Regression Analysis In Medical Research: For Starters And 2nd Levelers

Preface to the Second Edition......Page 5
Preface to the First Edition......Page 6
Contents......Page 7
1 Introduction, History, and Background......Page 14
1.2 Extension of Regression Theories and Terminologies......Page 15
1.3 More Modern Times......Page 16
2 Data Example......Page 17
4 Defining the Intercept ``a´´ and the Regression Coefficient ``b´´ from the Regression Equation y = a + bx......Page 18
5 Correlation Coefficient (R) Varies Between -1 and + 1......Page 19
6 Computing R, Intercept ``a´´ and Regression Coefficient ``b´´: Ordinary Least Squares and Matrix Algebra......Page 20
7 SPSS Statistical Software for Windows for Regression Analysis......Page 24
8 A Significantly Positive Correlation, X Significant Determinant of Y......Page 26
9 Simple Linear Regression Uses the Equation y = a+bx......Page 27
10 Multiple Regression with Three Variables Uses Another Equation......Page 28
11 Real Data Example......Page 29
12 SPSS Statistical Software for Windows for Regression Analysis......Page 30
13 Summary of Multiple Regression Analysis of 3 Variables......Page 31
14 Purposes of Multiple Linear Regression......Page 32
15 Multiple Regression with an Exploratory Purpose, First Purpose......Page 33
16 Multiple Regression for the Purpose of Increasing Precision, Second Purpose......Page 39
17 Multiple Regression for Adjusting Confounding, Third Purpose......Page 44
18 Multiple Regression for Adjusting Interaction, Fourth Purpose......Page 47
Reference......Page 52
1 Introduction, History and Background......Page 53
1.1 Logistic Regression......Page 54
1.2 Cox Regression......Page 56
2 Logistic Regression......Page 57
3 Cox Regression......Page 69
4 Conclusion......Page 73
References......Page 74
1 Introduction, History, and Background......Page 75
2 High Performance Regression Analysis......Page 77
3 Example of a Multiple Linear Regression Analysis as Primary Analysis from a Controlled Trial......Page 78
4 Example of a Multiple Logistic Regression Analysis as Primary Analysis from a Controlled Trial......Page 80
5 Example of a Multiple Cox Regression Analysis as Primary Analysis from a Controlled Trial......Page 85
6 Conclusion......Page 86
Reference......Page 87
1 Introduction, History, and Background......Page 88
2 Binary Poisson Regression......Page 90
3 Negative Binomial Regression......Page 94
4 Probit Regression......Page 96
5 Tetrachoric Regression......Page 101
6 Quasi-Likelihood Regressions......Page 107
7 Conclusion......Page 116
Reference......Page 117
1 Introduction, History, and Background......Page 118
2 Multinomial Regression......Page 120
3 Ordinal Regression......Page 123
4 Negative Binomial and Poisson Regressions......Page 124
5 Random Intercepts Regression......Page 128
6 Logit Loglinear Regression......Page 132
7 Hierarchical Loglinear Regression......Page 136
8 Conclusion......Page 139
Reference......Page 140
1 Introduction, History, and Background......Page 141
2 Cox with Time Dependent Predictors......Page 142
3 Segmented Cox......Page 144
4 Interval Censored Regression......Page 147
5 Autocorrelations......Page 148
6 Polynomial Regression......Page 151
7 Conclusion......Page 155
Reference......Page 156
1 Introduction, History, and Background......Page 157
2 Little if any Difference Between Anova and Regression Analysis......Page 159
3 Paired and Unpaired Anovas......Page 162
Reference......Page 165
1 Introduction, History, and Background......Page 166
2 Repeated Measures Anova (Analysis of Variance)......Page 168
3 Repeated Measures Anova Versus Ancova......Page 171
4 Repeated Measures Anova with Predictors......Page 177
5 Mixed Linear Model Analysis......Page 178
6 Mixed Linear Model with Random Interaction......Page 182
7 Doubly Repeated Measures Multivariate Anova......Page 184
Reference......Page 189
1 Introduction, History, and Background......Page 190
2 Restructuring Categories into Multiple Binary Variables......Page 191
3 Variance Components Regressions......Page 194
4 Contrast Coefficients Regressions......Page 198
Reference......Page 204
1 Introduction, History, and Background......Page 205
2 Regression Analysis with Laplace Transformations with Due Respect to Those Clinical Pharmacologists Who Routinely Use it......Page 207
3 Laplace Transformations: How Does it Work......Page 208
4 Laplace Transformations and Pharmacokinetics......Page 209
5 Conclusion......Page 212
Reference......Page 213
1 Introduction, History, and Background......Page 214
2.1 Semi Variography......Page 216
2.2 Correlation Levels Between Observed Places and Unobserved Ones......Page 217
2.3 The Correlation Between the Known Places and the Place ``?´´......Page 218
3 Markov Regression......Page 220
Reference......Page 225
1 Introduction, History, and Background......Page 226
2 Path Analysis......Page 228
3 Structural Equation Modeling......Page 230
4 Bayesian Networks......Page 235
Reference......Page 238
