Online supplement
Long-term course of ADHD symptoms from childhood to early adulthood in a community sample
This online supplement contains further details on the statistical analysis and results for:(1) growth curve and growth mixture modelling using the accelerated longitudinal design, (2) the overlap among severity subgroups for symptoms of inattention (FBB-ADHS-Inatt) and hyperactivity-impulsivity (FBB-ADHS-HypImp), and (3) the comparisonsbetween subgroupsfor all three outcome measures on child and family variables.
Growth curve modelling and growth mixture modelling
Our aim was to analyse ADHD symptom trajectories over the age range 7 to 19 years. However, because of the timing of the three measurement points in this study (baseline to 2-year follow-up), none of the eleven birth cohorts (7 to 17 years old at baseline) provided information across the whole age span and each age cohort could provide longitudinal data for no longer than two years. To achieve the objectives of the study, data was analysed using an accelerated longitudinal design [1,2]. In this design, data from all cohorts were used to estimate a trajectory for the entire age range covered by the study (7 to 19 years). That is, the 7-year-old cohort provided data for the age period from 7 to 9 years, the 8-year-old cohort for the age period from 8 to 10 years and so on. The assumption underlying this approach is that all age cohorts follow the same (subgroup) trajectory and that there are no significant differences among age cohorts in the change over time. For growth curve models, the validity of this assumption was tested using age cohort as a predictor for the growth parameters (i.e., intercept, slope).Likewise, in growth mixture modelling, age cohortwas used a predictor for subgroup membership. When there is a common (subgroup) trajectory,age cohort will not be a significant predictor of, for example, change over time in the growth curve models or of subgroup membership in the growth mixture models.
For growth curve modelling and growth mixture modelling a series of models with increasing complexity was computed: (1) a fixed linear model investigated linear change over time under the assumption that there was no variance in the linear slope; (2) a random linear model identical to the first model was applied except thatthe variance term of the linear slope was estimated; and (3) a fixed quadratic, random linear model was applied with an additional fixed quadratic term to investigate curvilinear change over time. For all models, intercepts were random. In this analysis, time was coded such that the intercept indicated symptom severity for children aged 7 years.
For growth curve modelling in the total group, the model selection process was based on multiple criteria. Besides parameter estimates, severalmodel fit indices were inspected to evaluate the general model fit (e.g., chi-square test). Because all three models(fixed linear model, random linear model and fixed quadratic, random linear model) werenested, they were compared using the chi-square difference test.
For subgroup analyses based on growth mixture modelling, the most appropriate model was selected using the following criteria. First, we used the Bayesian information criterion (BIC), which is a measure of relative fit and reflects the balance of model fit and parsimony when two or more models are compared. Models with lower BIC values are preferred. Second, when age cohort membership was used as an additional predictor for subgroup membership, only solutions with none or only minor cohort differences between subgroups were taken into consideration (for details see paragraph below). Third, subgroups had to be meaningful; i.e., they either had to be consistent with prior assumptions or, if not previously expected, their size and course had to be reasonable and clearly interpretable.
Results of growth curve modelling
For inattention (FBB-ADHS-Inatt) and total symptoms (FBB-ADHS-Tot), the average trajectory was best described by the fixed linear model (see Table S1). This model demonstrated good fit measures and all parameters were in the reasonable range compared to the other models. For both outcome measures, the slope became significant, indicating a symptom reduction over time.
The threegrowth curve models estimated for hyperactivity-impulsivity (FBB-ADHS-HypImp) demonstrated good fit indices (see Table S1). Although the chi-square difference tests showed an advantage of the random linear model (2(2) = 43.60, p < .01) and the quadratic fixed, random linear model (2(3) = 50.65, p < .01)over the fixed linear model, the latter was chosen because the variance term of the linear slope was not significantfor either the random linear model or the quadratic fixed, random linear model. Furthermore, with 0.001 (p < 0.1) the quadratic term of the quadratic model was very small. The model of choice (fixed linear) indicated linear decreasing scores for hyperactivity-impulsivity (FBB-ADHS-HypImp) over time.
