Observational Studies

386 Pages·2002·8.568 MB·English

by  Paul R. Rosenbaum (auth.)

Springer Series in Statistics
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Paul R. Rosenbaum
Observational Studies
Second Edition
, Springer
Paul R.Rosenbaum
DepartmentofStatistics
The Wharton School
UniversityofPennsylvania
Philadelphia,PA 19104-6302
USA
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Rosenbaum,PaulR.
Observationalstudies/PaulR.Rosenbaum.-2nded.
p.em.- (Springerseriesinstatistics)
Includesbibliographicalreferencesandindex.
I.Experimentaldesign. 2.Analysisofvariance. I.Title. II.Series.
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ISBN 978-1-4419-3191-7 ISBN 978-1-4757-3692-2 (eBook)
DOI 10.1007/978-1-4757-3692-2
For Sarah, Hannah, and Aaron.
Preface
1. What the Book Is About: An Outline
An observational study is an empiric investigation of treatments, policies,
or exposures and the effects they cause, but it differs from an experiment
in that the investigator cannot control the assignment of treatments to
subjects. Observational studies are common in most fields that study the
effects of treatments or policies on people. Chapter 1 defines the subject
more carefully, presents several observational studies, and briefly indicates
some of the issues that structure the subject.
In an observational study, the investigator lacks experimental control;
therefore, it is important to begin by discussing the contribution ofexper
imental control to inference about treatment effects. The statistical theory
of randomized experiments is reviewed in Chapter 2.
Analytical adjustments are widely used inobservationalstudies inan ef
fort to remove overt biases,that is, differences between treated and control
groups, presentbeforetreatment,thatare visible inthedataathand.Chap
ter 3 discusses the simplest of these adjustments,which do littlemore than
compare subjects who appear comparable. Chapter 3 then examines the
circumstances under which the adjustments succeed. Alas, these circum
stances are not especially plausible, for they imply that the observational
study differs from an experiment only in ways that have been recorded. If
treated and control groups differed before treatment in ways not recorded,
there would be a hidden bias. Chapter 4discusses sensitivity analyses that
ask how thefindings ofa study might be altered by hidden biases ofvarious
viii Preface
magnitudes.It turns out that observational studies vary markedly in their
sensitivity to hidden bias. The degree of sensitivity to hidden bias is one
important consideration in judging whether the treatment caused its os
tensible effects or alternatively whether these seeming effects could merely
reflect a hidden bias. Chapter 5discusses models for treatment effects and
illustrates their use in sensitivity analysis.
Although asensitivityanalysis indicatesthe degree to whichconclusions
could be altered by hidden biases of various magnitudes, it does not indi
catewhether hiddenbias ispresent. Chapters6through8concernattempts
to detect hidden biases using devices such as multiple control groups, mul
tiple referent groups in a case-referent study, or known effects. Chapter 9
concernscoherenceinobservationalstudies,a concept that falls somewhere
between attempts to detect hidden bias and sensitivity analyses.
Chapter 10discusses methods and algorithms for matching and stratifi
cation for observed covariates. Chapters 3 and 10 both concern the control
of overt biases; however, Chapter 3 assumes that matched pairs, sets, or
strata are exactly homogeneous in the observed covariates.When there are
many covariates each taking many values, the exact matching in Chapter
3 is not practical. In contrast, the methods and algorithms in Chapter 10
willoften produce matched pairs, sets, or strata that balance many covari
ates simultaneously. The planning of observational studies is discussed in
Chapter 11. Chapter 12 discusses the relationship between the design of
an observational study and its intended audience.
2. Suggestions for the Reader
Chapter 1ismotivationand Chapter2islargely review.Chapter4depends
on Chapter 3. Chapter 10may be read immediately following Chapter 3.
Other chapters depend strongly on Chapter 4 but only weakly on each
other. Chapters 11and 12depend on all the previous chapters but may be
read at any time.
It is not necessary, perhaps not wise, to read from cover to cover. This
book discusses research design, scientific inference, concepts, methods, al
gorithms and technical results of statistics, together with many examples
that serve varied purposes. Different topics will interest different readers,
and some topics will be details for all readers. Several suggestions follow.
Chapters are organized by topic. For example, all of the material about
randomized experiments appears in Chapter 2, but not all of this material
isofequal importance, and parts can be skipped on the way to later chap
ters. Appendices and sections marked with an asterisk (*) provide some
suggestions about what can be skipped.
