Regression models as a tool in medical research:
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Boca Raton, Fla. [u.a.]
CRC Press
2013
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| Series: | Chapman & Hall book
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | XXI, 473 S. graph. Darst. |
| ISBN: | 9781466517486 1466517484 |
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| adam_text | Contents
Preface
xv
Acknowledgments
xix
About the Author
xxi
I The Basics
1
1
Why Use Regression Models?
3
1.1 Why Use Simple Regression Models?
3
1.2
Why Use Multiple Regression Models?
4
1.3
Some Basic Notation
6
2
An Introductory Example
9
2.1
A Single Line Model
9
2.2
Fitting a Single Line Model
11
2.3
Taking Uncertainty into Account
13
2.4
A Two-Line Model
14
2.5
How to Perform These Steps with
Stata
17
2.6
Exercise 5-HIAA and Serotonin
19
2.7
Exercise Haemoglobin
19
2.8
Exercise Scaling of Variables
19
3
The Classical Multiple Regression Model
21
4
Adjusted Effects
23
4.1
Adjusting for Confounding
23
4.2
Adjusting for Imbalances
26
4.3
Exercise Physical Activity in Schoolchildren
27
5
Inference for the Classkal Multiple Regression Model
29
5.1
The Traditional and the Modern Way of Inference
29
5.2
How to Perform the Modern Way of Inference with
Stata
34
5.3
How Valid and Good are Least Squares Estimates?
35
5.4
A Note on the Use and Interpretation of p-Values in Regression
Analyses
35
VIH
6
Logistic
Regression 39
6.1
The Definition of the Logistic Regression Model
39
6.2
Analysing a Dose Response Experiment by Logistic Regression
40
6.3
How to Fit a Dose Response Model with Stata
44
6.4
Estimating Odds Ratios and Adjusted Odds Ratios Using Logistic
Regression
45
6.5
How to Compute (Adjusted) Odds Ratios Using Logistic Regression
in State
49
6.6
Exercise Allergy in Children
50
6.7
More on Logit Scale and Odds Scale
51
7
Inference for the Logistic Regression Model
55
7.1
The Maximum Likelihood Principle
55
7.2
Properties of the ML Estimates for Logistic Regression
56
7.3
Inference for a Single Regression Parameter
57
7.4
How to Perform
Wald
Tests and Likelihood Ratio Tests in State
58
8
Categorical Covariates
63
8.1
Incorporating Categorical Covariates in a Regression Model
63
8.2
Some Technicalities in Using Categorical Covariates
65
8.3
Testing the Effect of a Categorical Covariate
67
8.4
The Handling of Categorical Covariates in
Stete 68
8.5
Presenting Results of a Regression Analysis Involving Categorical
Covariates in a Table
73
8.6
Exercise Physical Occupation and Back Pain
76
8.7
Exercise Odds Ratios and Categorical covariates
77
9
Handling Ordered Categories: A First Lesson in Regression Modelling
Strategies
79
10
The Cox
Proporţional
Hazards Model
85
10.1
Modelling the Risk of Dying
85
10.2
Modelling the Risk of Dying in Continuous Time
87
10.3
Using the Cox Proportional Hazards Model to Quantify the Differ¬
ence in Survival Between Groups
90
10.4
How to Fit a Cox Proportional Hazards Model with
Stete 91
10.5
Exercise Prognostic Factors in Breast Cancer Patients—Part
1 94
11
Common Pitfalls in Using Regression Models
97
11.1
Association versus Causation
97
11.2
Difference between Subjects versus Difference within Subjects
99
11.3
Real-World Models versus Statistical Models
100
11.4
Relevance versus Significance
102
11.5
Exercise Prognostic Factors in Breast Cancer Patients—Part
2 104
їх
11 Advanced Topics and Techniques
107
12
Some Useful Technicalities
109
12.1
Illustrating Models by Using Model-Based Predictions
109
12.2
How to Work with Predictions in
Stata
110
12.3
Residuals and the Standard Deviation of the Error Term
116
12.4
Working with Residuals and the RMSE in
Stata
118
12.5
Linear and Nonlinear Functions of Regression Parameters
119
12.6
Transformations of Regression Parameters
120
12.7
Centering of Covariate Values
121
12.8
Exercise Paternal Smoking versus Maternal Smoking
122
13
Comparing Regression Coefficients
123
13.1
Comparing Regression Coefficients among Continuous Covariates
123
13.2
Comparing Regression Coefficients among Binary Covariates
127
13.3
Measuring the Impact of Changing Covariate Values
128
13.4
Translating Regression Coefficients
130
13.5
How to Compare Regression Coefficients in
Stata
131
13.6
Exercise Health in Young People
137
14
Power and Sample Size
139
14.1
The Power of a Regression Analysis
139
14.2
Determinants of Power in Regression Models with a Single Covariate
140
14.3
Determinants of Power in Regression Models with Several Covari¬
ates
148
14.4
Power and Sample Size Calculations When a Sample from the
Covariate Distribution Is Given
152
14.5
Power and Sample Size Calculations Given a Sample from the
Covariate Distribution with Stata
154
14.6
The Choice of the Values of the Regression Parameters in a Simula¬
tion Study
165
14.7
Simulating a Covariate Distribution
166
14.8
Simulating a Covariate Distribution with Stata
169
14.9
Choosing the Parameters to Simulate a Covariate Distribution
177
M.lONecessary Sample Sizes to Justify Asymptotic Methods
178
14.11
Exercise Power Considerations for a Study on Neck Pain
178
14.
