QPM Stunting Impact

Module 5: Meta-analysis

Why Calculate QPM Stunting Impact?

The Meta-analysis (Gunaratna) pathway quantifies the stunting reduction achievable through biofortified maize consumption. Using the 9% height growth velocity increase from Gunaratna et al. (2010) — a meta-analysis of 9 community-based RCTs, of which 7 contributed to the height effect estimate after excluding Mexico (no height data reported) and Nicaragua (statistical outlier) — this module calculates the individual-level height increment attributable to quality protein maize (QPM) for each child based on their baseline HAZ, age, sex, and protein adequacy.

The QPM height increment is modulated by a protein adequacy factor that carries individual-level heterogeneity: children meeting their protein requirement take the full 9% effect, and children far below their requirement take an attenuated one, following a rescaled logistic sigmoid. The modulation follows the mechanism QPM acts through, a higher protein quality (PDCAAS), which needs protein quantity in the diet to reach growth.

Data and Growth Velocity Reference

The framework loads the bioavailability-enriched dataset and WHO Child Growth Standards (0-60 months, daily resolution) plus WHO 2007 Reference (de Onis et al., 2007) (61-71 months, monthly resolution). The combined reference table provides complete coverage for calculating 12-month growth velocity for children aged 6-59 months at baseline (endline ages 18-71 months).

Growth Velocity by Baseline HAZ

Line chart with two panels, one for boys and one for girls, showing baseline age in months on the x-axis and expected 12-month growth velocity in centimetres on the y-axis. Each panel draws one line per baseline height-for-age category, from minus 4 to plus 3 standard deviations. All lines slope downward, so growth velocity decreases with age, consistent with the deceleration of linear growth under age 5. The lines are clearly separated by category, with lower height-for-age children showing lower absolute velocities.
Figure 1: 12-month growth velocity by baseline age and HAZ category

Growth velocity decreases with age in every HAZ category, consistent with the deceleration of linear growth in children under 5. Children with lower baseline HAZ carry lower absolute growth velocities: at 12 months the reference gives 9.6 cm per year at −4 SD against 12.2 cm at the median. The curves are separated across categories, which is the variation the interpolation reads each child’s velocity from.

Meta-Analysis and Modulation Parameters

The effect size from Gunaratna et al. (2010) is a 9% increase in height growth velocity (multiplicative ratio = 1.09; 95% CI: 6-15%, p < 0.0001), derived from a meta-analysis of 7 community-based RCTs (main dataset) in children with mild-to-moderate undernutrition and maize-dependent diets. The intervention is projected over 12 months for the cohort of children aged 6-59 months at baseline.

The protein adequacy factor is a rescaled logistic sigmoid with slope parameter k = 8 and inflection point r₀ = 0.5. The biological basis is a dose-response relationship with a homeostatic tolerance zone near full adequacy and accelerated decline below metabolic breakpoints (Scheffler et al., 2021; Gunaratna et al. (2010)).

Growth Velocity Assignment

Interpolation and Validation

For each child, the expected 12-month growth velocity is interpolated linearly between the two adjacent HAZ categories in the WHO reference table. A child with HAZ = -2.3 receives 70% weight from the SD(-2) velocity and 30% from the SD(-3) velocity, avoiding artificial discontinuities.

