Multivariable model building: a pragmatic approach to regression analysis based on fractional polynomials for modelling continuous variables
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| Format: | Book |
| Language: | English |
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Chichester [u.a.]
Wiley
2008
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| Series: | Wiley series in probability and statistics
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 303 S. graph. Darst. |
| ISBN: | 9780470028421 0470028424 |
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| 245 | 1 | 0 | |a Multivariable model building |b a pragmatic approach to regression analysis based on fractional polynomials for modelling continuous variables |c Patrick Royston ; Willi Sauerbrei |
| 246 | 1 | |a Multivariable model-building | |
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| adam_text | MULTIVARIABLE MODEL-BUILDING A PRAGMATIC APPROACH TO REGRESSION ANALYSIS
BASED ON FRACTIONAL POLYNOMIALS FOR MODELLING CONTINUOUS VARIABLES
PATRICK ROYSTON CANCER AND STATISTICAL METHODOLOGY GROUPS, MRC CLINICAL
TRIALS UNIT, LONDON, UK WILLI SAUERBREI INSTITUTE OF MEDICAL BIOMETRY
AND MEDICAL INFORMATICS, UNIVERSITY MEDICAL CENTER, FREIBURG, GERMANY
JOHN WILEY & SONS, LTD CONTENTS PREFACE XV 1 INTRODUCTION 1.1 REAL-LIFE
PROBLEMS AS MOTIVATION FOR MODEL BUILDING, 1 1.1.1 MANY CANDIDATE
MODELS, 1 1.1.2 FUNCTIONAL FORM FOR CONTINUOUS PREDICTORS, 2 1.1.3
EXAMPLE 1: CONTINUOUS RESPONSE, 2 1.1.4 EXAMPLE 2: MULTIVARIABLE MODEL
FOR SURVIVAL DATA, 5 1.2 ISSUES IN MODELLING CONTINUOUS PREDICTORS, 8
1.2.1 EFFECTS OF ASSUMPTIONS, 8 1.2.2 GLOBAL VERSUS LOCAL INFLUENCE
MODELS, 9 1.2.3 DISADVANTAGES OF FRACTIONAL POLYNOMIAL MODELLING, 9
1.2.4 CONTROLLING MODEL COMPLEXITY, 10 1.3 TYPES OF REGRESSION MODEL
CONSIDERED, 10 1.3.1 NORMAL-ERRORS REGRESSION, 10 1.3.2 LOGISTIC
REGRESSION, 12 1.3.3 COX REGRESSION, 12 1.3.4 GENERALIZED LINEAR MODELS,
14 1.3.5 LINEAR AND ADDITIVE PREDICTORS, 14 1.4 ROLE OF RESIDUALS, 15
1.4.1 USES OF RESIDUALS, 15 1.4.2 GRAPHICAL ANALYSIS OF RESIDUALS, 15
1.5 ROLE OF SUBJECT-MATTER KNOWLEDGE IN MODEL DEVELOPMENT, 16 1.6 SCOPE
OF MODEL BUILDING IN OUR BOOK, 17 1.7 MODELLING PREFERENCES, 18 1.7.1
GENERAL ISSUES, 18 1.7.2 CRITERIA FOR A GOOD MODEL, 18 1.7.3 PERSONAL
PREFERENCES, 19 1.8 GENERAL NOTATION, 20 VI CONTENTS 2 SELECTION OF
VARIABLES 23 2.1 INTRODUCTION, 23 2.2 BACKGROUND, 24 2.3 PRELIMINARIES
FOR A MULTIVARIABLE ANALYSIS, 25 2.4 AIMS OF MULTIVARIABLE MODELS, 26
2.5 PREDICTION: SUMMARY STATISTICS AND COMPARISONS, 29 2.6 PROCEDURES
FOR SELECTING VARIABLES, 29 2.6.1 STRENGTH OF PREDICTORS, 30 2.6.2
