Summarization,smoothing,and inference in epidemiologic analysis

Abstract

In a recent article (Epidemiology 1990; 1: 421–429) I resurrected some historical criticisms of conventional statistics in non-randomized, non-randomly sampled studies, and suggested some improvements to current practice in response to these criticisms. Here, I propose that some resolution can be achieved by separating data analysis into summarization, smoothing, and inferential phases. Methods of statistical inference are in fact smoothing methods, as are many methods of descriptive statistics, and as such can be viewed as pattern-recognition devices. Scientific inference is not a statistical process, but instead concerns derivation of explanations for patterns detected by statistical methods. Improvements could be made to all three phases simply by keeping the phases distinct.

Keywords

Statistics epidemiologic methods

Get full access to this article

View all access options for this article.

References

1. Greenland S Randomization, statistics, and causal inference. Epidemiology 1990; 1: 421–9.

2. Tukey JW Exploratory data analysis. Reading, MA: Addison-Wesley, 1977.

3. Freedman DA , Lane D Significance testing in a non-stochastic setting. In: Bickel P , Doksum K , Hodges JL , eds. Lehman Festschrift. Belmont, CA: Wadsworth, 1983.

4. Box GEP , Tiao GC Bayesian inference in statistical analysis. Reading, MA: Addison-Wesley, 1973.

5. McCullagh P , Nelder J Generalized linear models. 2nd ed. New York: Chapman and Hall, 1989.

6. Gelfand AF , Smith AFM Sampling-based approaches to calculating marginal densities. J Am Stat Assoc 1990; 85: 398–409.

7. Hastie T , Tibshirani R Generalized additive models. New York: Chapman and Hall, 1990.

8. Grobbee DE , Rimm EB , Giovannucci E , et al Coffee, caffeine, and cardiovascular disease in men. N Eng J Med 1990; 323: 1026–32.

9. Klatsky AL , Friedman GA , Armstrong MA Coffee use prior to myocardial infarction restudied: heavier intake may increase risk. Am J Epidemiol 1990; 32: 479–88.

10.

10. Maclure M Popperian refutation in epidemiology. Am J Epidemiol 1985; 121: 343–50.

11.

11. Eysenck HJ

Were we really wrong?

Am J Epidemiol 1991; 133: 429–33.

12.

12. Wald NA Smoking. In: Vessey MP , Gray M , eds. Cancer risks and preventions. New York: Oxford, 1985, Ch. 3.

13.

13. Neyman J Foundations of behavioristic statistics. In: Godambe VP , Sprott DA , eds. Foundations of statistical inference. Toronto: Holt, Rinehart, Winston, 1971.

14.

14. Miller MI , Roysan B Bayesian image reconstruction for emission tomography incorporating Good's roughness prior on massively parallel processors. Proc Natl Acad Sci 1991; 88: 3223–7.

15.

15. Banfield, JD , Raftery AE Ice floe identification in satellite images using mathematical morphology and clustering about principal curves. J Am Stat Assoc 1992; 87: 7–16.

16.

16. Leamer EE Specification searches. New York: Wiley, 1978.

17.

17. Gale WA , ed. Artificial intelligence and statistics. Reading, MA: Addison-Wesley, 1986.

18.

18. Penrose R The emperor's new mind. New York: Oxford, 1989.

19.

19. Freedman DA Statistics and the scientific method. In: Mason W , Feinberg SE , eds. Cohort analysis in social research: beyond the identification problem. New York: Springer, 1985: 345–90.