Modeling Binary Correlated Responses using SAS, SPSS and R (eBook)

Preface 8
Part I: Introduction and Review of Modeling Uncorrelated Observations 10
Part II: Analyzing Correlated Data Through Random Component 11
Part III: Analyzing Correlated Data Through Systematic Components 15
Part IV: Analyzing Correlated Data Through the Joint Modeling of Mean and Variance 16
Contents 18
Part I: Introduction and Review of Modeling Uncorrelated Observations 25
Chapter 1: Introduction to Binary Logistic Regression 26
1.1 Motivating Example 26
1.2 Definition and Notation 27
1.2.1 Notations 27
1.2.2 Definitions 27
Categorical Variable in the Form of a Series of Binary Variables 28
Relationship Between Response and Predictor Variables 29
1.3 Exploratory Analyses 29
1.4 Statistical Models 31
1.4.1 Chapter 3: Standard Binary Logistic Regression Model 31
1.4.2 Chapter 4: Overdispersed Logistic Regression Model 31
1.4.3 Chapter 5: Survey Data Logistic Regression Model 32
1.4.4 Chapter 6: Generalized Estimating Equations Logistic Regression Model 32
1.4.5 Chapter 7: Generalized Method of Moments Logistic Regression Model 32
1.4.6 Chapter 8: Exact Logistic Regression Model 32
1.4.7 Chapter 9: Two-Level Nested Logistic Regression Model 33
1.4.8 Chapter 10: Hierarchical Logistic Regression Model 33
1.4.9 Chapter 11: Fixed Effects Logistic Regression Model 33
1.4.10 Chapter 12: Heteroscedastic Logistic Regression Model 33
1.5 Analysis of Data 34
1.5.1 SAS Programming 35
1.5.2 SPSS Programming 35
1.5.3 R Programming 35
1.6 Conclusions 36
1.7 Related Examples 37
1.7.1 Medicare Data 37
1.7.2 Philippines Data 37
1.7.3 Household Satisfaction Survey 38
1.7.4 NHANES: Treatment for Osteoporosis 38
References 39
Chapter 2: Short History of the Logistic Regression Model 40
2.1 Motivating Example 40
2.2 Definition and Notation 41
2.2.1 Notation 41
2.2.2 Definition 41
2.3 Exploratory Analyses 42
2.4 Statistical Model 43
2.5 Analysis of Data 45
2.6 Conclusions 45
References 46
Chapter 3: Standard Binary Logistic Regression Model 48
3.1 Motivating Example 49
3.1.1 Study Hypotheses 49
3.2 Definition and Notation 49
3.3 Exploratory Analyses 51
3.4 Statistical Models 54
3.4.1 Probability 55
3.4.2 Odds 55
3.4.3 Logits 56
3.4.4 Logistic Regression Versus Ordinary Least Squares 56
3.4.5 Generalized Linear Models 57
3.4.6 Response Probability Distributions 58
3.4.7 Log-Likelihood Functions 58
3.4.8 Maximum Likelihood Fitting 58
3.4.9 Goodness of Fit 59
3.4.10 Other Fit Statistics 59
3.4.11 Assumptions for Logistic Regression Model 60
3.4.12 Interpretation of Coefficients 60
3.4.13 Interpretation of Odds Ratio (OR) 60
3.4.14 Model Fit 61
3.4.15 Null Hypothesis 61
3.4.16 Predicted Probabilities 62
3.4.17 Computational Issues Encountered with Logistic Regression 63
3.5 Analysis of Data 63
3.5.1 Medicare Data 64
SAS Output 69
SAS Output 69
3.6 Conclusions 74
3.7 Related Examples 74
Appendix: Partial Medicare Data time=1 75
References 76
Part II: Analyzing Correlated Data Through Random Component 78
Chapter 4: Overdispersed Logistic Regression Model 79
4.1 Motivating Example 79
4.2 Definition and Notation 80
4.3 Exploratory Data Analyses 81
4.4 Statistical Model 82
4.4.1 Williams Method of Analysis 83
4.4.2 Overdispersion Factor 84
4.4.3 Datasets 85
4.4.4 Housing Satisfaction Survey 85
4.5 Analysis of Data 85
4.5.1 Standard Logistic Regression Model 86
4.5.2 Overdispersed Logistic Regression Model 89
4.5.3 Exchangeability Logistic Regression Model 95
4.6 Conclusions 99
4.7 Related Example 100
4.7.1 Use of Word Einai 100
References 100
Chapter 5: Weighted Logistic Regression Model 102
5.1 Motivating Example 103
5.2 Definition and Notation 103
5.3 Exploratory Analyses 104
5.3.1 Treatment for Osteoporosis 105
5.4 Statistical Model 106
5.5 Analysis of Data 107
5.5.1 Weighted Logistic Regression Model with Survey Weights 107
SAS Program 108
5.5.2 Weighted Logistic Regression Model with Strata and Clusters Identified 118
5.5.3 Comparison of Weighted Logistic Regression Models 121
5.6 Conclusions 121
5.7 Related Examples 121
References 122
Chapter 6: Generalized Estimating Equations Logistic Regression 124
6.1 Motivating Example 124
6.1.1 Description of the Rehospitalization Issues 124
Study Hypotheses 125
6.2 Definition and Notation 125
6.3 Exploratory Analyses 127
6.4 Statistical Models: GEE Logistic Regression 130
6.4.1 Medicare Data 130
6.4.2 Generalized Linear Model 131
6.4.3 Generalized Estimating Equations 131
6.4.4 Marginal Model 132
6.4.5 Working Correlation Matrices 132
6.4.6 Model Fit 133
6.4.7 Properties of GEE Estimates 134
6.5 Data Analysis 134
6.5.1 GEE Logistic Regression Model 134
SAS Output 139
GEE with INDEP and EXCH CORR structure 139
