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| Ïîèñê ïî óêàçàòåëÿì |
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| Hosmer D.W., Lemeshow S. — Applied survival analysis: regression modeling of time to event data |
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| Ïðåäìåòíûé óêàçàòåëü |
Martingale, counting process 360—362
Maximum likelihood approach 93—94
Maximum Likelihood Estimation 10—15
Maximum partial likelihood estimator 96—97
Mean: based on entire observed range 54—55
Mean: estimator 53—54
Mean: importance 52
Mean: sample estimator 55—56
Method of fractional polynomials 161—163 170
Model adequacy, assessment 196—239
Model adequacy, at risk process 204
Model adequacy, counting function 227
Model adequacy, counting process 200—203
Model adequacy, cumulative observed versus cumulative estimated expected number of events 227—228
Model adequacy, deleting subjects with extreme values 222—223
Model adequacy, goodness-of-fit tests and measures 225—230
Model adequacy, Grambsch and Themeau generalized least squares score test 207
Model adequacy, graphical approach 207—208
Model adequacy, identification of influential and poorly fit subjects 216—225
Model adequacy, interpretation and presentation of final model 230—239
Model adequacy, partial likelihood score test 207
Model adequacy, process of deleting and refitting models 222—223
Model adequacy, residuals 197—205
Model adequacy, score process residual 203—204
Model adequacy, stratified model 245
Model adequacy, two-step procedure 211
Model development: cloud of data 196
Model development: goal 196
Model, selection 1
Modeling paradigm, interval-censored survival data 267—268
Monotone likelihood 193—194
Multiple-covariate models 129—137
Multiple-covariate models, log-hazard function 130
Multiple-covariate models, log-hazard ratio 130—133
Multiple-covariate models, partial likelihood ratio test 134
Nelson — Aalen estimator 74—77
Nelson — Aalen estimator, cumulative hazard 361
Nested case-control studies 326—333
Nested case-control studies, baseline survivorship function estimator 332
Nested case-control studies, conditional logistic regression 330—331
Nested case-control studies, estimator of baseline function 330—331
Nested case-control studies, partial likelihood 328
Nested case-control studies, ratio of standard errors of coefficient estimates 327
Nested case-control studies, time-varying covariates 328
Nominal scale covariate See Scale covariate nominal
Observed information 97—98
Odds-ratio, log-logistic regression model 300
Offset variable 321
Parametric regression models 271—305. See also Exponential regression model
Parametric regression models, log-logistic regression model 299—304
Parametric regression models, other 304—305
Parametric regression models, Weibull regression model 289—299
Partial likelihood 95
Partial likelihood ratio test 98—99 119 121
Partial likelihood ratio test, addition of two interaction variables 208—211
Partial likelihood ratio test, approximate 171
Partial likelihood ratio test, deleted covariate 160
Partial likelihood ratio test, model development 162—163
Partial likelihood ratio test, multiple-covariate models 134
Partial likelihood ratio test, recurrent event models 314
Partial likelihood score test 207
Partial likelihood, estimator, regression coefficients 109
Partial likelihood, full stratified 244
Partial likelihood, interaction term inclusion 207
Partial likelihood, nested case-control studies 328
Partial likelihood, time-varying covariates 250
Peto — Prentice test 62 71
Point estimator 135—136
Point estimator, hazard ratio 118 234—235
Pointwise confidence bands, covariate-adjusted survivorship function 154—155
Pointwise confidence interval 43—44
Pointwise estimator, hazard function 81—82
Poisson distribution, approximated 227
Preliminary main effects model 160—161
Preliminary main effects model, fitting 174—177
Probability density function 82
Product limit estimator 28
Proportional hazards assumption 114
Proportional hazards assumption, assessment methods 205—216
Proportional hazards assumption, importance 205—206
Proportional hazards diagnostics, score residuals as 217—219
Proportional hazards function: conditional models 311
Proportional hazards function: for stratum 243—244
Proportional hazards model 91—92. See also Fitted proportional hazards regression model
Proportional hazards model, extensions 241—269
Proportional hazards model, extensions, model fitting 262—265
Proportional hazards model, extensions, stratified 243—248
Proportional hazards model, extensions, time-varying covariates 248—253
Proportional hazards model, extensions, truncated, left-censored and interval censored data 253—269
Proportional hazards model, fitted, assessment methods 197
Proportional hazards model, log-hazard function 205—206
Proportional hazards model, proportional hazard function 243—244
Proportional hazards model, ratio of survivorship function at successive interval endpoints 259
Proportional hazards model, stratified 243—248
Proportional hazards regression model 91
Proportional hazards regression model, best subsets selection 188—190
Proportional hazards regression model, estimator 108—111
Proportional hazards regression model, fitting 93—106
Proportional hazards regression model, fitting, Breslow approximation 106—108
