[Regression methods and causal inference: structural equations models]

The estimate of correlations among observed outcomes is crucial in biomedical research, especially when the aim of the study is to infer, from the magnitude of these correlations, the causal influence of certain, sometimes latent, factors. In such situations, a typical regression approach, known as "structural equation models" (SEM), which was introduced in the 1970s, becomes significant. These models allow hypotheses to be formulated quite clearly, thanks to some explicit and rigorous graphical representations, on which the "path analysis" is based. SEM, which were initially used in economics, have in the past decade been applied in a wide variety of fields, especially in genetic epidemiology. It's in this field that SEM are extraordinarily effective, representing a simple yet powerful means of estimating the contribution of genes and the environment to the phenotypic expression of a given disease. To this end, data on twins are particularly useful, and in this case the correlation between the outcomes describes the extent of similarity of the twin phenotypes. From this standpoint, SEM undoubtedly constitute one of the most promising statistical tools for family studies and quantitative genetic research. The method can be easily extended to traditional epidemiology, and some interesting applications have already been developed in occupational and social epidemiology. In this paper, we describe in detail the SEM approach and discuss the use of these models in genetic epidemiology, using twin studies as an example. We also discuss the application of SEM in fields other than genetic research.