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Sensitivity to Hidden Bias

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Observational Studies

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

Abstract

Cornfield, Haenszel, Hammond, Lilienfeld, Shimkin, and Wynder (1959) first conducted a formal sensitivity analysis in an observational study. Their paper is a survey of the evidence available in 1959 linking smoking with lung cancer. The paper asks whether the association between smoking and lung cancer is an effect caused by smoking or whether it is instead due to a hidden bias. Can lung cancer be prevented by not smoking? Or are the higher rates of lung cancer among smokers due to some other difference between smokers and nonsmokers?

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References

  • Aakvik, A. (2001) Bounding a matching estimator: The case of a Norwegian training program. Oxford Bulletin of Economics and Statistics, 63, 115–143.

    Article  Google Scholar 

  • Aiken, L. H., Smith, H. L., and Lake, E. T. (1994) Lower Medicare mortality among a set of hospitals known for good nursing care. Medical Care, 32, 771–787.

    Article  Google Scholar 

  • Armitage, P. (1977) Statistical Methods in Medical Research (fourth printing), Oxford, UK: Blackwell.

    Google Scholar 

  • Balke, A. and Pearl, J. (1997) Bounds on treatment effects from studies with imperfect compliance. Journal of the American Statistical Association, 92, 1172–1176.

    Article  Google Scholar 

  • Bickel, P. and van Zwet, (1978) Asymptotic expansions for the power of distribution free tests in the two-sample problem. Annals of Statistics, 6, 937–1004.

    Article  MathSciNet  MATH  Google Scholar 

  • Boston Collaborative Drug Pro j ect (1972) Excess of ampicillin rashes associated with allopurinol or hyperuricemia. New England Journal of Medicine, 286, 505–507.

    Article  Google Scholar 

  • Breslow, N. and Day, N. (1980) Statistical Methods in Cancer Research, I: The Analysis of Case-Control Studies. Lyon, France: International Agency for Research on Cancer.

    Google Scholar 

  • Bross, I. D. J. (1966) Spurious effects from an extraneous variable. Journal of Chronic Diseases, 19, 637–647.

    Article  Google Scholar 

  • Bross, I. D. J. (1967) Pertinency of an extraneous variable. Journal of Chronic Diseases, 20, 487–495.

    Article  Google Scholar 

  • Cameron, E. and Pauling, L. (1976) Supplemental ascorbate in the supportive treatment of cancer: Prolongation of survival times in terminal human cancer. Proceedings of the National Academy of Sciences (USA), 73, 3685–3689.

    Article  Google Scholar 

  • Copas, J. B. and Li, H. G. (1997) Inference for non-random samples (with discussion). Journal of the Royal Statistical Society, B, 59, 55–96.

    Article  MathSciNet  MATH  Google Scholar 

  • Cornfield, J., Haenszel, W., Hammond, E., Lilienfeld, A., Shimkin, M., and Wynder, E. (1959). Smoking and lung cancer: Recent evidence and a discussion of some questions. Journal of the National Cancer Institute, 22, 173–203.

    Google Scholar 

  • Davanzo, P., Thomas, M. A., Yue, K., Oshiro, T., Belin, T., Strober, M., and McCracken, J. (2001) Decreased anterior cingulate myoinositol/creatine spectoscopy resonance with lithium treatment in children with bipolar disorder. Neuropsychopharmacology, 24, 359 – 369.

    Article  Google Scholar 

  • Eaton, M. (1987) Lectures on Topics in Probability Inequalities. Amsterdam: Centrum voor Wiskunde en Informatica.

    MATH  Google Scholar 

  • Eidson, M., Philen, R. M., Sewell, C. M., Voorhees, R., and Kilbourne, E. M. (1990) L-tryptophan and eosinophilia-myalgia syndrome in New Mexico. Lancet, 335, 645–648.

    Article  Google Scholar 

  • Fisher, R.A. (1958) Lung cancer and cigarettes? Nature, 182, July 12, 108.

