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Causal Inference in Randomized Experiments

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Design of Observational Studies

Part of the book series: Springer Series in Statistics ((SSS))

Abstract

An observational study is an empiric investigation of treatment effects when random assignment to treatment or control is not feasible. Because observational studies are structured to resemble simple randomized experiments, an understanding of the role randomization plays in experiments is important as background. As a prelude to the discussion of observational studies in later chapters, the current chapter contains a brief review of the logic of causal inference in a randomized experiment. Only one simple case is discussed in detail, namely a randomized paired experiment in which subjects are paired before randomization and one subject in each pair is picked at random to receive treatment, the other receiving control. Although a foundation for later chapters, much of the material in this chapter is quite old, dating from Sir Ronald Fisher’s work in the 1920s and 1930s, and it is likely to be familiar from other contexts, such as a course in the design of experiments.

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References

  • Andrews, D.F., Bickel, P.J., Hampel, F.R., Huber, P.J., Rogers, W.H., Tukey, J.W.: Robust Estimates of Location. Princeton, NJ: Princeton University Press (1972)

    MATH  Google Scholar 

  • Bennett, D.M.: Confidence limits for a ratio using Wilcoxon’s signed rank test. Biometrics 21, 231–234 (1965)

    Article  MathSciNet  Google Scholar 

  • Boruch, R.: Randomized Experiments for Planning and Evaluation. Thousand Oaks, CA: Sage (1997)

    MATH  Google Scholar 

  • Cochran, W.G.: The planning of observational studies of human populations (with Discussion). J Roy Statist Soc A 128, 234–265 (1965)

    Article  Google Scholar 

  • Conover, W.J., Salsburg, D.S.: Locally most powerful tests for detecting treatment effects when only a subset of patients can be expected to ‘respond’ to treatment. Biometrics 44, 189–196 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  • Cook, T.D., Shadish, W.R.: Social experiments: Some developments over the past fifteen years. Annu Rev Psychol 45, 545–580 (1994)

    Article  Google Scholar 

  • Couch, K.A.: New evidence on the long-term effects of employment training programs. J Labor Econ 10, 380–388. (1992)

    Article  Google Scholar 

  • Cox, D.R.: Planning of Experiments. New York: Wiley (1958)

    MATH  Google Scholar 

  • Cox, D.R.: The interpretation of the effects of non-additivity in the Latin square. Biometrika 45, 69–73. (1958)

    MATH  Google Scholar 

  • Cox, D.R.: The role of significance tests. Scand J Statist 4, 49–62 (1977)

    MATH  MathSciNet  Google Scholar 

  • Cox, D.R., Reid, N.: The Theory of the Design of Experiments. New York: Chapman and Hall/CRC (2000)

    MATH  Google Scholar 

  • Dehejia, R.H., Wahba, W.: Causal effects in nonexperimental studies: Reevaluating the evaluation of training programs. J Am Statist Assoc 94, 1053–1062 (1999)

    Article  Google Scholar 

  • Fisher, R.A.: Design of Experiments. Edinburgh: Oliver and Boyd (1935)

    Google Scholar 

  • Frangakis, C.E., Rubin, D.B.: Principal stratification in causal inference. Biometrics 58, 21–29 (2002)

    Article  MathSciNet  Google Scholar 

  • Freedman, D.A.: Randomization does not justify logistic regression. Statist Sci 23, 237–249 (2008)

    Article  Google Scholar 

  • Friedman, L.M., DeMets, D.L., Furberg, C.D.: Fundamentals of Clinical Trials. New York: Springer (1998)

    Google Scholar 

  • Greevy, R., Lu, B., Silber, J.H., Rosenbaum, P.R.: Optimal matching before randomization. Biostatistics 5, 263–275 (2004)

    Article  MATH  Google Scholar 

  • Hämäläinen, K., Uusitalo, R., Vuori, J.: Varying biases in matching estimates: Evidence from two randomized job search training experiments. Labour Econ 15, 604–618 (2008)

