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Hosmer D.W., Lemeshow S. — Applied survival analysis: regression modeling of time to event data
Hosmer D.W., Lemeshow S. — Applied survival analysis: regression modeling of time to event data



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Íàçâàíèå: Applied survival analysis: regression modeling of time to event data

Àâòîðû: Hosmer D.W., Lemeshow S.

Àííîòàöèÿ:

A textbook for an introductory course in statistical methods for analyzing data typically encountered in health related studies that include events involving an element of time. Assumes previous courses in linear and logical regression. Emphasizes practical applications rather than mathematical theory, modeling data, and interpreting results. Also highlights the importance of incomplete or censored data and how that censoring may influence the selection of models and the interpretation of results. Mostly uses examples from STATA, but the methods are fairly ubiquitous among the currently available statistical software packages.


ßçûê: en

Ðóáðèêà: Ìàòåìàòèêà/Âåðîÿòíîñòü/Ñòàòèñòèêà è ïðèëîæåíèÿ/

Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö

ed2k: ed2k stats

Ãîä èçäàíèÿ: 1999

Êîëè÷åñòâî ñòðàíèö: 393

Äîáàâëåíà â êàòàëîã: 03.06.2005

Îïåðàöèè: Ïîëîæèòü íà ïîëêó | Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
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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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