3 47
48 4 16 1 48
49 4 18 3 49
50 4 20 3 50
51 4 22 3 51
52 4 24 3 52
53 5 0 1 53
54 5 2 1 54
55 5 4 1 55
56 5 6 1 56
57 5 8 1 57
58 5 10 1 58
59 5 12 1 59
60 5 14 1 60
61 5 16 2 61
62 5 18 2 62
63 5 20 2 63
64 5 22 3 64
65 5 24 3 65
66 6 0 1 66
67 6 2 1 67
68 6 4 1 68
69 6 6 1 69
70 6 8 1 70
71 6 10 1 71
72 6 12 1 72
73 6 14 1 73
74 6 16 1 74
75 6 18 1 75
76 6 20 2 76
77 6 22 2 77
78 6 24 2 78
79 7 0 1 79
80 7 2 1 80
81 7 4 1 81
82 7 6 1 82
83 7 8 1 83
84 7 10 1 84
85 7 12 3 85
86 7 14 3 86
87 7 16 3 87
88 7 18 3 88
89 7 20 3 89
90 7 22 3 90
91 7 24 2 91
92 8 0 1 92
93 8 2 1 93
94 8 4 1 94
95 8 6 1 95
96 8 8 1 96
97 8 10 1 97
98 8 12 1 98
99 8 14 1 99
100 8 16 1 100
101 8 18 1 101
102 8 20 1 102
103 8 22 1 103
104 8 24 1 104
105 9 0 1 105
106 9 2 1 106
107 9 4 1 107
108 9 6 1 108
109 9 8 1 109
110 9 10 1 110
111 9 12 2 111
112 9 14 2 112
113 9 16 2 113
114 9 18 1 114
115 9 20 1 115
116 9 22 1 116
117 9 24 1 117
118 10 0 1 118
119 10 2 1 119
120 10 4 2 120
121 10 6 2 121
122 10 8 2 122
123 10 10 2 123
124 10 12 2 124
125 10 14 2 125
126 10 16 2 126
127 10 18 2 127
128 10 20 2 128
129 10 22 2 129
130 10 24 2 130
131 11 0 1 131
132 11 2 1 132
133 11 4 1 133
134 11 6 1 134
135 11 8 1 135
136 11 10 1 136
137 11 12 1 137
138 11 14 1 138
139 11 16 1 139
140 11 18 1 140
141 11 20 1 141
142 11 22 1 142
143 11 24 1 143
144 12 0 1 144
145 12 2 1 145
146 12 4 1 146
147 12 6 1 147
148 12 8 1 148
149 12 10 2 149
150 12 12 2 150
151 12 14 2 151
152 12 16 2 152
153 12 18 2 153
154 12 20 2 154
155 12 22 2 155
156 12 24 2 156
157 13 0 1 157
158 13 2 1 158
159 13 4 2 159
160 13 6 2 160
161 13 8 2 161
162 13 10 2 162
163 13 12 3 163
164 13 14 3 164
165 13 16 3 165
166 13 18 3 166
167 13 20 3 167
168 13 22 3 168
169 13 24 3 169
170 14 0 1 170
171 14 2 1 171
172 14 4 2 172
173 14 6 2 173
174 14 8 1 174
175 14 10 3 175
176 14 12 3 176
177 14 14 3 177
178 14 16 3 178
179 14 18 3 179
180 14 20 3 180
181 14 22 3 181
182 14 24 3 182
183 15 0 1 183
184 15 2 1 184
185 15 4 2 185
186 15 6 3 186
187 15 8 3 187
188 15 10 3 188
189 15 12 3 189
190 15 14 3 190
191 15 16 3 191
192 15 18 3 192
193 15 20 3 193
194 15 22 3 194
195 15 24 3 195
196 16 0 1 196
197 16 2 1 197
198 16 4 1 198
199 16 6 1 199
200 16 8 2 200
201 16 10 2 201
202 16 12 2 202
203 16 14 3 203
204 16 16 3 204
205 16 18 2 205
206 16 20 2 206
207 16 22 2 207
208 16 24 2 208
209 17 0 1 209
210 17 2 1 210
211 17 4 2 211
212 17 6 2 212
213 17 8 2 213
214 17 10 1 214
215 17 12 1 215
216 17 14 1 216
217 17 16 1 217
218 17 18 3 218
219 17 20 3 219
220 17 22 3 220
221 17 24 3 221
222 18 0 1 222
223 18 2 1 223
224 18 4 1 224
225 18 6 1 225
226 18 8 1 226
227 18 10 1 227
228 18 12 1 228
229 18 14 1 229
230 18 16 1 230
231 18 18 2 231
232 18 20 2 232
233 18 22 2 233
234 18 24 2 234
235 19 0 1 235
236 19 2 2 236
237 19 4 2 237
238 19 6 2 238
239 19 8 2 239
240 19 10 2 240
