Paul R. Rosenbaum

• Paul R. Rosenbaum, An Introduction to the Theory of Observational Studies (Gewerbestrasse 11, 6330 Cham, Switzerland: Springer, 2025) Abstract

  This book is an introduction to the theory of causal inference in observational studies.   An observational study draws inferences about the effects caused by treatments or preventable exposures when randomized experimentation is unethical or infeasible.  An observational study is distinguished from an experiment by the problems that follow from the absence of randomized assignment of individuals to treatments.  Observational studies are common in most fields that study the effects of treatments or policies on people, including public health and epidemiology, economics and public policy, medicine and clinical psychology, and criminology and empirical legal studies.

   

   

  Description
  After Part I reviews causal inference in randomized experiments, the twelve short chapters in Parts II, III and IV introduce modern topics: the propensity score, ignorable treatment assignment, the principal unobserved covariate, algorithms for optimal matching, randomized reassignment techniques for appraising the covariate balance achieved by matching, covariance adjustment, sensitivity analysis, design sensitivity, ways to design an observational study to be insensitive to larger unmeasured biases, the large sample efficiency of a sensitivity analysis, quasi-experimental devices that provide observable information about unmeasured biases, evidence factors and complementary analyses to address unmeasured biases.   The book is accessible to anyone who has completed an undergraduate course in mathematical statistics.  The subject is developed with the aid of two simple empirical examples concerning the health benefits or harms caused by consuming alcohol.  The data for these examples and their reanalyses are freely available in an R package, iTOS, associated with Introduction to the Theory of Observational Studies.
• Paul R. Rosenbaum (2025), Tightening blocks in complementary analyses of observational studies: Optimization algorithm and examples, American Statistician, 9. 10.1080/00031305.2024.2393630 Abstract

  An observational block design has I blocks matched for covariates and J individuals per block, but treatments
  were not randomly assigned to individuals within blocks, as would have been done in an experiment.
  Tightening an observational block design means selecting J'< J individuals from each block, and possibly
  I’ ≤ I blocks, to construct a new observational block design that, in some way, addresses unmeasured
  biases from nonrandom treatment assignment. Tightening must preserve covariate balance while altering
  the design to achieve some additional objective. An optimization algorithm is introduced that achieves this
  while maintaining the block structure by finely balancing covariates across blocks and through optimal
  subset matching. An example is considered in detail, both to motivate and illustrate the tightening of an
  observational block design. Two tightened designs are built from a study of light daily alcohol consumption
  and its possible effects on HDL cholesterol. One tightened design adjusts for an outcome tentatively
  presuming it was unaffected by the treatment. The second tightened design uses a differential effect to
  remove bias from an unobserved general disposition that promotes several treatments. An R package
  tightenBlock implements the method, contains the data, and in that package the help-file for the
  function tighten reproduces the example.

  Related
  Links

  Link via DOI
• Paul R. Rosenbaum, Causal Inference (Cambridge, MA: MIT Press, 2023) Abstract

  A nontechnical guide to the basic ideas of modern causal inference, with illustrations from health, the economy, and public policy.

  Which of two antiviral drugs does the most to save people infected with Ebola virus? Does a daily glass of wine prolong or shorten life? Does winning the lottery make you more or less likely to go bankrupt? How do you identify genes that cause disease? Do unions raise wages? Do some antibiotics have lethal side effects? Does the Earned Income Tax Credit help people enter the workforce?

  Causal Inference provides a brief and nontechnical introduction to randomized experiments, propensity scores, natural experiments, instrumental variables, sensitivity analysis, and quasi-experimental devices. Ideas are illustrated with examples from medicine, epidemiology, economics and business, the social sciences, and public policy.