^Exercise Choosing between Two Outcomes
179
15
Selection of the Sample
181
15.1
Selection in Dependence on the Covariates
181
15.2
Selection in Dependence on the Outcome
183
15.3
Sampling in Dependence on Covariate Values
185
16
Selection of Covariates
187
16.1
Fitting Regression Models with Correlated Covariates
187
16.2
The Adjustment versus Power Dilemma
189
16.3
The Adjustment
Makes
Effects Small
Dilemma
191
16.4
Adjusting for Mediators
193
16.5
Adjusting for Confounding—A Useful Academic Game
1%
16.6
Adjusting for Correlated Confounders
198
16.7
Including Predictive Covariates
199
16.8
Automatic Variable Selection
201
16.9
How to Choose Relevant Sets of Covariates
202
ló.lOPreparing
the Selection of Covariates: Analysing the Association
Among Covariates
206
16.11
Preparing the Selection of Covariates: Univariate Analyses?
206
16.1
2Exercise Vocabulary Size in Young Children—Part
1 207
16.13
Preprocessing of the Covariate Space
208
16.1
4How to Preprocess the Covariate Space with
Stata
210
lo.^Exercise
Vocabulary Size in Young Children-Part
2 219
16.16
What Is a Confounder?
219
17
Modelling Nonlinear Effects
221
17.1
Quadratic Regression
221
17.2
Polynomial Regression
225
17.3
Splines
225
17.4
Fractional Polynomials
229
17.5
Gain in Power by Modelling Nonlinear Effects?
230
17.6
Demonstrating the Effect of a Covariate
232
17.7
Demonstrating a Nonlinear Effect
233
17.8
Describing the Shape of a Nonlinear Effect
234
17.9
Detecting Nonlinearity by Analysis of Residuals
237
17.
lOJudging of Nonlinearity May Require Adjustment
237
17.11
How to Model Nonlinear Effects in
Stata
238
17.12The Impact of Ignoring Nonlinearity
254
17.13
Modelling the Nonlinear Effect of Confounders
255
17.