    Article  Google Scholar 

  • Freidlin, B. and Gastwirth, J. L. (2000) Should the median test be retired from general use? American Statistician, 54, 161–164.

    Google Scholar 

  • Gastwirth, J. L. (1988) Statistical Reasoning in Law and Public Policy. New York: Academic.

    MATH  Google Scholar 

  • Gastwirth, J. L. (1992a) Employment discrimination: A statistician’s look at analysis of disparate impact claims. Law and Inequality, 11, 151 – 179.

    Google Scholar 

  • Gastwirth, J. L. (1992b) Methods for assessing the sensitivity of statistical comparisons used in Title VII cases to omitte variahles Jurimetrics Journal, 19–34.

    Google Scholar 

  • Gastwirth, J. L. and Greenhouse, S. (1987) Estimating a common relative risk: Application in equal employment. Journal of the American Statistical Association, 82, 38–45.

    Article  MathSciNet  MATH  Google Scholar 

  • Gastwirth, J. L., Krieger, A. M. and Rosenbaum, P. R. (1998a) Cornfield’s inequality. In: Encyclopedia of Biostatistics, P. Armitage and T. Colton, eds., New York: Wiley, pp. 952–955.

    Google Scholar 

  • Gastwirth, J. L., Krieger, A. M., and Rosenbaum, P. R. (1998b) Dual and simultaneous sensitivity analysis for matched pairs. Biometrika, 85, 907–920.

    Article  MATH  Google Scholar 

  • Gastwirth, J. L., Krieger, A. M., and Rosenbaum, P. R. (2000) Asymptotic separability in sensitivity analysis. Journal of the Royal Statistical Society, Series B, 62, 545–555.

    Article  MathSciNet  MATH  Google Scholar 

  • Gibbons, J. D. (1982) Brown-Mood median test. In: Encyclopedia of Statistical Sciences, Volume 1, S. Kotz and N. Johnson, eds., New York: Wiley, pp. 322–324.

    Google Scholar 

  • Graham, A. J., Macdonald, A. M., and Hawkes, C. H. (1997) British motor neuron disease twin study. Journal of Neurology, Neurosurgery and Psychiatry, 6, 562–569.

    Article  Google Scholar 

  • Greenhouse, S. (1982) Jerome Cornfield’s contributions to epidemiology. Biometrics, 38S, 33–46.

    Article  Google Scholar 

  • Greenland, S. (1996) Basic methods of sensitivity analysis of biases. International Journal of Epidemiology, 25, 1107–1116.

    Google Scholar 

  • Gu, X. S. and Rosenbaum, P. R. (1993) Comparison of multivariate matching methods: Structures, distances and algorithms. Journal of Computational and Grapical Statistics, 2, 405–420.

    Google Scholar 

  • Hájek, J., Sidák, Z. and Sen, P. K. (1999) Theory of Rank Tests (Second Edition) . New York: Academic.

    MATH  Google Scholar 

  • Hakulinen, T. (1981) A Mantel-Haenszel statistic for testing the association between a polychotomous exposure and a rare outcome. American Journal of Epidemiology, 113 ,192–197.

    Google Scholar 

  • Hammond, E. C. (1964) Smoking in relation to mortality and morbidity: Findings in first thirty-four months of follow-up in a prospective study started in 1959. Journal of the National Cancer Institute, 32, 1161 – 1188.

    Google Scholar 

  • Hannan, J. and Harkness, W. (1963) Normal approximation to the distribution of two independent binomials, conditional on a fixed sum. Annals of Mathematical Statistics, 34, 1593–1595.

    Article  MathSciNet  MATH  Google Scholar 

  • Harkness, W. (1965) Properties of the extended hypergeometric distribution. Annals of Mathematical Statistics, 36, 938–945.

    Article  MathSciNet  MATH  Google Scholar 

  • Herbst, A., Ulfelder, H., and Poskanzer, D. (1971) Adenocarcinoma of the vagina: Association of maternal stilbestrol therapy with tumor appearance in young women. New England Journal of Medicine, 284, 878–881.

