Statistical Methods in Medical Research 4ed

More documents

Recommendations

Info

18.10 Meta-analysis 647 the combined estimate of efficacy, ^u*, will have greater variance than the estimate y obtained from the fixed-effects model. A slightly more efficient procedure is to estimate by maximum likelihood, which involves an iterative calculation (see, for instance, Normand, 1999, equation (8)). Both these procedures are in the spirit of empirical Bayesian methods (§6.5), whereby the between-trial variation can be estimated from the available data. In contrast to this approach is the fully Bayesian analysis, in which (with the model described above) prior distributions are specified for the parameters vi, u* and v*, either based on specific prior judgements or using non-informative distributions to represent ignorance (Smith et al., 1995; Normand, 1999).
19 Statistical methods in epidemiology 19.1 Introduction The branch of medical science called epidemiology has been defined as `the study of the distribution and determinants of health-related states or events in specified populations, and the application of this study to control of health problems' (Last, 1995, p. 55). In broad terms epidemiology is concerned with the distribution of disease, or of a physiological condition, and of the factors that influence the distribution. It includes within its orbit the study of chronic diseases, as well as the communicable diseases which give rise to epidemics of the classical sort. The subject overlaps to some extent with social medicine, community medicine or public health, which would usually be understood to include social and administrative topics, such as the provision and use of health services. Epidemiology is concerned with certain characteristics of groups of individuals rather than single subjects, and inevitably gives rise to statistical problems. Many of these are conceptually similar to statistical problems arising in other branches of medical science, and, indeed, in the non-medical sciences, and can be approached by the methods of analysis described earlier in this book; several examples in earlier chapters have been drawn from epidemiological studies. Other methodological problems in epidemiology, although of statistical interest, are bound up with considerations of a non-statistical nature and cannot be discussed here. Examples are the interpretation of vital and health statistical data, which requires a close knowledge of administrative procedures for the recording of such data and of the classification of diseases and causes of death (Benjamin, 1968; World Health Organization, 1992); and the proper use and potential development of medical records of various sorts (Acheson, 1967). There is also a considerable body of literature concerned with the mathematical theory of epidemic disease; the monographs by Bailey (1975) and Becker (1989) provide useful summaries of this work. For general accounts of epidemiological methods, the reader may consult Kleinbaum et al. (1982), Miettinen (1985), Hennekens et al. (1987), Elwood (1988), Kelsey et al. (1996) and Rothman and Greenland (1998). In this chapter we consider briefly certain problems arising in epidemiological research for which special statistical methods have been developed. 648
Page 2 and 3:
To J.O. Irwin Mentor and friend
Page 4 and 5:
# 1971, 1987, 1994, 2002 by Blackwe
Page 6 and 7:
vi Contents 9.3 Factorial designs,
Page 9 and 10:
Preface to the fourth edition In th
Page 11 and 12:
Preface to the fourth edition xi Ho
Page 13 and 14:
2 The scope of statistics other pat
Page 15 and 16:
4 The scope of statistics groups is
Page 17 and 18:
6 The scope of statistics pressure
Page 19 and 20:
2 Describing data 2.1 Diagrams One
Page 21 and 22:
10 Describing data 1- 4 weeks Under
Page 23 and 24:
12 Describing data Table 2.1 Outcom
Page 25 and 26:
14 Describing data Your height: ...
Page 27 and 28:
16 Describing data be transferred f
Page 29 and 30:
18 Describing data extracted from t
Page 31 and 32:
20 Describing data many variables a
Page 33 and 34:
22 Describing data cannot be less t
Page 35 and 36:
24 Describing data Bufotenin (nmol/
Page 37 and 38:
26 Describing data Frequency 20 18
Page 39 and 40:
28 Describing data The number of as
Page 41 and 42:
30 Describing data Frequency Measur
Page 43 and 44:
32 Describing data may be abbreviat
Page 45 and 46:
34 Describing data variables follow
Page 47 and 48:
36 Describing data 107 01. The geom
Page 49 and 50:
38 Describing data If the number of
Page 51 and 52:
40 Describing data Therefore the me
Page 53 and 54:
42 Describing data xi x will then n
Page 55 and 56:
44 Describing data taking the antil
Page 57 and 58:
46 Describing data against their ef
Page 59 and 60:
48 Probability example, is sometime
Page 61 and 62:
50 Probability It will appear in du
Page 63 and 64:
52 Probability In general, pairs of
Page 65 and 66:
54 Probability the five types be cl
Page 67 and 68:
56 Probability converted to a ratio
Page 69 and 70:
58 Probability Correct Equivocal In
Page 71 and 72:
60 Probability Probability 1 . 0 0
Page 73 and 74:
62 Probability Probability density
Page 75 and 76:
64 Probability As a second example,
Page 77 and 78:
66 Probability coefficient. In the
Page 79 and 80:
68 Probability n r pr …1 p† n r
Page 81 and 82:
70 Probability π = 0 Probability .
Page 83 and 84:
72 Probability 0 } — T n Fig. 3.8
Page 85 and 86:
74 Probability Probability 0 . 4 0
Page 87 and 88:
76 Probability Table 3.4 Binomial a
Page 89 and 90:
78 Probability where exp(z) is a co
Page 91 and 92:
80 Probability approaches the shape
Page 93 and 94:
82 Probability Probabililty density
Page 95 and 96:
84 Analysing means and proportions
Page 97 and 98:
Page 99 and 100:
Page 101 and 102:
Page 103 and 104:
Page 105 and 106:
Page 107 and 108:
Page 109 and 110:
Page 111 and 112:
Page 113 and 114:
Page 115 and 116:
Page 117 and 118:
Page 119 and 120:
Page 121 and 122:
Page 123 and 124:
Page 125 and 126:
Page 127 and 128:
Page 129 and 130:
Page 131 and 132:
Page 133 and 134:
Page 135 and 136:
Page 137 and 138:
Page 139 and 140:
Page 141 and 142:
Page 143 and 144:
Page 145 and 146:
Page 147 and 148:
Page 149 and 150:
Page 151 and 152:
Page 153 and 154:
Page 155 and 156:
Page 157 and 158:
Page 159 and 160:
148 Analysing variances Probability
Page 161 and 162:
150 Analysing variances headings 0
Page 163 and 164:
152 Analysing variances Method AB N
Page 165 and 166:
154 Analysing variances Example 5.2
Page 167 and 168:
156 Analysing variances Comparison
Page 169 and 170:
158 Analysing variances With contin
Page 171 and 172:
160 Analysing variances Let y ˆ x1
Page 173 and 174:
162 Analysing variances p … log x
Page 175 and 176:
164 Analysing variances as expected
Page 177 and 178:
166 Bayesian methods This argument
Page 179 and 180:
168 Bayesian methods nothing of the
Page 181 and 182:
170 Bayesian methods in this way. F
Page 183 and 184:
172 Bayesian methods In some situat
Page 185 and 186:
174 Bayesian methods difference bet
Page 187 and 188:
176 Bayesian methods the distributi
Page 189 and 190:
178 Bayesian methods In the unpaire
Page 191 and 192:
180 Bayesian methods The examples d
Page 193 and 194:
182 Bayesian methods difference bet
Page 195 and 196:
184 Bayesian methods variation may
Page 197 and 198:
186 Bayesian methods The resulting
Page 199 and 200:
188 Regression and correlation Infa
Page 201 and 202:
190 Regression and correlation y x
Page 203 and 204:
192 Regression and correlation on s
Page 205 and 206:
194 Regression and correlation y ,
Page 207 and 208:
196 Regression and correlation y (a
Page 209 and 210:
198 Regression and correlation incr
Page 211 and 212:
200 Regression and correlation From