14Nonlinear Models
257
17.1
5Exercise Serum Markers for AMI
258
18
Transformation of Covariates
259
18.1
Transformations to Obtain a Linear Relationship
259
18.2
Transformation of Skewed Covariates
262
18.3
To Categorise or Not to Categorise
264
19
Effect Modification and Interactions
269
19.1
Modelling Effect Modification
269
19.2
Adjusted Effect Modifications
274
19.3
Interactions
276
19.4
Modelling Effect Modifications in Several Covariates
280
19.5
The Effect of a Covariate in the Presence of Interactions
281
19.6
Interactions as Deviations from Additivity
282
Xl
19.7
Scales and
Interactions
285
19.8
Ceiling Effects and Interactions
286
19.9
Hunting for Interactions
287
19.1
OHow to Analyse Effect Modification and Interactions with
Stata
290
19.11
Exercise Treatment Interactions in a Randomised Clinical Trial for
the Treatment of Malignant
Glioma
296
20
Applying Regression Models to Clustered Data
299
20.1
Why Clustered Data Can Invalidate Inference
299
20.2
Robust Standard Errors
300
20.3
Improving the Efficiency
301
20.4
Within-and Between-Cluster Effects
304
20.5
Some Unusual but Useful Usages of Robust Standard Errors in
Clustered Data
305
20.6
How to Take Clustering into Account in
Stata
307
21
Applying Regression Models to Longitudinal Data
313
21.1
Analysing Time Trends in the Outcome
313
21.2
Analysing Time Trends in the Effect of Covariates
316
21.3
Analysing the Effect of Covariates
317
21.4
Analysing Individual Variation in Time Trends
317
21.5
Analysing Summary Measures
321
21.6
Analysing the Effect of Change
322
21.7
How to Perform Regression Modelling of Longitudinal Data in
Stata
323
21.8
Exercise Increase of Body Fat in Adolescents
329
22
The Impact of Measurement Error
331
22.1
The Impact of Systematic and Random Measurement Error
331
22.2
The Impact of Misclassification
334
22.3
The Impact of Measurement Error in Confounders
335
22.4
The Impact of Differential Misclassification and Measurement Error
336
22.5
Studying the Measurement Error
337
22.6
Exercise Measurement Error and Interactions
338
23
The Impact of Incomplete Covariate Data
341
23.1
Missing Value Mechanisms
341
23.2
Properties of a Complete Case Analysis
342
23.3
Bias Due to Using ad hoc Methods
343
23.4
Advanced Techniques to Handle Incomplete Covariate Data
344
23.5
Handling of Partially Defined Covariates
345
III Risk Scores and Predictors
347
24
Risk Scores
349
24.1
What Is a Risk Score?
349
Xli
24.2
Judging the Usefulness of a Risk Score
352
24.3
The Precision of Risk Score Values
353
24.4
The Overall Precision of a Risk Score
356
24.5
Using Stata s predict Command to Compute Risk Scores
357
24.6
Categorisation of Risk Scores
368
24.7
Exercise Computing Risk Scores for Breast Cancer Patients
369
25
Construction of Predictors
371
25.1
From Risk Scores to Predictors
371
25.2
Predictions and Prediction Intervals for a Continuous Outcome
371
25.3
Predictions for a Binary Outcome
373
25.4
Construction of Predictions for Time-to-Event Data
376
25.5
How to Construct Predictions with
Stata
378
25.6
The Overall Precision of a Predictor
382
26
Evaluating the Predictive Performance
383
26.1
The Predictive Performance of an Existing Predictor
383
26.2
How to Assess the Predictive Performance of an Existing Predictor
in
Stata
385
26.3
Estimating the Predictive Performance of a New Predictor
387
26.4
How to Assess the Predictive Performance via Cross-Validation in
Stata
389
26.5
Exercise Assessing the Predictive Performance of a Prognostic Score
in Breast Cancer Patients
392
27
Outlook: Construction of Parsimonious Predictors
393
IV Miscellaneous
395
28
Alternatives to Regression Modelling
397
28.1
Stratification
397
28.2
Measures of Association: Correlation Coefficients
399
28.3
Measures of Association: The Odds Ratio
400
28.4
Propensity Scores
402
28.5
Classification and Regression Trees
404
29
Specific Regression Models
407
29.1
Probit
Regression for Binary Outcomes
407
29.2
Generalised Linear Models
408
29.3
Regression Models for Count Data
409
29.4
Regression Models for Ordinal Outcome Data
411
29.5
Quantité
Regression and Robust Regression
412
29.6
ANOVA and Regression
414
XIII
30
Specific
Usages
of Regression Models
415
30.1
Logistic Regression for the Analysis of Case-Control Studies
415
30.2
Logistic Regression for the Analysis of Matched Case-Control
Studies
417
30.3
Adjusting for Baseline Values in Randomised Clinical Trials
418
30.4
Assessing Predictive Factors
421
30.5
Incorporating Time-Varying Covariates in a Cox Model
422
30.6
Time-Dependent Effects in a Cox Model
424
30.7
Using the Cox Model in the Presence of Competing Risks
426
30.8
Using the Cox Model to Analyse Multi-State Models
427
31
What Is a Good Model?
429
31.1
Does the Model Fit the Data?
429
31.2
How Good Are Predictions?
430
31.3
Explained Variation
431
31.4
Goodness of Fit
432
31.5
Model Stability
434
31.6
The Usefulness of a Model
435
32
Final Remarks on the Role of Prespecified Models and Model Devel¬
opment
439
V Mathematical Details
443
A Mathematics Behind the Classical Linear Regression Model
445
A.
