INSEAD Library

Includes bibliographical references and index

Digitized

Observational Studies Contents 1 Observational Studies 1 1.1 What Are Observational Studies? 1 1.2 Some Observational Studies ............................................................................ 2 1.3 Purpose of This Book ...................................................................................... 10 1.4 Bibliographic Notes ........................................................................................... 11 1.5 References ............................................................................................................ 16 2 Randomized Experiments 2.1 Introduction and Example: A Randomized Clinical Trial . . 2.2 The Lady Tasting Tea ...................................................................................... 2.3 Randomized Experiments ............................................................................. 2.4 Testing the Hypothesis of No Treatment Effect .................................. 2.5 Simple Models for Treatment Effects ....................................................... 2.6 Confidence Intervals ........................................................................................ 19 19 21 23 27 40 44 2.7 Point Estimates .................................................................................................. 46 2.8 *More Complex Outcomes ............................................................................. 50 2.9 *Appendix: Effect Increasing Tests Under Alternatives . . . ..................54 2.10 *Appendix: The Set of Treatment Assignments ............................... 55 2.11 Bibliographic Notes ........................................................................................ 63 2.12 Problems ............................................................................................................. 64 2.13 References .......................................................................................................... 66 3 Overt Bias in Observational Studies 3.1 Introduction: An Example and Planning Adjustments . . . 71 71 xii Contents 3.2 Adjustments by Exact Stratification and Matching ........................... 77 3.3 Case-Referent Studies ......................................................................... 83 3.4 *Small Sample Inference with an Unknown Propensity Score........... 86 3.5 *Large Sample Inference with an Unknown Propensity Score ............ 90 3.6 *Inexact Matching Followed by Stratification ..................................... 92 3.7 Bibliographic Notes............................................................................... 99 3.8 Problems ............................................................................................ 100 3.9 References .......................................................................................... 100 4 Sensitivity to Hidden Bias 105 4.1 What Is a Sensitivity Analysis? 105 4.2 A Model for Sensitivity Analysis ......................................................... 106 4.3 Matched Pairs ................................................................................... 110 4.4 Sensitivity Analysis for Sign-Score Statistics ................................... 119 4.5 Multiple Controls and Continuous Responses ................................ 135 4.6 Sensitivity Analysis for Two Unmatched Groups ............................. 140 4.7 Appendix: Technical Results and Proofs ........................................... 151 4.8 Bibliographic Notes............................................................................. 158 4.9 Problems ............................................................................................ 158 4.10 References ........................................................................................ 163 5 Models for Treatment Effects 171 5.1 Effects That Vary from Person to Person .......................................... 171 5.2 Order Statistics ............................................................................... 173 5.3 Dilated Effects .................................................................................... 173 5.4 Instrumental Variables .................................................................... 180 5.5 Attributable Effects: Binary Responses ............................................ 188 5.6 Attributable Effects: Displacements ................................................. 192 5.7 Inference About a Quantile ............................................................... 195 5.8 Bibliographic Notes............................................................................. 198 5.9 Problems ............................................................................................ 198 5.10 Appendix: Minimum Wage Data ...................................................... 199 5.11 References ........................................................................................ 201 6 Known Effects 205 6.1 Detecting Hidden Bias Using Known Effects .................................... 205 6.2 An Outcome Known to Be Unaffected by the Treatment . ............... 214 6.3 An Outcome With Known Direction of Effect ..................................... 221 6.4 *The Behavior of T* with Nonnegative Effects .................................... 222 6.5 Bias of Known Direction ..................................................................... 223 6.6 Bibliographic Notes............................................................................. 226 6.7 Problems ............................................................................................ 226 6.8 References .......................................................................................... 227 7 Multiple Reference Groups in Case-Referent Studies 231 Contents xiii 7.1 Multiple Reference Groups.................................................................. 231 7.2 Matched Studies with Two Referent Groups ...................................... 7.3 *Appendix: Selection and Hidden Bias ............................................... 7.4 *Appendix: Derivation of Bounds for Sensitivity Analysis ................. 7.5 Bibliographic Notes............................................................................... 7.6 Problems ............................................................................................. 7.7 References ........................................................................................... 8 Multiple Control Groups 8.1 The Role of a Second Control Group ................................................... 8.2 Selecting Control Groups ................................................................... 8.3 Comparing Outcomes in Two Control Groups ................................... 8.4 Bibliographic Notes............................................................................... 8.5 Problems ............................................................................................. 237 244 246 248 249 250 253 253 263 265 269 270 8.6 References ........................................................................................... 272 9 Coherence and Focused Hypotheses 9.1 Coherent Associations ........................................................................ 9.2 Signed Rank Statistics for Coherent Predictions .............................. 9.3 Example: Do Anesthetic Gases Cause Mutations? ............................ 9.4 *Properties of the Coherent Signed Rank Test ................................... 9.5 Some Other Forms of Coherence ........................................................ 9.6 Strengths and Limitations of Coherence ........................................... 9.7 *Appendix: Arrangement-Increasing Functions of Matrices ............. 9.8 Bibliographic Notes............................................................................... 9.9 Problems ............................................................................................. 277 277 279 282 285 285 286 288 289 290 9.10 References ......................................................................................... 290 10 Constructing Matched Sets and Strata 295 10.1 Introduction: Propensity Scores, Structures, Algorithms . . 295 10.2 The Propensity Score ........................................................................ 296 10.3 Optimal Strata ................................................................................ 302 10.4 Optimal Matching ............................................................................. 311 10.5 Bibliographic Notes............................................................................. 322 10.6 Software ............................................................................................ 322 10.7 Problems ........................................................................................... 323 10.8 References ......................................................................................... 328 11 Planning an Observational Study 11.1 Introduction and Some Ground Rules ............................................ 11.2 Three Observational Studies ........................................................... 11.3 Choice of Research Hypothesis ........................................................ 11.4 A Control Group ................................................................................ 11.5 Defining Treated and Control Groups .............................................. 11.6 Competing Theories .......................................................................... 333 333 336 339 342 344 347 xiv Contents 11.7 Internal Replication ......................................................................... 11.8 Nondose Nonresponse: An Absent Association ................................ 11.9 Stability Analyses ............................................................................. 11.10 Abrupt, Short-Lived Treatments .................................................... 11.11 Natural Blocks ............................................................................... 11.12 Refute Several Alternative Explanations......................................... 11.13 Bibliographic Notes ......................................................................... 11.14 Problems ........................................................................................ 11.15 References ....................................................................................... 351 352 353 355 357 358 358 358 360 12 Some Strategic Issues 367 12.1 What Are Strategic Issues? .............................................................. 367 12.2 Some Specific Suggestions ............................................................... 368 12.3 References ......................................................................................... 369 Index 370