The problem of drawing causal inferences from retrospective case-control studies is
considered. A model for causal inference in prospective studies is reviewed and then
applied to retrospective studies. The limitations of case-control studies are formulated in
terms of the level of causally relevant parameters that can be estimated in such studies. An
example using data from a large retrospective study of coffee-drinking and myocardial
infarctions is used to illustrate the ideas of the article.
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References
1.
Basu, D. (1980) "Randomization analysis of experimental data: the Fisher Randomization Test." J. of the Amer. Stat. Assn.75: 575-582.
2.
Bishop, Y.M.M., S.E. Fienberg, and P.W. Holland (1975) Discrete Multivariate Analysis: Theory and Practice . Cambridge: MIT Press.
3.
Breslow, N.E. and N.E. Day (1980) Statistical Methods in Cancer Research, Vol. 1: The Analysis of Case-Control Studies . Lyon, France: International Agency for Research on Cancer.
4.
Cochran, W.G. (1965) "Planning of observational studies of human populations ." J. of the Royal Stat. Society series A, 128, part 2: 234-255.
5.
Cornfield, J. (1951) "A method of estimating comparative rates from clinical data, application to cancer of the lung, breast and cervix." J. of the National Cancer Institute11: 1269-1275.
6.
Cornfield, J. (1956) "A statistical problem arising from retrospective studies." Proceedings of the Third Berkeley Symposium4: 135-148.
7.
Cox, D.R. (1958) Planning of Experiments. New York: John Wiley.
8.
Fisher, R.A. (1935) The Design of Experiments. Edinburgh: Oliver & Boyd.
9.
Granger, C.W.J. (1969) "Investigating causal relations by econometric models and cross-spectral methods." Econometrica37: 424-438.
10.
Holland, P.W. (1986a) "Which comes first, cause or effect?" New York Statistician38: 1-6.
11.
Holland, P.W. (1986b) "Statistics and causal inference." J. of the Amer. Stat. Assn.81: 945-970.
12.
Holland, P.W. and D.B. Rubin (1983) "On Lord's Paradox," in Wainer and Messick (eds.) Principles of Modern Psychological Measurement. Hillsdale, NJ: Lawrence Erlbaum.
13.
Jick, H. et al. (1973) "Coffee and mycardial infarction." New England J. of Medicine289: 63-67.
14.
Kempthorne, O. (1952) The Design and Analysis of Experiments. New York: John Wiley.
15.
Kempthorne, O. (1976) Discussion of "On rereading R. A. Fisher" by Leonard J. Savage. Annals of Statistics4: 495-497.
16.
Kruskal, W. (1980) "The significance of Fisher." J. of the Amer. Stat. Assn.75: 1019-1030.
17.
Miettinen, O.S. (1976) "Stratification by a multivariate confounder score ." Amer. J. of Epidemiology104: 609-620.
18.
Rosenbaum, P.R. (1984a) "From association to causation in observational studies: the role of tests of strongly ignorable treatment assignment." J. of the Amer. Stat. Assn.79: 41-48.
19.
Rosembaum, P.R. (1984b) "The consequences of adjustment for a concomitant variable that has been affected by the treatment. " J. of the Royal Stat. Society series A, 147: 656-666.
20.
Rosenbaum, P.R. (1984c) "Conditional permutation tests and the propensity score in observational studies." J. of the Amer. Stat. Assn.79: 565-574.
21.
Rosenbaum, P.R. and D.B. Rubin (1983a) "The central role of the propensity score in observational studies for causal effects." Biometrika70: 41-55.
22.
Rosembaum, P.R. and D.B. Rubin (1983b) "Assessing sensitivity to an unobserved binary covariate in an observational study with binary outcome." J. of the Royal Stat. Society series B, 45: 212-218.
23.
Rosenbaum, P.R. and D.B. Rubin (1984a) Discussion of Pratt and Schlaifer "On the nature and discovery of structure." J. of the Amer. Stat. Assn.79: 26-28.
24.
Rosenbaum, P.R. and D.B. Rubin (1984b) "Reducing bias in observational studies using subclassification on the propensity score." J. of the Amer. Stat. Assn.79: 516-524.
25.
Rosenbaum, P.R. and D.B. Rubin (1985a) "Constructing a control group using multivariate matched sampling methods that incorporate the propensity score." Amer. Statistician39: 33-38.
26.
Rosenbaum, P.R. and D.B. Rubin (1985b) "The bias due to incomplete matching." Biometrics41: 103-116.
27.
Rubin, D.B. (1974) "Estimating causal effects of treatments in randomized and nonrandomized studies." J. of Educ. Psychology66: 688-701.
28.
Rubin, D.B. (1977) "Assignment of treatment group on the basis of a covariate." J. of Educ. Statistics2: 1-26.
29.
Rubin, D.B. (1978) "Bayesian inference for causal effects: the role of randomization." Annals of Statistics6: 34-58.
30.
Rubin, D.B. (1980) Discussion of "Randomization analysis of experimental data: the Fisher Randomization Test," by D. Basu.J. of the Amer. Stat. Assn.75: 591-593.
31.
Rubin, D.B. (1986) "Which ifs have causal answers." J. of the Amer. Stat. Assn.81, 961-962.