One hundred and twenty-four parent–child pairs were identified and invited to participate. Of these couples, 101 responded. The response rate was 81.5%, as indicated in a previous report with study flowchart [34]. All 101 participants remained during the 4-year follow-up period. Data on child attachment, average HbA1c, and HbA1c variability were collected for all patients (Table 1). Eight questionnaires assessing parental attachment were missing (ECR-RS, 7.8% of missing data), and we could calculate TIR for only 74 patients (26.7% of missing data), which affected further analyses. Baseline characteristics are shown in Table 1. Among the children, 50 (49.5%) were girls. Questionnaires were completed by mothers in 79.3%, fathers in 19.8%, and another caregiver (grandmother) in one case.

Differences were found between girls and boys in attachment to the mother. A higher percentage of secure attachment was found in girls compared to boys (Pearson Chi-Square (1) = 4.014, p = 0.045, Table 1). Otherwise, there were no differences between the two groups.

The majority of children (83, 82.2%) used an insulin pump. There were no differences between users of different glucose monitoring modalities (NCGM = 22, NBGM = 52) in average Hb1Ac (Mann–Whitney U = 287, p = 0.61) or HbA1c variability (Mann–Whitney U = 212, p = 0.36). There were significant differences in TIR (MCGM = 55.72, MBGM = 45.84, t (38) = -2.90, p = 0.006), so glucose monitoring modality was included in further analyses. There were no differences in average Hb1Ac (M-W U = 810, p = 0.58), HbA1c variability (M-W U = 612, p = 0.23), or TIR (t (16) = -0.92, p = 0.37) between those using insulin pumps or mechanical injectors.

Average HbA1c was significantly related to HbA1c variability (r (99) = 0.59, p < 0.001) and TIR (r (72) = -0.41, p < 0.001), but there was no relationship between HbA1c variability and TIR (r (72) = −0.09, p = 0.43). Finally, diabetes duration was not statistically significantly related to average HbA1c (r (99) = 0.04, p = 0.71), HbA1c variability (r (99) = −0.09, p = 0.36), and TIR (r (72) = 0.02, p = 0.85) and was not included in further analyses.

Because concordance between children's attachment to mother and attachment to father was high (95% of children had the same two-way classification for both parents), we used only attachment to mother in further analyses to avoid multicollinearity between the independent variables. There was also a moderate correlation between parent attachment anxiety and parent attachment avoidance (r (91) = 0.43, p < 0.001), so two regression models (a and b) were created for each dependent variable.

When multivariable linear regression models were built to identify independent predictors of average Hb1Ac, HbA1c variability, and TIR, parental attachment anxiety (a) and attachment avoidance (b) were included alternately to avoid multicollinearity in the models. All final models achieved adequate fit. Statistical data for the models is presented in the Additional file 1: Table S2, Additional file 2: Table S3, and Additional file 3: Table S4, and statistically significant results are summarized in the Additional file 4: Table S5.

In predicting the average HbA1c in the 4 years after inclusion Model 1a including ECR-RS anxiety achieved a global predictive power of R2 = 0.27, adjusted R2 = 0.18 (F(10, 78) = 2.981, p = 0.004) and Model 1b including ECR-RS avoidance had a global predictive power of R2 = 0.32, adjusted R2 = 0.24, F(10, 78) = 3.729, p < 0.001 (whole models are presented in Additional file 1: Table S2). Both models showed that a significant predictor of a higher average HbA1c was the older age of the child. The interaction between the child's attachment to the mother and the child's sex was statistically significant in both models. Simple slope analyses revealed that girls who were securely attached at baseline (CAI) had higher average HbA1c than girls who were insecurely attached (Model 1a: B = −0.61, t = −2.07, p = 0.04; Model 1b: B = −0.64, t = -2.25, p = 0.03, shown in Fig. 1). In boys, the opposite but statistically non-significant relationship was observed (Model 1a: B = 8.38, t = 1.39, p = 0.17).

