Detecting causal nonlinear exposure-response relations in epidemiological data.
The possibility of hormesis in individual dose-response relations undermines traditional epidemiological criteria and tests for causal relations between exposure and response variables. Non-monotonic exposure-response relations in a large population may lack aggregate consistency, strength, biological gradient, and other hallmarks of traditional causal relations. For example, a u-shaped or n-shaped curve may exhibit zero correlation between dose and response. Thus, possible hormesis requires new ways to detect potentially causal exposure-response relations. This paper introduces information-theoretic criteria for identifying potential causality in epidemiological data that may contain nonmonotonic or threshold dose-response nonlinearities. Roughly, exposure variable X is a potential cause of response variable Y if and only if: (a) X is INFORMATIVE about Y (i.e., the mutual information between X and Y, I(X; Y), measured in bits, is positive. This provides the required generalization of statistical association measures for monotonic relations); (b) UNCONFOUNDED: X provides information about Y that cannot be removed by conditioning on other variables. (c) PREDICTIVE: Past values of X are informative about future values of Y, even after conditioning on past values of Y; (d) CAUSAL ORDERING: Y is conditionally independent of the parents of X, given X. These criteria yield practical algorithms for detecting potential causation in cohort, case-control, and time series data sets. We illustrate them by identifying potential causes of campylobacteriosis, a foodborne bacterial infectious diarrheal illness, in a recent case-control data set. In contrast to previous analyses, our information-theoretic approach identifies a hitherto unnoticed, highly statistically significant, hormetic (U-shaped) relation between recent fast food consumption and women's risk of campylobacteriosis. We also discuss the application of the new information-theoretic criteria in resolving ambiguities and apparent contradictions due to confounding and information redundancy or overlap among variables in epidemiological data sets.
Cox
Louis Anthony
LA
Cox Associates and University of Colorado, 503 Franklin Street, Denver, CO, 80218, USA. tony@cox-associates.com