**3. Results**

All genotype frequencies did not significantly different from the Hardy–Weinberg equilibrium expectations in the OVERBMI group (*p*-values range from 0.10 to 1.00), CONBMI group (*p*-values range from 0.50 to 1.00), OVERFMI (*p*-values range from 0.56 to 1.00), CONFMI (*p*-values range from 0.47 to 1.00), and the case–control group (*p*-values range from 0.33 to 1.00; Table 4).


**Table 4.** The probability that the genotype frequencies do not differ from Hardy–Weinberg expectations and minor allele frequencies (MAF).

No significant association was found between *FTO* (rs9939609), *FABP2* (rs1799883), *LEP* (rs2167270), *LEPR* (rs1137101), *MC4R* (rs17782313) and the BMI value exceeding 25. All divisions were checked under four genetic models: codominant, dominant, recessive, and overdominant, *p*-values were between 0.11 and 0.98. The influence of single alleles on BMI division was also checked and no significant association was found (Table 5).

**Table 5.** Association analysis of the *FTO* (rs9939609) polymorphism with BMI.


OR—odds ratio; 95% CI—confidence interval; AIC—Akaike information criterion; *p*-value \*—adjusted by age *p*-value; q-value—FDR adjusted *p*-values.

The *FTO* gene polymorphism (rs9939609) was significantly associated with FMI exceeding 6 (Table 6). An association was found for the codominant (AA vs. TT), dominant (AT-AA vs. TT), and for the recessive genetic models (AA vs. TT-AT). The chance of being OVERFMI for the combination AA was over 4.7 times greater than for the combination TT in the codominant model (Fisher's exact test *p* = 0.01). The chance of being OVERFMI for the combination AT-AA was >2.7 times higher than for the combination TT in the dominant model (Fisher's exact test *p* = 0.02). The chance of being OVERFMI for the combination AA was >2.8 times higher than for the combination TT-AT in the codominant model (Fisher's exact test *p* = 0.02). Moreover, the chance of being OVERFMI was >2.0-fold higher for A allele with Pearson's chi-squared test *p*-value < 0.01. The model was supplemented with age as a potential factor influencing the result, because of statistical differences shown between groups for this variable (Table 6).

**Table 6.** Association analysis of the *FTO* (rs9939609) polymorphism with FMI.


OR—odds ratio; 95% CI—confidence interval; AIC—Akaike information criterion; *p*-value \*—adjusted by age *p*-value; q-value—FDR adjusted *p*-values.

Gene–gene interactions' influence on BMI and FMI division was calculated with the MDR function. The best two-locus model in all divisions was that involving *FTO* (rs9939609) and *LEPR* (rs1137101), indicating a potential gene–gene interaction between these two genes. For BMI division, when genotypes AT × AA, TT × AA, TT × AG (*FTO* × *LEPR*, respectively) appear the model sorts the observations to join the CONBMI group with a higher probability than joining the OVERBMI group (*p* = 0.02). For FMI division when the genotypes AT × GG, TT × AA, and TT × AG (*FTO* × *LEPR*, respectively) appear, the model sorts the observations to join the CONFMI group with a higher probability than joining the OVERFMIgroup (*p* < 0.01; Table 7).

**Number of Loci Best Combination Division Cross-Validation Consistency Testing Balance Accuracy** *p***-Value** 2 *FTO* × *LEPR* BMI 4/10 0.59 0.02 *FTO* × *LEPR* FMI 6/10 0.63 <0.01 3 *LEP* × *LEPR* × *MC4R* BMI 5/10 0.64 <0.01 *FTO* × *LEP* × *LEPR* FMI 6/10 0.70 <0.01 4 *FABP2* × *LEP* × *LEPR* × *MC4R* BMI 10/10 0.72 <0.01 *FTO* × *FABP2* × *LEP* × *LEPR* FMI 5/10 0.75 <0.01 5 *FTO* × *FABP2* × *LEP* × *LEPR* × *MC4R* BMI 10/10 0.78 <0.01 *FTO* × *FABP2* × *LEP* × *LEPR* × *MC4R* FMI 10/10 0.81 <0.01

**Table 7.** Best gene–gene interaction models, as identified by MDR.

The best chosen three-locus model for BMI division involved the genes *LEP* (rs2167270), *LEPR* (rs1137101), and *MC4R* (rs17782313). The genotypes GG × AA × TT, GG × AG × TC, GG × AG × CC, GG × GG × TT, AA × AA × TT, AA × AA × TC, AA × AG × TT, AA × AG × CC, AG × AA × TT, AG × AG × TT, and AG × GG × CC (*LEP* × *LEPR* × *MC4R*, respectively) were selected by an algorithm to join the CONBMI group (*p* < 0.01). For FMI division, the best three-locus model included the genes *FTO* (rs9939609), *LEPR* (rs1137101), and *MC4R* (rs17782313). The genotypes AT × GG × AA, AT × AG × GG, TT × GG × AG, TT × AG × AA, TT × AG × AG, and TT × AA × AG (*FTO* × *LEPR* × *MC4R*, respectively) were selected by an algorithm to join the control group with a higher probability (*p* < 0.01). When the genotypes TT × GG × GG, and TT × AA × AA (*FTO* × *LEPR* × *MC4R*, respectively) appeared, the model sorted the observations to join the CONFMI group (*p* < 0.01). In all divisions in the four-locus and five-locus models when genotype was chosen to join the control group in *FTO* (rs9939609), only TT and AT genotypes appeared (Table 7).