STEPWISE PROCEDURES, 31 2.6.3 ALL-SUBSETS MODEL SELECTION USING
INFORMATION CRITERIA, 32 2.6.4 FURTHER CONSIDERATIONS, 33 2.7 COMPARISON
OF SELECTION STRATEGIES IN EXAMPLES, 35 2.7.1 MYELOMA STUDY, 35 2.7.2
EDUCATIONAL BODY-FAT DATA, 36 2.7.3 GLIOMA STUDY, 38 2.8 SELECTION AND
SHRINKAGE, 40 2.8.1 SELECTION BIAS, 40 2.8.2 SIMULATION STUDY, 40 2.8.3
SHRINKAGE TO CORRECT FOR SELECTION BIAS, 42 2.8.4 POST-ESTIMATION
SHRINKAGE, 44 2.8.5 REDUCING SELECTION BIAS, 45 2.8.6 EXAMPLE, 46 2.9
DISCUSSION, 47 2.9.1 MODEL BUILDING IN SMALL DATASETS, 47 2.9.2 FULL,
PRE-SPECIFIED OR SELECTED MODEL? 47 2.9.3 COMPARISON OF SELECTION
PROCEDURES, 49 2.9.4 COMPLEXITY, STABILITY AND INTERPRETABILITY, 49
2.9.5 CONCLUSIONS AND OUTLOOK, 50 3 HANDLING CATEGORICAL AND CONTINUOUS
PREDICTORS 53 3.1 INTRODUCTION, 53 3.2 TYPES OF PREDICTOR, 54 3.2.1
BINARY, 54 3.2.2 NOMINAL, 54 3.2.3 ORDINAL, COUNTING, CONTINUOUS, 55
3.2.4 DERIVED, 55 3.3 HANDLING ORDINAL PREDICTORS, 55 3.3.1 CODING
SCHEMES, 55 3.3.2 EFFECT OF CODING SCHEMES ON VARIABLE SELECTION, 56 3.4
HANDLING COUNTING AND CONTINUOUS PREDICTORS: CATEGORIZATION, 58 3.4.1
OPTIMAL CUTPOINTS: A DANGEROUS ANALYSIS, 58 3.4.2 OTHER WAYS OF
CHOOSING A CUTPOINT, 59 3.5 EXAMPLE: ISSUES IN MODEL BUILDING WITH
CATEGORIZED VARIABLES, 60 3.5.1 ONE ORDINAL VARIABLE, 61 3.5.2 SEVERAL
ORDINAL VARIABLES, 62 CONTENTS VII 3.6 HANDLING COUNTING AND CONTINUOUS
PREDICTORS: FUNCTIONAL FORM, 64 3.6.1 BEYOND LINEARITY, 64 3.6.2 DOES
NONLINEARITY MATTER? 65 3.6.3 SIMPLE VERSUS COMPLEX FUNCTIONS, 66 3.6.4
INTERPRETABILITY AND TRANSPORTABILITY, 66 3.7 EMPIRICAL CURVE FITTING,
67 3.7.1 GENERAL APPROACHES TO SMOOTHING, 68 3.7.2 CRITIQUE OF LOCAL AND
GLOBAL INFLUENCE MODELS, 68 3.8 DISCUSSION, 69 3.8.1 SPARSE CATEGORIES,
69 3.8.2 CHOICE OF CODING SCHEME, 69 3.8.3 CATEGORIZING CONTINUOUS
VARIABLES, 70 3.8.4 HANDLING CONTINUOUS VARIABLES, 70 FRACTIONAL
POLYNOMIALS FOR ONE VARIABLE 71 4.1 INTRODUCTION, 72 4.2 BACKGROUND, 72
4.2.1 GENESIS, 72 4.2.2 TYPES OF MODEL, 73 4.2.3 RELATION TO BOX-TIDWELL
AND EXPONENTIAL FUNCTIONS, 73 4.3 DEFINITION AND NOTATION, 74 4.3.1
FRACTIONAL POLYNOMIALS, 74 4.3.2 FIRST DERIVATIVE, 74 4.4
CHARACTERISTICS, 75 4.4.1 FP1 AND FP2 FUNCTIONS, 75 4.4.2 MAXIMUM OR
MINIMUM OF A FP2 FUNCTION, 75 4.5 EXAMPLES OF CURVE SHAPES WITH FP1 AND
FP2 FUNCTIONS, 76 4.6 CHOICE OF POWERS, 78 4.7 CHOICE OF ORIGIN, 79 4.8
MODEL FITTING AND ESTIMATION, 79 4.9 INFERENCE, 79 4.9.1 HYPOTHESIS
TESTING, 79 4.9.2 INTERVAL ESTIMATION, 80 4.10 FUNCTION SELECTION
PROCEDURE, 82 4.10.1 CHOICE OF DEFAULT FUNCTION, 82 4.10.2 CLOSED TEST
PROCEDURE FOR FUNCTION SELECTION, 82 4.10.3 EXAMPLE, 83 4.10.4