1 Introduction, History, and Background......Page 239
2 Multivariate Analysis of Variance (Manova)......Page 242
3 Canonical Regression......Page 244
4 Conclusion......Page 248
Reference......Page 249
Chapter 14: More on Poisson Regressions......Page 250
1 Introduction, History, and Background......Page 251
2 Poisson Regression with Event Outcomes per Person per Period of Time......Page 252
3 Poisson Regression with Yes / No Event Outcomes per Population per Period of Time......Page 255
4 Poisson Regressions Routinely Adjusting Age and Sex Dependence, Intercept-Only Models......Page 256
5 Loglinear Models for Assessing Incident Rates with Varying Incident Risks......Page 258
Reference......Page 261
1 Introduction, History, and Background......Page 262
2 Linear Trend Testing of Continuous Data......Page 263
3 Linear Trend Testing of Discrete Data......Page 266
4 Conclusion......Page 267
Reference......Page 268
1 Introduction, History, Background......Page 269
2 Optimal Scaling with Discretization and Regularization versus Traditional Linear Regression......Page 272
3 Automatic Regression for Maximizing Relationships......Page 277
4 Conclusion......Page 280
Reference......Page 281
1 Introduction, History, and Background......Page 282
2 Linear and the Simplest Nonlinear Models of the Polynomial Type......Page 283
3 Spline Modeling......Page 287
4 Conclusion......Page 291
Reference......Page 292
Chapter 18: More on Nonlinear Regressions......Page 293
1 Introduction, History, and Background......Page 294
2 Testing for Linearity......Page 296
3 Logit and Probit Transformations......Page 298
4 ``Trial and Error´´ Method, Box Cox Transformation, ACE /AVAS Packages......Page 301
5 Sinusoidal Data with Polynomial Regressions......Page 302
6 Exponential Modeling......Page 303
7 Spline Modeling......Page 304
8 Loess Modeling......Page 308
9 Conclusion......Page 311
Appendix......Page 313
Reference......Page 314
Chapter 19: Special Forms of Continuous Outcomes Regressions......Page 315
2 Kernel Regressions......Page 316
3 Gamma and Tweedie Regressions......Page 324
4 Robust Regressions......Page 333
5 Conclusion......Page 338
Reference......Page 339
1 Introduction, History, and Background......Page 340
2 Example......Page 342
3 Deming Regression......Page 345
4 Passing-Bablok Regression......Page 347
5 Conclusion......Page 348
References......Page 349
Chapter 21: Regressions, a Panacee or at Least a Widespread Help for Clinical Data Analyses......Page 350
1 Introduction, History, and Background......Page 351
2 How Regressions Help You Make Sense of the Effects of Small Changes in Experimental Settings......Page 353
3 How Regressions Can Assess the Sensitivity of your Predictors......Page 354
4 How Regressions Can be Used for Data with Multiple Categorical Outcome and Predictor Variables......Page 360
5 How Regressions Are Used for Assessing the Goodness of Novel Qualitative Diagnostic Tests......Page 366
6 How Regressions Can Help you Find out about Data Subsets with Unusually Large Spread......Page 369
6.1 Maximum Likelihood Estimation......Page 370
6.2 Autocorrelations......Page 371
6.3 Weighted Least Squares......Page 374
6.4 Two Stage Least Squares......Page 377
6.5 Robust Standard Errors......Page 380
6.6 Generalized Least Squares......Page 382
Reference......Page 383
1 Introduction, History, and Background......Page 384
2 Data Example with a Continuous Outcome, More on the Principles of Regression Trees......Page 387
3 Automated Entire Tree Regression from the LDL Cholesterol Example......Page 388
4 Conclusion......Page 391
Reference......Page 392
Chapter 23: Regressions with Latent Variables......Page 393
1 Introduction, History, and Background......Page 394
2 Factor Analysis......Page 395
3 Partial Least Squares (PLS)......Page 402
4 Discriminant Analysis......Page 408
5 Conclusion......Page 413
References......Page 414
1 Introduction, History, and Background......Page 415
2 Data Example......Page 416
References......Page 420
1 Introduction, History, and Background......Page 422
2 Principles of Principal Components Analysis and Optimal Scaling, a Brief Review......Page 423
3.1 Principal Components Analysis......Page 426
3.2 Optimal Scaling with Spline Smoothing......Page 430
3.3 Optimal Scaling with Spline Smoothing Including Regularized Regression Using Either Ridge, Lasso, or Elastic Net Shrinkages......Page 431
4 Conclusion......Page 435
Reference......Page 436
1 Introduction, History, and Background......Page 437
2 Statistical Model......Page 438
3.1 Step 1 - Smoothing......Page 440
3.2 Step 2 - Functional Principal Components Analysis (FPCA)......Page 443
3.3 Step 3 - Regression Analysis......Page 445
4 Applications in Medical and Health Research......Page 448
References......Page 449
1 Introduction, History, and Background......Page 450
2 Traditional Linear and Robust Linear Regression Analysis......Page 452
3 Quantile Linear Regression Analysis......Page 457
Reference......Page 464
Index......Page 465