    Article  Google Scholar 

  • Hettmansperger, T. (1984) Statistical Inference Based on Ranks. New York: Wiley.

    MATH  Google Scholar 

  • Hodges, J. and Lehmann, E. (1962) Rank methods for combination of individual experiments in the analysis of variance. Annals of Mathematical Statistics, 33, 482–497.

    Article  MathSciNet  MATH  Google Scholar 

  • Hodges, J. and Lehmann, E. (1963) Estimates of location based on rank tests. Annals of Mathematical Statistics, 34, 598–611.

    Article  MathSciNet  MATH  Google Scholar 

  • Hollander, M., Proschan, F., and Sethuraman, J. (1977) Functions decreasing in transposition and their applications in ranking problems. Annals of Statistics, 5, 722–733.

    Article  MathSciNet  MATH  Google Scholar 

  • Hollander, M. and Wolfe, D. (1973, 1999) Nonparametric Statistical Methods. New York: Wiley.

    MATH  Google Scholar 

  • Holley, R. (1974) Remarks on the FKG inequalities. Communications in Mathematical Physics, 36, 227–231.

    Article  MathSciNet  Google Scholar 

  • Jick, H., Miettinen, O., Neff, R., et al. (1973) Coffee and myocardial infarction. New England Journal of Medicine, 289, 63–77.

    Article  Google Scholar 

  • Johnson, N., Kotz, S., and Kemp, A. (1992) Univariate Discrete Distributions. New York: Wiley.

    MATH  Google Scholar 

  • Kelsey, J. and Hardy, R. (1975) Driving of motor vehicles as a risk factor for acute herniated lumbar intervertebral disc. American Journal of Epidemiology, 102, 63–73.

    Google Scholar 

  • Kevekordes, S., Gebel, T. W., Hellwig, M., Dames, W., and Dunkelberg, H. (1998) Human effect monitoring in cases of occupational exposure to antineoplastic drugs: a method comparison. Occupational and Environmental Medicine, 55, 145–149.

    Article  Google Scholar 

  • Krieger, A. M. and Rosenbaum, P. R. (1994) A stochastic comparison for arrangement increasing functions. Combinatorics, Probability and Computing, 3, 345–348.

    Article  MathSciNet  MATH  Google Scholar 

  • Lehmann, E. (1975) Nonparametrics: Statistical Methods Based on Ranks. San Francisco: Holden-Day.

    MATH  Google Scholar 

  • Lin, D. Y., Psaty, B. M., and Kronmal, R. A. (1998) Assessing the sensitivity of regression results to unmeasured confounders in observational studies. Biometrics, 54, 948–963.

    Article  MATH  Google Scholar 

  • Mack, T., Pike, M., Henderson, B., Pfeffer, R., Gerkins, V., Arthur, B., and Brown, S. (1976) Estrogens and endometrial cancer in a retirement community. New England Journal of Medicine, 294, 1262–1267.

    Article  Google Scholar 

  • Mann, H. and Whitney, D. (1947) On a test of whether one of two random variables is stochastically larger than the other. Annals of Mathematical Statistics, 18, 50–60.

    Article  MathSciNet  MATH  Google Scholar 

  • Manski, C. (1990) Nonparametric bounds on treatment effects. American Economic Review, 319–323.

    Google Scholar 

  • Manski, C. (1995) Identification Problems in the Social Sciences. Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Mantel, N. and Haenszel, W. (1959) Statistical aspects of retrospective studies of disease. Journal of the National Cancer Institute, 22, 719–748.

    Google Scholar 

  • Marcus, S. (1997) Using omitted variable bias to assess uncertainty in the estimation of an AIDS education treatment effect. Journal of Educational and Behavioral Statistics, 22, 193–202.

    Google Scholar 

  • Marshall, A. and Olkin, I. (1979) Inequalities: Theory of Majorization and Its Applications. New York: Academic.

    MATH  Google Scholar 

  • McNemar, Q. (1947) Note on the sampling errorof the differences between correlated proportions or percentages. Psychometrika, 12, 153–157.