SEQUENTIAL PROCEDURE, 83 4.10.5 TYPE I ERROR AND POWER OF THE FUNCTION
SELECTION PROCEDURE, 84 4.11 SCALING AND CENTERING, 84 4.11.1
COMPUTATIONAL ASPECTS, 84 4.11.2 EXAMPLES, 85 4.12 FP POWERS AS
APPROXIMATIONS TO CONTINUOUS POWERS, 85 4.12.1 BOX-TIDWELL AND
FRACTIONAL POLYNOMIAL MODELS, 85 4.12.2 EXAMPLE, 85 VIII CONTENTS 4.13
PRESENTATION OF FRACTIONAL POLYNOMIAL FUNCTIONS, 86 4.13.1 GRAPHICAL, 86
4.13.2 TABULAR, 87 4.14 WORKED EXAMPLE, 89 4.14.1 DETAILS OF ALL
FRACTIONAL POLYNOMIAL MODELS, 89 4.14.2 FUNCTION SELECTION, 90 4.14.3
DETAILS OF THE FITTED MODEL, 90 4.14.4 STANDARD ERROR OF A FITTED VALUE,
91 4.14.5 FITTED ODDS RATIO AND ITS CONFIDENCE INTERVAL, 91 4.15
MODELLING COVARIATES WITH A SPIKE AT ZERO, 92 4.16 POWER OF FRACTIONAL
POLYNOMIAL ANALYSIS, 94 4.16.1 UNDERLYING FUNCTION LINEAR, 95 4.16.2
UNDERLYING FUNCTION FP1 OR FP2, 95 4.16.3 COMMENT, 96 4.17 DISCUSSION,
97 5 SOME ISSUES WITH UNIVARIATE FRACTIONAL POLYNOMIAL MODELS 99 5.1
INTRODUCTION, 99 5.2 SUSCEPTIBILITY TO INFLUENTIAL COVARIATE
OBSERVATIONS, 100 5.3 A DIAGNOSTIC PLOT FOR INFLUENTIAL POINTS IN FP
MODELS, 100 5.3.1 EXAMPLE 1: EDUCATIONAL BODY-FAT DATA, 101 5.3.2
EXAMPLE 2: PRIMARY BILIARY CIRRHOSIS DATA, 101 5.4 DEPENDENCE ON CHOICE
OF ORIGIN, 103 5.5 IMPROVING ROBUSTNESS BY PRELIMINARY TRANSFORMATION,
105 5.5.1 EXAMPLE 1: EDUCATIONAL BODY-FAT DATA, 106 5.5.2 EXAMPLE 2: PBC
DATA, 107 5.5.3 PRACTICAL USE OF THE PRE-TRANSFORMATION G S (X), 107 5.6
IMPROVING FIT BY PRELIMINARY TRANSFORMATION, 108 5.6.1 LACK OF FIT OF
FRACTIONAL POLYNOMIAL MODELS, 108 5.6.2 NEGATIVE EXPONENTIAL
PRE-TRANSFORMATION, 108 5.7 HIGHER ORDER FRACTIONAL POLYNOMIALS, 109
5.7.1 EXAMPLE 1: NERVE CONDUCTION DATA, 109 5.7.2 EXAMPLE 2: TRICEPS
SKINFOLD THICKNESS, 110 5.8 WHEN FRACTIONAL POLYNOMIAL MODELS ARE
UNSUITABLE, 111 5.8.1 NOT ALL CURVES ARE FRACTIONAL POLYNOMIALS, 111
5.8.2 EXAMPLE: KIDNEY CANCER, 112 5.9 DISCUSSION, 113 MFP: MULTIVARIABLE
MODEL-BUILDING WITH FRACTIONAL POLYNOMIALS 115 6.1 INTRODUCTION, 115 6.2
MOTIVATION, 116 6.3 THE MFP ALGORITHM, 117 6.3.1 REMARKS, 118 6.3.2
EXAMPLE, 118 CONTENTS IX 6.4 PRESENTING THE MODEL, 120 6.4.1 PARAMETER
ESTIMATES, 120 6.4.2 FUNCTION PLOTS, 121 6.4.3 EFFECT ESTIMATES, 121 6.5
MODEL CRITICISM, 123 6.5.1 FUNCTION PLOTS, 123 6.5.2 GRAPHICAL ANALYSIS
OF RESIDUALS, 124 6.5.3 ASSESSING FIT BY ADDING MORE COMPLEX FUNCTIONS,
125 6.5.4 CONSISTENCY WITH SUBJECT-MATTER KNOWLEDGE, 129 6.6 FURTHER
TOPICS, 129 6.6.1 INTERVAL ESTIMATION, 129 6.6.2 IMPORTANCE OF THE
NOMINAL SIGNIFICANCE LEVEL, 130 6.6.3 THE FULL MFP MODEL, 131 6.6.4 A
SINGLE PREDICTOR OF INTEREST, 132 6.6.5 CONTRIBUTION OF INDIVIDUAL
VARIABLES TO THE MODEL FIT, 134 6.6.6 PREDICTIVE VALUE OF ADDITIONAL
