The canonical correlation analysis between iron nutrition and thyroid hormone
We performed canonical correction analysis to explore the structure of correlation by using a method similar to multivariate analysis. The set of iron nutrition was assigned as X variables (X1 = SF and X2 = Hb). Meanwhile, the set of thyroid hormones was assigned as Y variables (Y1 = T3, Y2 = FT3, Y3 = T4, Y4 = FT4, and Y5 = TSH). There were two canonical functions. However, only the first canonical function was statistically significant (canonical coefficient = 0.431, P < 0.01). On the base of standardized canonical coefficients between the canonical function and all variables (U in iron status and V in thyroid hormones), the equations could be established as follows:
U1= -0.648X1 - 0.591X2
V1= 0.388Y1 - 0.970Y2 + 0.135Y3 - 0.308Y4 + 0.213Y5
The canonical correlation analysis showed that a significant positive correlation existed between iron nutrition and thyroid hormone. The proportion of explaining the variance attributed to a given canonical were 96.22% in the 1st canonical function (Table S2 ). U1 and V1 explained 35.6% and 65.1% of iron nutritional status and thyroid hormone variables, respectively. As shown in the illustration, the structure coefficients pointed that except the variable of TSH, other variables had positive correlations with iron nutrition variances (Fig. 2 andFig. S3). Moreover, the standardized coefficients of SF and FT3 were the highest in their respective subsets. The larger the standardized canonical coefficients are, the greater the weight in their respective typical variables is. Consistent with the former, the standardized canonical coefficients of SF and FT3 were the highest in their respective subsets as well. We next performed elastic network regression due to the fact that coefficient of SF was almost the same as the Hb in our results.