## Observational StudiesAn Observational study is an empiric investigation of the effects caused by a treatment, policy , or intervention in which it is not possible to assign subjects at random to treatment or control, as would be done in a controlled experiment. Observational studies are common in most fields that study the effects of treatments on people. The second edition of ¿Observational Studies¿ is about 50 percent longer than the first edition, with many new examples and methods. There are new chapters on nonadditive models for treatment effects (Chapter 5) and planning observational studies (Chapter 11) and Chapter 9, on coherence, has been extensively rewritten. Paul R. Rosenbaum is Robert G. Putzel Professor, Department of Statistics, The Wharton School of the University of Pennsylvania. He is a fellow of the American Statistical Association. |

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### Contents

Observational Studies | 1 |

12 Some Observational Studies | 2 |

13 Purpose of This Book | 10 |

14 Bibliographic Notes | 11 |

15 References | 16 |

Randomized Experiments | 19 |

22 The Lady Tasting Tea | 21 |

23 Randomized Experiments | 23 |

66 Bibliographic Notes | 226 |

68 References | 227 |

Multiple Reference Groups in CaseReferent Studies | 231 |

72 Matched Studies with Two Referent Groups | 237 |

Selection and Hidden Bias | 244 |

Derivation of Bounds for Sensitivity Analysis | 246 |

75 Bibliographic Notes | 248 |

76 Problems | 249 |

24 Testing the Hypothesis of No Treatment Effect | 27 |

25 Simple Models for Treatment Effects | 40 |

26 Confidence Intervals | 44 |

27 Point Estimates | 46 |

28 More Complex Outcomes | 50 |

Effect Increasing Tests Under Alternatives | 54 |

The Set of Treatment Assignments | 55 |

211 Bibliographic Notes | 63 |

212 Problems | 64 |

213 References | 66 |

Overt Bias in Observational Studies | 71 |

32 Adjustments by Exact Stratification and Matching | 77 |

33 CaseReferent Studies | 83 |

34 Small Sample Inference with an Unknown Propensity Score | 86 |

35 Large Sample Inference with an Unknown Propensity Score | 90 |

36 Inexact Matching Followed by Stratification | 92 |

37 Bibliographic Notes | 99 |

38 Problems | 100 |

Sensitivity to Hidden Bias | 105 |

42 A Model for Sensitivity Analysis | 106 |

43 Matched Pairs | 110 |

44 Sensitivity Analysis for SignScore Statistics | 119 |

45 Matching with Multiple Controls and Continuous Responses | 135 |

46 Sensitivity Analysis for Comparing Two Unmatched Groups | 140 |

Technical Results and Proofs | 151 |

48 Bibliographic Notes | 158 |

410 References | 163 |

Models for Treatment Effects | 171 |

52 Order Statistics | 173 |

54 Instrumental Variables | 180 |

Binary Responses | 188 |

Displacements | 192 |

57 Inference About a Quantile | 195 |

58 Bibliographic Notes | 198 |

511 References | 201 |

Known Effects | 205 |

62 An Outcome Known to Be Unaffected by the Treatment | 214 |

63 An Outcome With Known Direction of Effect | 221 |

64 The Behavior of T with Nonnegative Effects | 222 |

65 Bias of Known Direction | 223 |

Multiple Control Groups | 253 |

Systematic Variation and Bracketing | 263 |

83 Comparing Outcomes in Two Control Groups | 265 |

84 Bibliographic Notes | 269 |

85 Problems | 270 |

86 References | 272 |

Coherence and Focused Hypotheses | 277 |

92 Signed Rank Statistics for Coherent Predictions | 279 |

Do Anesthetic Gases Cause Mutations? | 282 |

94 Properties of the Coherent Signed Rank Test | 285 |

96 Strengths and Limitations of Coherence | 286 |

ArrangementIncreasing Functions of Matrices | 288 |

98 Bibliographic Notes | 289 |

99 Problems | 290 |

Constructing Matched Sets and Strata | 295 |

102 The Propensity Score | 296 |

103 Optimal Strata | 302 |

104 Optimal Matching | 311 |

105 Bibliographic Notes | 322 |

107 Problems | 323 |

328 | |

Planning an Observational Study | 333 |

112 Three Observational Studies | 336 |

113 Choice of Research Hypothesis | 339 |

114 A Control Group | 342 |

115 Defining Treated and Control Groups | 344 |

116 Competing Theories Not Null and Alternative Hypotheses | 347 |

Multiple Treatment Assignment Mechanisms | 351 |

An Absent Association | 352 |

119 Stability Analyses and Minimizing the Need for Stability Analyses | 353 |

Abrupt ShortLived Treatments | 355 |

1111 Natural Blocks | 357 |

1112 Refute Several Alternative Explanations | 358 |

1114 Problems | 359 |

360 | |

Some Strategic Issues | 367 |

122 Some Specific Suggestions | 368 |

123 References | 369 |

370 | |

### Common terms and phrases

A(xs absence of hidden adjusted responses arrangement-increasing biases binary case-referent study causal Chapter coherent compared confidence interval Consider control groups coordinates discussed disease distance dose Epidemiology example expectation and variance exposed exposure free of hidden full matching function Gastwirth hidden bias hypergeometric distribution increase inference instance instrumental variable Journal Krueger lung cancer matched pairs matched sets matching with multiple McNemar's test median median test methods minimum wage multiple controls null hypothesis observational studies optimal matching order statistics outcome pair matching partial order patients prob(Z probability problem propensity score Proposition random variables rank sum statistic rcsi receive the treatment referent groups Rosenbaum rTsi Rubin sample sensitivity analysis sensitivity to hidden sign-score statistics signed rank statistic significance level smoking strata stratification stratum Table test statistic theory treated and control treated group treated subjects treated unit treatment assignments treatment effect unobserved covariate upper bound