Table 1

Akaike Information Criterion (AIC), Shapiro–Wilk test (SW) for the residuals (e) and random-effects (RE) for Betti-0 (B0) and Betti-1 (B1) areas under the curve (AUC) at every developmental model

LME-Age8630.993 (0.71)0.984 (0.36)627.60.98 (0.04)0.974 (0.07)
LME-Age.Sex864.90.994 (0.82)0.984 (0.35)631.30.98 (0.04)0.974 (0.07)
GAMM-Age861.40.994 (0.79)0.987 (0.53)627.70.986 (0.18)0.981 (0.22)
GAMM-Age.Sex862.90.994 (0.82)0.986 (0.49)630.90.987 (0.21)0.981 (0.22)
GAMM-PDS858.30.992 (0.65)0.983 (0.31)625.60.989 (0.36)0.988 (0.63)
GAMM-PDS.Sex859.50.991 (0.57)0.979 (0.15)633.10.985 (0.14)0.984 (0.37)
GAMM-AgePDS859.40.994 (0.82)0.983 (0.3)625.90.991 (0.54)0.987 (0.53)
GAMM-AgePDS.Sex862.50.993 (0.74)0.983 (0.3)631.70.991 (0.57)0.979 (0.17)
  • Developmental models: linear mixed-effects models for age (LME-Age) and age-sex interaction (LME-Age.Sex), generalized additive mixed models with smooth splines for age (GAMM-Age) and age-by-sex (GAMM-Age.Sex), PDS (GAMM-PDS) and PDS-by-sex (GAMM-PDS.Sex), and age-PDS interaction (GAMM-AgePDS) and age-PDS interaction-by-sex (GAMM-AgePDS.Sex). Akaike Information Criterion (AIC) and Shapiro–Wilk tests (SW) for the residuals (e) and random-effects (RE) of the Betti-0 (B0) and Betti-1 (B1) areas under the curve (AUC) for every developmental model.

  • Concerning the developmental effects at the functional network level, the PDS term showed strong effects in the fronto-parietal (FPN) and moderate effects in the auditory (AUD), sensorimotor-hand (SMH), and subcortical (SUB) networks for the B0-AUC (Fig. 5). Only the FPN had a significant effect after FDR correction (F = 6.84; EDF = 2.09; p = 0.001), which shows a nonlinear trend similar to the whole brain network (Fig. 6). No effects (even uncorrected) were found for the B1-AUC.