In many nutritional studies the probability of obtaining a certain disease is believed to be related to a certain predictor variable. In order to test for the relationship between the predictor variable and the disease it is important to obtain accurate measurements on the predictor variable. In measuring food intake, three common methods are used: 24-hour recalls, food frequency questionnaires and food records. Food records are often thought to be the most reliable, but they are difficult and expensive to obtain. The question of interest to us is to use the food records to examine possible systematic biases in questionnaires as a measure of usual food intake. Such an examination allows us to validate the use of the less expensive questionnaires as measures of dietary intake. Many problems can arise in a validation study we will address a few of these. First, we investigate the possibility of time dependent data. In Freedman, et al. (1991), the authors assume that all measurements on a given individual have the same mean and variance. However, such assumptions may be violated in at least two circumstances. First, some studies occur over a period of years, and diets may change over the course of the study. Second, measurements might be taken at different times of the year, and it is known that diets differ on the basis of seasonal factors. We suggest new models incorporating mean and variance offsets, i.e., changes in the population mean and variance for observations taken at different time points. The parameters in the model are estimated by simple methods, and the theory of unbiased estimating equations (M -estimates) is used to derive asymptotic covariance matrix estimates. A second problem is that of obtaining precise estimates of correlation between true intake and a surrogate for true intake and intraindividual correlation between two surrogates for true intake measured close together in time...
