Binary regression in truncated samples, with application to comparing dietary instruments in a large prospective study

We examine two issues of importance in nutritional epidemiology: the relationship between dietary fat intake and breast cancer, and the comparison of different dietary assessment instruments, in our case the food frequency questionnaire (FFQ) and the multiple-day food record (FR). The data we use come from women participants in the control group of the Dietary Modification component of the Women's Health Initiative (WHI) Clinical Trial. The difficulty with the analysis of this important data set is that it comes from a truncated sample, namely those women for whom fat intake as measured by the FFQ amounted to 32% or more of total calories. We describe methods that allow estimation of logistic regression parameters in such samples, and also allow comparison of different dietary instruments. Because likelihood approaches that specify the full multivariate distribution can be difficult to implement, we develop approximate methods for both our main problems that are simple to compute and have high efficiency. Application of these approximate methods to the WHI study reveals statistically significant fat and breast cancer relationships when a FR is the instrument used, and demonstrate a marginally significant advantage of the FR over the FFQ in the local power to detect such relationships.