An outline of graphical Markov models in dentistry

In the usual multiple regression model there is one response variable and one block of several explanatory variables. In contrast, in reality there may be a block of several possibly interacting response variables one would like to explain. In addition, the explanatory variables may split into a sequence of several blocks, each block containing several interacting variables. The variables in the second block are explained by those in the first block; the variables in the third block by those in the first and the second block etc.

During recent years methods have been developed allowing analysis of problems where the data set has the above complex structure. The models involved are called graphical models or graphical Markov models. The main result of an analysis is a picture, a conditional independence graph with precise statistical meaning, consisting of circles representing variables and lines or arrows representing significant conditional associations. The absence of a line between two circles signifies that the corresponding two variables are independent conditional on the presence of other variables in the model.

An example from epidemiology is presented in order to demonstrate application and use of the models. The data set in the example has a complex structure consisting of successive blocks: the variable in the first block is year of investigation; the variables in the second block are age and gender; the variables in the third block are indices of calculus, gingivitis and mutans streptococci and the final response variables in the fourth block are different indices of caries. Since the statistical methods may not be easily accessible to dentists, this article presents them in an introductory form.

Graphical models may be of great value to dentists in allowing analysis and visualisation of complex structured multivariate data sets consisting of a sequence of blocks of interacting variables and, in particular, several possibly interacting responses in the final block.