241 19 12 2 241
242 19 14 2 242
243 19 16 2 243
244 19 18 3 244
245 19 20 3 245
246 19 22 2 246
247 19 24 3 247
248 20 0 1 248
249 20 2 2 249
250 20 4 2 250
251 20 6 2 251
252 20 8 2 252
253 20 10 2 253
254 20 12 2 254
255 20 14 3 255
256 20 16 3 256
257 20 18 3 257
258 20 20 2 258
259 20 22 3 259
260 20 24 3 260
261 21 0 1 261
262 21 2 1 262
263 21 4 1 263
264 21 6 1 264
265 21 8 1 265
266 21 10 1 266
267 21 12 1 267
268 21 14 2 268
269 21 16 3 269
270 21 18 3 270
271 21 20 1 271
272 21 22 2 272
273 21 24 3 273
274 22 0 1 274
275 22 2 2 275
276 22 4 2 276
277 22 6 3 277
278 22 8 3 278
279 22 10 3 279
280 22 12 3 280
281 22 14 3 281
282 22 16 3 282
283 22 18 3 283
284 22 20 3 284
285 22 22 3 285
286 22 24 3 286
287 23 0 1 287
288 23 2 1 288
289 23 4 1 289
290 23 6 1 290
291 23 8 2 291
292 23 10 1 292
293 23 12 1 293
294 23 14 1 294
295 23 16 1 295
296 23 18 1 296
297 23 20 1 297
298 23 22 3 298
299 23 24 3 299
300 24 0 1 300
301 24 2 2 301
302 24 4 2 302
303 24 6 3 303
304 24 8 3 304
305 24 10 3 305
306 24 12 3 306
307 24 14 3 307
308 24 16 3 308
309 24 18 2 309
310 24 20 2 310
311 24 22 2 311
312 24 24 2 312
313 25 0 1 313
314 25 2 2 314
315 25 4 2 315
316 25 6 2 316
317 25 8 2 317
318 25 10 2 318
319 25 12 2 319
320 25 14 2 320
321 25 16 2 321
322 25 18 2 322
323 25 20 2 323
324 25 22 2 324
325 25 24 1 325
326 26 0 1 326
327 26 2 1 327
328 26 4 2 328
329 26 6 2 329
330 26 8 2 330
331 26 10 2 331
332 26 12 2 332
333 26 14 2 333
334 26 16 2 334
335 26 18 3 335
336 26 20 2 336
337 26 22 2 337
338 26 24 2 338
339 27 0 1 339
340 27 2 1 340
341 27 4 1 341
342 27 6 1 342
343 27 8 1 343
344 27 10 1 344
345 27 12 1 345
346 27 14 1 346
347 27 16 1 347
348 27 18 1 348
349 27 20 1 349
350 27 22 1 350
351 27 24 1 351
352 28 0 1 352
353 28 2 1 353
354 28 4 1 354
355 28 6 1 355
356 28 8 1 356
357 28 10 2 357
358 28 12 3 358
359 28 14 3 359
360 28 16 3 360
361 28 18 3 361
362 28 20 3 362
363 28 22 2 363
364 28 24 2 364
365 29 0 1 365
366 29 2 1 366
367 29 4 1 367
368 29 6 1 368
369 29 8 1 369
370 29 10 1 370
371 29 12 1 371
372 29 14 1 372
373 29 16 1 373
374 29 18 1 374
375 29 20 1 375
376 29 22 1 376
377 29 24 2 377
378 30 0 1 378
379 30 2 1 379
380 30 4 1 380
381 30 6 1 381
382 30 8 2 382
383 30 10 3 383
384 30 12 3 384
385 30 14 2 385
386 30 16 2 386
387 30 18 2 387
388 30 20 2 388
389 30 22 3 389
390 30 24 3 390
391 31 0 1 391
392 31 2 1 392
393 31 4 1 393
394 31 6 1 394
395 31 8 1 395
396 31 10 1 396
397 31 12 3 397
398 31 14 3 398
399 31 16 2 399
400 31 18 2 400
401 31 20 2 401
402 31 22 2 402
403 31 24 2 403
404 32 0 1 404
405 32 2 2 405
406 32 4 2 406
407 32 6 2 407
408 32 8 2 408
409 32 10 3 409
410 32 12 3 410
411 32 14 3 411
412 32 16 3 412
413 32 18 3 413
414 32 20 3 414
415 32 22 3 415
416 32 24 3 416
417 33 0 1 417
418 33 2 1 418
419 33 4 1 419
420 33 6 1 420
421 33 8 1 421