VARIABLES, 136 6.7 FURTHER EXAMPLES, 138 6.7.1 EXAMPLE 1: ORAL CANCER,
138 6.7.2 EXAMPLE 2: DIABETES, 139 6.7.3 EXAMPLE 3: WHITEHALL I, 140 6.8
SIMPLE VERSUS COMPLEX FRACTIONAL POLYNOMIAL MODELS, 144 6.8.1 COMPLEXITY
AND MODELLING AIMS, 144 6.8.2 EXAMPLE: GBSG BREAST CANCER DATA, 144 6.9
DISCUSSION, 146 6.9.1 PHILOSOPHY OF MFP, 147 6.9.2 FUNCTION COMPLEXITY,
SAMPLE SIZE AND SUBJECT-MATTER KNOWLEDGE, 148 6.9.3 IMPROVING ROBUSTNESS
BY PRELIMINARY COVARIATE TRANSFORMATION, 148 6.9.4 CONCLUSION AND
FUTURE, 149 7 INTERACTIONS 151 7.1 INTRODUCTION, 151 7.2 BACKGROUND, 152
7.3 GENERAL CONSIDERATIONS, 152 7.3.1 EFFECT OF TYPE OF PREDICTOR, 152
7.3.2 POWER, 153 7.3.3 RANDOMIZED TRIALS AND OBSERVATIONAL STUDIES, 153
7.3.4 PREDEFINED HYPOTHESIS OR HYPOTHESIS GENERATION, 153 7.3.5
INTERACTIONS CAUSED BY MISMODELLING MAIN EFFECTS, 154 7.3.6 THE
TREATMENT-EFFECT PLOT, 154 7.3.7 GRAPHICAL CHECKS, SENSITIVITY AND
STABILITY ANALYSES, 154 7.3.8 CAUTIOUS INTERPRETATION IS ESSENTIAL, 155
7.4 THE MFPI PROCEDURE, 155 7.4.1 MODEL SIMPLIFICATION, 156 7.4.2 CHECK
OF THE RESULTS AND SENSITIVITY ANALYSIS, 156 CONTENTS 7.5 EXAMPLE 1:
ADVANCED PROSTATE CANCER, 157 7.5.1 THE FITTED MODEL, 158 7.5.2 CHECK OF
THE INTERACTIONS, 160 7.5.3 FINAL MODEL, 161 7.5.4 FURTHER COMMENTS AND
INTERPRETATION, 162 7.5.5 FP MODEL SIMPLIFICATION, 163 7.6 EXAMPLE 2:
GBSG BREAST CANCER STUDY, 163 7.6.1 OESTROGEN RECEPTOR POSITIVITY AS A
PREDICTIVE FACTOR, 163 7.6.2 A PREDEFINED HYPOTHESIS:
TAMOXIFEN-OESTROGEN RECEPTOR INTERACTION, 163 7.7 CATEGORIZATION, 165
7.7.1 INTERACTION WITH CATEGORIZED VARIABLES, 165 7.7.2 EXAMPLE: GBSG
STUDY, 166 7.8 STEPP, 167 7.9 EXAMPLE 3: COMPARISON OF STEPP WITH MFPI,
168 7.9.1 INTERACTION IN THE KIDNEY CANCER DATA, 168 7.9.2 STABILITY
INVESTIGATION, 168 7.10 COMMENT ON TYPE I ERROR OF MFPI, 171 7.11
CONTINUOUS-BY-CONTINUOUS INTERACTIONS, 172 7.11.1 MISMODELLING MAY
INDUCE INTERACTION, 173 7.11.2 MFPIGEN: AN FP PROCEDURE TO INVESTIGATE
INTERACTIONS, 174 7.11.3 EXAMPLES OF MFPIGEN, 175 7.11.4 GRAPHICAL
PRESENTATION OF CONTINUOUS-BY-CONTINUOUS INTERACTIONS, 179 7.11.5
SUMMARY, 180 7.12 MULTI-CATEGORY VARIABLES, 181 7.13 DISCUSSION, 181
MODEL STABILITY 183 8.1 INTRODUCTION, 183 8.2 BACKGROUND, 184 8.3 USING
THE BOOTSTRAP TO EXPLORE MODEL STABILITY, 185 8.3.1 SELECTION OF
VARIABLES WITHIN A BOOTSTRAP SAMPLE, 185 8.3.2 THE BOOTSTRAP INCLUSION
FREQUENCY AND THE IMPORTANCE OF A VARIABLE, 186 8.4 EXAMPLE 1: GLIOMA
DATA, 186 8.5 EXAMPLE 2: EDUCATIONAL BODY-FAT DATA, 188 8.5.1 EFFECT OF
INFLUENTIAL OBSERVATIONS ON MODEL SELECTION, 189 8.6 EXAMPLE 3: BREAST
CANCER DIAGNOSIS, 190 8.7 MODEL STABILITY FOR FUNCTIONS, 191 8.7.1