• Paul R. Rosenbaum (2022), A new transformation of treated-control matched-pair differences for graphical display, American Statistician, 7. 10.1080/00031305.2022.2063944 Abstract

  A new transformation is proposed for treated-minus-control matched pair differences that leaves the center of their distribution untouched, but symmetrically and smoothly transforms and shortens the tails. In this way, the center of the distribution is interpretable, undistorted and uncompressed, yet outliers are clear and distinct along the periphery. The transformation of pair differences, y↦ϱ(y),is strictly increasing, continuous, differentiable and odd, ϱ(−y)=−ϱ(y), so its action in the extreme upper tail mirrors its action in the extreme lower tail. Moreover, the center of the distribution—typically 90% or 95% of the distribution—is not transformed, with ϱ(y)=y for −β≤y≤β, yet the nonlinear transformation of the tails is barely perceptible as it begins at ±β, in the sense that 1=ϱ′(β)=ϱ′(−β), where ϱ′(·) is the derivative of ϱ(·). The transformation is applied to an observational study of the effect of light daily alcohol consumption on the level of HDL cholesterol. The study has three control groups intended to address specific unmeasured biases; so, several types of pair differences require coordinated depiction focused on unmeasured bias, not outliers. An R package tailTransform implements the method, contains the data, and reproduces aspects of the graphs and data analysis.

  Related
  Links

  Access via Publisher Taylor and Fancis
• Jeffrey H. Silber, Paul R. Rosenbaum, Joseph G. Reiter, Alexander Hill, Siddarth Jain, David Wolk, Dylan Small, Sean Hashemi, Lee A. Fleisher, Bijan A. Niknam, Mark D. Neuman, Roderic Eckenhoff (2022), Alzheimer’s dementia after exposure to anesthesia and surgery in the elderly: a matched natural experiment using appendicitis, Annals of Surgery, 11. 10.1097/SLA.0000000000004632 Abstract

  Objective:

  The aim of this study was to determine whether surgery and anesthesia in the elderly may promote Alzheimer disease and related dementias (ADRD).

  Background:

  There is a substantial conflicting literature concerning the hypothesis that surgery and anesthesia promotes ADRD. Much of the literature is confounded by indications for surgery or has small sample size. This study examines elderly patients with appendicitis, a common condition that strikes mostly at random after controlling for some known associations.

  Methods:

  A matched natural experiment of patients undergoing appendectomy for appendicitis versus control patients without appendicitis using Medicare data from 2002 to 2017, examining 54,996 patients without previous diagnoses of ADRD, cognitive impairment, or neurological degeneration, who developed appendicitis between ages 68 through 77 years and underwent an appendectomy (the ‘‘Appendectomy’’ treated group), matching them 5:1 to 274,980 controls, examining the subsequent hazard for developing ADRD.

  Results:

  The hazard ratio (HR) for developing ADRD or death was lower in the Appendectomy group than controls: HR = 0.96 [95% confidence interval (CI) 0.94–0.98], P < 0.0001, (28.2% in Appendectomy vs 29.1% in controls, at 7.5 years). The HR for death was 0.97 (95% CI 0.95–0.99), P = 0.002, (22.7% vs 23.1% at 7.5 years). The HR for developing ADRD alone was 0.89 (95% CI 0.86–0.92), P < 0.0001, (7.6% in Appendectomy vs 8.6% in controls, at 7.5 years). No subgroup analyses found significantly elevated rates of ADRD in the Appendectomy group.

  Conclusion:

  In this natural experiment involving 329,976 elderly patients, exposure to appendectomy surgery and anesthesia did not increase the subsequent rate of ADRD.

  Related
  Links

  Public Access via NIH
• Katherine Brumberg, Dylan Small, Paul R. Rosenbaum (2022), Using randomized rounding of linear programs to obtain unweighted natural strata that balance many covariates, Journal of the Royal Statistical Society Series A: Statistics in Society, 21. 10.1111/rssa.12848 Abstract

