Separating effects of foods and of food components in nutritional epidemiology I have data on average long-term intake of common foods of a medium/large cohort (n=500+). It was assessed semi-quantitatively (that is, interval-censored). From these about 100 food items and their rough intake frequency I have, using a food database, calculated each cohort member's average intake of about 150 food components as weighted sums of the food intakes.
Now I'd like to relate time-to-event data on my disease of interest in this cohort to dietary behaviour. The problem is that since the components are weighted sums of the foods, some foods and some components are highly correlated. Often, the components are more significantly associated with my outcome, but I'm uncertain whether this really reflects their health impact. The foods can be expected to have been assessed with quite some error, probably inducing some regression dilution bias, which should be alleviated in the components as they are kind of an average.
Is there something that can be done about this from a statistical point of view?
 A: See the food composition matrix approach in
@Article{gre00whe,
  author =       {Greenland, Sander},
  title =        {When should epidemiologic regressions use random coefficients?},
  journal =      Biometrics,
  year =         2000,
  volume =       56,
  pages =        {915-921},
  doi = {10.1111/j.0006-341X.2000.00915.x},
  annote =       {Bayesian methods;causal inference;empirical Bayes estimators;epidemiologic method;hierarchical regression;mixed models;multilevel modeling;random-coefficient regression;shrinkage;variance components;use of statistics in epidemiology is largely primitive;stepwise variable selection on confounders leaves important confounders uncontrolled;composition matrix;example with far too many significant predictors with many regression coefficients absurdly inflated when overfit;lack of evidence for dietary effects mediated through constituents;shrinkage instead of variable selection;larger effect on confidence interval width than on point estimates with variable selection;uncertainty about variance of random effects is just uncertainty about prior opinion;estimation of variance is pointless;instead the analysis should be repeated using different values;``if one feels compelled to estimate $\tau^2$, I would recommend giving it a proper prior concentrated amount contextually reasonable values'';claim about ordinary MLE being unbiased is misleading because it assumes the model is correct and is the only model entertained;shrinkage towards compositional model;``models need to be complex to capture uncertainty about the relations...an honest uncertainty assessment requires parameters for all effects that we know may be present.  This advice is implicit in an antiparsimony principle often attributed to L. J. Savage 'All models should be as big as an elephant (see Draper, 1995)'''.  See also gus06per.}

}