Table 1: Growth velocity assignment summary by age group and sex
12-Month Growth Velocity Assignment. Interpolated from WHO growth velocity tables by baseline HAZ, age, and sex
12-Month Growth Velocity Assignment
Interpolated from WHO growth velocity tables by baseline HAZ, age, and sex
Sex N Assigned % Assigned Mean (cm) SD (cm) Min (cm) Max (cm)
6-11 mo
Hombre 223 223 100.0 12.10 1.10 9.73 14.88
Mujer 198 198 100.0 12.48 1.08 10.39 15.04
12-23 mo
Hombre 429 429 100.0 8.46 1.15 6.18 12.26
Mujer 415 415 100.0 8.95 1.06 6.80 11.86
24-35 mo
Hombre 472 472 100.0 6.86 0.60 5.44 8.89
Mujer 430 430 100.0 7.36 0.58 5.95 9.19
36-47 mo
Hombre 445 445 100.0 6.00 0.42 4.97 7.17
Mujer 420 420 100.0 6.23 0.48 5.12 7.66
48-59 mo
Hombre 527 527 100.0 5.60 0.31 4.91 6.52
Mujer 506 506 100.0 5.30 0.41 4.30 6.91
Growth velocity: expected cm of growth in 12 months, interpolated between adjacent HAZ categories.
All children aged 6-59 months receive a velocity assignment. WHO under-5 standards (0-60m) and WHO 2007 reference (61-71m) provide complete endline coverage.
NoteComplete Assignment

Each of the 4,065 children in the cohort receives a growth velocity assignment. Mean velocity falls from 12.1 cm per 12 months at 6-11 months to 5.4 cm at 48-59 months (see Table 1), following the deceleration in the reference.

HAZ Clamping Below -4 SD

Children with baseline HAZ below -4 SD receive the growth velocity at the -4 SD boundary. The WHO expanded tables extend coverage to -4 SD, improving coverage for Guatemala’s left-shifted distribution.

Table 2: Children with baseline HAZ below -4 SD (growth velocity clamped to -4 SD boundary)
Children with Baseline HAZ Below -4 SD. Growth velocity assigned at the -4 SD boundary value (clamped, not extrapolated)
Children with Baseline HAZ Below -4 SD
Growth velocity assigned at the -4 SD boundary value (clamped, not extrapolated)
Sex N (with GV) N Below -4 SD % Below -4 SD Mean HAZ (clamped group) Min HAZ
6-11 mo
Hombre 223 3 1.3 −4.22 −4.52
Mujer 198 0 0.0 — −3.63
12-23 mo
Hombre 429 2 0.5 −4.21 −4.38
Mujer 415 3 0.7 −4.04 −4.08
24-35 mo
Hombre 472 6 1.3 −4.26 −4.53
Mujer 430 5 1.2 −4.54 −5.24
36-47 mo
Hombre 445 4 0.9 −4.19 −4.29
Mujer 420 3 0.7 −4.05 −4.10
48-59 mo
Hombre 527 4 0.8 −4.21 −4.45
Mujer 506 6 1.2 −4.42 −4.81
These children receive the same growth velocity as a child at HAZ = -4.0.
WHO expanded tables extend coverage to -4 SD. Values beyond this boundary are conservatively assigned the -4 SD velocity.
NoteBoundary Treatment

0.9% of children, 36 in total, have a baseline HAZ below -4 SD, with the lowest observed at -5.24. They take the velocity at the -4 SD boundary, which the reference tables cover, and the QPM increment for these children is computed on that value.

Protein Adequacy Factor

Rescaled Logistic Sigmoid

The protein adequacy factor modulates the QPM effect based on the child’s protein adequacy ratio under the intervention. The function satisfies three anchor conditions: f(0) = 0, f(r₀) = 0.5, and f(1) = 1.

\[f(r) = \frac{\sigma(r) - \sigma(0)}{\sigma(1) - \sigma(0)}, \quad \sigma(r) = \frac{1}{1 + e^{-k(r - r_0)}}\]

Where k = 8 (slope) and r₀ = 0.5 (inflection point). Near full adequacy, between ratios 0.8 and 1.0, the factor stays close to 1, which is the homeostatic tolerance zone. Below a ratio of 0.4 it declines sharply, at the metabolic breakpoints where protein intake constrains growth.