422 33 10 1 422
423 33 12 1 423
424 33 14 1 424
425 33 16 1 425
426 33 18 1 426
427 33 20 1 427
428 33 22 1 428
429 33 24 1 429
430 34 0 1 430
431 34 2 1 431
432 34 4 1 432
433 34 6 1 433
434 34 8 1 434
435 34 10 2 435
436 34 12 3 436
437 34 14 3 437
438 34 16 3 438
439 34 18 1 439
440 34 20 1 440
441 34 22 2 441
442 34 24 2 442
443 35 0 1 443
444 35 2 1 444
445 35 4 1 445
446 35 6 1 446
447 35 8 1 447
448 35 10 1 448
449 35 12 1 449
450 35 14 1 450
451 35 16 1 451
452 35 18 1 452
453 35 20 1 453
454 35 22 3 454
455 35 24 3 455
456 36 0 1 456
457 36 2 1 457
458 36 4 1 458
459 36 6 1 459
460 36 8 1 460
461 36 10 1 461
462 36 12 1 462
463 36 14 2 463
464 36 16 2 464
465 36 18 2 465
466 36 20 2 466
467 36 22 2 467
468 36 24 2 468
469 37 0 1 469
470 37 2 1 470
471 37 4 1 471
472 37 6 1 472
473 37 8 1 473
474 37 10 1 474
475 37 12 1 475
476 37 14 1 476
477 37 16 1 477
478 37 18 1 478
479 37 20 1 479
480 37 22 1 480
481 37 24 2 481
482 38 0 1 482
483 38 2 1 483
484 38 4 2 484
485 38 6 3 485
486 38 8 3 486
487 38 10 3 487
488 38 12 3 488
489 38 14 3 489
490 38 16 3 490
491 38 18 3 491
492 38 20 3 492
493 38 22 3 493
494 38 24 3 494
495 39 0 1 495
496 39 2 1 496
497 39 4 1 497
498 39 6 1 498
499 39 8 2 499
500 39 10 2 500
501 39 12 1 501
502 39 14 2 502
503 39 16 2 503
504 39 18 3 504
505 39 20 3 505
506 39 22 2 506
507 39 24 2 507
508 40 0 1 508
509 40 2 1 509
510 40 4 2 510
511 40 6 2 511
512 40 8 2 512
513 40 10 3 513
514 40 12 3 514
515 40 14 3 515
516 40 16 2 516
517 40 18 2 517
518 40 20 2 518
519 40 22 2 519
520 40 24 2 520
521 41 0 1 521
522 41 2 2 522
523 41 4 3 523
524 41 6 3 524
525 41 8 3 525
526 41 10 3 526
527 41 12 3 527
528 41 14 3 528
529 41 16 3 529
530 41 18 3 530
531 41 20 3 531
532 41 22 3 532
533 41 24 3 533
534 42 0 1 534
535 42 2 1 535
536 42 4 1 536
537 42 6 1 537
538 42 8 1 538
539 42 10 2 539
540 42 12 2 540
541 42 14 2 541
542 42 16 2 542
543 42 18 2 543
544 42 20 1 544
545 42 22 2 545
546 42 24 2 546
547 43 0 1 547
548 43 2 1 548
549 43 4 1 549
550 43 6 1 550
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920 71 18 1 920
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924 72 0 1 924
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930 72 12 1 930
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937 73 0 1 937
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950 74 0 1 950
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970 75 14 2 970
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978 76 4 1 978
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980 76 8 2 980
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987 76 22 2 987
988 76 24 2 988
989 77 0 1 989
990 77 2 1 990
991 77 4 1 991
992 77 6 1 992
993 77 8 1 993
994 77 10 2 994
995 77 12 2 995
996 77 14 3 996
997 77 16 3 997
998 77 18 3 998
999 77 20 3 999
1000 77 22 2 1000
