Discussion

Discussion

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1. ABO blood-type genes

Page 83, bottom:
The text suggest that brothers of female breast cancer cases could provide information on the ABO blood-type distribution in the source population. Brothers of females in the source population might provide this information, but not the brothers of cases, since siblings tend to share genes. If brothers of cases were selected as controls, they would represent a matched control group, with matching on sibship. A valid result could still be obtained, by taking the matching into account in the analysis, but matching was not the topic of the example.

Svend Juul, Department of Epidemiology and Social Medicine University of Aarhus, Denmark.

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2. Rate of change of random error with study size

Page 95, figure 5-1:
Wouldn't the figure be more instructive if the random error curve were drawn to be upward concave? It would then illustrate more reasonably the relation between study size and random error and would make it clearer that the random error of an estimate approaches zero when the study size increases.

Svend Juul, Department of Epidemiology and Social Medicine University of Aarhus, Denmark.

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3. Plane through three-dimensional space

Page 183, equation 10-1:
The text states that equation 10-1 can be depicted as a straight line in a three dimensional space. It is actually a plane. It might be instructive to include a graphical example, and maybe to comment that with more dimensions a graphical display becomes either impossible or incomprehensible. Figure 5-4 is a related example, although the age-risk association in figure 5-4 is non-linear.

Svend Juul, Department of Epidemiology and Social Medicine University of Aarhus, Denmark.

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4. Stepwise models in epidemiologic analysis

(box, page 194)

While Epidemiology: An Introduction1 inspires an epidemiologic mindset, unsophisticated readers might use it to justify indiscriminant stepwise regression, because it mentions that stepwise regression is more appropriate for prediction models than for causal models.1, p. 194 This could encourage mindlessness in epidemiologic data analysis.2 I believe that stepwise regression methods are rarely indicated, even for prediction models.

Reason 13-5: a) different subsets can be identified, dependent on the method (forward or backward); b) best subset searches are more efficient (Mallow's Cp etc.); c) stepwise methods underestimate variance.

Reason 2: The text implies that stepwise regression could be useful to predict individual risks, like the previous example.1, pp. 192-193 Here, an individual risk point estimate is computed rather than the prediction interval, which seems inconsistent with promotion of effect interval estimation over p-value statistical significance, because effect intervals convey both strength and precision. Variable selection methods would influence prediction interval estimation.

Reason 3: Use of automatic stepwise regression methods implies that the nature of confounding is completely unknown and therefore, for the superset of subsets of causal models, each causal model is probabilistically equivalent. In most epidemiologic models, however, this is not the case.

One justification for use of stepwise models: Stepwise polynomial models in epidemiology. In most cases, fractional polynomial selection, an alternative to categorical analysis to examine dose-response6, is not known a priori. In this case, stepwise methods could be useful.

References:

1. Rothman KJ. Epidemiology: An Introduction. New York: Oxford University Press, 2002.
2. Hertz-Picciotto I. What you should have learned about epidemiologic data analysis. Epidemiology 1999; 10(6):778-83.
3. Goldberger AS, Jochems DB. Note on stepwise least squares. JASA 1961; 56(293)105-110.
4. Goldberger AS. Stepwise least squares: residual analysis and specification error. JASA 1961; 56(296)998-1000.
5. http://www.pitt.edu/~wpilib/statfaq/regrfaq.html
6. Greenland S. Dose-response and trend analysis in epidemiology: alternatives to categorical analysis. Epidemiology. 1995; 6(4):356-65.
7. Corinne C. Aragaki, Ph.D., University of Texas School of Public Health, Houston