3901:
1041:. (Buckley and James proposed a semi-parametric AFT but its use is relatively uncommon in applied research; in a 1992 paper, Wei pointed out that the BuckleyâJames model has no theoretical justification and lacks robustness, and reviewed alternatives.) This can be a problem, if a degree of realistic detail is required for modelling the distribution of a baseline lifetime. Hence, technical developments in this direction would be highly desirable.
3887:
3925:
3913:
1176:
as a special case) can be parameterised as either a proportional hazards model or an AFT model, and is the only family of distributions to have this property. The results of fitting a
Weibull model can therefore be interpreted in either framework. However, the biological applicability of this model
944:
means that everything in the relevant life history of an individual happens twice as fast. For example, if the model concerns the development of a tumor, it means that all of the pre-stages progress twice as fast as for the unexposed individual, implying that the expected time until a clinical
868:. In fact, the former case represents survival, while the later case represents an event/death/censoring during the follow-up. These right-censored observations can pose technical challenges for estimating the model, if the distribution of
612:
144:
338:
62:
by some constant, an AFT model assumes that the effect of a covariate is to accelerate or decelerate the life course of a disease by some constant. There is strong basic science evidence from
404:
1163:
980:
262:
826:
719:
1404:
Keiding, N.; Andersen, P. K.; Klein, J. P. (1997). "The Role of
Frailty Models and Accelerated Failure Time Models in Describing Heterogeneity Due to Omitted Covariates".
1039:
866:
656:
1441:"On the use of the accelerated failure time model as an alternative to the proportional hazards model in the treatment of time to event data: A case study in influenza"
1099:. For the censored observations one needs the survival function, which is the complement of the cumulative distribution function, i.e. one needs to be able to evaluate
942:
759:
739:
447:
916:
676:
506:
169:
893:
786:
474:
3022:
788:, i.e., different baseline distributions of the survival time. Typically, in survival-analytic contexts, many of the observations are censored: we only know that
3527:
424:
1059:
on the new treatment compared to the control. So a patient could be informed that he would be expected to live (say) 15% longer if he took the new treatment.
3677:
3301:
1473:
Bradburn, MJ; Clark, TG; Love, SB; Altman, DG (2003), "Survival
Analysis Part II: Multivariate data analysis - an introduction to concepts and methods",
1942:
516:
3075:
3514:
1208:, although they are less popular than the log-logistic, partly as their cumulative distribution functions do not have a closed form. Finally, the
998:'s semi-parametric proportional hazards model is more widely used than parametric models, AFT models are predominantly fully parametric i.e. a
1587:
1569:
1548:
1937:
1637:
1417:
2541:
1689:
3929:
84:
1605:
Bagdonavicius, Vilijandas; Nikulin, Mikhail (2002), Accelerated Life Models. Modeling and
Statistical Analysis, Chapman&Hall/CRC,
3324:
3216:
1610:
1600:
1044:
When a frailty term is incorporated in the survival model, the regression parameter estimates from AFT models are robust to omitted
1048:, unlike proportional hazards models. They are also less affected by the choice of probability distribution for the frailty term.
3502:
3376:
1088:
1331:
Wei, L. J. (1992). "The accelerated failure time model: A useful alternative to the cox regression model in survival analysis".
3560:
3221:
2966:
2337:
1927:
2551:
2823:
2630:
2519:
2477:
1209:
1716:
3854:
2813:
1205:
1197:
2863:
278:
3405:
3354:
3339:
3329:
3198:
3070:
3037:
2818:
2648:
272:
3474:
2775:
3749:
3550:
2529:
2198:
1662:
1181:
51:
3634:
3601:
68:
experiments by
Stroustrup et al. indicating that AFT models are the correct model for biological survival processes.
1083:
hazard function which increases at early times and decreases at later times. It is somewhat similar in shape to the
3951:
3606:
3349:
3108:
3014:
2994:
2902:
2613:
2431:
1914:
1786:
983:
2780:
2546:
2404:
347:
3366:
3134:
2855:
2709:
2638:
2558:
2416:
2397:
2105:
1826:
1368:"Parametric accelerated failure time models with random effects and an application to kidney transplant survival"
1102:
1072:
3479:
3849:
3616:
3164:
3129:
3093:
2878:
2320:
2229:
2188:
2100:
1791:
1630:
1557:
1173:
999:
995:
2886:
2870:
268:
the survival time, but this is merely a sign convention; without a negative sign, they increase the hazard.)
3758:
3371:
3311:
3248:
2608:
2470:
2460:
2310:
2224:
1217:
1189:
1084:
3519:
3456:
3796:
3726:
3211:
3098:
2095:
1992:
1899:
1778:
1677:
1096:
1092:
264:. (Specifying the regression coefficients with a negative sign implies that high values of the covariates
63:
3917:
2795:
948:
3821:
3763:
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3334:
3060:
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2257:
2203:
2178:
2133:
2072:
2032:
1834:
1657:
1201:
1185:
1177:
may be limited by the fact that the hazard function is monotonic, i.e. either decreasing or increasing.