In general, the good fit for the models of choice indicated that the assumption of a common developmental trajectory across age cohorts was reasonable. To further investigate the suitability of the accelerated longitudinal design, we used age cohort as a predictor for the intercept, which(in contrast to the linear slope) was not fixed and where significant inter-individual variability was observedfor both outcome measures. Although we detected some cohort differences, the proportion of variance explained was low: 0.8% for inattention (FBB-ADHS-Inatt),1.5% for hyperactivity-impulsivity (FBB-ADHS-HypImp) and 1.3% for total symptoms (FBB-ADHS-Tot).
Results of growth mixture modelling
Table S2 shows that a three-class solution of the fixed linear model was preferred for the data on inattention (FBB-ADHS-Inatt), hyperactivity-impulsivity (FBB-ADHS-HypImp), and total symptoms (FBB-ADHS-Tot).The subgroups were labelled as low, moderate and high based on their overall symptom levels over time.The subgroup trajectories had a clearly interpretable meaning and, when age cohort was used as a predictor of subgroup membership, neither of the regression coefficients became significantfor hyperactivity-impulsivity (FBB-ADHS-HypImp). For inattention (FBB-ADHS-Inatt) and total symptoms (FBB-ADHS-Tot), some cohort differences were observed that could be attributed to the 7-year-old cohort (FBB-ADHS-Inattand FBB-ADHS-Tot) and 17-year-old cohort (only for FBB-ADHS-Tot).In comparison to some other age cohorts, the 7-year-old cohort had a higher likelihood of being in the low group (when the moderate group was the reference group) and the 17-year-old cohort had a higher likelihood of being in the moderate group (when the high group was the reference group). Odds ratios (OR) were computed to further describe cohort differences in subgroup membership. The OR was up to 2.94 for hyperactivity-impulsivity (FBB-ADHS-Inatt) and up to 4.42 for total symptoms (FBB-ADHS-Tot).
For all outcome measures (FBB-ADHS-Inat, FBB-ADHS-HypImp, FBB-ADHS-Tot), the four-class solution of the fixed linear model was rejected primarily because of severe cohort differences among subgroups or a very small group that was additionally obtained for inattention (FBB-ADHS-Inatt; 0.2%) or hyperactivity-impulsivity (FBB-ADHS-HypImp; 0.7%). The random linear models with additional variance in the slope did not offer any reasonable advantage over the three-class solution of the fixed linear model, because the variance term of the linear slope did not became significant in either case and small, non-admissible values were obtainedseveral times.Startingfrom the three-class solution of the quadratic fixed, random linear model, subgroup trajectories for inattention (FBB-ADHS-Inatt), hyperactivity-impulsivity (FBB-ADHS-HypImp) and total symptoms (FBB-ADHS-Tot) were not in line with the expectations derived from previous research orclinical experience and, furthermore, several cohort differences were obtained, calling the validity of the solutions of the quadratic models into question.
Overlap among subgroups of inattention (FBB-ADHS-Inatt) and hyperactivity-impulsivity (FBB-ADHS-HypImp)
To investigate the overlap among the subgroups of inattention (FBB-ADHS-Inatt) and hyperactivity-impulsivity (FBB-ADHS-HypImp), we computed their joint frequencies (based on most likely class membership). Results are presented in Table S3. About three-quarters of all children and adolescents (75.1%) followed a low trajectory for both inattention (FBB-ADHS-Inatt) and hyperactivity-impulsivity (FBB-ADHS-HypImp). A low/high subgroup combination was the least common combination, occurring at a rate of 0.2% for inattention/hyperactivity-impulsivity or 0.5% for hyperactivity-impulsivity/inattention.
