Simultaneously modelling clustered marginal counts and multinomial proportions with zero inflation with application to analysis of osteoporotic fractures data

Osteoporotic fractures are known to be highly recurring. We investigate bone‐dependent and bone‐independent risk factors of osteoporotic fracture frequency and relative proportions at various body locations by using the data from the osteoporotic fracture study that was conducted by the National Health and Nutrition Examination Survey, 2007–2008. We propose a new zero‐inflated baseline category multinomial mixed model to characterize the clustered count responses and multinomial proportions by subject simultaneously while taking account of zero inflation and randomness of cluster sizes. Our approach gives additional insights into the risk factors of osteoporotic fracture frequencies at various body locations. This joint modelling of fracture frequency also allows us to characterize relative proportion patterns at various body locations by subject between men and women across age. These findings have clear policy relevance to appropriate osteoporotic fracture prevention and resource allocation.