    Article  Google Scholar 

  • Miettinen, O. (1969) Individual matching with multiple controls in the case of all or none responses. Biometrics, 22, 339–355.

    Article  MathSciNet  Google Scholar 

  • Ming, K. and Rosenbaum, P. R. (2000) Substantial gains in bias reduction from matching with a variable number of controls. Biometrics, 56, 118–124.

    Article  MATH  Google Scholar 

  • Moertel, C., Fleming, T., Creagan, E., Rubin, J., O’Connell, M., and Ames, M. (1985) High-dose vitamin C vs placebo in the treatment of patients with advanced cancer who have had no prior chemotherapy: A randomized double-blind comparison. New England Journal of Medicine, 312, 137–141.

    Article  Google Scholar 

  • Morton, D., Saah, A., Silberg, S., Owens, W., Roberts, M., and Saah, M. (1982) Lead absorption in children of employees in a lead related industry. American Journal of Epidemiology, 115, 549–555.

    Google Scholar 

  • Mosteller, F. and Tukey, J. (1977) Data Analysis and Regression. Reading, MA: Addison-Wesley.

    Google Scholar 

  • Nicholson, W., Selikoff, I., Seidman, H., Lilis, R., and Formby, P. (1979) Long-term mortality experience of chrysotile miners and millers in Thetford Mines, Quebec. Annals of the New York Academy of Sciences, 330, 11–21.

    Article  Google Scholar 

  • Normand, S. T., Landrum, M. B., Guadagnoli, E., Ayanian, J. Z., Ryan, T. J., Cleary, P. D., and McNeil, B. J. (2001) Validating recommendations for coronary angiography following acute myocardial infarction in the elderly: A matched analysis using propensity scores. Journal of Clinical Epidemiology, 54, 387–398.

    Article  Google Scholar 

  • O’Brien, P. C. and Fleming, T. R. (1987) A paired Prentice-Wilcoxon test for censored paired data. Biometrics, 43, 169–180.

    Article  Google Scholar 

  • Pearl, J. (2000) Causality. New York: Cambridge University Press.

    MATH  Google Scholar 

  • Peters, J. M., Preston-Martin, S., and Yu, M. C. (1981) Brain tumors in children and occupational exposure of parents. Science, 213, 235–236.

    Article  Google Scholar 

  • Plackett, R. L. (1981) The Analysis of Categorical Data (second edition). New York: Macmillan.

    MATH  Google Scholar 

  • Psaty, B. M., Koepsell, T. D., Lin, D., Weiss, N., Siscovick, D. S., Rosendaal, F. R., Pahor, M., and Furberg, C. D. (1999) Assessment and control for confounding by indication in observational studies. Journal of the American Geriatrics Society, 47, 749–754.

    Google Scholar 

  • Quade, D. (1979) Using weighted rankings in the analysis of complete blocks with additive block effects. Journal of the American Statistical Association, 74, 680–683.

    Article  MathSciNet  MATH  Google Scholar 

  • Rosenbaum, P. R. (1986) Dropping out of high school in the United States: An observational study. Journal of Educational Statistics, 11, 207–224.

    Article  Google Scholar 

  • Rosenbaum, P. R. (1987) Sensitivity analysis for certain permutation inferences in matched observational studies. Biometrika, 74, 13–26.

    Article  MathSciNet  MATH  Google Scholar 

  • Rosenbaum, P. R. (1988) Sensitivity analysis for matching with multiple controls. Biometrika, 75, 577–581.

    Article  MathSciNet  MATH  Google Scholar 

  • Rosenbaum, P. R. (1989) On permutation tests for hidden biases in observational studies: An application of Holley’s inequality to the Savage lattice. Annals of Statistics, 17, 643–653.

    Article  MathSciNet  MATH  Google Scholar 

  • Rosenbaum, P. R. (1991a) Sensitivity analysis for matched case-control studies. Biometrics, 47, 87–100.