Conditional probabilities were computed to further investigate the coincidence of certain subgroups. As expected from the results of the joint frequencies (s. Table S3), children and adolescents from a low subgroup (either inattention or hyperactivity-impulsivity) had a very high probability of also being on a low trajectory for the second outcome domain (P(HypImplow|Inatt low) = .93; P(Inattlow|HypImp low) = .89). In contrast, children and adolescents following a high trajectory on either outcome domain were more likely to be members of a moderate subgroup (P(HypImpmoderate|Inatt high) = .36; P(Inattmoderate|HypImp high) = .47) or a high subgroup (P(HypImphigh|Inatt high) = .46; P(Inatthigh|HypImp high) = .44) on the second outcome measure. Children and adolescents of a moderate subgroup (either inattention or hyperactivity-impulsivity) had a high probability to follow either a low (P(HypImplow|Inatt moderate) = .56; P(Inattlow|HypImp moderate) = .45) or a moderate (P(HypImpmoderate|Inatt moderate) = .36; P(Inattlow|HypImp moderate) = .47) trajectory on the second outcome domain.
Description of subgroups
Subgroups for inattention(FBB-ADHS-Inatt), hyperactivity-impulsivity (FBB-ADHS-HypImp) and total symptoms (FBB-ADHS-Tot)were further compared by child variables of sex, externalizing behaviour, emotional symptoms, quality of life and by family SES, all assessed at the first measurement point (baseline).
For unordered categorical variables, subgroups were analysed using chi-square tests.For continuous variables, they were compared using analysis of covariance (ANCOVA). Where there was a significant main effect, pairwise comparisons between subgroups were performed using the least significance difference method (LSD).Assignment of children and adolescents to the low, moderate and high subgroups was based on their most likely class membership.
Measures used to describe subgroups
Child externalizing behaviour was assessed using the parent-rated externalizing problems scale of the German version of the Child Behavior Checklist for Ages 4-18 (CBCL/4-18) [3], which has been proven to have factorial validity and internal consistency (Cronbach’s = .87) [4,5]. Each of the 33 items are rated on a 3-point scale (0–2), with higher scores indicating more severe symptoms. The scale score (range 0–66) represents the sum of the individual item scores.
Informationon child internalizing symptoms was obtained through parent reports using the emotional symptoms scale of the Strengths and Difficulties Questionnaire (SDQ)[6,7]. Five items are each rated on a 3-point scale (0–2), with higher scores indicating more severe symptoms. The scale score (range 0–10) represents the sum of the individual item scores. The SDQ is a valid instrument [8,9] and, for the emotional symptom scale,the reported Cronbach’s is .72 in parent rating [8].
To quantify child quality of life, the total score of the Questionnaire for Measuring Health-Related Quality of Life in Children and Adolescents KINDL-R [10] in parent ratings was used. Each of the 24 items are rated on a 5-point scale (1–5), with higher scores indicating higher quality of life. The scale score (range 1–5) represents the sum of the individual item scores divided by the number of items. KINDL-R has been demonstrated to be a valid instrument [11,12]with good internal consistency for the total score (Cronbach’s = .90) [10].
Family SES reported by the parents was operationalized using the Winkler’s socioeconomic index [13], which considers the three dimensions of income, education and occupational status, each scored on a 7-point scale (1–7). The index is the sum of the three dimension scores (range 3–21).
Results of subgroup descriptions
On a descriptive level, boys were more likely to be members of subgroups with more severe symptoms. For inattention (FBB-ADHS-Inatt), the proportion of boys per subgroup was 47.3%for the low subgroup, 68.7% for the medium subgroup and 75.4% for the high subgroup. For hyperactivity-impulsivity (FBB-ADHS-HypImp), the corresponding proportions of boys were 48.6%, 66.8% and 70.8% in the low, medium and high subgroups, and for total symptoms (FBB-ADHS-Tot) were 48.1%, 69.6% and 74.7%, respectively. Chi-square tests further confirmed that sex was not equally distributed across the severity groups for inattention (2(2) = 80.87, p < .01), hyperactivity-impulsivity (2(2) = 48.29, p < .01) or total symptoms (2(2) = 68.78, p < .01).
