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Background  Multifactor dimensionality reduction (MDR) is a powerful method for analysis of gene-gene interactions and has been successfully applied to many genetic studies of complex diseases. However, the main application of MDR has been limited to binary traits, while traits having ordinal features are commonly observed in many genetic studies (e.g., obesity classification - normal, pre-obese, mild obese and severe obese).    Methods  We propose ordinal MDR (OMDR) to facilitate gene-gene interaction analysis for ordinal traits. As an alternative to balanced accuracy, the use of tau-b, a common ordinal association measure, was suggested to evaluate interactions. Also, we generalized cross-validation consistency (GCVC) to identify multiple best interactions. GCVC can be practically useful for analyzing complex traits, especially in large-scale genetic studies.    Results and conclusions  In simulations, OMDR showed fairly good performance in terms of power, predictability and selection stability and outperformed MDR. For demonstration, we used a real data of body mass index (BMI) and scanned 1~4-way interactions of obesity ordinal and binary traits of BMI via OMDR and MDR, respectively. In real data analysis, more interactions were identified for ordinal trait than binary traits. On average, the commonly identified interactions showed higher predictability for ordinal trait than binary traits. The proposed OMDR and GCVC were implemented in a C/C++ program, executables of which are freely available for Linux, Windows and MacOS upon request for non-commercial research institutions.

Identification of multiple gene-gene interactions for ordinal phenotypes