Causality: a Statistical View

Statistical aspects of causality are reviewed in simple form and the impact of recent work discussed. Three distinct notions of causality are set out and implications for densities and for linear dependencies explained. The importance of appreciating the possibility of effect modifiers is stressed, be they intermediate variables, background variables or unobserved confounders. In many contexts the issue of unobserved confounders is salient. The difficulties of interpretation when there are joint effects are discussed and possible modifications of analysis explained. The dangers of uncritical conditioning and marginalization over intermediate response variables are set out and some of the problems of generalizing conclusions to populations and individuals explained. In general terms the importance of search for possibly causal variables is stressed but the need for caution is emphasized.

[1]  G. Yule,et al.  On the association of attributes in statistics, with examples from the material of the childhood society, &c , 1900, Proceedings of the Royal Society of London.

[2]  G. Yule.  On the Association of Attributes in Statistics: With Illustrations from the Material of the Childhood Society, &c , 1900 .

[3]  R Fisher,et al.  Design of Experiments , 1936 .

[4]  W. G. Cochran.  The Omission or Addition of an Independent Variate in Multiple Linear Regression , 1938 .

[5]  Illtyd Trethowan.  Causality , 1938 .

[6]  William G. Cochran,et al.  The analysis of groups of experiments , 1938, The Journal of Agricultural Science.

[7]  I NICOLETTI,et al.  The Planning of Experiments , 1936, Rivista di clinica pediatrica.

[8]  D. A. Bell,et al.  Applied Statistics , 1953, Nature.

[9]  I. Good.  A CAUSAL CALCULUS (I)* , 1961, The British Journal for the Philosophy of Science.

[10]  I. Good.  A CAUSAL CALCULUS (II)* , 1961, The British Journal for the Philosophy of Science.

[11]  Education Welfare.,et al.  Smoking and Health. Report of the Advisory Committee to the Surgeon General of the Public Health Service. , 1964 .

[12]  W. G. Cochran.  The Planning of Observational Studies of Human Populations , 1965 .

[13]  A. B. Hill.  The Environment and Disease: Association or Causation? , 1965, Proceedings of the Royal Society of Medicine.

[14]  G. Box.  Use and Abuse of Regression , 1966 .

[15]  C. Fletcher,et al.  Smoking and health. , 1970, WHO chronicle.

[16]  Tore Schweder,et al.  Composable Markov processes , 1970, Journal of Applied Probability.

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

[18]  Derek Fraser,et al.  Education and Welfare , 1973 .

[19]  D. Rubin.  Estimating causal effects of treatments in randomized and nonrandomized studies. , 1974 .

[20]  R. Lucas.  Econometric policy evaluation: A critique , 1976 .

[21]  T. Cooper.  Department of Health, Education, and Welfare. , 1976, Military medicine.

[22]  David R. Cox,et al.  Present Position and Potential Developments: Some Personal Views Design of Experiments and Regression , 1984 .

[23]  D. Topping,et al.  Smoking and health , 1984, The Medical journal of Australia.

[24]  P. Holland.  Statistics and Causal Inference , 1985 .

[25]  Odd O. Aalen,et al.  Dynamic modelling and causality , 1987 .

[26]  D. Francis.  An introduction to structural equation models. , 1988, Journal of clinical and experimental neuropsychology.

[27]  R. Prentice.  Surrogate endpoints in clinical trials: definition and operational criteria. , 1989, Statistics in medicine.

[28]  N. Kiviat,et al.  Nephrogenic rests, nephroblastomatosis, and the pathogenesis of Wilms' tumor. , 1990, Pediatric pathology.

[29]  T. Speed,et al.  On the Application of Probability Theory to Agricultural Experiments. Essay on Principles. Section 9 , 1990 .

[30]  A. Dempster.  Causality and statistics , 1990 .

[31]  N. Wermuth,et al.  On Substantive Research Hypotheses, Conditional Independence Graphs and Graphical Chain Models , 1990 .

[32]  D. Rubin.  [On the Application of Probability Theory to Agricultural Experiments. Essay on Principles. Section 9.] Comment: Neyman (1923) and Causal Inference in Experiments and Observational Studies , 1990 .

[33]  A. Goldberger.  A course in econometrics , 1991 .

[34]  D. Cox.  Causality : some statistical aspects , 1992 .

[35]  Rory A. Fisher,et al.  The Arrangement of Field Experiments , 1992 .

[36]  N. Wermuth,et al.  Linear Dependencies Represented by Chain Graphs , 1993 .

[37]  Richard Scheines,et al.  An introduction to Causal Inference , 1996 .

[38]  James M. Robins,et al.  Causal Inference from Complex Longitudinal Data , 1997 .

[39]  J. Goldthorpe.  Causation, statistics, and sociology , 1998 .

[40]  T. Shakespeare,et al.  Observational Studies , 2003 .

[41]  J M Violanti,et al.  Cellular phones and fatal traffic collisions. , 1998, Accident; analysis and prevention.

[42]  Michael I. Jordan.  Graphical Models , 2003 .

[43]  D. Freedman.  From association to causation: some remarks on the history of statistics , 1999 .

[44]  D. Cox,et al.  Some Remarks on Failure-times, Surrogate Markers, Degradation, Wear, and the Quality of Life , 1999, Lifetime data analysis.

[45]  A. P. Dawid,et al.  Causal inference without counterfactuals (with Discussion) , 2000 .

[46]  A. Dawid.  Causal Inference without Counterfactuals , 2000 .

[47]  K. Hoover.  Causality in Macroeconomics , 2001 .

[48]  N. McAlister Gregg,et al.  Congenital cataract following German measles in the mother , 2001 .

[49]  C. Granger.  Investigating causal relations by econometric models and cross-spectral methods , 1969 .

[50]  Steffen L. Lauritzen,et al.  Causal Inference from Graphical Models , 2001 .

[51]  D. Lindley.  Seeing and Doing: the Concept of Causation , 2002 .

[52]  D. Rubin,et al.  Principal Stratification in Causal Inference , 2002, Biometrics.

[53]  A. Dawid.  Influence Diagrams for Causal Modelling and Inference , 2002 .

[54]  R. Doll.  Proof of Causality: Deduction from Epidemiological Observation , 2002, Perspectives in biology and medicine.

[55]  Steffen L. Lauritzen,et al.  Graphical Models for Surrogates , 2003 .

[56]  Tom Burr,et al.  Causation, Prediction, and Search , 2003, Technometrics.

[57]  Nanny Wermuth,et al.  A general condition for avoiding effect reversal after marginalization , 2003 .

[58]  James M. Robins,et al.  Unified Methods for Censored Longitudinal Data and Causality , 2003 .

[59]  N. Wermuth,et al.  Joint response graphs and separation induced by triangular systems , 2004 .