    Article  MathSciNet  MATH  Google Scholar 

  • Rosenbaum, P. R. (1991b) Discussing hidden bias in observational studies. Annals of Internal Medicine, 115, 901–905.

    Google Scholar 

  • Rosenbaum, P. R. (1991c) A characterization of optimal designs for observational studies. Journal of the Royal Statistical Society, Series B,53, 597–610.

    MathSciNet  MATH  Google Scholar 

  • Rosenbaum, P. R. (1993) Hodges-Lehmann point estimates of treatment effect in observational studies. Journal of the American Statistical Association, 88, 1250–1253.

    Article  MathSciNet  MATH  Google Scholar 

  • Rosenbaum, P. R. (1995) Quantiles in nonrandom samples and observational studies. Journal of the American Statistical Association, 90, 11424–1431.

    Article  MathSciNet  Google Scholar 

  • Rosenbaum, P. R. (1999a) Using combined quantile averages in matched observational studies. Applied Statistics, 48, 63–78.

    MATH  Google Scholar 

  • Rosenbaum, P. R. (1999b) Reduced sensitivity to hidden bias at upper quantiles in observational studies with dilated effects. Biometrics, 55, 560–564.

    Article  MATH  Google Scholar 

  • Rosenbaum, P. R. (1999) Holley’s inequality. In: Encyclopedia of Statistical Sciences, Update Volume 3, S. Kotz, C. B. Read, and D. L. Banks, eds., New York: Wiley, pp. 329–331.

    Google Scholar 

  • Rosenbaum, P. R. (2001) Effects attributable to treatment: Inference in experiments and observational studies with a discrete pivot. Biometrika, 88, 219–232.

    Article  MathSciNet  MATH  Google Scholar 

  • Rosenbaum, P. R. and Krieger, A. M. (1990) Sensitivity analysis for twosample permutation inferences in observational studies. Journal of the American Statistical Association, 85, 493–498.

    Article  MATH  Google Scholar 

  • Rosenbaum, P. R. and Rubin, D. B. (1983) Assessing sensitivity to an unobserved binary covariate in an observational study with binary outcome. Journal of the Royal Statistical Society, Series B,45, 212 –218.

    Google Scholar 

  • Rubin, D. B. (1978) Bayesian inference for causal effects: The role of randomization. Annals of Statistics, 6, 34–58.

    Article  MathSciNet  MATH  Google Scholar 

  • Savage, I. R. (1964) Contributions to the theory of rank order statistics: Applications of lattice theory. Review of the International Statistical Institute, 32, 52–63.

    Article  MathSciNet  MATH  Google Scholar 

  • Schlesselmann, J. J. (1978) Assessing the effects of confounding variables. American Journal of Epidemiology, 108, 3–8.

    Google Scholar 

  • Skerfving, S., Hansson, K., Mangs, C., Lindsten, J., and Ryman, N. (1974) Methylmercury-induced chromosome damage in man. Environmental Research, 7, 83–98.

    Article  Google Scholar 

  • Smith, H. L. (1997) Matching with multiple controls to estimate treatment effects in observational studies. Sociological Methodology, 27, 325 – 353.

    Article  Google Scholar 

  • Stevens, W. L. (1951) Mean and variance of an entry in a contingency table. Biometrika, 38, 468–470.

    MathSciNet  MATH  Google Scholar 

  • Tardif, S. (1987) Efficiency and optimality results for tests based on weighted rankings. Journal of the American Statistical Association, 82, 637–644.

    Article  MathSciNet  MATH  Google Scholar 

  • Tukey, J. W. (1957) Sums of random partitions of ranks. Annals of Mathematical Statistics, 28, 987–992.

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Statistics, The Wharton School, University of Pennsylvania, 19104-6302, Philadelphia, PA, USA

    Paul R. Rosenbaum

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Rosenbaum, P.R. (2002). Sensitivity to Hidden Bias. In: Observational Studies. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3692-2_4

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  • DOI: https://doi.org/10.1007/978-1-4757-3692-2_4

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4419-3191-7

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