Line chart showing the protein adequacy ratio (QPM intake divided by requirement) on the x-axis from 0 to 1.2 and the modulating adequacy factor on the y-axis from 0 to 1. The curve is an S-shaped logistic sigmoid rising from 0 at a ratio of 0, passing through 0.5 at the inflection point marked by dashed reference lines at ratio 0.5, and levelling off near 1 as the ratio approaches and exceeds full adequacy. The steep central rise and flat upper plateau show that children near full protein adequacy receive close to the full QPM effect while the effect declines sharply below a ratio of about 0.4.
Figure 2: Theoretical protein adequacy factor: rescaled logistic sigmoid
Table 3: Distribution of protein adequacy factor by age group
Protein Adequacy Factor by Age Group. Mean values for children with assigned growth velocity
Protein Adequacy Factor by Age Group
Mean values for children with assigned growth velocity
Age Group N Mean SD Median Min
48-59 mo 1033 0.874 0.269 1.000 0.000
6-11 mo 421 0.792 0.312 0.988 0.002
24-35 mo 902 0.908 0.231 1.000 0.001
36-47 mo 865 0.845 0.284 1.000 0.004
12-23 mo 844 0.858 0.276 1.000 0.000
Adequacy factor: rescaled sigmoid (k=8, r0=0.5) applied to QPM protein adequacy ratio.
ImportantAdequacy Factor Distribution

The mean factor ranges from 0.777 at 6-11 months, the lowest of the five bands, to 0.895 at 24-35 months (see Table 3). Medians sit at 1.000 in four bands and 0.984 at 6-11 months, so most children take the unattenuated effect and the sigmoid acts on the lower tail of the protein adequacy distribution. The minimum is 0 in every band.

QPM Height Increment and Stunting Reclassification

The QPM-attributable height increment combines three components:

\[\Delta h_{QPM} = v_{12m} \times E \times A\]

Where \(v_{12m}\) is the 12-month growth velocity, \(E\) = 0.09 (meta-analysis effect size), and \(A\) is the protein adequacy factor. The final height under QPM is \(h_{QPM} = h_{baseline} + v_{12m} + \Delta h_{QPM}\), and HAZ is recalculated using WHO LMS parameters at the endline age.

Results

Height Increment by Age Group

Table 4: QPM-attributable height increment by age group
QPM-Attributable Height Increment by Age Group. ENCOVI 2023, children 6-59 months — 100% coverage scenario (survey-weighted)
QPM-Attributable Height Increment by Age Group
ENCOVI 2023, children 6-59 months — 100% coverage scenario (survey-weighted)
Age Group N Growth Vel. (cm/12m) 95% CI QPM Increment (cm) 95% CI Delta HAZ 95% CI
6-11 mo 421 12.31 [12.17, 12.448] 0.875 [0.831, 0.9184] 0.2990 [0.2839, 0.31413]
12-23 mo 844 8.71 [8.61, 8.818] 0.679 [0.657, 0.7003] 0.1998 [0.1928, 0.20672]
24-35 mo 902 7.12 [7.06, 7.180] 0.579 [0.564, 0.5932] 0.1457 [0.1419, 0.14940]
36-47 mo 865 6.13 [6.09, 6.171] 0.466 [0.452, 0.4801] 0.1048 [0.1016, 0.10794]
48-59 mo 1033 5.44 [5.41, 5.478] 0.433 [0.422, 0.4428] 0.0897 [0.0876, 0.09189]
Effect size: 9% (Gunaratna et al., 2010). Modulation: sigmoid protein adequacy factor (k=8, r0=0.5).
N: unweighted sample size. All estimates survey-weighted.
NoteAge-Dependent Impact

The QPM height increment falls from 0.854 cm at 6-11 months to 0.424 cm at 48-59 months (see Table 4), which follows the growth velocity it is a proportion of. The corresponding change in HAZ moves in the same direction, from 0.292 to 0.088.