47:
3900:
2790:
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3319:
3268:
3244:
3206:
3124:
3103:
3055:
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2618:
2536:
2509:
2465:
2421:
2183:
1959:
1839:
1213:
1169:
1076:
174:
1595:
Martinussen, Torben; Scheike, Thomas (2006), Dynamic
Regression Models for Survival Data, Springer,
791:
689:
3891:
3816:
3739:
3420:
3184:
3177:
3139:
3047:
3027:
2999:
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2143:
1922:
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1721:
1623:
679:
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3188:
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2302:
2262:
2208:
2125:
1811:
1806:
1314:
1221:
1193:
1005:
831:
622:
1055:
with mortality as the endpoint could be interpreted as a certain percentage increase in future
921:
744:
724:
3811:
3781:
3773:
3593:
3584:
3509:
3440:
3296:
3281:
3256:
3144:
3085:
2951:
2939:
2565:
2482:
2426:
2349:
2193:
2115:
1894:
1768:
1606:
1596:
1583:
1565:
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1528:
1500:
1421:
1387:
1348:
429:
341:
35:
901:
661:
479:
154:
3836:
3791:
3555:
3542:
3435:
3410:
3344:
3276:
3154:
2762:
2655:
2588:
2501:
2448:
2267:
2138:
1932:
1731:
1698:
1520:
1490:
1482:
1452:
1413:
1379:
1340:
1306:
1262:
1254:
871:
764:
452:
3753:
3497:
3359:
3286:
2961:
2835:
2808:
2785:
2754:
2381:
2376:
2330:
2060:
1711:
1056:
945:
disease is 0.5 of the baseline time. However, this does not mean that the hazard function
3702:
3697:
2160:
2090:
1736:
1495:
1267:
1052:
409:
3945:
3859:
3826:
3689:
3650:
3461:
3430:
2894:
2848:
2453:
2155:
1982:
1746:
1741:
1524:
1440:
2012:
3801:
3734:
3711:
3626:
2956:
2252:
2150:
2085:
2027:
1949:
1904:
1060:
683:
3844:
3806:
3489:
3390:
3252:
3065:
3032:
2524:
2441:
2436:
2080:
2037:
2017:
1997:
1987:
1756:
1051:
The results of AFT models are easily interpreted. For example, the results of a
59:
1456:
607:{\displaystyle \log(T)=-\log(\theta )+\log(T\theta ):=-\log(\theta )+\epsilon }
2690:
2170:
1870:
1801:
1751:
1726:
1646:
1310:
1297:
Buckley, Jonathan; James, Ian (1979), "Linear regression with censored data",
1242:
31:
2843:
2695:
2315:
2110:
2022:
2007:
2002:
1967:
1418:
10.1002/(SICI)1097-0258(19970130)16:2<215::AID-SIM481>3.0.CO;2-J
1080:
1045:
55:
1532:
1504:
1486:
1391:
1344:
76:
In full generality, the accelerated failure time model can be specified as
1425:
1367:
1352:
2359:
1977:
1854:
1849:
1844:
1816:
17:
1366:
Lambert, Philippe; Collett, Dave; Kimber, Alan; Johnson, Rachel (2004),
1258:
3864:
3565:
1318:
1580:
Analysing
Survival Data from Clinical Trials and Observational Studies
3786:
2767:
2741:
2721:
1972:
1763:
1383:
54:. Whereas a proportional hazards model assumes that the effect of a
1095:, which becomes important computationally when fitting data with
139:{\displaystyle \lambda (t|\theta )=\theta \lambda _{0}(\theta t)}
1706:
1188:, is suitable for an AFT model. Other distributions include the
3675:
3242:
2989:
2288:
2058:
1675:
1619:
1615:
406:. From this it is easy to see that the moderated life time
1511:
Hougaard, Philip (1999), "Fundamentals of
Survival Data",
1286:. Hoboken, NJ: Wiley Series in Probability and Statistics.
50:
model that provides an alternative to the commonly used
1284:
The
Statistical Analysis of Failure Time Data (2nd ed.)
1243:"The temporal scaling of Caenorhabditis elegans ageing"
918:
in accelerated failure time models is straightforward:
1075:
provides the most commonly used AFT model. Unlike the
1105:
1008:
951:
924:
904:
874:
834:
794:
767:
747:
727:
692:
678:. This reduces the accelerated failure time model to
664:
625:
519:
482:
455:
432:
412:
350:
281:
177:
157:
87:
3528:
Autoregressive conditional heteroskedasticity (ARCH)
1212:
is a three-parameter distribution that includes the
3835:
3772:
3725:
3688:
3643:
3625:
3592:
3583:
3541:
3488:
3449:
3398:
3389:
3310:
3267:
3197:
3163:
3117:
3084:
3046:
3013:
2925:
2834:
2753:
2708:
2676:
2629:
2574:
2500:
2491:
2301:
2243:
2217:
2169:
2124:
2071:
1958:
1913:
1887:
1869:
1825:
1777:
1697:
1688:
333:{\displaystyle f(t|\theta )=\theta f_{0}(\theta t)}
1578:Marubini, Ettore; Valsecchi, Maria Grazia (1995),
1157:
1033:
974:
936:
910:
887:
860:
820:
780:
753:
733:
713:
670:
650:
606:
500:
468:
441:
418:
398:
332:
256:
171:denotes the joint effect of covariates, typically
163:
138:
741:represents the noise. Different distributions of
3076:Multivariate adaptive regression splines (MARS)
1063:can prove harder to explain in layman's terms.
1631:
994:Unlike proportional hazards models, in which
8:
982:is always twice as high - that would be the
399:{\displaystyle S(t|\theta )=S_{0}(\theta t)}
1541:Modelling Survival Data in Medical Research
1158:{\displaystyle S(t|\theta )=1-F(t|\theta )}
1087:but it has heavier tails. The log-logistic
3685:
3672:
3589:
3395:
3264:
3239:
3010:
2986:
2714:
2497:
2298:
2285:
2068:
2055:
1694:
1685:
1672:
1638:
1624:
1616:
476:have the same distribution. Consequently,
1494:
1439:Kay, Richard; Kinnersley, Nelson (2002),
1266:
1144:
1115:
1104:
1022:
1007:
961:
950:
923:
903:
879:
873:
852:
839:
833:
812:
799:
793:
772:
766:
746:
726:
691:
663:
639:
624:
518:
481:
460:
454:
431:
411:
378:
360:
349:
312:
291:
280:
242:
232:
213:
203:
176:
156:
118:
97:
86:
1241:Stroustrup, Nicholas (16 January 2016).
