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Supplementary Information
Supplemental Information on Participants and Procedures
Families were recruited through local media outlets, community organizations, and pediatric clinics in and around San Diego, California. Child and parent exclusion criteria included medical or psychiatric disturbances that would preclude treatment participation; use of appetite- and/or weight-affecting medications; and concurrent involvement in weight loss or psychological treatment. A total of 204 families entered family-based treatment (FBT), and 150 were randomized to the maintenance treatments (MTs). Two statistical outliers were identified, who showed extreme child z-BMI values at 2-year follow-up. Both cases were highly influential on the primary outcome analysis, and therefore, were excluded from the present study. Thus, the present study utilized the remaining sample of 148 parent-child dyads randomized to a maintenance condition. As noted in the primary report from this trial (reference removed for blind review), the study sample closely matched the racial and ethnic makeup of San Diego County at the time of recruitment.
FBT and both active MT conditions consisted of 20-minute individual family (parent-child dyad) sessions, and 40-minute concurrent child and parent group sessions. Group session content was similar for parents and children, except that parents were provided with additional information on effective parenting skills related to the content. Family sessions reinforced group session content and provided more individualized treatment (e.g., addressing barriers to compliance). Behavioral change strategies included self-monitoring of food intake, physical activity, and weight; parental modeling of healthy weight-related behaviors; positive reinforcement; and environmental control (e.g., changing the home environment). The dietary component of treatment utilized the Traffic Light Diet approach (Epstein, 2003) to reduce caloric intake to approximately 1200 to 1500 calories per day, change taste preferences, and improve nutrient quality. The Traffic Light Diet divides foods into the colors of the traffic light, representing stop and think (RED foods), approach with caution (YELLOW foods), and go (GREEN foods). Physical activity was mastery-based with an ultimate goal of 90 minutes of moderate to intense activity at least 5 days/week. Children and parents chose activities from a list to meet calorie expenditure goals. Self-monitoring of dietary intake was introduced during week 1 of FBT, and PA self-monitoring was introduced during week 4.
Although both MTs focused on achieving energy balance for weight maintenance, they were theoretically and procedurally distinct: BSM focused on helping families develop behavioral weight maintenance skills, and SFM focused on helping families change their social environment and body image to support weight maintenance. The control group received no further treatment contact after FBT. The two active maintenance conditions did not differ in their specific dietary aims. Across BSM and SFM, parents and children were encouraged to increase caloric intake to a level to promote weight maintenance, rather than weight loss; to increase the frequency, duration, and intensity of physical activity to yield energy balance; and to maintain a 3-lb (1.35-kg) weight range around their weight at the outset of the weight maintenance phase.
Supplemental Measures
Demographics. Parents completed a brief demographics questionnaire to report on their child’s and their own race/ethnicity, age, and sex.
Dietary Intake. Children’s and parents’ dietary intake was measured via self-report in the form of four-day food diaries (including at least one weekend day). Prior to each assessment time point, participants were provided with paper-based diary entries (one for each day), which allowed them to provide the date, time of day, and description for all food items consumed over the course of the day. To enhance accuracy, participants were given self-monitoring training to carefully record intake. At baseline, children completed 53% of their own food records (with parents completing the remainder) but completed a larger percentage of their own food records at later assessments (63% at month 29), which makes sense because they had aged two years and had experience (from treatment) self-monitoring their food intake. Diaries were reviewed for completeness in person at each assessment time point by a trained researcher. Depending on the time point, 93% - 96% of child records and 98% - 99% of parent records listed at least five foods or beverages per day. All coders of the dietary records were trained together so that it was ensured that all coders received identical content. Coders practiced coding diaries, responses were reviewed and compared, and coders received feedback together.
