Bounding Causal Effects Under Uncontrolled Confounding Using Counterfactuals

Common sensitivity analysis methods for unmeasured confounders provide a corrected point estimate of causal effect for each specified set of unknown parameter values. This article reviews alternative methods for generating deterministic nonparametric bounds on the magnitude of the causal effect using linear programming methods and potential outcomes models. The bounds are generated using only the observed table. We then demonstrate how these bound widths may be reduced through assumptions regarding the potential outcomes under various exposure regimens. We illustrate this linear programming approach using data from the Cooperative Cardiovascular Project. These bounds on causal effect under uncontrolled confounding complement standard sensitivity analyses by providing a range within which the causal effect must lie given the validity of the assumptions.

[1]  E. C. Hammond,et al.  Smoking and lung cancer: recent evidence and a discussion of some questions. , 1959, Journal of the National Cancer Institute.

[2]  I. Bross,et al.  Pertinency of an extraneous variable. , 1967, Journal of chronic diseases.

[3]  J. Copas.  Randomization models for the matched and unmatched 2 × 2 tables , 1973 .

[4]  J. Schlesselman.  Assessing effects of confounding variables. , 1978, American journal of epidemiology.

[5]  N. Breslow,et al.  Statistical methods in cancer research: volume 1- The analysis of case-control studies , 1980 .

[6]  R Neutra,et al.  An analysis of detection bias and proposed corrections in the study of estrogens and endometrial cancer. , 1981, Journal of chronic diseases.

[7]  Takashi Yanagawa,et al.  Case-control studies: Assessing the effect of a confounding factor , 1984 .

[8]  J M Robins,et al.  Identifiability, exchangeability, and epidemiological confounding. , 1986, International journal of epidemiology.

[9]  M. Gail,et al.  Indirect corrections for confounding under multiplicative and additive risk models. , 1988, American journal of industrial medicine.

[10]  C. Manski.  Nonparametric Bounds on Treatment Effects , 1989 .

[11]  W. Flanders,et al.  Indirect Assessment of Confounding: Graphic Description and Limits on Effect of Adjusting for Covariates , 1990, Epidemiology.

[12]  Joshua D. Angrist,et al.  Identification of Causal Effects Using Instrumental Variables , 1993 .

[13]  H. Krumholz,et al.  Quality of care for Medicare patients with acute myocardial infarction. A four-state pilot study from the Cooperative Cardiovascular Project. , 1995, JAMA.

[14]  Alexander Balke,et al.  Probabilistic counterfactuals: semantics, computation, and applications , 1996 .

[15]  James J. Heckman,et al.  Identification of Causal Effects Using Instrumental Variables: Comment , 1996 .

[16]  David Maxwell Chickering,et al.  A Clinician's Tool for Analyzing Non-Compliance , 1996, AAAI/IAAI, Vol. 2.

[17]  A. Hjalmarson,et al.  Effects of beta blockade on sudden cardiac death during acute myocardial infarction and the postinfarction period. , 1997, The American journal of cardiology.

[18]  J. Pearl,et al.  Bounds on Treatment Effects from Studies with Imperfect Compliance , 1997 .

[19]  D. Rubin,et al.  Bayesian inference for causal effects in randomized experiments with noncompliance , 1997 .

[20]  R. Kronmal,et al.  Assessing the sensitivity of regression results to unmeasured confounders in observational studies. , 1998, Biometrics.

[21]  Palmer.  Encyclopedia of biostatistics , 1999, BMJ.

[22]  J Schwartz,et al.  Air pollution and hospital admissions for heart disease in eight U.S. counties. , 1998, Epidemiology.

[23]  J. Pearl,et al.  Causal diagrams for epidemiologic research. , 1999, Epidemiology.

[24]  J. Pearl,et al.  Confounding and Collapsibility in Causal Inference , 1999 .

[25]  K A Schulman,et al.  The effect of race and sex on physicians' recommendations for cardiac catheterization. , 1999, The New England journal of medicine.

[26]  J. Pearl.  Causality: Models, Reasoning and Inference , 2000 .

[27]  H. Lawson,et al.  Treatment of acute myocardial infarction and 30-day mortality among women and men. , 2000, The New England journal of medicine.

[28]  J. Robins.  Data, Design, and Background Knowledge in Etiologic Inference , 2001, Epidemiology.

[29]  A. Zaslavsky,et al.  Racial disparities in the quality of care for enrollees in medicare managed care. , 2002, JAMA.

[30]  S. Greenland,et al.  Estimating causal effects. , 2002, International journal of epidemiology.

[31]  Sander Greenland,et al.  An overview of relations among causal modelling methods. , 2002, International journal of epidemiology.

[32]  Carl V Phillips,et al.  Quantifying and Reporting Uncertainty from Systematic Errors , 2003, Epidemiology.

[33]  Timothy L Lash,et al.  Semi-Automated Sensitivity Analysis to Assess Systematic Errors in Observational Data , 2003, Epidemiology.

[34]  Richard F MacLehose,et al.  Quality of care for acute myocardial infarction in rural and urban US hospitals. , 2004, The Journal of rural health : official journal of the American Rural Health Association and the National Rural Health Care Association.

[35]  S. Wacholder.  The impact of a prevention effort on the community. , 2005, Epidemiology.

[36]  Chittaranjan Andrade,et al.  Confounding , 2007, Indian journal of psychiatry.