The Geometry of Statistical Models for Two-Way Contingency Tables with   Fixed Odds Ratios
  We study the geometric structure of the statistical models for two-by-two contingency tables. One or two odds ratios are fixed and the corresponding models are shown to be a portion of a ruled quadratic surface or a segment. Some pointers to the general case of two-way contingency tables are also given and an application to case-control studies is presented. 
Enrico Carlini and Fabio Rapallo