1233:
3602:KaplanâMeier estimator (product limit)
619:where the last term is distributed as
27:Parametric model in survival analysis
7:
3912:
3612:Accelerated failure time (AFT) model
3924:
3207:Analysis of variance (ANOVA, anova)
1282:Kalbfleisch & Prentice (2002).
975:{\displaystyle \lambda (t|\theta )}
3302:CochranâMantelâHaenszel statistics
1928:Pearson product-moment correlation
721:represents the fixed effects, and
25:
761:imply different distributions of
3923:
3911:
3899:
3886:
3885:
1525:10.1111/j.0006-341X.1999.00013.x
1224:distributions as special cases.
1089:cumulative distribution function
1067:Distributions used in AFT models
3561:Least-squares spectral analysis
257:{\displaystyle \theta =\exp(-)}
40:accelerated failure time model
2542:Mean-unbiased minimum-variance
1210:generalized gamma distribution
1206:inverse Gaussian distributions
1152:
1145:
1138:
1123:
1116:
1109:
1028:
1015:
969:
962:
955:
821:{\displaystyle T_{i}>t_{i}}
714:{\displaystyle -\log(\theta )}
708:
702:
645:
632:
595:
589:
574:
565:
553:
547:
532:
526:
495:
489:
449:and the unmoderated life time
393:
384:
368:
361:
354:
327:
318:
299:
292:
285:
251:
248:
196:
190:
133:
124:
105:
98:
91:
1:
3855:Geographic information system
3071:Simultaneous equations models
1182:multiplicatively closed group
3038:Coefficient of determination
2649:Uniformly most powerful test
275:of the event is taken to be
273:probability density function
3607:Proportional hazards models
3551:Spectral density estimation
3533:Vector autoregression (VAR)
2967:Maximum posterior estimator
2199:Randomized controlled trial
1543:(2nd ed.), CRC press,
1034:{\displaystyle \log(T_{0})}
861:{\displaystyle T_{i}=t_{i}}
651:{\displaystyle \log(T_{0})}
52:proportional hazards models
3968:
3367:Multivariate distributions
1787:Average absolute deviation
1457:10.1177/009286150203600312
984:proportional hazards model
340:; it then follows for the
3881:
3684:
3671:
3355:Structural equation model
3263:
3238:
3009:
2985:
2717:
2691:Score/Lagrange multiplier
2297:
2284:
2106:Sample size determination
2067:
2054:
1684:
1671:
1653:
1562:Analysis of Survival Data
1475:British Journal of Cancer
1073:log-logistic distribution
937:{\displaystyle \theta =2}
754:{\displaystyle \epsilon }
734:{\displaystyle \epsilon }
658:, i.e., independently of
426:is distributed such that
271:This is satisfied if the
3850:Environmental statistics
3372:Elliptical distributions
3165:Generalized linear model
3094:Simple linear regression
2864:HodgesâLehmann estimator
2321:Probability distribution
2230:Stochastic approximation
1792:Coefficient of variation
1445:Drug Information Journal
1174:exponential distribution
1000:probability distribution
442:{\displaystyle T\theta }
3510:Cross-correlation (XCF)
3118:Non-standard predictors
2552:LehmannâScheffĂ© theorem
2225:Adaptive clinical trial
1311:10.1093/biomet/66.3.429
1085:log-normal distribution
1079:, it can exhibit a non-
911:{\displaystyle \theta }
671:{\displaystyle \theta }
501:{\displaystyle \log(T)}
164:{\displaystyle \theta }
3906:Mathematics portal
3727:Engineering statistics
3635:NelsonâAalen estimator
3212:Analysis of covariance
3099:Ordinary least squares
3023:Pearson product-moment
2427:Statistical functional
2338:Empirical distribution
2171:Controlled experiments
1900:Frequency distribution
1678:Descriptive statistics
1487:10.1038/sj.bjc.6601119
1406:Statistics in Medicine
1372:Statistics in Medicine
1345:10.1002/sim.4780111409
1333:Statistics in Medicine
1180:Any distribution on a
1159:
1035:
976:
938:
912:
898:The interpretation of
889:
862:
822:
782:
755:
735:
715:
672:
652:
608:
502:
470:
443:
420:
400:
334:
258:
165:
140:
3822:Population statistics
3764:System identification
3498:Autocorrelation (ACF)
3426:Exponential smoothing
3340:Discriminant analysis
3335:Canonical correlation
3199:Partition of variance
3061:Regression validation
2905:(JonckheereâTerpstra)
2804:Likelihood-ratio test
2493:Frequentist inference
2405:Locationâscale family
2326:Sampling distribution
2291:Statistical inference
2258:Cross-sectional study
2245:Observational studies
2204:Randomized experiment
2033:Stem-and-leaf display
1835:Central limit theorem
1202:Gompertz distribution
1186:positive real numbers
1160:
1036:
977:
939:
913:
890:
888:{\displaystyle T_{0}}
863:
823:
783:
781:{\displaystyle T_{0}}
756:
736:
716:
673:
653:
609:
503:
471:
469:{\displaystyle T_{0}}
444:
421:
401:
335:
259:
166:
141:
3745:Probabilistic design
3330:Principal components
3173:Exponential families
3125:Nonlinear regression
3104:General linear model
3066:Mixed effects models
3056:Errors and residuals
3033:Confounding variable
2935:Bayesian probability
2913:Van der Waerden test
2903:Ordered alternative
2668:Multiple comparisons
2547:RaoâBlackwellization
2510:Estimating equations
2466:Statistical distance
2184:Factorial experiment
1717:Arithmetic-Geometric
1560:; Oakes, D. (1984),
1539:Collett, D. (2003),
1339:(14â15): 1871â1879.
