Distribution of in vivo insulin action in Pima Indians as mixture of three normal distributions

Abstract

If a single gene produced insulin resistance, with environmental effects creating some additional variance, insulin action might be distributed as a mixture of two normal distributions if the gene is dominant or recessive or as a mixture of three normal distributions if the gene is codominant. To estimate maximal insulin-stimulated glucose uptake rates (MaxMs), hyperinsulinemic-euglycemic clamps were performed on 245 nondiabetic Pima Indians (126 men, 119 women). Five models (for 1, 2, 3, 4, or 5 components each, normally distributed with a common variance) were fitted to the frequency distribution of MaxM by iterative maximum-likelihood estimation. The three-component model fit the data significantly better than a single normal distribution (chi 2 = 14.3 with 4 df P less than .01) or a mixture of two normal distributions (chi 2 = 9.9 with 2 df, P less than .01). Mixtures of four or five normal distributions did not fit the data significantly better than a mixture of three normal distributions. The first component of the distribution comprised 23%, the second 48%, and the third 29% of the total distribution. Similarly, the frequency distributions of fasting plasma insulin concentrations and a principal component score derived from MaxM and fasting insulin were best fitted by a mixture of three normal distributions. These results are consistent with the hypothesis that among Pimas, insulin resistance is determined by a single gene with a codominant mode of inheritance. Segregation analyses of studies performed in pedigrees are indicated to prove or disprove this genetic hypothesis.