  In causal inference, natural strata are a new compromise between conventional strata and matching in a fixed ratio, say pair matching or matching two controls to each treated individual. Like matching in a fixed ratio, natural strata: (a) do not require weights, (b) balance many measured covariates beyond those that define the strata and (c) provide closer balance for a measured continuous covariate coarsely cut to form strata. Unlike matching in a fixed ratio, the ratio of controls to treated individuals need not be an integer, so if the data permit a fixed ratio comparison of 1-to-2.5 or even 1-to-0.75, then these ratios are possible using natural strata. Optimal natural strata are defined by a moderate number of fixed strata plus an integer program that minimizes the imbalance in many other measured covariates that are not used to specify the strata. Solving large integer programs is computationally difficult. A tool in the theory of approximation algorithms is ‘randomized rounding of a linear program’ to produce an integer solution: a fractional solution to a linear program defines a probability distribution for an integer-valued random variable which is sampled. We apply this tool in a new way to produce natural strata and develop new properties of randomize rounding in this context. When proportional strata are impractical, we approximate them by minimizing the earthmover distance to proportionality. The method is applied to study birth outcomes for older and younger mothers in the United States in 2018. An R package natstrat is available at CRAN.

  Related
  Links

  Access via Oxford University Press
• Ruoqi Yu and Paul R. Rosenbaum (2022), Graded Matching for Large Observational Studies, Journal of Computational and Graphical Statistics , 10. 10.1080/10618600.2022.2058001 Abstract

  Observational studies of causal effects often use multivariate matching to control imbalances in measured covariates. For instance, using network optimization, one may seek the closest possible pairing for key covariates among all matches that balance a propensity score and finely balance a nominal covariate, perhaps one with many categories. This is all straightforward when matching thousands of individuals, but requires some adjustments when matching tens or hundreds of thousands of individuals. In various senses, a sparser network—one with fewer edges—permits optimization in larger samples. The question is: What is the best way to make the network sparse for matching? A network that is too sparse will eliminate from consideration possible pairings that it should consider. A network that is not sparse enough will waste computation considering pairings that do not deserve serious consideration. We propose a new graded strategy in which potential pairings are graded, with a preference for higher grade pairings. We try to match with pairs of the best grade, incorporating progressively lower grade pairs only to the degree they are needed. In effect, only sparse networks are built, stored and optimized. Two examples are discussed, a small example with 1567 matched pairs from clinical medicine, and a slightly larger example with 22,111 matched pairs from economics. The method is implemented in an R package RBestMatch available at https://github.com/ruoqiyu/RBestMatch. Supplementary materials for this article are available online.

  Related
  Links

  Access via Publisher Taylor & Francis
• Siddharth Jain, Paul R. Rosenbaum, Joseph G. Reiter, Alexander S. Hill, David A. Wolk, Sean Hashemi, Lee A. Fleisher, Roderic Eckenhoff, Jeffrey H. Silber (2022), Risk of Parkinson’s disease after anaesthesia and surgery, British Journal of Anaesthesia , 3. Abstract

  We previously examined the association between the exposure of surgery and anaesthesia for appendicitis and the subsequent development of Alzheimer’s disease and related dementias (ADRD).^1,2 We chose to focus on appendicectomy because appendicitis appears to occur fairly randomly (acting as a natural experiment), and its sequelae are generally not long term, unlike other procedures possibly needed as a result of underlying illnesses that may affect long-term outcomes. Literature has suggested that there are common pathways of neurodegeneration in Parkinson’s disease (PD) and ADRD.^3–5 We used the same cohort of patients who received an appendicectomy for appendicitis with similarly matched patients who did not have an appendicectomy, to investigate an association between exposure to surgery and anaesthesia and PD.

  Related
  Links

  NIH Public Access
• Ruoqi Yu, Dylan Small, Paul R. Rosenbaum (2021), The Information in Covariate Imbalance in Studies of Hormone Replacement Therapy, Annals of Applied Statistics, 15 (4), pp. 2023-2042.
• Ruoqi Yu, Dylan Small, David Harding, Jose Alvarez, Paul R. Rosenbaum (2021), Optimal Matching for Observational Studies that Integrate Quantitative and Qualitative Research, Statistics and Public Policy , 8 (p.p. 42-52).
• All Research from Paul R. Rosenbaum »

Past Courses

• BSTA5500 - Applied Reg & Analy Var

  An applied graduate level course in multiple regression and analysis of variance for students who have completed an undergraduate course in basic statistical methods. Emphasis is on practical methods of data analysis and their interpretation. Covers model building, general linear hypothesis, residual analysis, leverage and influence, one-way anova, two-way anova, factorial anova. Primarily for doctoral students in the managerial, behavioral, social and health sciences. Permission of instructor required to enroll.