    Article  Google Scholar 

  • Heckman, J.J., Hotz, V.J.: Choosing among alternative nonexperimental methods for estimating the impact of social programs: The case of manpower training (with Discussion). J Am Statist Assoc 84, 862–874 (1989)

    Article  Google Scholar 

  • Hodges, J.L., Lehmann, E.L.: Rank methods for combination of independent experiments in analysis of variance. Ann Math Statist 33, 482–497 (1962)

    Article  MATH  MathSciNet  Google Scholar 

  • Hodges, J.L., Lehmann, E.L.: Estimates of location based on ranks. Ann Math Statist 34, 598–611 (1963)

    Article  MATH  MathSciNet  Google Scholar 

  • Hoeffding, W.: A class of statistics with asymptotically normal distributions. Ann Math Statist 19, 293–325 (1948)

    Article  MATH  MathSciNet  Google Scholar 

  • Holland, P.W.: Statistics and causal inference. J Am Statist Assoc 81, 945–960 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  • Hollister, R., Kemper, P., Maynard, R., eds.: The National Supported Work Demonstration. Madison: University of Wisconsin Press (1984)

    Google Scholar 

  • Huber, P.J.: Robust estimation of a location parameter. Ann Math Statist 35, 73–101 (1964)

    Article  MATH  MathSciNet  Google Scholar 

  • Hudgens, M.G., Halloran, M.E.: Toward causal inference with interference. J Am Statist Assoc 482, 832–842 (2008)

    Google Scholar 

  • Jurečková, J., Sen, P.K.: Robust Statistical Procedures. New York: Wiley (1996)

    MATH  Google Scholar 

  • Kempthorne, O.: Design and Analysis of Experiments. New York: Wiley (1952)

    MATH  Google Scholar 

  • LaLonde, R.J.: Evaluating the econometric evaluations of training programs with experimental data. Am Econ Rev 76, 604–620 (1986)

    Google Scholar 

  • LaLonde, R.J.: The promise of public sector-sponsored training programs. J Econ Perspec 9, 149–168 (1995)

    Google Scholar 

  • Lehmann, E.L.: Testing Statistical Hypotheses. New York: Wiley (1959)

    MATH  Google Scholar 

  • Lehmann, E.L.: Nonparametrics. San Francisco: Holden-Day (1975)

    MATH  Google Scholar 

  • Maritz, J.S.: A note on exact robust confidence intervals for location. Biometrika 66, 163–166 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  • Maritz, J.S.: Distribution-Free Statistical Methods. London: Chapman and Hall (1995)

    Google Scholar 

  • Neyman, J.: On the application of probability theory to agricultural experiments: Essay on principles, Section 9.\ In Polish, but reprinted in English with Discussion by T. Speed and D. B. Rubin in Statist Sci 5, 463–480 (1923, reprinted 1990)

    Google Scholar 

  • Nichols, T.E., Holmes, A.P.: Nonparametric permutation tests for functional neuroimaging. Human Brain Mapping 15, 1–25.

    Google Scholar 

  • Pagano, M., Tritchler, D.: On obtaining permutation distributions in polynomial time. J Am Statist Assoc 78, 435–440 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  • Piantadosi, S.: Clinical Trials. New York: Wiley (2005)

    Book  MATH  Google Scholar 

  • Pratt, J.W., Gibbons, J.D.: Concepts of Nonparametric Theory. New York: Springer (1981)

    MATH  Google Scholar 

  • Robinson, J.: The large sample power of permutation tests for randomization models. Ann Statist 1, 291–296 (1973)

    Article  MATH  MathSciNet  Google Scholar 

  • Rosenbaum, P.R.: The consequences of adjustment for a concomitant variable that has been affected by the treatment. J Roy Statist Soc A 147, 656–666 (1984)

    Google Scholar 

  • Rosenbaum, P.R.: Effects attributable to treatment: Inference in experiments and observational studies with a discrete pivot. Biometrika 88, 219–231 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  • Rosenbaum, P.R.: Attributing effects to treatment in matched observational studies. J Am Statist Assoc 97, 183–192 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  • Rosenbaum, P.R.: Observational Studies (2nd ed.). New York: Springer (2002)