Proportional hazards regression model, fitting, Efron approximation 106—108
Proportional hazards regression model, fitting, inverse of negative of second derivative 97
Proportional hazards regression model, fitting, log partial likelihood function 96 99
Proportional hazards regression model, fitting, log partial likelihood ratio 103—104
Proportional hazards regression model, fitting, maximum partial likelihood estimator, tied survival times 107
Proportional hazards regression model, fitting, multiple variable Wald test statistic 104
Proportional hazards regression model, fitting, partial likelihood ratio test 98—99
Proportional hazards regression model, fitting, ratio of derivative 100
Proportional hazards regression model, fitting, score test 100
Proportional hazards regression model, fitting, score test statistic 104
Proportional hazards regression model, fitting, time-dependent covariates 101
Proportional hazards regression model, fitting, univariate Wald tests 104
Proportional hazards regression model, fitting, Wald statistic 99—100
Proportional hazards regression model, fitting, Wald-statistic-based interval 100—101
Proportional hazards regression model, fitting, with tied survival times 106—108
Proportional hazards regression model, hazard function 114 161
Proportional hazards regression model, high leverage 219
Proportional hazards regression model, log-hazard function 114
Proportional hazards regression model, survivorship function 93
Proportional hazards regression model, time-varying covariate notation 249—250
Random effects 307
Recurrent event models 308—317
Recurrent event models, conditional models 310—311 316
Recurrent event models, counting process 308—309 314—315
Recurrent event models, estimated hazard ratio 315—316
Recurrent event models, Grennesby — Borgan goodness-of-fit test 313
Recurrent event models, marginal event-specific model 311—312
Recurrent event models, marginal model 316—317
Recurrent event models, partial likelihood ratio tests 314
Recurrent event models, time-varying covariates 311—312
Reference cell coding 120 122 126
Regression coefficient: additive models 336
Regression coefficient: cumulative, additive models 337—338 342—348
Regression coefficient: partial likelihood estimator 109
Regression diagnostic statistics 216
Regression models 1—26 64 87—111.
Regression models, arbitrarily interval-censored survival time 257—261
Regression models, censoring mechanisms 17—22
Regression models, development 158—194
Regression models, development, 15 percent rule 185
Regression models, development, adding design variables 178
Regression models, development, covariates See also Covariates purposeful
Regression models, development, covariates, best subsets selection 187—193
Regression models, development, covariates, stepwise selection 180—187
Regression models, development, covariates, subset selection 158—159
Regression models, development, fitting of reduced model 160
Regression models, development, five best methods 190—193
Regression models, development, graphs of estimated coefficients versus group midpoints 169 171
Regression models, development, interaction terms 177—180
Regression models, development, larger interactions model 180
Regression models, development, largest log partial likelihood 162
| Regression models, development, log-hazard function 161—162
Regression models, development, method of fractional polynomials 161—163 170
Regression models, development, modeling strategies 168—169
Regression models, development, numerical problems 193—194
Regression models, development, partial likelihood ratio test 162—163
Regression models, development, preliminary main effects model 160—161
Regression models, development, scale of continuous covariates 160—161 169
Regression models, fully parametric 89
Regression models, hazard function 90
Residuals See also Specific residuals
Residuals: covariate-specific 204—205
Residuals: definition 197—198
Residuals: for dichotomous covariate 209
Residuals: martingale 163 172—173
Residuals: model adequacy assessment 197—205
Right censoring 18
Right truncation 21
risk score 144—146
Risk score, equation 147
SAS: lifetest procedure 67—68
SAS: variance estimator 60—61
Scale covariate: continuous 127—129
Scale covariate: nominal 115—127
Scale covariate: nominal, estimator 120—121
Scale covariate: nominal, hazard ratio 116—118
Scale covariate: nominal, log-hazard function 121
Scale covariate: nominal, partial likelihood ratio test 121
Scale covariate: nominal, point estimator of hazard ratio 118
Scale covariate: nominal, Wald statistic-based confidence interval 119
Scale covariate: nominal, Wald test 124—125
Scale parameter 290
scatterplot 5—7
Schoenfeld residual 203
Schoenfeld residual, estimator 198—199
Schoenfeld residual, scaled 199 206
Schoenfeld residual, smoothed 208—212 214—215 242
Schoenfeld residual, vector 199
Score equation 203
Score equation, shape parameter 291
Score process residual 203—204
Score residual 203
Score residual, as proportional hazards diagnostics 217—219
Score residual, scaled 219—220
Score residual, scaled, exponential regression model 281—284
Score residual, shape parameter 294
Score test 100 167
Score test statistic 104
Score test, for model significance 191—192
Score test, inclusion of decile-of-risk design variables 226—227
