The author responds:
I thank Dr. Stang1 for commenting on several points. First, he is correct that the P value refers to the probability of having obtained results as or more extremely divergent from the null, assuming the null hypothesis is true. This makes the formal scenario even farther removed from the substantive questions we would like to answer than I had suggested when focusing only on the result obtained.
Second, in acknowledging the difficulty of grasping patterns of trend or interaction using point estimates and confidence intervals, I should have said “less easily integrated” rather than “less familiar.” The challenge is to summarize, in your mind, an array of results to evaluate how persuasively they support a particular pattern, with a P value constituting a single (admittedly imperfect) summary number. This is much like the balance between using an index versus examining the individual items that make up that index.
Third, I acknowledge that nonmonotonic associations can reflect causal associations. Still, with limited understanding of the underlying biological process (as is often the case in epidemiologic studies), a graded response to exposure has particular credibility, given how often causal relations seem to generate such a pattern.
Fourth, he raises an interesting question regarding whether data-driven, hypothesis-free studies such as genome-wide association studies should be held to the traditional standards of epidemiologic research to assess causality. There seems to be a continuum between hypothesis-driven and data-driven research, and as one moves across that spectrum, the conventional epidemiologic principles guiding interpretation of results erode and call for different conceptual and statistical tools to assess results.
David A. Savitz
Department of Epidemiology
1. Stang A. Reconciling theory and practice regarding P
values [letter]. Epidemiology. 2013;24:781