Page 213 and 214:
202 Regression and correlation y ,
Page 215 and 216:
204 Regression and correlation Valu
Page 217 and 218:
206 Regression and correlation disc
Page 219 and 220:
8 Comparison of several groups 8.1
Page 221 and 222:
210 Comparison of several groups P
Page 223 and 224:
212 Comparison of several groups s
Page 225 and 226:
214 Comparison of several groups to
Page 227 and 228:
216 Comparison of several groups sh
Page 229 and 230:
218 Comparison of several groups s
Page 231 and 232:
220 Comparison of several groups su
Page 233 and 234:
222 Comparison of several groups No
Page 235 and 236:
224 Comparison of several groups yc
Page 237 and 238:
226 Comparison of several groups Q
Page 239 and 240:
228 Comparison of several groups te
Page 241 and 242:
230 Comparison of several groups Ta
Page 243 and 244:
232 Comparison of several groups Ta
Page 245 and 246:
234 Comparison of several groups th
Page 247 and 248:
9 Experimental design 9.1 General r
Page 249 and 250:
238 Experimental design the estimat
Page 251 and 252:
240 Experimental design Table 9.1 N
Page 253 and 254:
242 Experimental design Similarly,
Page 255 and 256:
244 Experimental design The sum of
Page 257 and 258:
246 Experimental design If, in a tw
Page 259 and 260:
248 Experimental design Table 9.5 S
Page 261 and 262:
250 Experimental design interaction
Page 263 and 264:
252 Experimental design difference
Page 265 and 266:
254 Experimental design Table 9.7 C
Page 267 and 268:
256 Experimental design interaction
Page 269 and 270:
258 Experimental design litters and
Page 271 and 272:
260 Experimental design randomizati
Page 273 and 274:
262 Experimental design rows, colum
Page 275 and 276:
264 Experimental design type of des
Page 277 and 278:
266 Experimental design Main unit S
Page 279 and 280:
268 Experimental design categories
Page 281 and 282:
270 Experimental design Example 9.6
Page 283 and 284:
10 Analysing non-normal data 10.1 D
Page 285 and 286:
274 Analysing non-normal data The s
Page 287 and 288:
276 Analysing non-normal data Estim
Page 289 and 290:
278 Analysing non-normal data betwe
Page 291 and 292:
Table 10.1 Some properties of three
Page 293 and 294:
282 Analysing non-normal data This
Page 295 and 296:
284 Analysing non-normal data High
Page 297 and 298:
286 Analysing non-normal data which
Page 299 and 300:
288 Analysing non-normal data Table
Page 301 and 302:
290 Analysing non-normal data 1 It
Page 303 and 304:
292 Analysing non-normal data It is
Page 305 and 306:
294 Analysing non-normal data proba
Page 307 and 308:
296 Analysing non-normal data Fract
Page 309 and 310:
298 Analysing non-normal data h=…
Page 311 and 312:
300 Analysing non-normal data This
Page 313 and 314:
302 Analysing non-normal data Boots
Page 315 and 316:
304 Analysing non-normal data more
Page 317 and 318:
306 Analysing non-normal data Sampl
Page 319 and 320:
308 Analysing non-normal data 3 squ
Page 321 and 322:
310 Analysing non-normal data mG ˆ
Page 323 and 324:
11 Modelling continuous data 11.1 A
Page 325 and 326:
314 Modelling continuous data Examp
Page 327 and 328:
316 Modelling continuous data n k i
Page 329 and 330:
318 Modelling continuous data consi
Page 331 and 332:
320 Modelling continuous data basis
Page 333 and 334:
322 Modelling continuous data 11.4
Page 335 and 336:
324 Modelling continuous data var
Page 337 and 338:
326 Modelling continuous data Table
Page 339 and 340:
328 Modelling continuous data Again
Page 341 and 342:
330 Modelling continuous data SSq D
Page 343 and 344:
332 Modelling continuous data Two g
Page 345 and 346:
334 Modelling continuous data which
Page 347 and 348:
336 Modelling continuous data the i
Page 349 and 350:
338 Modelling continuous data predi
Page 351 and 352:
340 Modelling continuous data equat
Page 353 and 354:
Page 355 and 356:
344 Modelling continuous data Somet
Page 357 and 358:
