Change in diet includes temporality, i.e. a particular individual had some diet pattern at a specific point of time, but after some period the time, his/her diet pattern changed. To examine the effect of this change on 'disease control', you need data for both two points of time, which is not possible with cross-sectional data. Hence causality cannot be established using the cross-sectional data.
However, you can use some sophisticated statistical methods that will help you, like "Propensity Score Matching (PSM)", which will give you the average treatment effect of diet pattern change using a counterfactual model.