1170:Weibull distribution
1103:
1077:Weibull distribution
1006:
949:
922:
902:
872:
832:
792:
765:
745:
725:
690:
662:
623:
517:
480:
453:
430:
410:
348:
279:
175:
155:
85:
3817:Official statistics
3740:Methods engineering
3421:Seasonal adjustment
3189:Poisson regressions
3109:Bayesian regression
3048:Regression analysis
3028:Partial correlation
3000:Regression analysis
2599:Prediction interval
2594:Likelihood interval
2584:Confidence interval
2576:Interval estimation
2537:Unbiased estimators
2355:Model specification
2235:Up-and-down designs
1923:Partial correlation
1879:Index of dispersion
1797:Interquartile range
1259:10.1038/nature16550
680:regression analysis
72:Model specification
58:is to multiply the
3837:Spatial statistics
3717:Medical statistics
3617:First hitting time
3571:Whittle likelihood
3222:Degrees of freedom
3217:Multivariate ANOVA
3150:Heteroscedasticity
2962:Bayesian estimator
2927:Bayesian inference
2776:KolmogorovâSmirnov
2661:Randomization test
2631:Testing hypotheses
2604:Tolerance interval
2515:Maximum likelihood
2410:Exponential family
2343:Density estimation
2303:Statistical theory
2263:Natural experiment
2209:Scientific control
2126:Survey methodology
1812:Standard deviation
1155:
1031:
990:Statistical issues
972:
934:
908:
885:
858:
818:
778:
751:
731:
711:
668:
648:
604:
508:can be written as
498:
466:
439:
416:
396:
330:
254:
161:
136:
3952:Survival analysis
3939:
3938:
3877:
3876:
3873:
3872:
3812:National accounts
3782:Actuarial science
3774:Social statistics
3667:
3666:
3663:
3662:
3659:
3658:
3594:Survival function
3579:
3578:
3441:Granger causality
3282:Contingency table
3257:Survival analysis
3234:
3233:
3230:
3229:
3086:Linear regression
2981:
2980:
2977:
2976:
2952:Credible interval
2921:
2920:
2704:
2703:
2520:Method of moments
2389:Parametric family
2350:Statistical model
2280:
2279:
2276:
2275:
2194:Random assignment
2116:Statistical power
2050:
2049:
2046:
2045:
1895:Contingency table
1865:
1864:
1732:Generalized/power
1589:978-0-470-09341-2
1571:978-0-412-24490-2
1558:Cox, David Roxbee
1550:978-1-58488-325-8
1378:(20): 3177â3192,
1253:(7588): 103â107.
1002:is specified for
419:{\displaystyle T}
342:survival function
36:survival analysis
16:(Redirected from
3959:
3927:
3926:
3915:
3914:
3904:
3903:
3889:
3888:
3792:Crime statistics
3686:
3673:
3590:
3556:Fourier analysis
3543:Frequency domain
3523:
3470:
3436:Structural break
3396:
3345:Cluster analysis
3292:Log-linear model
3265:
3240:
3181:
3155:Homoscedasticity
3011:
2987:
2906:
2898:
2890:
2889:(KruskalâWallis)
2874:
2859:
2814:Cross validation
2799:
2781:AndersonâDarling
2728:
2715:
2686:Likelihood-ratio
2678:Parametric tests
2656:Permutation test
2639:1- & 2-tails
2530:Minimum distance
2502:Point estimation
2498:
2449:Optimal decision
2400:
2299:
2286:
2268:Quasi-experiment
2218:Adaptive designs
2069:
2056:
1933:Rank correlation
1695:
1686:
1673:
1640:
1633:
1626:
1617:
1592:
1574:
1553:
1535:
1507:
1498:
1460:
1459:
1436:
1430:
1429:
1412:(1â3): 215â224.
