Different statistical methods to adjust the effect of macronutrient intake for total energy intake are currently being used to analyze epidemiologic studies of diet and disease. This research examines the statistical properties of these methods. Accepted for publication was a paper which interprets the regression coefficients of three alternative regression models; we show that four different effects of interest (related to either adding calories to the diet or substituting sources of calories in the diet) are estimable by each model and we derive the standard errors of these estimates. Our research also examines the behavior of these methods when the study subjects are categorized into a small number of groups according to their nutrient intake. When the true macronutrient intakes and their inter-relationships are known without error, one result of this investigation shows Willett's """"""""residual"""""""" method to be more powerful than the """"""""standard"""""""" method (both measuring the effect of calorie substitution) and very similar to the """"""""density"""""""" method. Many regression procedures involve multi-step model building based on the use of repeated tests of significance. Theory has been developed to address problems resulting from repeated testing for a forward selection procedure. After step 1, the commonly used F-ratio does not have a conventional F-distribution but an appropriate conditioning helps in developing the """"""""correct"""""""" testing procedure. Application of exploratory analyses for selecting the 'best' regression predictor model affects statistical properties of conventional Mean Square Error of Prediction estimators and, in particular, can lead to substantial bias. Different bootstrap-type estimators have been studied using theory and Monte-Carlo Simulations.