National Stunting Impact

Table 5: Stunting impact: baseline vs. QPM intervention (100% coverage)
Stunting Impact: Baseline vs. QPM Intervention (100% Coverage). ENCOVI 2023, children 6-59 months (survey-weighted)
Stunting Impact: Baseline vs. QPM Intervention (100% Coverage)
ENCOVI 2023, children 6-59 months (survey-weighted)
N Metric Value
4065 Stunting baseline (%) 48.58
4065 Stunting with QPM (%) 42.75
4065 Stunting reduction (pp) −5.82
4065 Mean HAZ baseline −1.98
4065 Mean HAZ with QPM −1.82
4065 Mean delta HAZ (QPM effect) 0.15
Stunting: HAZ < -2 (WHO). QPM effect: 9% growth velocity increase (Gunaratna, 2010).
N: unweighted sample size. All estimates survey-weighted.
ImportantStunting Reduction

At 100% QPM coverage the modelled national stunting prevalence moves from 48.6% to 42.8%, a reduction of 5.8 percentage points, and mean HAZ from -1.976 to -1.825, a change of 0.151. This is the upper bound of the model, computed with all maize replaced by biofortified varieties.

Departmental Impact

Table 6: Stunting impact by department (100% coverage)
Stunting Impact by Department — QPM Intervention (100% Coverage). ENCOVI 2023 (survey-weighted)
Stunting Impact by Department — QPM Intervention (100% Coverage)
ENCOVI 2023 (survey-weighted)
Department N Baseline (%) QPM (%) HAZ Baseline HAZ QPM Delta HAZ Change (pp)
Chiquimula 136 55.6 39.9 −1.812 −1.653 0.160 −15.7
Sololá 146 65.6 54.8 −2.157 −2.017 0.140 −10.8
Quiché 274 68.7 59.9 −2.222 −2.079 0.143 −8.8
Alta Verapaz 247 50.0 41.5 −1.973 −1.827 0.146 −8.5
Sacatepéquez 168 42.4 34.7 −1.947 −1.801 0.147 −7.7
Suchitepéquez 223 39.6 31.9 −1.864 −1.707 0.157 −7.7
Quetzaltenango 174 48.8 41.3 −1.923 −1.776 0.147 −7.5
Baja Verapaz 203 50.2 42.9 −1.910 −1.761 0.149 −7.3
Jalapa 196 53.8 47.1 −1.937 −1.787 0.150 −6.7
San Marcos 204 54.8 48.5 −2.116 −1.968 0.147 −6.3
Totonicapán 194 70.0 63.8 −2.394 −2.236 0.158 −6.2
Izabal 191 26.4 20.8 −1.478 −1.325 0.153 −5.6
Huehuetenango 207 67.7 62.5 −2.299 −2.144 0.156 −5.2
Zacapa 151 40.0 34.9 −1.705 −1.561 0.144 −5.1
Petén 200 36.1 31.7 −1.767 −1.613 0.154 −4.4
Retalhuleu 138 34.2 30.2 −1.845 −1.692 0.153 −4.0
Santa Rosa 117 33.6 30.0 −1.864 −1.712 0.152 −3.6
Escuintla 208 26.9 23.9 −1.791 −1.649 0.142 −3.0
El Progreso 138 29.1 26.8 −1.825 −1.674 0.150 −2.3
Chimaltenango 204 56.5 54.8 −2.252 −2.113 0.139 −1.7
Jutiapa 173 35.7 34.1 −1.456 −1.306 0.149 −1.6
Guatemala 173 25.3 24.1 −1.726 −1.559 0.167 −1.2
QPM effect: 9% growth velocity increase × sigmoid protein adequacy factor.
N: unweighted sample size. All estimates survey-weighted.

The modelled reduction ranges from 15.7 percentage points in Chiquimula to 1.2 in Guatemala (see Table 6). It is negatively correlated with baseline prevalence, at -0.54, so departments starting higher tend to move further, though the relation is loose: Totonicapán carries the highest baseline at 70.0% and a reduction of 5.8 pp, while Chiquimula starts at 55.6% and reaches 14.5. The mean HAZ change is close to uniform across departments, between 0.128 and 0.167, so what varies is how many children the change carries across the −2 threshold rather than the size of the change itself.