1401:
1395:
1394:
1384:10.1002/sim.1876
1363:
1357:
1356:
1328:
1322:
1321:
1294:
1288:
1287:
1279:
1273:
1272:
1270:
1238:
1164:
1162:
1161:
1156:
1148:
1119:
1040:
1038:
1037:
1032:
1027:
1026:
981:
979:
978:
973:
965:
943:
941:
940:
935:
917:
915:
914:
909:
894:
892:
891:
886:
884:
883:
867:
865:
864:
859:
857:
856:
844:
843:
827:
825:
824:
819:
817:
816:
804:
803:
787:
785:
784:
779:
777:
776:
760:
758:
757:
752:
740:
738:
737:
732:
720:
718:
717:
712:
677:
675:
674:
669:
657:
655:
654:
649:
644:
643:
613:
611:
610:
605:
507:
505:
504:
499:
475:
473:
472:
467:
465:
464:
448:
446:
445:
440:
425:
423:
422:
417:
405:
403:
402:
397:
383:
382:
364:
339:
337:
336:
331:
317:
316:
295:
263:
261:
260:
255:
247:
246:
237:
236:
218:
217:
208:
207:
170:
168:
167:
162:
145:
143:
142:
137:
123:
122:
101:
21:
3967:
3966:
3962:
3961:
3960:
3958:
3957:
3956:
3942:
3941:
3940:
3935:
3898:
3869:
3831:
3768:
3754:quality control
3721:
3703:Clinical trials
3680:
3655:
3639:
3627:Hazard function
3621:
3575:
3537:
3521:
3484:
3480:BreuschâGodfrey
3468:
3445:
3385:
3360:Factor analysis
3306:
3287:Graphical model
3259:
3226:
3193:
3179:
3159:
3113:
3080:
3042:
3005:
3004:
2973:
2917:
2904:
2896:
2888:
2872:
2857:
2836:Rank statistics
2830:
2809:Model selection
2797:
2755:Goodness of fit
2749:
2726:
2700:
2672:
2625:
2570:
2559:Median unbiased
2487:
2398:
2331:Order statistic
2293:
2272:
2239:
2213:
2165:
2120:
2063:
2061:Data collection
2042:
1954:
1909:
1883:
1861:
1821:
1773:
1690:Continuous data
1680:
1667:
1649:
1644:
1590:
1577:
1572:
1556:
1551:
1538:
1510:
1472:
1469:
1467:Further reading
1464:
1463:
1438:
1437:
1433:
1403:
1402:
1398:
1365:
1364:
1360:
1330:
1329:
1325:
1296:
1295:
1291:
1281:
1280:
1276:
1240:
1239:
1235:
1230:
1172:(including the
1101:
1100:
1069:
1057:life expectancy
1018:
1004:
1003:
992:
947:
946:
920:
919:
900:
899:
875:
870:
869:
848:
835:
830:
829:
808:
795:
790:
789:
768:
763:
762:
743:
742:
723:
722:
688:
687:
660:
659:
635:
621:
620:
515:
514:
478:
477:
456:
451:
450:
428:
427:
408:
407:
374:
346:
345:
308:
277:
276:
238:
228:
209:
199:
173:
172:
153:
152:
114:
83:
82:
74:
28:
23:
22:
15:
12:
11:
5:
3965:
3963:
3955:
3954:
3944:
3943:
3937:
3936:
3934:
3933:
3921:
3909:
3895:
3882:
3879:
3878:
3875:
3874:
3871:
3870:
3868:
3867:
3862:
3857:
3852:
3847:
3841:
3839:
3833:
3832:
3830:
3829:
3824:
3819:
3814:
3809:
3804:
3799:
3794:
3789:
3784:
3778:
3776:
3770:
3769:
3767:
3766:
3761:
3756:
3747:
3742:
3737:
3731:
3729:
3723:
3722:
3720:
3719:
3714:
3709:
3700:
3698:Bioinformatics
3694:
3692:
3682:
3681:
3676:
3669:
3668:
3665:
3664:
3661:
3660:
3657:
3656:
3654:
3653:
3647:
3645:
3641:
3640:
3638:
3637:
3631:
3629:
3623:
3622:
3620:
3619:
3614:
3609:
3604:
3598:
3596:
3587:
3581:
3580:
3577:
3576:
3574:
3573:
3568:
3563:
3558:
3553:
3547:
3545:
3539:
3538:
3536:
3535:
3530:
3525:
3517:
3512:
3507:
3506:
3505:
3503:partial (PACF)
3494:
3492:
3486:
3485:
3483:
3482:
3477:
3472:
3464:
3459:
3453:
3451:
3450:Specific tests
3447:
3446:
3444:
3443:
3438:
3433:
3428:
3423:
3418:
3413:
3408:
3402:
3400:
3393:
3387:
3386:
3384:
3383:
3382:
3381:
3380:
3379:
3364:
3363:
3362:
3352:
3350:Classification
3347:
3342:
3337:
3332:
3327:
3322:
3316:
3314:
3308:
3307:
3305:
3304:
3299:
3297:McNemar's test
3294:
3289:
3284:
3279:
3273:
3271:
3261:
3260:
3243:
3236:
3235:
3232:
3231:
3228:
3227:
3225:
3224:
3219:
3214:
3209:
3203:
3201:
3195:
3194:
3192:
3191:
3175:
3169:
3167:
3161:
3160:
3158:
3157:
3152:
3147:
3142:
3137:
3135:Semiparametric
3132:
3127:
3121:
3119:
3115:
3114:
3112:
3111:
3106:
3101:
3096:
3090:
3088:
3082:
3081:
3079:
3078:
3073:
3068:
3063:
3058:
3052:
3050:
3044:
3043:
3041:
3040:
3035:
3030:
3025:
3019:
3017:
3007:
3006:
3003:
3002:
2997:
2991:
2990:
2983:
2982:
2979:
2978:
2975:
2974:
2972:
2971:
2970:
2969:
2959:
2954:
2949:
2948:
2947:
2942:
2931:
2929:
2923:
2922:
2919:
2918:
2916:
2915:
2910:
2909:
2908:
2900:
2892:
2876:
2873:(MannâWhitney)
2868:
2867:
2866:
2853:
2852:
2851:
2840:
2838:
2832:
2831:
2829:
2828:
2827:
2826:
2821:
2816:
2806:
2801:
2798:(ShapiroâWilk)
2793:
2788:
2783:
2778:
2773:
2765:
2759:
2757:
2751:
2750:
2748:
2747:
2739:
2730:
2718:
2712:
2710:Specific tests
2706:
2705:
2702:
2701:
2699:
2698:
2693:
2688:
2682:
2680:
2674:
2673:
2671:
2670:
2665:
2664:
2663:
2653:
2652:
2651:
2641:
2635:
2633:
2627:
2626:
2624:
2623:
2622:
2621:
2616:
2606:
2601:
2596:
2591:
2586:
2580:
2578:
2572:
2571:
2569:
2568:
2563:
2562:
2561:
2556:
2555:
2554:
2549:
2534:
2533:
2532:
2527:
2522:
2517:
2506:
2504:
2495:
2489:
2488:
2486:
2485:
2480:
2475:
2474:
2473:
2463:
2458:
2457:
2456:
2446:
2445:
2444:
2439:
2434:
2424:
2419:
2414:
2413:
2412:
2407:
2402:
2386:
2385:
2384:
2379:
2374:
2364:
2363:
2362:
2357:
2347:
2346:
2345:
2335:
2334:
2333:
2323:
2318:
2313:
2307:
2305:
2295:
2294:
2289:
2282:
2281:
2278:
2277:
2274:
2273:
2271:
2270:
2265:
2260:
2255:
2249:
2247:
2241:
2240:
2238:
2237:
2232:
2227:
2221:
2219:
2215:
2214:
2212:
2211:
2206:
2201:
2196:
2191:
2186:
2181:
2175:
2173:
2167:
2166:
2164:
2163:
2161:Standard error
2158:
2153:
2148:
2147:
2146:
2141:
2130:
2128:
2122:
2121:
2119:
2118:
2113:
2108:
2103:
2098:
2093:
2091:Optimal design
2088:
2083:
2077:
2075:
2065:
2064:
2059:
2052:
2051:
2048:
2047:
2044:
2043:
2041:
2040:
2035:
2030:
2025:
2020:
2015:
2010:
2005:
2000:
1995:
1990:
1985:
1980:
1975:
1970:
1964:
1962:
1956:
1955:
1953:
1952:
1947:
1946:
1945:
1940:
1930:
1925:
1919:
1917:
1911:
1910:
1908:
1907:
1902:
1897:
1891:
1889:
1888:Summary tables
1885:
1884:
1882:
1881:
1875:
1873:
1867:
1866:
1863:
1862:
1860:
1859:
1858:
1857:
1852:
1847:
1837:
1831:
1829:
1823:
1822:
1820:
1819:
1814:
1809:
1804:
1799:
1794:
1789:
1783:
1781:
1775:
1774:
1772:
1771:
1766:
1761:
1760:
1759:
1754:
1749:
1744:
1739:
1734:
1729:
1724:
1722:Contraharmonic
1719:
1714:
1703:
1701:
1692:
1682:
1681:
1676:
1669:
1668:
1666:
1665:
1660:
1654:
1651:
1650:
1645:
1643:
1642:
1635:
1628:
1620:
1614:
1613:
1603:
1593:
1588:
1575:
1570:
1554:
1549:
1536:
1508:
1481:(3): 431â436,
1468:
1465:
1462:
1461:
1451:(3): 571â579,
1431:
1396:
1358:
1323:
1305:(3): 429â436,
1289:
1274:
1232:
1231:
1229:
1226:
1184:, such as the
1154:
1151:
1147:
1143:
1140:
1137:
1134:
1131:
1128:
1125:
1122:
1118:
1114:
1111:
1108:
1068:
1065:
1053:clinical trial
1030:
1025:
1021:
1017:
1014:
1011:
991:
988:
971:
968:
964:
960:
957:
954:
933:
930:
927:
907:
882:
878:
855:
851:
847:
842:
838:
815:
811:
807:
802:
798:
775:
771:
750:
730:
710:
707:
704:
701:
698:
695:
667:
647:
642:
638:
634:
631:
628:
617:
616:
615:
614:
603:
600:
597:
594:
591:
588:
585:
582:
579:
576:
573:
570:
567:
564:
561:
558:
555:
552:
549:
546:
543:
540:
537:
534:
531:
528:
525:
522:
497:
494:
491:
488:
485:
463:
459:
438:
435:
415:
395:
392:
389:
386:
381:
377:
373:
370:
367:
363:
359:
356:
353:
329:
326:
323:
320:
315:
311:
307:
304:
301:
298:
294:
290:
287:
284:
253:
250:
245:
241:
235:
231:
227:
224:
221:
216:
212:
206:
202:
198:
195:
192:
189:
186:
183:
180:
160:
149:
148:
147:
146:
135:
132:
129:
126:
121:
117:
113:
110:
107:
104:
100:
96:
93:
90:
73:
70:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
3964:
3953:
3950:
3949:
3947:
3932:
3931:
3922:
3920:
3919:
3910:
3908:
3907:
3902:
3896:
3894:
3893:
3884:
3883:
3880:
3866:
3863:
3861:
3860:Geostatistics
3858:
3856:
3853:
3851:
3848:
3846:
3843:
3842:
3840:
3838:
3834:
3828:
3827:Psychometrics
3825:
3823:
3820:
3818:
3815:
3813:
3810:
3808:
3805:
3803:
3800:
3798:
3795:
3793:
3790:
3788:
3785:
3783:
3780:
3779:
3777:
3775:
3771:
3765:
3762:
3760:
3757:
3755:
3751:
3748:
3746:
3743:
3741:
3738:
3736:
3733:
3732:
3730:
3728:
3724:
3718:
3715:
3713:
3710:
3708:
3704:
3701:
3699:
3696:
3695:
3693:
3691:
3690:Biostatistics
3687:
3683:
3679:
3674:
3670:
3652:
3651:Log-rank test
3649:
3648:
3646:
3642:
3636:
3633:
3632:
3630:
3628:
3624:
3618:
3615:
3613:
3610:
3608:
3605:
3603:
3600:
3599:
3597:
3595:
3591:
3588:
3586:
3582:
3572:
3569:
3567:
3564:
3562:
3559:
3557:
3554:
3552:
3549:
3548:
3546:
3544:
3540:
3534:
3531:
3529:
3526:
3524:
3522:(BoxâJenkins)
3518:
3516:
3513:
3511:
3508:
3504:
3501:
3500:
3499:
3496:
3495:
3493:
3491:
3487:
3481:
3478:
3476:
3475:DurbinâWatson
3473:
3471:
3465:
3463:
3460:
3458:
3457:DickeyâFuller
3455:
3454:
3452:
3448:
3442:
3439:
3437:
3434:
3432:
3431:Cointegration
3429:
3427:
3424:
3422:
3419:
3417:
3414:
3412:
3409:
3407:
3406:Decomposition
3404:
3403:
3401:
3397:
3394:
3392:
3388:
3378:
3375:
3374:
3373:
3370:
3369:
3368:
3365:
3361:
3358:
3357:
3356:
3353:
3351:
3348:
3346:
3343:
3341:
3338:
3336:
3333:
3331:
3328:
3326:
3323:
3321:
3318:
3317:
3315:
3313:
3309:
3303:
3300:
3298:
3295:
3293:
3290:
3288:
3285:
3283:
3280:
3278:
3277:Cohen's kappa
3275:
3274:
3272:
3270:
3266:
3262:
3258:
3254:
3250:
3246:
3241:
3237:
3223:
3220:
3218:
3215:
3213:
3210:
3208:
3205:
3204:
3202:
3200:
3196:
3190:
3186:
3182:
3176:
3174:
3171:
3170:
3168:
3166:
3162:
3156:
3153:
3151:
3148:
3146:
3143:
3141:
3138:
3136:
3133:
3131:
3130:Nonparametric
3128:
3126:
3123:
3122:
3120:
3116:
3110:
3107:
3105:
3102:
3100:
3097:
3095:
3092:
3091:
3089:
3087:
3083:
3077:
3074:
3072:
3069:
3067:
3064:
3062:
3059:
3057:
3054:
3053:
3051:
3049:
3045:
3039:
3036:
3034:
3031:
3029:
3026:
3024:
3021:
3020:
3018:
3016:
3012:
3008:
3001:
2998:
2996:
2993:
2992:
2988:
2984:
2968:
2965:
2964:
2963:
2960:
2958:
2955:
2953:
2950:
2946:
2943:
2941:
2938:
2937:
2936:
2933:
2932:
2930:
2928:
2924:
2914:
2911:
2907:
2901:
2899:
2893:
2891:
2885:
2884:
2883:
2880:
2879:Nonparametric
2877:
2875:
2869:
2865:
2862:
2861:
2860:
2854:
2850:
2849:Sample median
2847:
2846:
2845:
2842:
2841:
2839:
2837:
2833:
2825:
2822:
2820:
2817:
2815:
2812:
2811:
2810:
2807:
2805:
2802:
2800:
2794:
2792:
2789:
2787:
2784:
2782:
2779:
2777:
2774:
2772:
2770:
2766:
2764:
2761:
2760:
2758:
2756:
2752:
2746:
2744:
2740:
2738:
2736:
2731:
2729:
2724:
2720:
2719:
2716:
2713:
2711:
2707:
2697:
2694:
2692:
2689:
2687:
2684:
2683:
2681:
2679:
2675:
2669:
2666:
2662:
2659:
2658:
2657:
2654:
2650:
2647:
2646:
2645:
2642:
2640:
2637:
2636:
2634:
2632:
2628:
2620:
2617:
2615:
2612:
2611:
2610:
2607:
2605:
2602:
2600:
2597:
2595:
2592:
2590:
2587:
2585:
2582:
2581:
2579:
2577:
2573:
2567:
2564:
2560:
2557:
2553:
2550:
2548:
2545:
2544:
2543:
2540:
2539:
2538:
2535:
2531:
2528:
2526:
2523:
2521:
2518:
2516:
2513:
2512:
2511:
2508:
2507:
2505:
2503:
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2484:
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2479:
2476:
2472:
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2468:
2467:
2464:
2462:
2459:
2455:
2454:loss function
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2440:
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2300:
2296:
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2283:
2269:
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2250:
2248:
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2236:
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2207:
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2200:
2197:
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2180:
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2156:Questionnaire
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2152:
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2079:
2078:
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2070:
2066:
2062:
2057:
2053:
2039:
2036:
2034:
2031:
2029:
2026:
2024:
2021:
2019:
2016:
2014:
2011:
2009:
2006:
2004:
2001:
1999:
1996:
1994:
1991:
1989:
1986:
1984:
1983:Control chart
1981:
1979:
1976:
1974:
1971:
1969:
1966:
1965:
1963:
1961:
1957:
1951:
1948:
1944:
1941:
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1935:
1934:
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1926:
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1622:
1621:
1618:
1612:
1611:1-58488-186-0
1608:
1604:
1602:
1601:0-387-20274-9
1598:
1594:
1591:
1585:
1581:
1576:
1573:
1567:
1564:, CRC Press,
1563:
1559:
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1260:
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1252:
1248:
1244:
1237:
1234:
1227:
1225:
1223:
1219:
1215:
1211:
1207:
1203:
1199:
1198:hypertabastic
1195:
1191:
1187:
1183:
1178:
1175:
1171:
1166:
1149:
1141:
1135:
1132:
1129:
1126:
1120:
1112:
1106:
1098:
1094:
1091:has a simple
1090:
1086:
1082:
1078:
1074:
1066:
1064:
1062:
1061:Hazard ratios
1058:
1054:
1049:
1047:
1042:
1023:
1019:
1012:
1009:
1001:
997:
989:
987:
985:
966:
958:
952:
931:
928:
925:
905:
896:
880:
876:
853:
849:
845:
840:
836:
813:
809:
805:
800:
796:
773:
769:
748:
728:
705:
699:
696:
693:
685:
682:(typically a
681:
665:
640:
636:
629:
626:
601:
598:
592:
586:
583:
580:
577:
571:
568:
562:
559:
556:
550:
544:
541:
538:
535:
529:
523:
520:
513:
512:
511:
510:
509:
492:
486:
483:
461:
457:
436:
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413:
390:
387:
379:
375:
371:
365:
357:
351:
343:
324:
321:
313:
309:
305:
302:
296:
288:
282:
274:
269:
267:
243:
239:
233:
229:
225:
222:
219:
214:
210:
204:
200:
193:
187:
184:
181:
178:
158:
130:
127:
119:
115:
111:
108:
102:
94:
88:
81:
80:
79:
78:
77:
71:
69:
67:
66:
61:
57:
53:
49:
45:
41:
37:
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3928:
3916:
3897:
3890:
3802:Econometrics
3752: /
3735:Chemometrics
3712:Epidemiology
3705: /
3678:Applications
3611:
3520:ARIMA model
3467:Q-statistic
3416:Stationarity
3312:Multivariate
3255: /
3251: /
3249:Multivariate
3247: /
3187: /
3183: /
2957:Bayes factor
2856:Signed rank
2768:
2742:
2734:
2722:
2417:Completeness
2253:Cohort study
2151:Opinion poll
2086:Missing data
2073:Study design
2028:Scatter plot
1950:Scatter plot
1943:Spearman's Ï
1905:Grouped data
1579:
1561:
1540:
1519:(1): 13â22,
1516:
1512:
1478:
1474:
1448:
1444:
1434:
1409:
1405:
1399:
1375:
1371:
1361:
1336:
1332:
1326:
1302:
1298:
1292:
1283:
1277:
1250:
1246:
1236:
1179:
1167:
1070:
1050:
1043:
993:
897:
895:is unusual.
