Nonassociative Group Decisions: Application to Bone Mineral Density

摘要

To find genes that cause diseases, geneticists test whether a change or variation in a gene is associated with a disease or an increased susceptibility. It was reported in 1994 that a slight variation in the vitamin D receptro gene (VDRGP) is associated with a significant change in our bone mineral density (BMD). By Jan. 1997, seventy-five independent investigations had been published, and no consensus had been reached as to whether BMD is really associated with VDRGP. In [3], we analyzed all 75 publications using a fuzzy mathematics approach to address thsi issue. We used two methods, one based on preference relations, and the other based on p-values. Fifty-five studies on spinal BMD and 73 on hip BMD were analyzed. Results from method I showed that VDRGP affect spinal BMD strongly among pre-menopausal populations, and moderately among post-menopausal populations, and popullations with pre-and post-menopausal women combined. No relations were found among populations with males and females combiend. VDRGP was associated with hip BMD among pre-menopausal, but not any other, populations. Using method two, we found that VDRGP was associated with spinal BMD only in pre-menopausal women, and VDRGP was somewhat associated with VDRGO in certain populations, but not in others. Heterogeneity of populations studied seems to be responsible for the discrepancies.