    MATH  Google Scholar 

  • Rosenbaum, P.R.: Covariance adjustment in randomized experiments and observational studies (with Discussion). Statist Sci 17, 286–327 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  • Rosenbaum, P.R.: Exact confidence intervals for nonconstant effects by inverting the signed rank test. Am Statistician 57, 132–138 (2003)

    Article  MathSciNet  Google Scholar 

  • Rosenbaum, P.R.: Interference between units in randomized experiments. J Am Statist Assoc 102, 191–200 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  • Rosenbaum, P.R.: Sensitivity analysis for m-estimates, tests, and confidence intervals in matched observational studies. Biometrics 63, 456–464 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  • Rosenbaum, P.R.: Confidence intervals for uncommon but dramatic responses to treatment. Biometrics 63, 1164–1171 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  • Rubin, D.B. : Estimating causal effects of treatments in randomized and nonrandomized studies. J Educ Psychol 66, 688–701 (1974)

    Article  Google Scholar 

  • Rubin, D.B., Stuart, E.A., Zanutto, E.L. : A potential outcomes view of value-added assessment in education. J Educ Behav Statist 29, 103–116 (2004)

    Article  Google Scholar 

  • Salsburg, D.S.: Alternative hypotheses for the effects of drugs in small-scale clinical studies. Biometrics 42, 671–674 (1986)

    Article  Google Scholar 

  • Salsburg, D.S.: The Use of Restricted Significance Tests in Clinical Trials. New York: Springer (1992)

    MATH  Google Scholar 

  • Shadish, W. R., Cook, T. D., Campbell, D. T.: Experimental and Quasi-Experimental Designs for Generalized Causal Inference. Boston: Houghton-Mifflin (2002)

    Google Scholar 

  • Shaffer, J.P.: Bidirectional unbiased procedures. J Am Statist Assoc 69, 437–439 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  • Small, D., Ten Have, T.R., Rosenbaum, P.R.: Randomization inference in a group-randomized trial of treatments for depression: covariate adjustment, noncompliance and quantile effects. J Am Statist Assoc 103, 271–279 (2007)

    Article  MathSciNet  Google Scholar 

  • Smith, J.A., Todd, P.E.: Does matching overcome LaLonde’s critique of nonexperimental estimators? J Econometrics 125, 305–353 (2005)

    Article  MathSciNet  Google Scholar 

  • Sobel, M.E.: What do randomized studies of housing mobility demonstrate?: Causal inference in the face of interference. J Am Statist Assoc 476, 1398–1407 (2006)

    Google Scholar 

  • Stephenson, W.R.: A general class of one-sample nonparametric test statistics based on subsamples. J Am Statist Assoc 76, 960–966 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  • Tobin, J.: Estimation of relationships for limited dependent variables. Econometrica 26, 24–36 (1958)

    Article  MATH  MathSciNet  Google Scholar 

  • Weiss, L.: A note on confidence sets for random variables. Ann Math Statist 26, 142–144 (1955)

    Article  MATH  MathSciNet  Google Scholar 

  • Welch, B.L.: On the z-test in randomized blocks and Latin squares. Biometrika 29, 21–52 (1937)

    MATH  Google Scholar 

  • Wilcoxon, F.: Individual comparisons by ranking methods. Biometrics 1, 80–83 (1945)

    Article  Google Scholar 

  • Wilk, M.B.: The randomization analysis of a generalized randomized block design. Biometrika 42, 70–79 (1955)

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Statistics Department Wharton School, University of Pennsylvania, 19104-6340, Philadelphia, PA, USA

    Paul R. Rosenbaum

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  1. Paul R. Rosenbaum
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Correspondence to Paul R. Rosenbaum .

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Rosenbaum, P.R. (2010). Causal Inference in Randomized Experiments. In: Design of Observational Studies. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-1213-8_2

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