1
Computing Regression Parameters in Simple Linear Regression
445
A.2 Computing Regression Parameters in the Classical Multiple Regres¬
sion Model
446
A.3 Estimation of the Standard Error
448
A.4 Construction of Confidence Intervals and p-Values
450
В
Mathematics Behind the Logistic Regression Model
453
B.I The Least Squares Principle as a Maximum Likelihood Principle
453
B.2 Maximising the Likelihood of a Logistic Regression Model
454
B.3 Estimating the Standard Error of the ML Estimates
457
B.4 Testing Composite Hypotheses
458
С
The Modern Way of Inference
461
C.
1
Robust Estimation of Standard Errors
461
C.2 Robust Estimation of Standard Errors in the Presence of Clustering
461
D
Mathematics for Risk Scores and Predictors
463
D.I Computing Individual Survival Probabilities after Fitting a Cox
Model
463
D.2 Standard Errors for Risk Scores
463
XIV
D.3 The Delta
Rule
464
Bibliography
465
Index
471
Statistics
Regression Models
as a Tool
in Medical Research
While regression models have become standard tools in medical research,
understanding how to properly apply the models and interpret the results is often
challenging for beginners. Regression Models as a Tool in Medical Research
presents the fundamental concepts and important aspects of regression models
most commonly used in medical research, including the classical regression model
for continuous outcomes, the logistic regression model for binary outcomes,
and the Cox proportional hazards model for survival data. The text emphasizes
adequate use, correct interpretation of results, appropriate presentation of results,
and avoidance of potential pitfalls.
After reviewing popular models and basic methods, the book focuses on advanced
topics and techniques. It considers the comparison of regression coefficients, the
selection of covariates, the modeling of nonlinear and
nonadditive
effects, and the
analysis of clustered and longitudinal data, highlighting the impact of selection
mechanisms, measurement error, and incomplete covariate data. The text then
covers the use of regression models to construct risk scores and predictors. It
also gives an overview of more specific regression models and their applications
as well as alternatives to regression modeling.
Features
•
Helps readers improve their understanding of the role of regression models
in the medical field
•
Illustrates each technique with a concrete example, enabling readers to
better appreciate the properties and theory of the methods
•
Uses
Stata
to demonstrate the practical use of the models
•
Discusses how and when regression models can fail
•
Describes the basic principles behind statistical computations, with more
mathematical details given in the appendices
|
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| id | DE-604.BV040457257 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:24:20Z |
| institution | BVB |
| isbn | 9781466517486 1466517484 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025304768 |
| oclc_num | 815944004 |
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| owner | DE-355 DE-BY-UBR |
| owner_facet | DE-355 DE-BY-UBR |
| physical | XXI, 473 S. graph. Darst. |
| publishDate | 2013 |
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| publisher | CRC Press |
| record_format | marc |
| series2 | Chapman & Hall book |
| spelling | Vach, Werner Verfasser (DE-588)111242738 aut Regression models as a tool in medical research Werner Vach Boca Raton, Fla. [u.a.] CRC Press 2013 XXI, 473 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Chapman & Hall book Regressionsmodell (DE-588)4127980-3 gnd rswk-swf Medizinische Statistik (DE-588)4127563-9 gnd rswk-swf Regressionsmodell (DE-588)4127980-3 s Medizinische Statistik (DE-588)4127563-9 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025304768&sequence=000005&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025304768&sequence=000006&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Vach, Werner Regression models as a tool in medical research Regressionsmodell (DE-588)4127980-3 gnd Medizinische Statistik (DE-588)4127563-9 gnd |
| subject_GND | (DE-588)4127980-3 (DE-588)4127563-9 |
| title | Regression models as a tool in medical research |
| title_auth | Regression models as a tool in medical research |
| title_exact_search | Regression models as a tool in medical research |
| title_full | Regression models as a tool in medical research Werner Vach |
| title_fullStr | Regression models as a tool in medical research Werner Vach |
| title_full_unstemmed | Regression models as a tool in medical research Werner Vach |
| title_short | Regression models as a tool in medical research |
| title_sort | regression models as a tool in medical research |
| topic | Regressionsmodell (DE-588)4127980-3 gnd Medizinische Statistik (DE-588)4127563-9 gnd |
| topic_facet | Regressionsmodell Medizinische Statistik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025304768&sequence=000005&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025304768&sequence=000006&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT vachwerner regressionmodelsasatoolinmedicalresearch |