Sections marked with an asterisk (*) may be skipped. Sections receive
asterisks for widely varied reasons. An asterisk signals one thing only: the
Preface ix
material in the section is not needed later in the book. A topic that is
unconventional, or nonstandard, or technical, or a necessary but tiresome
detail, or an unnecessary but interesting digression, is likely to receive an
asterisk. Readers who skip these sections may suffer immediate loss, but
without future peril.
Appendicesdiscussideas thatareprimarilyofinterest topeoplewhocre
ate statistical methods, rather than to people who use them. Appendices
are leisurely and detailed, but they are aimed at a minority of readers.
Sensitivity analyses-an important topic in the book- involve obtaining
sharp bounds on certain probabilitydistributions usingaesthetically pleas
ing tools such as Holley's inequality and arrangement increasingfunctions.
Topics of this sort are discussed in appendices.
A reader who wishes to understand all of the central concepts while
minimizing the technical formalities should focus on matched pairs. It
turns out that, for purely technical reasons, the case of matched pairs
involves success-or-failure binary trials, so that the formalities are quite
elementary. Ifa reader focuses on discussionsofMcNemar's test for paired
binary outcomes and Wilcoxon's signed rank test for paired continuous
outcomes, then the reader will encounter all of the important concepts,
but will stay with probability distributions for binary trials. For example,
such a reader might read only the first threesectionsofChapter 4,thereby
completely covering the case of matched pairs, before moving on to later
chapters. Also, it is often possible to pick up concepts from the discussion
of examples. Many chapters begin with an example, and many methods
are illustrated with an example.
To be briefly introduced to the concepts underlying observationalstud
ies without formal mathematics, read the overview in Chapter 1, and read
about randomized experiments in §2.1of Chapter 2, adjustments for overt
bias in §3.1, sensitivity analysis in §4.1, detecting hidden bias in §6.1, co
herence in §9.1, multivariate matching and stratification in §10.1,planning
an observational study in Chapter 11, and strategic issues in Chapter 12.
In the index, there is a list of examples under "examples," a list of
mathematical symbols under "symbols," and a bits about software under
"software."
The second edition of Observational Studies is about 50% longer than
the first edition. There are two new chapters, namely, Chapter 5 about
nonadditive models for treatment effects and Chapter 11 about planning
observational studies. Chapter 9 about coherence has been completely
rewritten. There are substantial additions to the other chapters, for ex
ample, §3.5 about covariance adjustment of rank tests using an estimated
propensity score, §4.5 about sensitivity analysis based on asymptotic sep
arability, and §6.5 about bias of known direction. There are many new
examples and problems, and a few errors have been corrected.
x Preface
3. Acknowledgments
To grow older as an academic is to accumulate intellectual debts, and to
associate these debts with fond memories. I would like to acknowledge
several people who have helped with this book and also collaborators on
journal articles that are discussed here. My thanks go to Joe Gastwirth,
Sam Gu, Daniel Heitjan, Bob Hornik, Abba Krieger, Marshall Joffe, Yunfei
PaulLi, BoLu, SueMarcus,KeweiMing, KatePropert, Don Rubin, Jeffrey
Silber, and Elaine Zanutto.
Thiswork wassupportedinpart by theUSNationalScience Foundation.
The second edition was prepared while I was on sabbatical leave at the
Center for Advanced Study in the Behavioral Sciences, and the Center's
hospitality and support are gratefully acknowledged.
Chapter 11isadapted from my article, "Choiceas alternative to control
in observational studies" which appeared with discussion in Statistical Sci
ence, 1999, 14,259--304. I am grateful to the editor, Leon GIeser, and the
discussants, Charles Manski, James Robins, Thomas Cook, and William
Shadish for their comments. Also, I am grateful to the Institute of Math
ematical Statistics for their copyright policy which permits use by authors
ofpublications in IMSjournals, and for their specific encouragement to do
so with this article.
Most of all, I'd like to thank Sarah, Hannah, Aaron, and Judy.
The Wharton School
University of Pennsylvania
October 2001 Paul R. Rosenbaum
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 19
2.1 Introduction and Example:A Randomized Clinical Trial 19
2.2 The Lady Tasting Tea . . . . . . . . . . . . . . 21
2.3 Randomized Experiments . . . . . . . . . . . . 23
2.4 Testing the Hypothesis of NoTreatment Effect 27
2.5 Simple Models for Treatment Effects 40
2.6 Confidence Intervals . . . . 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 ofTreatment Assignments 55
2.11 Bibliographic Notes . 63
2.12 Problems . 64
2.13 References. . . . . . 66
3 Overt Bias in Observational Studies 71
3.1 Introduction: An Example and Planning Adjustments 71