Simple slope analysis for the interaction between child sex and attachment from multivariable regression Models 1a and 1b. Statistically significant results appear in bold

In Model 1b, higher parental attachment avoidance was associated with higher average HbA1c in boys (B = 0.51, t = 2.90, p = 0.005, shown in Fig. 2). For parents with high attachment avoidance (+ 1 SD), boys had higher average HbA1c than girls (B = 0.68, t = 2.34, p = 0.022), whereas for parents with low attachment avoidance (-1 SD), girls had higher average HbA1c than boys (B = −0.52, t = −2.02, p = 0.047).

Simple slope analysis for statistically significant interaction between child sex and parent attachment style (ECR-RS anxiety or ECR-RS avoidance) from multivariable regression Models 1b, 2b, 3a and 3b. Statistically significant results appear in bold. Graphical results for Models 1a and 2a were not calculated because the interactions were not statistically significant

The final models for predicting HbA1c Variability achieved adequate fit, Model 2a including ECR-RS anxiety with a global predictive power of R2 = 0.23, adjusted R2 = 0.16, F(8, 78) = 2.978 p = 0.006, and Model 2b including ECR-RS avoidance with a global predictive power of R2 = 0.28, adjusted R2 = 0.19, F(9, 77) = 3.299, p = 0.002 (whole models are presented in Additional file 2: Table S3). Both models showed that a significant predictor of higher HbA1c variability was older age of the child. In Model 2a, an independent predictor of higher HbA1c variability was also female sex.

Interactions in Model 2a showed higher HbA1c variability in children with the lowest morning serum cortisol levels (−1 SD) when their parents reported higher attachment anxiety (B = 0.013, t = 2.167, p = 0.033).

The following interactions statistically significantly predicted higher HbA1c variability in Model 2b: male sex in parents with higher attachment avoidance (B = 0.017, t = 2.595, p = 0.011, shown in Fig. 2), higher parental attachment avoidance in children with lowest cortisol levels (−1 SD) (B = 0.015, t = 2.750, p = 0.007) similar to Model 2a. In addition, in those whose parents reported low attachment avoidance (−1 SD) girls had higher HbA1c variability than boys (B = −0.031, t = −3.153, p = 0.002), and higher morning cortisol levels were associated with higher HbA1c variability (B = 7e-5, t = 2.144, p = 0.035).

Participants differed in TIR according to glucose monitoring modality, so CGM/BGM was included as an independent variable in the prediction of TIR. Both models achieved adequate fit, Model 3a including ECR-RS anxiety with a global predictive power of R2 = 0.41, adjusted R2 = 0.26, F(12, 50) = 2.846, p = 0.005, and Model 3b including ECR-RS avoidance with a global predictive power of R2 = 0.37, adjusted R2 = 0.22, F(12, 50) = 2.475 p = 0.013 (whole models are presented in Additional file 3: Table S4). In Model 3a, those who used BGM had a lower TIR than those who used CGM. Higher parental attachment anxiety predicted lower TIR in boys (B = −8.543, t = −3.231, p = 0.002; shown in Fig. 2) and in children with secure attachment to the mother (CAI) (B = −6.254, t = −2.094, p = 0.041). In children who have insecure attachment to their mothers (CAI), TIR decreased with increasing morning cortisol levels (B = −0.041, t = -2.193, p = 0.033). For children whose parents reported high attachment anxiety (+ 1 SD), girls had higher TIR than boys (B = −13.251, t = -2.451, p = 0.018).

Model 3b showed that higher child age significantly predicted lower TIR. Among participants with intermediate or higher (+ 1 SD) morning cortisol levels, use of CGM predicted higher TIR than use of BGM (intermediate cortisol: B = -9.895, t = −2.702, p = 0.009; + 1SD cortisol: B = −20.036, t = −3.336, p = 0.002). Among those whose parents reported high attachment avoidance (+ 1 SD), girls had higher TIR than boys (B = −11.350, t = −2.281, p = 0.027).