SUMMARIZING VARIATION BETWEEN CURVES, 191 8.7.2 MEASURES OF CURVE
INSTABILITY, 192 8.8 EXAMPLE 4: GBSG BREAST CANCER DATA, 193 8.8.1
INTERDEPENDENCIES AMONG SELECTED VARIABLES AND FUNCTIONS IN SUBSETS, 193
CONTENTS XI 8.8.2 PLOTS OF FUNCTIONS, 193 8.8.3 INSTABILITY MEASURES,
195 8.8.4 STABILITY OF FUNCTIONS DEPENDING ON OTHER VARIABLES INCLUDED,
196 8.9 DISCUSSION, 197 8.9.1 RELATIONSHIP BETWEEN INCLUSION FRACTIONS,
198 8.9.2 STABILITY OF FUNCTIONS, 198 9 SOME COMPARISONS OF MFP WITH
SPLINES 201 9.1 INTRODUCTION, 201 9.2 BACKGROUND, 202 9.3 MVRS: A
PROCEDURE FOR MODEL BUILDING WITH REGRESSION SPLINES, 203 9.3.1
RESTRICTED CUBIC SPLINE FUNCTIONS, 203 9.3.2 FUNCTION SELECTION
PROCEDURE FOR RESTRICTED CUBIC SPLINES, 205 9.3.3 THE MVRS ALGORITHM,
205 9.4 MVSS: A PROCEDURE FOR MODEL BUILDING WITH CUBIC SMOOTHING
SPLINES, 205 9.4.1 CUBIC SMOOTHING SPLINES, 205 9.4.2 FUNCTION SELECTION
PROCEDURE FOR CUBIC SMOOTHING SPLINES, 206 9.4.3 THE MVSS ALGORITHM, 206
9.5 EXAMPLE 1: BOSTON HOUSING DATA, 207 9.5.1 EFFECT OF REDUCING THE
SAMPLE SIZE, 208 9.5.2 COMPARING PREDICTORS, 212 9.6 EXAMPLE 2: GBSG
BREAST CANCER STUDY, 214 9.7 EXAMPLE 3: PIMA INDIANS, 215 9.8 EXAMPLE 4:
PBC, 217 9.9 DISCUSSION, 219 9.9.1 SPLINES IN GENERAL, 220 9.9.2
COMPLEXITY OF FUNCTIONS, 221 9.9.3 OPTIMAL FIT OR TRANSFERABILITY? 221
9.9.4 REPORTING OF SELECTED MODELS, 221 9.9.5 CONCLUSION, 222 10 HOW TO
WORK WITH MFP 223 10.1 INTRODUCTION, 223 10.2 THE DATASET, 223 10.3
UNIVARIATE ANALYSES, 226 10.4 MFP ANALYSIS, 227 10.5 MODEL CRITICISM,
228 10.5.1 FUNCTION PLOTS, 228 10.5.2 RESIDUALS AND LACK OF FIT, 228
10.5.3 ROBUSTNESS TRANSFORMATION AND SUBJECT-MATTER KNOWLEDGE, 229
10.5.4 DIAGNOSTIC PLOT FOR INFLUENTIAL OBSERVATIONS, 230 10.5.5 REFINED
MODEL, 231 10.5.6 INTERACTIONS, 231 10.6 STABILITY ANALYSIS, 232 XII
CONTENTS 10.7 FINAL MODEL, 235 10.8 ISSUES TO BE AWARE OF, 235 10.8.1
SELECTING THE MAIN-EFFECTS MODEL, 235 10.8.2 FURTHER COMMENTS ON
STABILITY, 236 10.8.3 SEARCHING FOR INTERACTIONS, 238 10.9 DISCUSSION,
238 11 SPECIAL TOPICS INVOLVING FRACTIONAL POLYNOMIALS 241 11.1
TIME-VARYING HAZARD RATIOS IN THE COX MODEL, 241 11.1.1 THE FRACTIONAL
POLYNOMIAL TIME PROCEDURE, 242 11.1.2 THE MFP TIME PROCEDURE, 243 11.1.3
PROGNOSTIC MODEL WITH TIME-VARYING EFFECTS FOR PATIENTS WITH BREAST
CANCER, 243 11.1.4 CATEGORIZATION OF SURVIVAL TIME, 245 11.1.5
DISCUSSION, 246 11.2 AGE-SPECIFIC REFERENCE INTERVALS, 247 11.2.1
EXAMPLE: FETAL GROWTH, 247 11.2.2 USING FP FUNCTIONS AS SMOOTHERS, 248
11.2.3 MORE SOPHISTICATED DISTRIBUTIONAL ASSUMPTIONS, 249 11.2.4
DISCUSSION, 249 11.3 OTHER TOPICS, 250 11.3.1 QUANTITATIVE RISK