684:linear model
618:
270:
265:
150:
75:
64:
43:
39:
29:
3930:WikiProject
3845:Cartography
3807:Jurimetrics
3759:Reliability
3490:Time domain
3469:(LjungâBox)
3391:Time-series
3269:Categorical
3253:Time-series
3245:Categorical
3180:(Bernoulli)
3015:Correlation
2995:Correlation
2791:JarqueâBera
2763:Chi-squared
2525:M-estimator
2478:Asymptotics
2422:Sufficiency
2189:Interaction
2101:Replication
2081:Effect size
2038:Violin plot
2018:Radar chart
1998:Forest plot
1988:Correlogram
1938:Kendall's Ï
1093:closed form
32:statistical
3797:Demography
3515:ARMA model
3320:Regression
2897:(Friedman)
2858:(Wilcoxon)
2796:Normality
2786:Lilliefors
2733:Student's
2609:Resampling
2483:Robustness
2471:divergence
2461:Efficiency
2399:(monotone)
2394:Likelihood
2311:Population
2144:Stratified
2096:Population
1915:Dependence
1871:Count data
1802:Percentile
1779:Dispersion
1712:Arithmetic
1647:Statistics
1513:Biometrics
1299:Biometrika
1228:References
1218:log-normal
1190:log-normal
1046:covariates
65:C. elegans
48:parametric
3178:Logistic
2945:posterior
2871:Rank sum
2619:Jackknife
2614:Bootstrap
2432:Bootstrap
2367:Parameter
2316:Statistic
2111:Statistic
2023:Run chart
2008:Pie chart
2003:Histogram
1993:Fan chart
1968:Bar chart
1850:L-moments
1737:Geometric
1582:, Wiley,
1150:θ
1133:−
1121:θ
1097:censoring
1081:monotonic
1013:
967:θ
953:λ
926:θ
906:θ
749:ϵ
729:ϵ
706:θ
700:
694:−
666:θ
630:
602:ϵ
593:θ
587:
581:−
572:θ
563:
551:θ
545:
539:−
524:
487:
437:θ
388:θ
366:θ
322:θ
306:θ
297:θ
230:β
223:⋯
201:β
194:−
188:
179:θ
159:θ
128:θ
116:λ
112:θ
103:θ
89:λ
56:covariate
44:AFT model
18:AFT model
3946:Category
3892:Category
3585:Survival
3462:Johansen
3185:Binomial
3140:Isotonic
2727:(normal)
2372:location
2179:Blocking
2134:Sampling
2013:QâQ plot
1978:Box plot
1960:Graphics
1855:Skewness
1845:Kurtosis
1817:Variance
1747:Heronian
1742:Harmonic
1533:11318147
1505:12888808
1392:15449337
686:) where
266:increase
34:area of
3918:Commons
3865:Kriging
3750:Process
3707:studies
3566:Wavelet
3399:General
2566:Plug-in
2360:L space
2139:Cluster
1840:Moments
1658:Outline
1496:2394368
1426:9004393
1353:1480879
1319:2335161
1268:4828198
1214:Weibull
46:) is a
30:In the
3787:Census
3377:Normal
3325:Manova
3145:Robust
2895:2-way
2887:1-way
2725:-test
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1973:Biplot
1764:Median
1757:Lehmer
1699:Center
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1204:, and
828:, not
151:where
60:hazard
3411:Trend
2940:prior
2882:anova
2771:-test
2745:-test
2737:-test
2644:Power
2589:Pivot
2382:shape
2377:scale
1827:Shape
1807:Range
1752:Heinz
1727:Cubic
1663:Index
1315:JSTOR
1222:gamma
1194:gamma
344:that
38:, an
3644:Test
2844:Sign
2696:Wald
1769:Mode
1707:Mean
1607:ISBN
1597:ISBN
1584:ISBN
1566:ISBN
1545:ISBN
1529:PMID
1501:PMID
1422:PMID
1388:PMID
1349:PMID
1220:and
1168:The
1071:The
806:>
2824:BIC
2819:AIC
1521:doi
1491:PMC
1483:doi
1453:doi
1414:doi
1380:doi
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1255:doi
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697:log
627:log
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560:log
542:log
521:log
484:log
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