346 Modelling continuous data multi
Page 359 and 360:
348 Modelling continuous data (i) D
Page 361 and 362:
350 Modelling continuous data The r
Page 363 and 364:
352 Modelling continuous data In th
Page 365 and 366:
354 Modelling continuous data The c
Page 367 and 368:
356 Modelling continuous data If th
Page 369 and 370:
358 Modelling continuous data at th
Page 371 and 372:
360 Modelling continuous data about
Page 373 and 374:
362 Modelling continuous data y −
Page 375 and 376:
364 Modelling continuous data y −
Page 377 and 378:
366 Modelling continuous data outli
Page 379 and 380:
Page 381 and 382:
370 Modelling continuous data Patie
Page 383 and 384:
372 Modelling continuous data Norma
Page 385 and 386:
374 Modelling continuous data Cumul
Page 387 and 388:
Page 389 and 390:
12 Further regression models for a
Page 391 and 392:
380 Further regression models Table
Page 393 and 394:
382 Further regression models repre
Page 395 and 396:
384 Further regression models where
Page 397 and 398:
386 Further regression models Popul
Page 399 and 400:
388 Further regression models and S
Page 401 and 402:
390 Further regression models s(x)
Page 403 and 404:
392 Further regression models SS ˆ
Page 405 and 406:
394 Further regression models A…a
Page 407 and 408:
396 Further regression models and t
Page 409 and 410:
398 Further regression models that
Page 411 and 412:
400 Further regression models Regre
Page 413 and 414:
402 Further regression models M…T
Page 415 and 416:
404 Further regression models a0
Page 417 and 418:
406 Further regression models Maxim
Page 419 and 420:
408 Further regression models using
Page 421 and 422:
410 Further regression models suppo
Page 423 and 424:
412 Further regression models Dose
Page 425 and 426:
414 Further regression models Condu
Page 427 and 428:
416 Further regression models the p
Page 429 and 430:
418 Further regression models To be
Page 431 and 432:
420 Further regression models 9.5.
Page 433 and 434:
422 Further regression models in Ex
Page 435 and 436:
424 Further regression models param
Page 437 and 438:
426 Further regression models namel
Page 439 and 440:
428 Further regression models All t
Page 441 and 442:
430 Further regression models A not
Page 443 and 444:
432 Further regression models Appro
Page 445 and 446:
434 Further regression models form
Page 447 and 448:
436 Further regression models times
Page 449 and 450:
438 Further regression models block
Page 451 and 452:
440 Further regression models This
Page 453 and 454:
442 Further regression models Here
Page 455 and 456:
444 Further regression models follo
Page 457 and 458:
446 Further regression models missi
Page 459 and 460:
448 Further regression models probl
Page 461 and 462:
450 Further regression models perio
Page 463 and 464:
452 Further regression models betwe
Page 465 and 466:
454 Further regression models Spell
Page 467 and 468:
456 Multivariate methods 13.2 Princ
Page 469 and 470:
458 Multivariate methods High loadi
Page 471 and 472:
Table 13.1 Correlation matrix of 20
Page 473 and 474:
462 Multivariate methods eigenvalue
Page 475 and 476:
464 Multivariate methods The place
Page 477 and 478:
466 Multivariate methods allocation
Page 479 and 480:
468 Multivariate methods would pred
Page 481 and 482:
470 Multivariate methods and We fol
Page 483 and 484:
472 Multivariate methods In the dis
Page 485 and 486:
474 Multivariate methods Paired dat
Page 487 and 488:
476 Multivariate methods Mean SE (m
Page 489 and 490:
478 Multivariate methods x (3) x (5
Page 491 and 492:
480 Multivariate methods Allocation
Page 493 and 494:
482 Multivariate methods diagram in
Page 495 and 496:
484 Multivariate methods explanator
Page 497 and 498:
486 Modelling categorical data In t
Page 499 and 500:
488 Modelling categorical data calc
Page 501 and 502:
490 Modelling categorical data as t
Page 503 and 504:
