Compositional data analysis and diversity indicies: different approaches to define the role of nutrients in the study of diet-cancer relationship

In epidemiological studies the relationship between diet and risk of disease is usually investigated considering the absolute intake of nutrients/foods (often opportunely coded in categories of increasing consumption). The total intake of a nutrient is usually scattered among different food items and the modalities of intake could influence the impact on the risk. In order to evaluate the impact of nutrient dispersion on risk we suggest two different approaches: a) in the first each nutrient is described with a couple of variables rapresenting the estimated absolute intake (Z) and a diversity index (d) measuring the dispersion intake on different dietary sources; b) the second approach is based on standard techniques used in analysis of compositional data