Describing a craniofacial anomaly: finite elements and the biometrics of landmark locations.

An intergroup comparison of cephalometric landmark configurations by the finite-element method elegantly depicts the algebra of some of the size and shape change measures that one may define by reference to those landmarks. In studies of mean differences between groups, the statistical analysis of these finite elements is equivalent to competent statistical analysis of the same data using any other geometric metaphor, such as properly standardized vector descriptions of landmark "movement" or scalar measures, size and shape variables, taken in sufficient variety. In applications to landmark data, the reality of finite-element depictions is purely statistical rather than phenomenological. In the absence of additional evidence, they should not be held either more or less biologically meaningful than other descriptions of the same landmark changes to which they lead. These propositions are exemplified using landmark data from 13 cases of Apert syndrome.