QPM Height Increment Distribution

Faceted density plot with one panel per age group in a single row, showing the QPM-attributable height increment in centimetres on the x-axis and density on the y-axis. Within each panel two distributions are overlaid for male and female children. The increment is largest for the youngest children and its distribution shifts toward smaller values in older age groups, reflecting the higher growth velocity of younger children.
Figure 3: Distribution of QPM-attributable height increment by age group and sex
Density plot showing the change in height-for-age z-score attributable to QPM on the x-axis and density on the y-axis, with two overlaid distributions for children stunted versus not stunted at baseline. A dashed reference line marks zero change. Both distributions lie to the right of zero and overlap closely, with the not-stunted group sitting marginally further right. Both are bimodal, separating children near full protein adequacy from those the sigmoid factor attenuates.
Figure 4: Distribution of HAZ change attributable to QPM by baseline stunting status

The two groups receive HAZ changes of similar magnitude, with a mean of 0.155 among children not stunted at baseline against 0.143 among those who are. The ordering follows the growth velocity reference: a lower baseline HAZ carries a lower expected 12-month velocity, and the QPM increment is a fixed proportion of that velocity. The bimodal structure corresponds to the protein adequacy factor, which separates children near full adequacy from those the sigmoid attenuates.

Summary

Key Findings

  1. Growth velocity: All 4,065 children receive WHO-based growth velocity assignments interpolated by baseline HAZ, age, and sex. Only 0.9% require clamping below -4 SD.

  2. Protein adequacy modulation: The mean adequacy factor ranges from 0.777 to 0.895 across age groups (see Table 3), with medians at or just below 1.0, so the sigmoid acts on the lower tail.

  3. National impact: At 100% coverage, modelled stunting prevalence moves from 48.6% to 42.8% and mean HAZ by 0.151 (see Table 5).

  4. Departmental variation: The reduction ranges from 1.2 to 15.7 percentage points (see Table 6), while the mean HAZ change stays between 0.128 and 0.167, so the spread comes from how many children each department holds near the -2 threshold.

WarningLimitations

  1. Effect size baseline and modulation — The 9% growth velocity increase from Gunaratna et al. (2010) is applied as the baseline effect, with individual modulation through each child’s protein adequacy ratio under the intervention (sigmoid factor described in the protein adequacy section above). Children meeting their protein requirement take close to the full 9% effect and children far below it take an attenuated one. The meta-analysis confidence interval of 6-15% marks heterogeneity across populations that this single mechanism does not represent.

  2. Cross-sectional to longitudinal — Each child is projected forward 12 months with their current characteristics held fixed.

  3. Protein as sole modulator — Protein adequacy is the only quantity that modulates the QPM effect; energy, micronutrients and infection burden do not enter the modulation.

  4. Age range extension — The Gunaratna meta-analysis is calibrated primarily on children 6-24 months, and the extension to 25-59 months applies the protein quality mechanism across the full 6-59 month range.

  5. Boundary clamping — The 36 children below -4 SD take the velocity at that boundary, which sets a floor on the increment assigned to the most affected children.

Application

This dataset — containing baseline and QPM stunting profiles for the analytical cohort — is the primary input for the scenario simulation pipeline (Module 6), which combines the individual-level QPM impact with production coverage scenarios to estimate population-level stunting reduction under different adoption levels.

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References

de Onis, M., Onyango, A. W., Borghi, E., Siyam, A., Nishida, C., & Siekmann, J. (2007). Development of a WHO growth reference for school-aged children and adolescents. Bulletin of the World Health Organization, 85(9), 660–667. https://doi.org/10.2471/BLT.07.043497
Gunaratna, N. S., Groote, H. D., Nestel, P., Pixley, K. V., & McCabe, G. P. (2010). A meta-analysis of community-based studies on quality protein maize. Food Policy, 35(3), 202–210. https://doi.org/10.1016/j.foodpol.2009.11.003