Weighted three-way log-ratio analysis: analysing gender differences in patients with type 1 diabetes and cardiovascular disease

High rates of cardiovascular disease are prevalent among individuals with diabetes. Weight variability has been identified as a distinct risk factor for cardiovascular disease (CVD) in the general population, and there is preliminary evidence suggesting its significance extends to those with type 1 diabetes as well, regardless of gender. Utilising data from the Swedish National Diabetes Register, we investigate the association between visit-to-visit body weight fluctuations and the risk of cardiovascular diseases in males and females with type 1 diabetes who had no pre-existing cardiovascular conditions at the start of the study. To assess the relationship between cardiovascular risk, weight variability, and gender, we propose a generalisation of weighted log-ratio analysis for a three-way contingency table. Weighted log-ratio analysis offers several advantages over other categorical data analysis techniques. These include the computation and visual representation of the odds ratios (ORs) upon which the analysis relies. Interestingly, the association between CVD and weight variability differs between males and females. The three-way log-ratio analysis method presented in this paper gives a visual description of these conditional ORs in terms of point distances on a biplot, illustrating the association between types of CVD, weight variability and gender.