A Mixture‐of‐Genotypes Model for the Distribution of Thermostable Phenol Sulfotransferase Activity

A statistical method for parametric density estimation based upon a mixture‐of‐genotypes model is developed for the thermostable phenol sulfotransferase (SULT1A1) activity which has a putative role in modifying risk for colon and prostate cancer/polyps. The EM algorithm for the general mixture model is modified to accommodate the genetic constraints and is used to estimate genotype frequencies from the distribution of the SULT1A1 phenotype. A parametric bootstrap likelihood ratio test is considered as a testing method for the number of mixing components. The size and power of the test is then investigated and compared with the conventional chi‐squared test. The relative risk associated with genotypes defined by this model is also investigated through the generalized linear model. This analysis revealed that a genotype with the highest mean value of SULT1A1 activity has greater impact on cancer risk than others. This result suggests that the phenotype with a higher SULT1A1 activity might be important in studying the association between the cancer risk and SULT1A1 activity. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)