1001 77 24 2 1001
1002 78 0 1 1002
1003 78 2 2 1003
1004 78 4 2 1004
1005 78 6 2 1005
1006 78 8 2 1006
1007 78 10 2 1007
1008 78 12 3 1008
1009 78 14 3 1009
1010 78 16 2 1010
1011 78 18 2 1011
1012 78 20 2 1012
1013 78 22 2 1013
1014 78 24 1 1014
1015 79 0 1 1015
1016 79 2 1 1016
1017 79 4 1 1017
1018 79 6 1 1018
1019 79 8 1 1019
1020 79 10 1 1020
1021 79 12 2 1021
1022 79 14 2 1022
1023 79 16 2 1023
1024 79 18 2 1024
1025 79 20 2 1025
1026 79 22 2 1026
1027 79 24 2 1027
1028 80 0 1 1028
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1030 80 4 1 1030
1031 80 6 1 1031
1032 80 8 2 1032
1033 80 10 2 1033
1034 80 12 2 1034
1035 80 14 2 1035
1036 80 16 2 1036
1037 80 18 2 1037
1038 80 20 2 1038
1039 80 22 2 1039
1040 80 24 1 1040
1041 81 0 1 1041
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1044 81 6 1 1044
1045 81 8 1 1045
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1050 81 18 2 1050
1051 81 20 2 1051
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1053 81 24 2 1053
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1059 82 10 3 1059
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1067 83 0 1 1067
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1070 83 6 1 1070
1071 83 8 1 1071
1072 83 10 1 1072
1073 83 12 1 1073
1074 83 14 1 1074
1075 83 16 2 1075
1076 83 18 1 1076
1077 83 20 1 1077
1078 83 22 1 1078
1079 83 24 1 1079
1080 84 0 1 1080
1081 84 2 1 1081
1082 84 4 1 1082
1083 84 6 1 1083
1084 84 8 2 1084
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1086 84 12 3 1086
1087 84 14 3 1087
1088 84 16 3 1088
1089 84 18 2 1089
1090 84 20 1 1090
1091 84 22 1 1091
1092 84 24 1 1092
1093 85 0 1 1093
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1095 85 4 1 1095
1096 85 6 1 1096
1097 85 8 2 1097
1098 85 10 1 1098
1099 85 12 2 1099
1100 85 14 2 1100
1101 85 16 2 1101
1102 85 18 2 1102
1103 85 20 2 1103
1104 85 22 2 1104
1105 85 24 2 1105
1106 86 0 1 1106
1107 86 2 1 1107
1108 86 4 1 1108
1109 86 6 1 1109
1110 86 8 2 1110
1111 86 10 1 1111
1112 86 12 1 1112
1113 86 14 1 1113
1114 86 16 1 1114
1115 86 18 1 1115
1116 86 20 2 1116
1117 86 22 2 1117
1118 86 24 2 1118
1119 87 0 1 1119
1120 87 2 1 1120
1121 87 4 1 1121
1122 87 6 2 1122
1123 87 8 2 1123
1124 87 10 2 1124
1125 87 12 2 1125
1126 87 14 2 1126
1127 87 16 3 1127
1128 87 18 3 1128
1129 87 20 3 1129
1130 87 22 3 1130
1131 87 24 3 1131
1132 88 0 1 1132
1133 88 2 1 1133
1134 88 4 1 1134
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1137 88 10 2 1137
1138 88 12 2 1138
1139 88 14 1 1139
1140 88 16 1 1140
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1143 88 22 2 1143
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1145 89 0 1 1145
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1147 89 4 2 1147
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1150 89 10 1 1150
1151 89 12 2 1151
