Models for Treatment Effects

  • Paul R. Rosenbaum
Part of the Springer Series in Statistics book series (SSS)


The effect of a treatment may vary from one person to the next. One person may benefit or suffer greatly from treatment, while another person may experience little or no effect. In other words, the effect of the treatment on the ith person in stratum s, namely r Tsi - r Csi , may not be constant, but may change with i and s.


Minimum Wage Instrumental Variable Potential Response Treated Subject Dilate Effect 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Angrist, J. D. (1998) Estimating the labor market impact of voluntary military service using social security data on military applicants. Econometrica, 66, 249–288.zbMATHCrossRefGoogle Scholar
  2. Angrist, J. D. and Imbens, G. W. (1994) Identification and estimation of local average treatment effects. Econometrica, 62, 467–475.zbMATHCrossRefGoogle Scholar
  3. Angrist, J. D., Imbens, G. W., and Rubin, D. B. (1996) Identification of causal effects using instrumental variables (with discussion). Journal of the American Statistical Association, 91, 444–455.zbMATHCrossRefGoogle Scholar
  4. Bickel, P. and Lehmann, E. (1976) Descriptive statistics for nonparametric problems, IV: Spread. In Contributions to Statistics, J. Juneckova, ed., Dordrecht, Holland: Reidel, pp. 33–40.Google Scholar
  5. Card, D. and Krueger, A. (1994) Minimum wages and employment: A case study of the fast-food industry in New Jersey and Pennsylvania. American Economic Review, 84, 772–793.Google Scholar
  6. Card, D. and Krueger, A. (1995) Myth and Measurement: The New Economics of the Minimum Wage. Princeton, NJ: Princeton University Press.Google Scholar
  7. Card, D. and Krueger, A. (1998) A reanalysis of the effect of the New Jersey minimum wage increase on the fast-food industry with representative payroll data. National Bureau of Economic Research, Working Paper 6386.Google Scholar
  8. Card, D. and Krueger, A. (2000) Minimum wages and employment: A case study of the fast-food industry in New Jersey and Pennsylvania: Reply. American Economic Review, 90, 1397–1420.CrossRefGoogle Scholar
  9. Coats, T. J. and Walter, D. P. (1999) Effect of station design on death in the London Underground: Observational study. British Medical Journal, 319, 957.CrossRefGoogle Scholar
  10. Doksum, K. (1974) Empirical probability plots and statistical inference for nonlinear models in the two-sample case. Annals of Statistics, 2, 267–277.MathSciNetzbMATHCrossRefGoogle Scholar
  11. Doksum, K. and Sievers, G. (1976) Plotting with confidence: Graphical comparisons of two populations. Biometrika, 63, 421–434.MathSciNetzbMATHCrossRefGoogle Scholar
  12. Gart, J. J. (1963) A median test with sequential application. Biometrika, 50, 55–62.MathSciNetzbMATHGoogle Scholar
  13. Gastwirth, J. L. (1968) The first-median test: A two-sided version of the control median test. Journal of the American Statistical Association, 63, 692–706.MathSciNetzbMATHCrossRefGoogle Scholar
  14. Hamilton, M. A. (1979). Choosing the parameter for 2 × 2 and 2 × 2 × 2 table analysis. American Journal of Epidemiology, 109, 362–375.Google Scholar
  15. Harkness, W. (1965) Properties of the extended hypergeometric distribution. Annals of Mathematical Statistics, 36, 938–945.MathSciNetzbMATHCrossRefGoogle Scholar
  16. Holland, P. W. (1988) Causal inference, path analysis, and recursive structural equation models (with discussion). Sociological Methodology, 449–476.Google Scholar
  17. Lehmann, E. (1975) Nonparametrics: Statistical Methods Based on Ranks. San Francisco: Holden-Day.zbMATHGoogle Scholar
  18. Li, G., Tiwari, R.C., and Wells, M.T. (1996) Quantile comparison functions in two-sample problems, with application to comparisons of diagnostic markers. Journal of the American Statistical Association, 91, 689–698.MathSciNetzbMATHCrossRefGoogle Scholar
  19. MacMahon, B. and Pugh, T. F. (1970) Epidemiology: Principles and Methods. Boston: Little, Brown.Google Scholar
