Introduction

Study on the effects of vitamin A vitamin supplementation on growth

• field studies conducted between September 1989 and December 1991
• cohort of 2258 rural Nepalese children 12-60 months of age were randomized to receive vitamin A supplements or a placebo-control, and were followed once every for 4 months for 16 months (11290 total observations)
• some visits contained missing data (9552 complete records on 2215 children)
• study objectives were to:
  • characterize growth patterns of Nepalease children
  • investigate dependence of growth on child age, gender, and maternal covariates
• authors found that while vitamin A supplementation had no effect on weight gain or growth, arm circumference and muscle area growth improved

West KP, Jr., LeClerq SC, Shrestha SR, Wu LS, Pradhan EK, Khatry SK, Katz J, Adhikari R, Sommer A. Effects of vitamin A on growth of vitamin A deficient children: field studies in Nepal.J Nutr 1997;10:1957-1965.

Methods

Data

• subset of the larger dataset representing the control arm of the trial (first 1000 records)
• some visits contained missing data
• 200 total children, 5 visits each (1000 visits)
  • 874 with complete visit information
  • 535 boys, 465 girls
• variables measured each visit:
  • weight in kilograms
  • current level of breastfeed (non, <10 times/day, 10 or more times/day)
  • age in months

Methods

Analyses

• Explored effect of breastfeeding across time on child weight
• Models used: GLS, LME, FEM
• Correlation structure
• Cross-sectional and longitudinal effects
• Model fit comparisons

Results

Cross-sectional effect of age and breastfeeding on childhood weight

Results

Results

Covariance structure: within-subject correlation

• all highly correlated, although measures taken closer together are (slightly) more correlated
• data may have autoregressive variance-covariance AR(1) structure

Model: GLS

\[ \begin{aligned} Y_{ij}\ &= \alpha_i + \beta_2 Age_{ij} + \end{aligned} \]

\[ \begin{aligned} \beta_3 Breast Feeding_{ij} \times \beta_2 Age_{ij} + \varepsilon_{ij} \end{aligned} \]

gls.ind <- gls (wt ~ age + bf*age, data = nepal, na.action = na.omit)

• Generalized least squares model

GLS Models

Model: LME with random intercepts

\[ \begin{aligned} Y_{ij}\ &= \beta_0 + b_i \beta_1 Age_{ij} + \end{aligned} \]

\[ \begin{aligned} \beta_2 Breast Feeding_{ij} \times \beta_1 Age_{ij} + \varepsilon_{ij} \end{aligned} \]

• Linear mixed effects model with randomly varying intercepts
• Accounts for individual effects through random effect (\(b_i\))

Model: LME with random intercepts and cross-sectional effect

\[ \begin{aligned} Y_{ij}\ &= \beta_0 + b_i + \beta_1 InitialAge_{ij} + \beta_2 (InitialAge-Age)_{ij} + \end{aligned} \]

\[ \begin{aligned} \beta_3 Breast Feeding_{ij} \times \beta_2 (InitialAge-Age)_{ij} + \varepsilon_{ij} \end{aligned} \]

• Accounts for cross-sectional effect of initial age

LME Models

Methods: FEM

\[ \begin{aligned} Y_{ij}\ &= \alpha_i + \beta_2 (InitialAge-Age)_{ij} + \end{aligned} \]

\[ \begin{aligned} \beta_3 Breast Feeding_{ij} \times \beta_2 (InitialAge-Age)_{ij} + \varepsilon_{ij} \end{aligned} \]

fem1 <- lm(wt ~ -1 + factor(id) + (age-iniAge) + bf*(age-iniAge) + bf*(age-iniAge), data=nepal)

• Fixed effects model
• Controls for all unmeasured confounders

FEM model results

Model diagnostics: comparing GLS and LME

Model diagnostics: comparing GLS and LME

Comparing GLS, LME and FEM

Discussion

Best fit: LME

• LME w/ AR(1) performed better than GLS and FEM

Interpretation:

• For every month increase after the baseline visit, there was about a 0.14 kg increase in weight (p < 0.001). Age and breastfeeding interaction was significant, indicating that breastfeeding status varied across time, and breastfeeding had a surprisingly negative effect on weight. It’s possible that more sickly and skinnier children were breastfed longer than healthier children.