Results of ANCOVA and the LSD tests are reported in Table S4. Covariates of ANCOVA were child’s sex, age, externalizing (CBCL/4-18) and emotional symptoms(SDQ), quality of life(KINDL-R) and family SES(Winkler’s socioeconomic index) unless they were the dependent variable.For all dependent variables, ANCOVA revealed significant main effects for the subgroups of inattention (FBB-ADHS-Inatt), hyperactivity-impulsivity (FBB-ADHS-HypImp) and total symptoms (FBB-ADHS-Tot). On average, children and adolescents in the low subgroups demonstrated the least externalizing (CBCL/4-18) and internalizing symptoms (SDQ), the highest quality of life (KINDL-R) and their family had the highest SES (Winkler’s socioeconomic index), compared with either or both of the other two subgroups (moderate, high). Furthermore, for all three outcome domains,the high subgroup demonstrated more severe externalizing (CBCL/4-18) and internalizing symptoms (SDQ) and had a lower quality of life (KINDL-R) (only true for inattention), compared with the corresponding moderate subgroup. Family SES (Winkler’s socioeconomic index) could not distinguish between the moderate and high subgroups for any symptom domain.
References
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Table S1. Fit indices for the growth curve models for inattention (n = 2,591), hyperactivity-impulsivity (n = 2,588) and total symptoms (n = 2,587) to describe the average trajectory in the total groupModel / 2 / df / p / CFI / RMSEA / BIC
Inattention
A1. Fixed linear / 101.92 / 33 / < .01 / .98 / .03 / 4985
A2. Random lineara,b / 95.22 / 31 / < .01 / .98 / .03 / 4994
A3. Fixed quadratic, random lineara,b,c / 93.75 / 30 / < .01 / .98 / .03 / 5000
Hyperactivity-impulsivity
B1. Fixed linear / 159.08 / 33 / < .01 / .96 / .04 / 2147
B2. Random linearb / 115.48 / 31 / < .01 / .97 / .03 / 2119
B3. Fixed quadratic, random linearb / 108.43 / 30 / < .01 / .97 / .03 / 2120
Total symptoms
C1. Fixed linear / 120.16 / 33 / < .01 / .98 / .03 / 1712
C2. Random lineara,b / 96.22 / 31 / < .01 / .98 / .03 / 1704
C3. Fixed quadratic, random lineara,b,c / 95.46 / 30 / < .01 / .98 / .03 / 1711
Note. For all models intercepts were random.
2 = Chi-square value; df = degrees of freedom; CFI = Comparative fit index; RMSEA = Root mean square error of approximation; BIC = Bayesian information criterion; Inattention = Subscale of the ADHD Symptom Checklist (FBB-ADHS-Inatt); Hyperactivity-impulsivity = Subscale of the ADHD Symptom Checklist (FBB-ADHS-HypImp); Total symptoms = Total symptom score ADHD Symptom Checklist (FBB-ADHS-Tot).
a Variance of the linear slope is negative (Heywood case).
b Variance of the linear slope is non-significant.
c Quadratic term is non-significant.
Table S2. BIC values for growth mixture models with 1, 2, 3 or 4 classes for the detection of subgroups in inattention (n = 2,591), hyperactivity-impulsivity (n = 2,588) and total symptoms (n = 2,587)
Number of classes
Model / 1 / 2 / 3 / 4
Inattention
D1. Fixed linear / 4985 / 4618 / 4538 / 4509
D2. Random linear / 4994a / 4631a / 4552 / 4514b
D3. Fixed quadratic, random linear / 5000a / 4642 / 4515 / 4462
Hyperactivity-impulsivity
E1. Fixed linear / 2147 / 1329 / 1056 / 949
E2. Random linear / 2119 / 1318 / 1044a / 930a
E3. Fixed quadratic, random linear / 2120 / 1319 / 1031 / 898b
Total symptoms
F1. Fixed linear / 1712 / 1093 / 953 / 901
F2. Random linear / 1704a / 1098 / 959 / 913
F3. Fixed quadratic, random linear / 1711 / 1106 / 896 / 838
Note. For all models intercepts were random. Bold numbers indicate the model of choice.
Inattention = Subscale of the ADHD Symptom Checklist (FBB-ADHS-Inatt); Hyperactivity-impulsivity = Subscale of the ADHD Symptom Checklist (FBB-ADHS-HypImp); Total symptoms = Total symptom score ADHD Symptom Checklist (FBB-ADHS-Tot).
a Heywood case – non-admissible parameter values obtained (e.g., negative variance slope).
b Best log-likelihood value was not replicated.