  20. Orban, J. and Wolfe, D. A. (1982) A class of distribution-free two-sample tests based on placements. Journal of the American Statistical Association, 77, 666–672.MathSciNetzbMATHCrossRefGoogle Scholar
  21. Manski, C. (1990) Nonparametric bounds on treatment effects. American Economic Review, 319–323.Google Scholar
  22. Manski, C. (1995) Identification Problems in the Social Sciences. Cambridge, MA: Harvard University Press.Google Scholar
  23. Rosenbaum, P. R. (1995) Quantiles in nonrandom samples and observational studies. Journal of the American Statistical Association, 90, 1424–1431.MathSciNetzbMATHCrossRefGoogle Scholar
  24. Rosenbaum, P. R. (1996a) Observational studies and nonrandomized experiments. In: Handbook of Statistics, Volume 13, Design of Experiments, Chapter 6, S. Ghosh and C. R. Rao, eds., New York: Elsevier, pp. 181–197.Google Scholar
  25. Rosenbaum, P. R. (1996b) Comment on “Identification of causal effects using instrumental variables” by Angrist, Imbens, and Rubin. Journal of the American Statistical Association, 91, 465–468.Google Scholar
  26. Rosenbaum, P. R. (1997) Discussion of a paper by Copas and Li. Journal of the Royal Statistical Society, Series B, 59, 90.Google Scholar
  27. Rosenbaum, P. R. (1999a) Reduced sensitivity to hidden bias at upper quantiles in observational studies with dilated effects. Biometrics, 55, 560–564.zbMATHCrossRefGoogle Scholar
  28. Rosenbaum, P. R. (1999b) Using combined quantile averages in matched observational studies. Applied Statistics, 48, 63–78.zbMATHGoogle Scholar
  29. Rosenbaum, P. (2001) Effects attributable to treatment: Inference in experiments and observational studies with a discrete pivot. Biometrika, 88, 219–232.MathSciNetzbMATHCrossRefGoogle Scholar
  30. Rubin, D. B. (1974) Estimating the causal effects of treatments in randomized and nonrandomized studies. Journal of Educational Psychology, 66, 688–701.CrossRefGoogle Scholar
  31. Shaked, M. (1982) Dispersive ordering of distributions. Journal of Applied Probability, 19, 310–320.MathSciNetzbMATHCrossRefGoogle Scholar
  32. Sedransk, J. and Meyer, J. (1978) Confidence intervals for the quantiles of finite populations: simple random and stratified random sampling. Journal of the Royal Statistical Society, Series B, 40, 239–252.MathSciNetzbMATHGoogle Scholar
  33. Sheiner, L. B. and Rubin, D. B. (1995) Intention-to-treat analysis and the goals of clinical trials. Clinical Pharmacology and Therapeutics, 57, 6–15.CrossRefGoogle Scholar
  34. Skerfving, S., Hansson, K., Mangs, C., Lindsten, J., and Ryman, N. (1974) Methylmercury-induced chromosome damage in man. Environmental Research, 7, 83–98.CrossRefGoogle Scholar
  35. Sommer, A. and Zeger, S. L. (1991) On estimating efficacy from clinical trials. Statistics in Medicine, 10, 45–52.CrossRefGoogle Scholar
  36. Switzer, P. (1976) Confidence procedures for two-sample problems. Biometrika, 63, 13–25.MathSciNetzbMATHCrossRefGoogle Scholar
  37. Thun, M. (1993) Kidney dysfunction in cadmium workers. In: Case Studies in Occupational Epidemiology, K. Steenland, ed., New York: Oxford University Press, pp. 105–126.Google Scholar
  38. Thun, M., Osorio, A., Schober, S., et al. (1989) Nephropathy in cadmium workers: Assessment of risk from airborne occupational exposure to cadmium. British Journal of Industrial Medicine, 46, 689–697.Google Scholar
  39. Tunca, B. T. and Egeli, U. (1996) Cytogenetic findings on shoe workers exposed long-term to benzene. Environmental Health Perspectives, 104, supplement 6, 1313–1317.Google Scholar
  40. Walter, S. D. (1975) The distribution of Levin’s measure of attributable risk. Biometrika, 62, 371–375.zbMATHCrossRefGoogle Scholar
  41. Wilks, S. (1962) Mathematical Statistics. New York: Wiley.zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Paul R. Rosenbaum
    • 1
  1. 1.Department of Statistics, The Wharton SchoolUniversity of PennsylvaniaPhiladelphiaUSA

Personalised recommendations