Supplementary Statistical Analyses
Descriptive statistics and regression analyses were computed using SPSS 22 (IBM Corporation, 2013). Examination of long-term changes in diet and weight during the maintenance phase of treatment was estimated using latent growth curve modeling (LGCM) in Mplus 7 (Múthen & Múthen, 2012). The advantage of this approach over the computation of change scores (e.g., final score minus baseline) is that it uses data from all four maintenance time points (i.e., months 5, 9, 17, and 29) to estimate a trajectory of change for each participant. Moreover, it uses maximum likelihood estimation to include data from all randomized dyads, which produces less biased estimates under the assumption that data are missing at random and retains statistical power by using the entire randomized sample compared to deletion of cases with missing data (Enders, 2013). Little’s MCAR test was not significant, χ2 (1304) = 1384.03, p > .05, which indicates that data were missing completely at random (Little, 1988). Thus, the missing data assumption associated with maximum likelihood estimation was met. Repeated assessments of a variable are used to determine a latent intercept (the initial status on the variable) and a latent slope (the amount of change in the variable over time). Across variables, the slope factor loading at randomization was fixed at 0 and the slope factor loading at 2-year follow-up was fixed at 1. This ensured that the resulting latent slope beta coefficient represented the overall change in the variable from randomization to the 2-year follow-up. Slope factors for the intermediate time points (i.e., post weight maintenance and 1-year follow-up) were fixed in a non-linear fashion based on the mean of the sample or were allowed to be freely estimated, depending upon which provided the better model fit (see Table S1). Acceptable model fit was obtained as indicated by root mean square error of approximation ≤.08 and comparative fit index ≥.95 (Hu & Bentler, 1999). The long-term maintenance slopes derived from the LGCMs were saved in order to create the regression models described in the main text and to compute similarity scores. Similarity scores were computed by standardizing each variable against the sample mean and standard deviation, and then the parent-standardized score was subtracted from the child-standardized score. Scores close to zero indicate high similarity in change (whether weight or diet). The sample size of 148 provided >80% power to detect a change in explained variance of at least 5% in a regression model with a total explained variance of 15% (Faul, Erdfelder, Buchner, & Lang, 2009).
Supplemental Results
Table S2 provides the means, standard deviations, and number of observations available at each time point for each of the observed study variables. Forty-five children (30% of randomized sample) provided complete data across all time points, whereas 75 children (51%) provided complete data at randomization and 2-year follow-up. Thirty-eight parents (26% of randomized sample) provided complete data across all time points, whereas 71 parents (48% of randomized sample) provided complete data at randomization and 2-year follow-up. Results of t-tests revealed significant average change in many of the study variables during the 2-year maintenance phase (see Table S1 under “Slope value” column). Both child BMI z-score and parent BMI increased significantly during the maintenance phase. Similarly, child and parent RED food intake increased during the maintenance phase. The proportion of the diet consisting of fruits and vegetables but did not change during the maintenance period. There was significant inter-individual variation in all variables (see Table S1 under “Slope variance” column), which demonstrates that, as would be expected, there was between-subject heterogeneity in the amount of change that occurred in these variables.
Given that parents completed a proportion of their children’s food records, sensitivity analyses were run to determine whether the primary findings (see Tables 1 and 2 in the main text document) held when only including those dyads in which children completed at least 50% of their own food records at randomization and 2-year follow-up (n = 50). The motivation for these analyses was to diminish the possibility that the correlation between parent and child changes was driven by shared method variance (i.e., that parents completed their own food records and their children’s food records). These analyses largely confirmed the primary findings. In this subset, children’s long-term weight maintenance was predicted by their long-term changes in RED food intake (β = .32, p < .05) but not by their long-term changes in fruits and vegetables (β = .22, p = .16). Children’s long-term RED food changes were predicted by parents’ long-term RED food changes (β = .33, p = .04). Moreover, the similarity in weight maintenance between parent and child could be accounted for by the similarity in changes in RED food intake (β = .30, p = .04) but not by the similarity in changes to fruit and vegetable intake (β = -.14, p = .32). The one effect that did not replicate was that parents’ changes in fruit and vegetable intake did not predict their children’s changes in fruit and vegetable intake (β = .10, p = .56).
