The correlation between major disease factors and sample size remains an important question in clinical investigations. A small sample size results in the selection of falsely significant risk factors that are not derived from population data. This problem is more serious in studies on multifactorial diseases based on polymorphisms and environmental factors because these studies require combination analysis. In the present study, we defined threshold lines to identify risk factors comprising complex interactions based on sample size. These threshold lines were constructed by a simulation study based on a resampling method that comprised a large data set (1441 case subjects with myocardial infarction and 979 control subjects). Finally, we demonstrated that these threshold lines could be used to identify risk factors for different data sets. In conclusion, these threshold lines enable us to design an association study of multifactorial diseases based on combination analysis.

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The blue moon ensemble method (Carter et al., 1989, Chem. Phys. Lett. 156, 472; Sprik & Ciccotti, 1998, J. Chem. Phys., 109, 7737) calculates the free energy profile of a chemical reaction along a specified reaction coordinate. The explicit algorithms for two simple reaction coordinates ("distance between two particles" and "difference between two distances") are derived. The derived algorithms are presented by Fortran-like codes to facilitate their implementation in arbitrary programs.

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