Fig. 3

Identification of molecular signatures for early HT using gut microbiota and clinical indicators. RDA/CCA analysis was utilized to examine the impact of environmental factors on the composition of gut microbiota in early HT patients and healthy subjects, with Monte Carlo permutations (999 permutations) determining the significance of this influence. CCA (Canonical Correspondence Analysis) and RDA (Redundancy Analysis) were employed, where sample groups were represented by different colors, and environmental factors were indicated by arrows originating from the origin. The choice between RDA and CCA was determined by the size of the first axis of Axis-lengths (a intermediate value during calculation, not shown here); a value ≥ 3.5 indicated CCA, while < 3.5 indicated RDA. Based on the intermediate value, we chose CCA for this analysis. The length of the arrows indicated the degree of influence of the environmental factors on the gut microbiota composition. The angle between the arrows reflected positive (acute angle) or negative correlation (obtuse angle), while the vertical distance from the sample point to the arrows represented the intensity of the influence on the samples. A shorter distance indicated a stronger influence. The right bar charts showed the significance of the correlation between each environmental factor (TPO-Ab, TG-Ab, SWE, TSH, age, FT3, FT4, and thyroid volume) and gut microbiota composition (A). Spearman rank correlation analysis identified the top 10 genera with the strongest correlation to clinical indicators, ranked by number of significant environmental factors and p-value magnitude. Positive and negative correlations were depicted by red and blue modules, respectively. Significance levels: *p < 0.05, **p < 0.01, ***p < 0.001 (B). Random forest analysis ranked species based on their importance in characterizing early HT (C). The cross-validation curve showed the correlation between model error and number of species used, indicating that 2–5 significant species are adequate for optimal regression outcomes (D)