6.6 Conclusions 149
6.7 Related Examples 150
References 151
Chapter 7: Generalized Method of Moments Logistic Regression Model 152
7.1 Motivating Example 152
7.1.1 Description of the Case Study 152
Study Hypotheses 153
7.2 Definition and Notation 153
7.3 Exploratory Analyses 154
7.4 Statistical Model 157
7.4.1 GEE Models for Time-Dependent Covariates 158
7.4.2 Lai and Small GMM Method 159
Types of Classification of Time-Dependent Covariates 159
7.4.3 Lalonde Wilson and Yin Method 161
7.5 Analysis of Data 162
7.5.1 Modeling Probability of Rehospitalization 162
7.5.2 SAS Results 163
7.5.3 SAS OUTPUT (Partial) 164
7.6 Conclusions 165
7.7 Related Examples 166
References 166
Chapter 8: Exact Logistic Regression Model 168
8.1 Motivating Example 168
8.2 Definition and Notation 169
8.3 Exploratory Analysis 170
8.3.1 Artificial Data for Clustering 170
8.3.2 Standard Logistic Regression 171
Sparse and Skewed Correlated Binary Data 171
8.3.3 Two-Stage Clustered Data 172
8.4 Statistical Models 173
8.4.1 Independent Observations 173
8.4.2 One-Stage Cluster Model 173
8.4.3 Two-Stage Cluster Exact Logistic Regression Model 175
8.5 Analysis of Data 176
8.5.1 Exact Logistic Regression for Independent Observations 176
8.5.2 Exact Logistic Regression for One-Stage Clustered Data 183
8.5.3 Exact Logistic Regression for Two-Stage Clustered Data 184
8.6 Conclusions 184
8.7 Related Examples 185
8.7.1 Description of the Data 185
8.7.2 Clustering 185
References 186
Part III: Analyzing Correlated Data Through Systematic Components 188
Chapter 9: Two-Level Nested Logistic Regression Model 189
9.1 Motivating Example 189
9.1.1 Description of the Case Study 189
9.1.2 Study Hypotheses 190
9.2 Definition and Notation 190
9.3 Exploratory Analyses 191
9.3.1 Medicare 193
9.4 Statistical Model 193
9.4.1 Marginal and Conditional Models 194
9.4.2 Two-Level Nested Logistic Regression with Random Intercept Model 195
9.4.3 Interpretation of Parameter Estimates 196
9.4.4 Two-Level Nested Logistic Regression Model with Random Intercept and Slope 197
9.4.5 Analysis of Data 198
9.4.6 Comparisons of Procedures (PROC NLMIXED Versus PROC GLIMMIX) 198
9.4.7 Model 1: Two-Level Nested Logistic Regression Model with Random Intercepts 199
SPSS Model 1: Logistic Regression Model with Random Intercepts 207
9.4.8 Two-Level Nested Logistic Regression Model Random Intercept and Slope 211
9.4.9 Model 2: Logistic Regression with Random Intercept/Random Slope for LOS 217
9.5 Conclusions 218
9.6 Related Examples 218
9.6.1 Multicenter Randomized Controlled Data (Beitler and Landis, 1985) 218
References 219
Chapter 10: Hierarchical Logistic Regression Models 221
10.1 Motivation 221
10.1.1 Description of Case Study 221
10.1.2 Study Hypotheses 222
10.2 Definitions and Notations 222
10.3 Exploratory Analyses 223
10.4 Statistical Model 224
10.4.1 Multilevel Modeling Approaches with Binary Outcomes 225
10.4.2 Potential Problems 225
10.4.3 Three-Level Logistic Regression Models with Multiple Random Intercepts 226
10.4.4 Three-Level Logistic Regression Models with Random Intercepts and Random Slopes 227
10.4.5 Nested Higher Level Logistic Regression Models 229
10.4.6 Cluster Sizes and Number of Clusters 229
10.4.7 Parameter Estimations 229
10.5 Analysis of Data 230
10.5.1 Modeling Random Intercepts for Levels 2 and 3 230
Graphical Representation 235
Three-Level Logistic Regression Model with Random Slopes 235
Graphical Representation 240
10.5.2 Interpretation 241
Binary Outcomes 242
10.6 Conclusions 242
10.7 Related Examples 243
References 244
Chapter 11: Fixed Effects Logistic Regression Model 245
11.1 Motivating Example 245
11.2 Definition and Notation 246
11.3 Exploratory Analysis 247
11.3.1 Philippine´s Data 247
11.4 Statistical Models 248
11.4.1 Fixed Effects Regression Models with Two Observations per Unit 249
11.4.2 Modeling More than Two Observations per Unit: Conditional Logistic 250
11.5 Analysis of Data 251
11.5.1 Fixed Effects Logistic Regression Model with Two Observations per Unit 251
Fixed Effects Logistic Regression Model with More than Two Observations 260
11.6 Conclusions 264
11.7 Related Examples 265
References 265
Part IV: Analyzing Correlated Data Through the Joint Modeling of Mean and Variance 267
Chapter 12: Heteroscedastic Logistic Regression Model 268
12.1 Motivating Example 268
12.2 Definitions and Notations 269
12.3 Exploratory Analyses 270
12.3.1 Dispersion Sub-model 273
12.4 Statistical Model 274
12.5 Analysis of Data 276
12.5.1 Heteroscedastic Logistic Regression Model 276
12.5.2 Standard Logistic Regression Model 279
12.5.3 Model Comparisons Mean Sub-model Versus Joint Modeling 280
12.6 Conclusions 281
12.7 Related Examples 281
References 283