Using Mutual Information to Measure the Impact of Multiple Genetic Factors on AIDS

Summary: Since the discovery of the 32-base-pair deletion in the CCR5 chemokine receptor gene (CCR5-Δ32) and its effect on HIV-1 infection and AIDS progression, many genetic factors affecting AIDS have been identified. Here we quantify the impact of 13 of these factors on AIDS progression using a new statistic based on the mutual information between causal factors and disease, the explained fraction. The influence of causal factors on disease is commonly measured by the attributable fraction statistic, but the attributable fraction is a poor measure of the extent to which a factor explains disease because it considers only whether a factor is necessary, not whether it is sufficient. The definition of the explained fraction, which is analogous to R2 or the explained variation for regression models, extends naturally to multiple factor levels. Because the explained fraction is approximately additive, it can be used to estimate how much of epidemiological data is explained by known genetic or environmental factors, and conversely how much is yet to be explained by unknown factors. We show that 13 genetic factors can cumulatively explain 9% of slow progression to AIDS, an effect comparable to the effect of smoking on lung cancer