Characteristics of studied population

The clinical features of infertile women undergoing IVF/ICSI procedure are summarized in Table 1. By conducting Shapiro–Wilk normality test, we determined all data as nonparametric, except age and FSH level which were considered as parametric. Levene’s test demonstrated no variance difference in parametric data. We compared the clinical data among women with different ovarian response using ANOVA for parametric data (age and FSH level), and using Mann–Whitney U test for nonparametric data (other parameters). The median age was 32 years for women with normal ovarian response (n = 46), 33 years for women with low ovarian response (n = 72), and 31 years for women with high ovarian response (n = 26), and there was no statistically significant difference. Results showed that women with high ovarian response had significantly lower FSH level (p = 0.006), and significantly higher AMH level (p < 0.001), and also significantly higher LH/FSH ratio (p < 0.001) in comparison with other two studied groups (Table 1).

Table 1 Clinical characteristics of the studied groupsFSHB rs10835638 and FSHR rs6166 variants are not associated with ovarian response

In this study, we analyzed genotypes distribution of FSHB rs10835638 and FSHR rs6166 variants in 144 infertile women undergoing IVF/ICSI procedure aged from 24 to 42 years. Genotype frequency distribution for rs10835638 was as follows: GG—73% (n = 105), GT—24% (n = 35), and TT—3% (n = 4). This was determined to be consistent with HWE (p = 0.604). Genotypes frequency distribution for rs6166 was as follows: AA—42% (n = 60), AG—39% (n = 56), GG—19% (n = 28), and did not correspond to HWE (p = 0.029). Table 2 shows genotypes and alleles distribution of FSHB rs10835638 and FSHR rs6166 variants among women with normal (n = 46), low (n = 72), and high (n = 26) ovarian response. Chi-square test demonstrated no statistically significant differences in the genotype’s distribution between groups when genes variants investigated independently.

Table 2 Genotypes and alleles frequency of FSHB rs10835638 and FSHR rs6166 variants among women with different ovarian response

The combined assessment of the FSHB rs10835638 and FSHR rs6166 intergenic interactions was carried out using MDR analysis. Thus, optimal models of gene–gene interactions were selected to estimate the co-effect of studied variants in increasing risk of low and high ovarian response (Table 3). A two-factor combination of FSHB rs10835638 / FSHR rs6166, carried out for low ovarian response risk estimation, characterized by 100% reproducibility and prediction accuracy of 59.21% (p = 0.002). A two-factor combination of FSHB rs10835638 / FSHR rs6166, carried out for high ovarian response risk estimation, characterized by 100% reproducibility and prediction accuracy of 58.19% (p = 0.006). Results showed a synergetic interaction between the two studied genetic variants (red color) (Fig. 1). FSHB rs10835638 variant played a greater role (0.62%) in increasing susceptibility of low ovarian response (Fig. 2a), and FSHR rs6166 variant played a greater role (2.91%) in increasing susceptibility of high ovarian response (Fig. 2b).

Table 3 Results of MDR analysis for FSHB rs10835638 / FSHR rs6166 interactions in the development of increasing risk of low and high ovarian responseFig. 1

A dendrogram graph of intergenic interactions between FSHB rs10835638 and FSHR rs6166 variants in studied groups; red color stands for synergism

Fig. 2

A Fruchterman-Reingold graph of intergenic interactions between FSHB rs10835638 and FSHR rs6166 variants in women with normal and low ovarian response (2a), or in women with normal and high ovarian response (2b). Red color stands for synergism

To minimize the type 1 statistical error in the analysis of intergenic interactions, a Bonferroni correction was introduced. Bonferroni significance level was calculated by dividing the initial significance level (α = 0.05) by the number of studied combinations of genotypes of the two loci which is equal to 8 (due to the lack of FSHB/FSHR TT/AA combined genotype). Differences were considered significant if the corresponding p-value was less than pbonf = 0.006. The genotype of the highest risk to develop low ovarian response was determined; however, there was no statistical significance. It was a two-locus of heterozygous GT/AG genotype of the FSHB rs10835638 / FSHR rs6166 variants (OR (95% CI) = 6.43 (0.79 − 52.56); p = 0.086, pbonf = 0.006) (Fig. 3a). The protective genotype against risk of high response was also determined; however, there was also no statistical significance. It was a two-locus of GG/AG genotype of FSHB rs10835638 / FSHR rs6166 variants (OR (95% CI) = 0.34 (0.11 − 1.06); p = 0.071, pbonf = 0.006) (Fig. 3b). Further studies with larger sample size are required to confirm the results.