ASSESSMENT IN DEVELOPMENTAL TOXICITY STUDIES, 250 11.3.2 MODEL
UNCERTAINTY FOR FUNCTIONS, 251 11.3.3 RELATIVE SURVIVAL, 252 11.3.4
APPROXIMATING SMOOTH FUNCTIONS, 253 11.3.5 MISCELLANEOUS APPLICATIONS,
254 12 EPILOGUE 255 12.1 INTRODUCTION, 255 12.2 TOWARDS RECOMMENDATIONS
FOR PRACTICE, 255 12.2.1 VARIABLE SELECTION PROCEDURE, 255 12.2.2
FUNCTIONAL FORM FOR CONTINUOUS COVARIATES, 257 12.2.3 EXTREME VALUES OR
INFLUENTIAL POINTS, 257 12.2.4 SENSITIVITY ANALYSIS, 257 12.2.5 CHECK
FOR MODEL STABILITY, 258 12.2.6 COMPLEXITY OF A PREDICTOR, 258 12.2.7
CHECK FOR INTERACTIONS, 258 12.3 OMITTED TOPICS AND FUTURE DIRECTIONS,
258 12.3.1 MEASUREMENT ERROR IN COVARIATES, 258 12.3.2 META-ANALYSIS,
258 12.3.3 MULTI-LEVEL (HIERARCHICAL) MODELS, 259 12.3.4 MISSING
COVARIATE DATA, 259 12.3.5 OTHER TYPES OF MODEL, 259 12.4 CONCLUSION,
259 CONTENTS XIII APPENDIX A: DATA AND SOFTWARE RESOURCES 261 A.I
SUMMARIES OF DATASETS, 261 A.2 DATASETS USED MORE THAN ONCE, 262 A.2.1
RESEARCH BODY FAT, 262 A.2.2 GBSG BREAST CANCER, 262 A.2.3 EDUCATIONAL
BODY FAT, 263 A.2.4 GLIOMA, 264 A.2.5 PROSTATE CANCER, 264 A.2.6
WHITEHALL I, 265 A.2.7 PBC, 265 A.2.8 ORAL CANCER, 266 A.2.9 KIDNEY
CANCER, 266 A. 3 SOFTWARE, 267 APPENDIX B: GLOSSARY OF ABBREVIATIONS 269
REFERENCES 271 INDEX 285
|
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| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV036072350 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:10:53Z |
| institution | BVB |
| isbn | 9780470028421 0470028424 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018963601 |
| oclc_num | 191697435 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM DE-11 DE-83 |
| owner_facet | DE-19 DE-BY-UBM DE-11 DE-83 |
| physical | XVII, 303 S. graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Wiley |
| record_format | marc |
| series2 | Wiley series in probability and statistics |
| spelling | Royston, Patrick Verfasser aut Multivariable model building a pragmatic approach to regression analysis based on fractional polynomials for modelling continuous variables Patrick Royston ; Willi Sauerbrei Multivariable model-building Chichester [u.a.] Wiley 2008 XVII, 303 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and statistics Analyse de régression Analyse de régression ram Polynômes Polynômes ram Variables (Mathématiques) Variables (mathématiques) ram Regression analysis Polynomials Variables (Mathematics) Regressionsanalyse (DE-588)4129903-6 gnd rswk-swf Polynom (DE-588)4046711-9 gnd rswk-swf Regressionsanalyse (DE-588)4129903-6 s Polynom (DE-588)4046711-9 s DE-604 Sauerbrei, Wilhelm F. Verfasser (DE-588)142589128 aut HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018963601&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Royston, Patrick Sauerbrei, Wilhelm F. Multivariable model building a pragmatic approach to regression analysis based on fractional polynomials for modelling continuous variables Analyse de régression Analyse de régression ram Polynômes Polynômes ram Variables (Mathématiques) Variables (mathématiques) ram Regression analysis Polynomials Variables (Mathematics) Regressionsanalyse (DE-588)4129903-6 gnd Polynom (DE-588)4046711-9 gnd |
| subject_GND | (DE-588)4129903-6 (DE-588)4046711-9 |
| title | Multivariable model building a pragmatic approach to regression analysis based on fractional polynomials for modelling continuous variables |
| title_alt | Multivariable model-building |
| title_auth | Multivariable model building a pragmatic approach to regression analysis based on fractional polynomials for modelling continuous variables |
| title_exact_search | Multivariable model building a pragmatic approach to regression analysis based on fractional polynomials for modelling continuous variables |
| title_full | Multivariable model building a pragmatic approach to regression analysis based on fractional polynomials for modelling continuous variables Patrick Royston ; Willi Sauerbrei |
| title_fullStr | Multivariable model building a pragmatic approach to regression analysis based on fractional polynomials for modelling continuous variables Patrick Royston ; Willi Sauerbrei |
| title_full_unstemmed | Multivariable model building a pragmatic approach to regression analysis based on fractional polynomials for modelling continuous variables Patrick Royston ; Willi Sauerbrei |
| title_short | Multivariable model building |
| title_sort | multivariable model building a pragmatic approach to regression analysis based on fractional polynomials for modelling continuous variables |
| title_sub | a pragmatic approach to regression analysis based on fractional polynomials for modelling continuous variables |
| topic | Analyse de régression Analyse de régression ram Polynômes Polynômes ram Variables (Mathématiques) Variables (mathématiques) ram Regression analysis Polynomials Variables (Mathematics) Regressionsanalyse (DE-588)4129903-6 gnd Polynom (DE-588)4046711-9 gnd |
| topic_facet | Analyse de régression Polynômes Variables (Mathématiques) Variables (mathématiques) Regression analysis Polynomials Variables (Mathematics) Regressionsanalyse Polynom |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018963601&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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