• PSYC6110 - Applied Reg & Analy Var

  An applied graduate level course in multiple regression and analysis of variance for students who have completed an undergraduate course in basic statistical methods. Emphasis is on practical methods of data analysis and their interpretation. Covers model building, general linear hypothesis, residual analysis, leverage and influence, one-way anova, two-way anova, factorial anova. Primarily for doctoral students in the managerial, behavioral, social and health sciences. Permission of instructor required to enroll.

• PSYC6120 - Int To Nonp & Loglin Mod

  An applied graduate level course for students who have completed an undergraduate course in basic statistical methods. Covers two unrelated topics: loglinear and logit models for discrete data and nonparametric methods for nonnormal data. Emphasis is on practical methods of data analysis and their interpretation. Primarily for doctoral students in the managerial, behavioral, social and health sciences. Permission of instructor required to enroll.

• STAT5000 - Applied Reg & Analy Var

  An applied graduate level course in multiple regression and analysis of variance for students who have completed an undergraduate course in basic statistical methods. Emphasis is on practical methods of data analysis and their interpretation. Covers model building, general linear hypothesis, residual analysis, leverage and influence, one-way anova, two-way anova, factorial anova. Primarily for doctoral students in the managerial, behavioral, social and health sciences. Permission of instructor required to enroll.

• STAT5010 - Int To Nonp & Loglin Mod

  An applied graduate level course for students who have completed an undergraduate course in basic statistical methods. Covers two unrelated topics: loglinear and logit models for discrete data and nonparametric methods for nonnormal data. Emphasis is on practical methods of data analysis and their interpretation. Primarily for doctoral students in the managerial, behavioral, social and health sciences. Permission of instructor required to enroll.

• STAT9950 - Dissertation

  Dissertation

• Marvin Zelen Leadership Award in Statistical Science, 2026
• Medallion Lecture, Institute of Mathematical Statistics, 2020
• Long-Term Excellence Award from the Health Policy Statistics Section of the American Statistical Association, 2018
• C. G. Khatri Lecture, Penn State University, 2017
• Nathan Mantel Award from the Section on Statistics in Epidemiology of the American Statistical Association, 2017
• Nelder Lecture, Imperial College, 2016
• George W. Snedecor Award from COPSS, 2003
• Fellow, American Statistical Association, 1992
• R.A. Fisher Award and Lecture from COPSS, 1970

Knowledge @ Wharton

• How Forced Labor Scrutiny Shapes Supply Chain Transparency, Knowledge @ Wharton - 06/23/2026
• The Science of Perfect Timing: Using Chronobiology, Knowledge @ Wharton - 06/23/2026
• Would You Trust AI for Ethical Advice?, Knowledge @ Wharton - 06/23/2026
• The Business of National Reputation, Knowledge @ Wharton - 06/23/2026
• Peanut Butter Raises and the Pay Equity Debate, Knowledge @ Wharton - 06/19/2026
• How Liquid Death Builds Marketing That Wins the Internet, Knowledge @ Wharton - 06/18/2026
• SpaceX’s Historic IPO and the Future of Space, Knowledge @ Wharton - 06/17/2026
• What Unexpected Champions Teach Us About Sports, Knowledge @ Wharton - 06/17/2026
• How Mortgage Lock-In Is Quietly Pushing Up House Prices, Knowledge @ Wharton - 06/16/2026
• Does Q&A Boost Engagement?, Knowledge @ Wharton - 06/16/2026