Fig. 3

Genotypes distribution of two-locus FSHB rs10835638 and FSHR rs6166 between women with normal and low ovarian response (3a), or women with normal and high ovarian response (3b). The light column in each cell represents women with normal ovarian response. GG, AA—homozygotes for the major allele; GT, AG—heterozygotes; TT, GG—homozygotes for the minor allele

FSHR rs6166 variant, but not FSHB rs10835638, is associated with gonadotropin levels

The clinical parameters of patients were analyzed based on FSHB rs10835638 and FSHR rs6166 genotypes. Due to low number of FSHB rs10835638 TT carriers (n = 4), patients with TT and GT genotypes were unified into one group for further analysis. The clinical parameters did not differ among women with different FSHB rs10835638 genotypes (Table 4). However, FSHR rs6166 genotypes were associated with significant differences in the clinical parameters (Table 5). FSH, LH and progesterone levels were significantly higher in FSHR rs6166 GG genotype carriers, compared to allele A carriers (p = 0.039, p = 0.029 and p = 0.058, respectively) (Fig. 4).

Table 4 Clinical parameters of the infertile women according to the FSHB rs10835638 genotypesTable 5 Clinical parameters of the infertile women according to the FSHR rs6166 genotypesFig. 4

Hormone levels of the infertile women according to the FSHR rs6166 genotypes. FSH, LH and progesterone levels significantly differed between FSHR rs6166 AA + AG and GG genotypes carriers (p = 0.039, p = 0.029 and p = 0.058, respectively)

A highly specific logistic regression models for predicting both low and high ovarian response

A multiple linear regression model was used to evaluate relationships between the dependent variable and predictor variables. The general multiple linear regression model looks as follows:

$$y \, = \, b_ + \, b_ * \, x_ + \, b_ * \, x_ + \, \ldots \, + \, b_ * \, x_ ,$$

where bn is the regression coefficient of the corresponding predictor, and xn is the value of the corresponding predictor.

The disadvantage of the multiple regression model is that its function returns a continuous value (y), and not a categorical variable indicating the object’s belonging to a certain class (in this case—low or normal ovarian response group; high or normal ovarian response group). To calculate the chances of the object to belong to a certain class, a logistic transformation of the multiple regression model was carried out:

where e is the base of natural logarithm, and y is the value of multiple linear regression function.

Two models containing regression coefficients and clinical parameter values were calculated for predicting the chances of both low and high ovarian response outcomes. A low response was considered to be less than 10 follicles. A high response was considered to be more than 16 follicles. FSH, LH, AMH, progesterone, free testosterone levels, as much as age, AFC and BMI values, and FSHB rs10835638 and FSHR rs6166 alleles were used as independent predictor variables to calculate models. All predictors used were checked for the presence of correlation interactions between themselves, which should be excluded when building a logistic regression model. The correlation coefficient between AMH and AFC was very high, thus only one of these predictors could be used in the model. According to logistic regressive analysis, both AMH and AFC are highly sensitive as predictors, but AFC is much more specific, therefore AFC was included in the model, while AMH was not.

A highly specific logistic regression model containing age, AFC, free testosterone level and FSHR rs6166 minor alleles number as predictors was calculated for predicting low ovarian response. The model is as follows:

$$}_}}}=1/(1+e^}+0.2688243*}+0.03912184*}-0.347912*})}).$$

The plow value obtained under 0.5 stands for the higher probability of a low ovarian response (less than 10 follicles). According to logistic regression analysis, the sensitivity of this model is 81.7%, and the specificity is 71.4%.

A highly specific logistic regression model containing AFC and LH/FSH ratio as predictors was also calculated for predicting high ovarian response. The model is as follows:

$$}_}}} = 1/(1 + e^} + 1.656675*}/})}).$$

The phigh value obtained over 0.5 stands for the higher probability of a high ovarian response (more than 16 follicles). According to logistic regression analysis, the sensitivity of this model is 95.8%, and the specificity is 76.9%.

Logistic regression models have been validated with the sample from the present study: low ovarian response group (n = 72) and high ovarian response group (n = 26) (Table 6).

Table 6 Results of developed logistic regressive models validation

To assess the sensitivity and specificity of the developed models on sample from this study, the following formulas were used:

Thus, the assessment based on sample from this study showed that the sensitivity of the developed low ovarian response model is 81.9%, and the specificity is 69.4%. Regarding the high ovarian response model, the assessment showed that the sensitivity is 76.9%, and the specificity is 90.9%.