492 Modelling categorical data DF.
Page 505 and 506:
494 Modelling categorical data in a
Page 507 and 508:
496 Modelling categorical data if p
Page 509 and 510:
498 Modelling categorical data When
Page 511 and 512:
500 Modelling categorical data Tabl
Page 513 and 514:
502 Modelling categorical data The
Page 515 and 516:
504 Empirical methods for categoric
Page 517 and 518:
Page 519 and 520:
Page 521 and 522:
Page 523 and 524:
Page 525 and 526:
Page 527 and 528:
Page 529 and 530:
Page 531 and 532:
Page 533 and 534:
Page 535 and 536:
Page 537 and 538:
Page 539 and 540:
16 Further Bayesian methods 16.1 Ba
Page 541 and 542:
530 Further Bayesian methods Analyt
Page 543 and 544:
532 Further Bayesian methods compli
Page 545 and 546:
534 Further Bayesian methods One ap
Page 547 and 548:
536 Further Bayesian methods result
Page 549 and 550:
538 Further Bayesian methods (i) th
Page 551 and 552:
540 Further Bayesian methods From (
Page 553 and 554:
542 Further Bayesian methods A stra
Page 555 and 556:
544 Further Bayesian methods the st
Page 557 and 558:
546 Further Bayesian methods but ma
Page 559 and 560:
548 Further Bayesian methods σ 30
Page 561 and 562:
550 Further Bayesian methods practi
Page 563 and 564:
552 Further Bayesian methods which
Page 565 and 566:
554 Further Bayesian methods Densit
Page 567 and 568:
556 Further Bayesian methods recurr
Page 569 and 570:
558 Further Bayesian methods a ˆ m
Page 571 and 572:
560 Further Bayesian methods values
Page 573 and 574:
562 Further Bayesian methods distri
Page 575 and 576:
564 Further Bayesian methods the se
Page 577 and 578:
566 Further Bayesian methods probab
Page 579 and 580:
17 Survival analysis 17.1 Introduct
Page 581 and 582:
570 Survival analysis Table 17.1 Cu
Page 583 and 584:
572 Survival analysis Table 17.2 Li
Page 585 and 586:
574 Survival analysis otherwise the
Page 587 and 588:
576 Survival analysis qtj ˆ dj=n 0
Page 589 and 590:
578 Survival analysis quantities in
Page 591 and 592:
580 Survival analysis Survival % 10
Page 593 and 594:
582 Survival analysis logrank test
Page 595 and 596:
584 Survival analysis the mean surv
Page 597 and 598:
586 Survival analysis the death rat
Page 599 and 600:
588 Survival analysis McGilchrist a
Page 601 and 602:
590 Survival analysis The martingal
Page 603 and 604:
592 Clinical trials trials. In drug
Page 605 and 606:
594 Clinical trials first type of e
Page 607 and 608: 596 Clinical trials . Proposed numb
Page 609 and 610: 598 Clinical trials If the response
Page 611 and 612: 600 Clinical trials methods of Baye
Page 613 and 614: 602 Clinical trials represented by
Page 615 and 616: 604 Clinical trials physicians find
Page 617 and 618: 606 Clinical trials very minor proc
Page 619 and 620: 608 Clinical trials each patient's
Page 621 and 622: 610 Clinical trials Table 18.1 Resu
Page 623 and 624: 612 Clinical trials solution is ava
Page 625 and 626: 614 Clinical trials Administrative
Page 627 and 628: 616 Clinical trials non-sequential
Page 629 and 630: 618 Clinical trials Table 18.3 Maxi
Page 631 and 632: 620 Clinical trials Standardized de
Page 633 and 634: 622 Clinical trials A somewhat diff
Page 635 and 636: 624 Clinical trials A trial showing
Page 637 and 638: 626 Clinical trials Publication bia
Page 639 and 640: 628 Clinical trials on different oc
Page 641 and 642: 630 Clinical trials Table 18.5 Numb
Page 643 and 644: 632 Clinical trials Treatment perio
Page 645 and 646: 634 Clinical trials in cases where
Page 647 and 648: 636 Clinical trials independent, an
Page 649 and 650: 638 Clinical trials Sample size The
Page 651 and 652: 640 Clinical trials and the restric
Page 653 and 654: 642 Clinical trials original data.
