The estimated spline functions (and 95% confidence intervals) for boys from the GAM.

<p>The seasonal functions (<b>a</b>) , (<b>b</b>) and (<b>c</b>) for WAZ and HAZ increments and diarrhea. The age functions in the absence of supplementary food (<b>d</b>) , (<b>e</b>) and (<b>f</b>) for WAZ and HAZ increments and diarrhea. The age functions due to ITT (<b>g</b>) , (<b>h</b>) and (<b>i</b>) for WAZ and HAZ increments and diarrhea.</p

Quantifying and Exploiting the Age Dependence in the Effect of Supplementary Food for Child Undernutrition

<div><p>Motivated by the lack of randomized controlled trials with an intervention-free control arm in the area of child undernutrition, we fit a trivariate model of weight-for-age z score (WAZ), height-for-age z score (HAZ) and diarrhea status to data from an observational study of supplementary feeding (100 kCal/day for children with WAZ ) in 17 Guatemalan communities. Incorporating time lags, intention to treat (i.e., to give supplementary food), seasonality and age interactions, we estimate how the effect of supplementary food on WAZ, HAZ and diarrhea status varies with a child’s age. We find that the effect of supplementary food on all 3 metrics decreases linearly with age from 6 to 20 mo and has little effect after 20 mo. We derive 2 food allocation policies that myopically (i.e., looking ahead 2 mo) minimize either the underweight or stunting severity – i.e., the sum of squared WAZ or HAZ scores for all children with WAZ or HAZ . A simulation study based on the statistical model predicts that the 2 derived policies reduce the underweight severity (averaged over all ages) by 13.6–14.1% and reduce the stunting severity at age 60 mo by 7.1–8.0% relative to the policy currently in use, where all policies have a budget that feeds % of children. While these findings need to be confirmed on additional data sets, it appears that in a low-dose (100 kCal/day) supplementary feeding setting in Guatemala, allocating food primarily to 6–12 mo infants can reduce the severity of underweight and stunting.</p></div

For boys, the left tails, <i>P</i>(WAZ <<i>θ</i>) for <i>θ</i> equals (a) −2, (b) −2.5, (c) −3 vs. age under the various policies.

<p>For boys, the left tails, <i>P</i>(WAZ <<i>θ</i>) for <i>θ</i> equals (a) −2, (b) −2.5, (c) −3 vs. age under the various policies.</p

For boys, the PDFs of the percent reduction of the severity indices of (a)-(b) the derived WAZ policy relative to the current policy, and (c)-(d) the current policy relative to the no food policy.

<p>For boys, the PDFs of the percent reduction of the severity indices of (a)-(b) the derived WAZ policy relative to the current policy, and (c)-(d) the current policy relative to the no food policy.</p

The estimated parameters for boys from the GAM.

<p>For each variable, we give the estimated coefficient (Est.), the standard error (S.E.) and the p-value.</p

Food allocation policies.

<p>A description of the food allocation policies and their severity indices for boys, which measure the average of squared shortfalls below the reference median (i.e., zero) for WAZ averaged over all 28 measured ages (underweight) and for HAZ at age 60 mo (stunting).</p

For boys, the left tails, <i>P</i>(HAZ <<i>θ</i>) for <i>θ</i> equals (a) −2, (b) −2.5, (c) −3, (d) −3.5, (e) −4, (f) −4.5 vs. age under the various policies.

<p>For boys, the left tails, <i>P</i>(HAZ <<i>θ</i>) for <i>θ</i> equals (a) −2, (b) −2.5, (c) −3, (d) −3.5, (e) −4, (f) −4.5 vs. age under the various policies.</p

The proportion of boys by age who receive food under the various allocation policies.

<p>The proportion of boys by age who receive food under the various allocation policies.</p