Semiparametric proportional hazards model 120 197
Semiparametric regression models 90—93
Shape parameter 290
Shape parameter, score equation 291
Shape parameter, score residuals 294
Shape parameter, Wald test 293—294
Shared frailty models 319
Software packages: diagnostic statistics 283
Software packages: fitting additive relative hazard models 335
Software packages: residuals 198
Software packages: standard error 237
Software packages: variance estimator 60—61
Spline functions 164
Standard error 124
Stata 14 16
STATA, fractional polynomial routine 163
Stratified model, assessment 245
Sum-of-squares matrix 199—200
Survival probability: model-based estimation 150
Survival probability: subject-specific estimated 226
Survival time 87—88
Survival time, definition 17—18
Survival time, distribution, quartile boundaries 47—49
Survival time, tied, proportional hazards model fitting 106—108
Survivorship function 11
Survivorship function, baseline, estimator 138 332
Survivorship function, baseline, interval censored 265—266
Survivorship function, comparison 57—73
Survivorship function, comparison, age groups 68—70
Survivorship function, comparison, BMDP package 68—69
Survivorship function, comparison, bronchopulmonary dysplasia study 70—73
Survivorship function, comparison, contingency table of group by status 59
Survivorship function, comparison, decision about results reporting 71
Survivorship function, comparison, functions crossing one another 62
Survivorship function, comparison, Kaplan — Meier estimator graph 57—58
Survivorship function, comparison, log-rank test 60—61 67—68
Survivorship function, comparison, Mantel — Haenszel analysis 73
Survivorship function, comparison, more than two groups 43—70
Survivorship function, comparison, raised to a power 62
Survivorship function, comparison, ratio of weighted sums over observed survival times 60
Survivorship function, comparison, significant difference 58—59
Survivorship function, comparison, significant difference, K groups 65—67
Survivorship function, comparison, tests for the equality 59 63—64
Survivorship function, comparison, Wilcoxon rank sum test 60—62
Survivorship function, confidence interval, endpoints 44
Survivorship function, confidence interval, estimate 40—42
Survivorship function, covariate-adjusted 137—152 238 252 265
Survivorship function, covariate-adjusted, additive models 339
Survivorship function, covariate-adjusted, center continuous covariates 143—144
Survivorship function, covariate-adjusted, confidence interval estimators 149 152—156
Survivorship function, covariate-adjusted, controlling for age 141—142
Survivorship function, covariate-adjusted, direct adjusted estimate 149—150
Survivorship function, covariate-adjusted, implicit model-based extrapolation 140
Survivorship function, covariate-adjusted, inappropriate extrapolation 140—141
Survivorship function, covariate-adjusted, pointwise confidence bands 154—155
Survivorship function, covariate-adjusted, risk score 144—146
Survivorship function, covariate-adjusted, variance estimator 152—153
Survivorship function, Cox model 93
Survivorship function, definition 27
Survivorship function, estimated, using 40—57
Survivorship function, estimated, using, counting process approach 42—43
Survivorship function, estimated, using, estimates of quantiles 47
Survivorship function, estimation 28—39. See also Hazard function
Survivorship function, estimation, graph 31—32
Survivorship function, estimation, histogram 36—37
Survivorship function, estimation, Kaplan — Meier estimator, cumulative hazard function 75
Survivorship function, estimation, life-table estimator 36—39
Survivorship function, estimation, Nelson — Aalen estimator 74—77
Survivorship function, estimation, not going to zero 33
Survivorship function, estimator, proportional hazards regression model 108—111
Survivorship function, exponential regression model 274
Survivorship function, log-log 43—44
Survivorship function, modified risk score-adjusted 147—148
Survivorship function, plotting from complex model 146—149
Survivorship function, second estimated 143
Survivorship function, semiparametric hazard function 92—93
Survivorship function, stratum-specific modified risk-score-adjusted 246—247
Survivorship probability scale 140
Tarone — Ware test 71
Taylor series expansion 354
Time ratio: exponential regression model 274 277—279 288
Time ratio: log-logistic regression model 300—301
Time ratio: Weibull regression model 290 297
Time-varying coefficient model 207 209 212
Time-varying covariates 101 241—242 248—253
Time-varying covariates, additive models 341
Time-varying covariates, internal and external 249
Time-varying covariates, modeling 251
Time-varying covariates, nested case-control studies 328
Time-varying covariates, notation 249—250
Time-varying covariates, recurrent event models 311—312
Truncated data 253—256
Truncated observation, definition 18
UMARU IMPACT Study 22—24 129—130
Univariate analysis 21
University of Massachusetts Aids Research Unit IMPACT Study 22—24 129—130
Variance estimator, delta method 356
Variance estimator, SAS 60—61
Variance parameter, significance test 323
Wald statistic 99—100
Wald statistic-based confidence interval 100—101 119 277
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