Page 655 and 656: 644 Clinical trials if the odds rat
Page 657: 646 Clinical trials 3 2 1 0 -1 -2 -
Page 661 and 662: 650 Statistical methods in epidemio
Page 675 and 676: Table 19.1 Death rate for two popul
Page 709 and 710:
698 Statistical methods in epidemio
Page 711 and 712:
Page 713 and 714:
Page 715 and 716:
Page 717 and 718:
Page 719 and 720:
Page 721 and 722:
Page 723 and 724:
Page 725 and 726:
Page 727 and 728:
Page 729 and 730:
718 Laboratory assays such cases, t
Page 731 and 732:
720 Laboratory assays and YT ˆ yT
Page 733 and 734:
722 Laboratory assays significant a
Page 735 and 736:
724 Laboratory assays The general p
Page 737 and 738:
726 Laboratory assays This relation
Page 739 and 740:
728 Laboratory assays Proportion po
Page 741 and 742:
730 Laboratory assays P contribute
Page 743 and 744:
732 Laboratory assays transformatio
Page 745 and 746:
734 Laboratory assays Table 20.1 Es
Page 747 and 748:
736 Laboratory assays P m iˆ1 ri l
Page 749 and 750:
738 Laboratory assays synthesize hi
Page 751 and 752:
740 Laboratory assays estimate of a
Page 754 and 755:
Appendix tables 743
Page 756 and 757:
2 0 0 02275 0 02222 0 02169 0 02118
Page 758 and 759:
16 6 91 93 1 11 91 153 4 19 3 7 23
Page 760 and 761:
16 0 128 0 258 0 392 0 535 0 690 0
Page 762 and 763:
5 0 05 6 61 5 79 5 41 5 19 5 05 4 9
Page 764 and 765:
3 0 0 05 4 17 3 32 2 92 2 69 2 53 2
Page 766 and 767:
14 0.05 3 03 3 70 4 11 4 41 4 64 4
Page 768 and 769:
Table A7 Percentage points for the
Page 770 and 771:
Table A9 Sample size for detecting
Page 772 and 773:
Bailey N.T.J. (1975) The Mathematic
Page 774 and 775:
Buyse M.E., Staquet M.J. and Sylves
Page 776 and 777:
eceptor interactions. J. Ster. Bioc
Page 778 and 779:
Etzioni R.D. and Weiss N.S. (1998)
Page 780 and 781:
Goetghebeur E. and Lapp K. (1997) T
Page 782 and 783:
sample data in randomized block and
Page 784 and 785:
Lehmann E.L. (1975) Nonparametrics:
Page 786 and 787:
Mehta C.R. (1994) The exact analysi
Page 788 and 789:
Peto R., Pike M., Day N. et al. (19
Page 790 and 791:
Scott J.E.S., Hunter E.W., Lee R.E.
Page 792 and 793:
Thompson S.G. and Barber J.A. (2000
Page 794 and 795:
Zhang H., Crowley J., Sox H.C. and
Page 796 and 797:
786 Author Index Brooks, S.P. 549,
Page 798 and 799:
788 Author Index Gart, J.J. 127, 67
Page 800 and 801:
790 Author Index Laurence, D.R. 519
Page 802 and 803:
792 Author Index RamoÂn, J.M. 536
Page 804 and 805:
794 Author Index Westley-Wise, V.J.
Page 806 and 807:
796 Subject Index Assays (cont.) ra
Page 808 and 809:
798 Subject Index Chronic obstructi
Page 810 and 811:
800 Subject Index Continuous variab
Page 812 and 813:
802 Subject Index Dot diagram 23, 2
Page 814 and 815:
804 Subject Index Growth curves 409
Page 816 and 817:
806 Subject Index McNemar's test 12
Page 818 and 819:
808 Subject Index Normal (cont.) st
Page 820 and 821:
810 Subject Index Proportions Bayes
Page 822 and 823:
812 Subject Index Roughness penalty
Page 824 and 825:
814 Subject Index Standard (cont.)
Page 826:
816 Subject Index Tumour (cont.) in
show all

Statistical Methods in Medical Research 4ed

Create successful ePaper yourself

Delete template?

Save as template?