1152 89 14 2 1152
1153 89 16 2 1153
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1155 89 20 2 1155
1156 89 22 2 1156
1157 89 24 2 1157
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1160 90 4 1 1160
1161 90 6 1 1161
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1163 90 10 1 1163
1164 90 12 1 1164
1165 90 14 1 1165
1166 90 16 1 1166
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1169 90 22 3 1169
1170 90 24 2 1170
1171 91 0 1 1171
1172 91 2 1 1172
1173 91 4 1 1173
1174 91 6 1 1174
1175 91 8 1 1175
1176 91 10 1 1176
1177 91 12 1 1177
1178 91 14 1 1178
1179 91 16 2 1179
1180 91 18 1 1180
1181 91 20 1 1181
1182 91 22 1 1182
1183 91 24 1 1183
1184 92 0 1 1184
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1186 92 4 1 1186
1187 92 6 1 1187
1188 92 8 1 1188
1189 92 10 1 1189
1190 92 12 1 1190
1191 92 14 1 1191
1192 92 16 1 1192
1193 92 18 1 1193
1194 92 20 1 1194
1195 92 22 1 1195
1196 92 24 2 1196
1197 93 0 1 1197
1198 93 2 1 1198
1199 93 4 1 1199
1200 93 6 1 1200
1201 93 8 1 1201
1202 93 10 1 1202
1203 93 12 1 1203
1204 93 14 1 1204
1205 93 16 1 1205
1206 93 18 1 1206
1207 93 20 1 1207
1208 93 22 2 1208
1209 93 24 3 1209
1210 94 0 1 1210
1211 94 2 1 1211
1212 94 4 1 1212
1213 94 6 2 1213
1214 94 8 2 1214
1215 94 10 2 1215
1216 94 12 2 1216
1217 94 14 2 1217
1218 94 16 2 1218
1219 94 18 2 1219
1220 94 20 2 1220
1221 94 22 2 1221
1222 94 24 2 1222
1223 95 0 1 1223
1224 95 2 1 1224
1225 95 4 1 1225
1226 95 6 1 1226
1227 95 8 1 1227
1228 95 10 1 1228
1229 95 12 1 1229
1230 95 14 1 1230
1231 95 16 1 1231
1232 95 18 1 1232
1233 95 20 3 1233
1234 95 22 3 1234
1235 95 24 2 1235
1236 96 0 1 1236
1237 96 2 1 1237
1238 96 4 1 1238
1239 96 6 1 1239
1240 96 8 1 1240
1241 96 10 1 1241
1242 96 12 1 1242
1243 96 14 1 1243
1244 96 16 1 1244
1245 96 18 1 1245
1246 96 20 1 1246
1247 96 22 1 1247
1248 96 24 2 1248
1249 97 0 1 1249
1250 97 2 2 1250
1251 97 4 2 1251
1252 97 6 2 1252
1253 97 8 2 1253
1254 97 10 1 1254
1255 97 12 2 1255
1256 97 14 2 1256
1257 97 16 2 1257
1258 97 18 1 1258
1259 97 20 1 1259
1260 97 22 1 1260
1261 97 24 1 1261
1262 98 0 1 1262
1263 98 2 1 1263
1264 98 4 1 1264
1265 98 6 1 1265
1266 98 8 1 1266
1267 98 10 1 1267
1268 98 12 1 1268
1269 98 14 1 1269
1270 98 16 1 1270
1271 98 18 1 1271
1272 98 20 1 1272
1273 98 22 1 1273
1274 98 24 1 1274
1275 99 0 1 1275
1276 99 2 1 1276
1277 99 4 3 1277
1278 99 6 3 1278
1279 99 8 3 1279
1280 99 10 3 1280
1281 99 12 3 1281
1282 99 14 1 1282
1283 99 16 1 1283
1284 99 18 1 1284
1285 99 20 1 1285
1286 99 22 1 1286
1287 99 24 1 1287
1288 100 0 1 1288
1289 100 2 1 1289
1290 100 4 1 1290
1291 100 6 1 1291
1292 100 8 2 1292
1293 100 10 2 1293
1294 100 12 1 1294
1295 100 14 1 1295
1296 100 16 1 1296
1297 100 18 1 1297
1298 100 20 1 1298
1299 100 22 1 1299
1300 100 24 3 1300
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