This thesis is concerned with the identification of vertebral fractures from measurements made of the anterior, mid and posterior heights of individual vertebrae. Two distinct problems are addressed: identifying deformities that exist at a particular moment in time from a single radiograph (prevalent deformities); and identifying deformities that have occurred between two consecutive radiographs (incident deformities). A number of different statistical models for the vertebral heights are proposed, and compared to two existing methods in common use. The new models proposed are: 1. A number of polynomial models. 2. A factor analysis model. 3. An imputation based regression model. The polynomial models were fitted using both least squares and a robust method. In the simplest polynomial model, a single magnification factor was fitted for each subject, allowing for variation in size of the spine, but not variation in shape. More complex models in which the magnification factor was allowed to vary within an individual were also used. In addition, an outlier detection method is also applied to the data to detect subjects with fractures, and this method is also compared to the existing methods. Models were compared not only on how well they predicted vertebral heights. but also on how well they can identify fractured vertebrae and identify individuals with fractures. Two approaches to identifying incident fractures are presented: • Identify vertebrae that are classed as prevalent fractures on the second radiograph but not on the first radiograph; • Identify vertebrae in which at least one height has shown a substantial reduction in height between the two radiographs. It is shown that combining these two approaches has advantages over using either approach individually.