Analysis of compositional bone density data using log ratio transformations

In skeletal research, one of the techniques available to measure bone mineralization produces compositional data, which consist of vectors of ordered proportions of bone sample in prespecified density intervals. We investigated the value of two multivariate data transformations, the cumulative log ratio and the continuation log ratio, in the analysis of an experimental study of the dose-response effect of a drug treatment on bone mineralization. Based on a comparison of alternative approaches to the analysis of compositional bone mineralization data in the application and in a simulation study, we recommend the use of the average of the cumulative log ratios over all the density intervals to detect change in the density distribution. We also recommend the use of one of the continuation log ratios when a specific density interval of interest can be specified a priori.