Table S3. Joint frequencies (percentages reported in parentheses) among subgroups of inattention and hyperactivity-impulsivity
Hyperactivity-Impulsivity
low / moderate / high
Inattention / n / (%) / n / (%) / n / (%)
low / 1942 / (75.1) / 145 / (5.6) / 6 / (0.2)
moderate / 239 / (9.2) / 151 / (5.8) / 34 / (1.3)
high / 12 / (0.5) / 25 / (1.0) / 32 / (1.2)
Notes. The analysis was based on 2,586 families with available data for inattention as well as hyperactivity-impulsivity.
Inattention = Subscale of the ADHD Symptom Checklist (FBB-ADHS-Inatt); Hyperactivity-impulsivity = Subscale of the ADHD Symptom Checklist (FBB-ADHS-HypImp).
Table S4. Analysis of covariance (ANCOVA) and least significance difference method (LSD) results testing for mean differences between subgroups of inattention (n = 2,591) hyperactivity-impulsivity (n = 2,588) and total symptoms (n = 2,587)
Subgroup
low / moderate / high / ANCOVA
Dependent variable / Mean / (SD) / Mean / (SD) / Mean / (SD) / F
Inattention
Child
Externalizing / 6.79a / (5.50) / 13.97a / (8.44) / 21.08a / (10.06) / 178.23*
Emotional / 1.51a / (1.60) / 2.67a / (2.20) / 4.07a / (2.28) / 11.50*
Quality of life / 4.13a / (0.35) / 3.83a / (0.41) / 3.51a / (0.45) / 33.27*
Family SES / 12.15a,b / (4.20) / 10.98a / (4.00) / 9.75b / (3.57) / 5.61*
Hyperactivity-impulsivity
Child
Externalizing / 6.79a / (5.46) / 15.53a / (7.99) / 23.42a / (8.69) / 359.99*
Emotional / 1.61a / (1.71) / 2.40b / (2.07) / 3.72a,b / (2.49) / 3.79*
Quality of life / 4.11a / (0.37) / 3.87a / (0.40) / 3.63 / (0.52) / 5.03*
Family SES / 12.13a,b / (4.19) / 10.77a / (3.89) / 9.78b / (4.15) / 6.29*
Total symptoms
Child
Externalizing / 6.74a / (5.30) / 15.81a / (8.27) / 23.03a / (9.14) / 344.64*
Emotional / 1.56a / (1.65) / 2.73b / (2.16) / 3.73a,b / (2.50) / 5.95*
Quality of life / 4.12a,b / (0.36) / 3.80a / (0.41) / 3.62b / (0.52) / 17.57*
Family SES / 12.13a,b / (4.20) / 10.86a / (3.82) / 9.55b / (3.81) / 5.73*
Notes. Degrees of freedom for F values are 2, 2583 for all analyses of inattention subgroups, 2, 2580 for all analyses of hyperactivity-impulsivity subgroups and 2, 2579 for all analyses of total symptoms subgroups. The covariates for ANCOVA were child’s sex, age, externalizing behaviour, emotional symptoms, quality of life and family socioeconomic status (SES) unless being used as the dependent variable. All variables were assessed at first measurement point (baseline).
SD = Standard deviation; Inattention = Subscale of the ADHD Symptom Checklist (FBB-ADHS-Inatt); Hyperactivity-impulsivity = Subscale of the ADHD Symptom Checklist (FBB-ADHS-HypImp); Total symptoms = Total symptom score ADHD Symptom Checklist (FBB-ADHS-Tot); Externalizing = Externalizing scale Child Behavior Checklist for Ages 4-18 (CBCL/4-18); Emotional = Emotional symptoms scale Strengths and Difficulties Questionnaire (SDQ); Quality of life = Total score Questionnaire for Measuring Health-Related Quality of Life in Children and Adolescents (KINDL-R); Family SES = Assessed by the Winkler’s socioeconomic index.
a,b For each dependent variable, subgroup means with the same superscript differ significantly according to the least significance difference method (LSD) (p < .05).
*p < .05
1