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Table S1. Summary of results from latent growth curve models.
Assessment Month / Model Fit / Slope value / Slope variance5 / 9 / 17 / 29 / CFI / RMSEA
Child variables
BMI z-score / 0 / .4 / 1.1 / 1 / .99 / .06 / 0.05** / 0.04***
RED food intake (proportion) / 0 / .7 / .9 / 1 / 1.00 / .00 / 0.13*** / 0.03***
Fruit & vegetable intake (proportion) / 0 / #0 / 1 / 1 / 1.00 / .00 / -0.02 / 0.01***
Parent Variables
BMI / 0 / .2 / 1.1 / 1 / .98 / .08 / 1.20*** / 4.83***
RED food intake (proportion) / 0 / .5 / .9 / 1 / .99 / .01 / 0.12*** / 0.02***
Fruit & vegetable intake (proportion) / 0 / 1.4 / 1.9 / 1 / .99 / .04 / -0.01 / 0.003***
Notes. # = slope parameter was allowed to be freely estimated using the number following the asterisk as the starting value. BMI = body mass index (kg/m2). CFI = comparative fit index. RMSEA = root mean square error of approximation.
** p < .01. *** p < .001.
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Table S2. Means (standard deviations) and numbers of observations at each assessment point for variables of interest.
Baseline(month 0) / Randomization
(month 5) / Post-MT
(month 9) / 1-year
Follow-up
(month 17) / 2-year
Follow-up
(month 29)
Child variables
BMI z-score / 2.20 (0.30)
N = 148 / 1.99 (0.38)
N = 148 / 1.98 (0.41)
N = 143 / 2.03 (0.43)
N = 135 / 2.03 (0.46)
N = 122
RED food intake
(proportion of diet) / 0.50 (0.13)
N = 148 / 0.30 (0.15)
N = 137 / 0.38 (0.15)
N = 95 / 0.42 (0.16)
N = 93 / 0.43 (0.17)
N = 96
Fruit & vegetable intake
(proportion of diet) / 0.15 (0.07)
N = 148 / 0.18 (0.09)
N = 137 / 0.17 (0.10)
N = 95 / 0.17 (0.09)
N = 93 / 0.17 (0.10)
N = 96
Parent Variables
BMI / 34.8 (6.2)
N = 148 / 32.8 (5.9)
N = 148 / 32.9 (6.2)
N = 135 / 34.0 (6.5)
N = 126 / 33.8 (6.1)
N = 119
RED food intake
(proportion of diet) / 0.40 (0.13)
N = 146 / 0.23 (0.13)
N = 133 / 0.30 (0.15)
N = 88 / 0.33 (0.15)
N = 90 / 0.35 (0.15)
N = 90
Fruit & vegetable intake
(proportion of diet) / 0.20 (0.09)
N = 146 / 0.23 (0.09)
N = 133 / 0.22 (0.10)
N = 88 / 0.22 (0.10)
N = 90 / 0.22 (0.10)
N = 90
Notes. BMI = body mass index (kg/m2). MT = maintenance treatment.
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Supplemental References
Enders, Craig K. (2013). Dealing With Missing Data in Developmental Research. Child Development Perspectives, 7(1), 27-31. doi: 10.1111/cdep.12008
Epstein, L. H. (2003). Development of evidence-based treatments for pediatric obesity. In A. E. Kazdin & J. R. Weisz (Eds.), Evidence-Based Psychotherapies for Children and Adolescents (pp. 374-388). New York: Guilford Publications, Inc.
Faul, F., Erdfelder, E., Buchner, A., & Lang, A. G. (2009). Statistical power analyses using G*Power 3.1: tests for correlation and regression analyses. Behav Res Methods, 41(4), 1149-1160. doi: 10.3758/BRM.41.4.1149
Hu, Li-tze, & Bentler, Peter M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6(1), 1-55.
Little, R. J. A. (1988). A test of missing completely at random for multivariate daata with missing values. Journal of the American Statistical Association, 83, 1198-1202.