Child Growth Failure Risk Effects 2021
Risk Overview
Child growth failure (CGF) is estimated using three risk exposures: stunting or low height for age (HAZ), wasting or low weight got height (WHZ), and underweight or low weight for age (WAZ).
The risk effects are found for each of these risk exposures based on categorical definitions using the WHO 2006 growth standards for children 0-59 months. They are: mild (<-1 to -2 Z score), moderate (<-2 to -3 Z score), and severe (<-3 Z score).
All three metrics are a measure of acute malnutrition and are associated with increased mortality and susceptibility to infectious disease. More information can be found in the CGF risk exposure model document.
GBD Modeling Strategy
In the GBD 2021 model, there were significant changes from the prior 2019 risk effects. Prior GBD models used a simulated joint distribution of stunting, underweight, and wasting measures from the [Olofin_2013] meta-analysis.
In GBD 2021, GBD created age-specific joint distributions of stunting, underweight, and wasting measures from 15 longitudinal studies (from 26 locations) in the Bill and Melinda Gates Foundation’s Knowledge Integration (Ki) database. The RR adjustment method was also strengthened in GBD 2021 by constraining optimisation in two ways. These changes result in a couple of differences relevant to our simulation:
There are now separate RR values for incidence and mortality
Malaria was identified as an affected cause
The incidence and mortality RR values from GBD are for incidence and CSMR. For this model, we will convert to incidence and EMR relative risks. More information on this conversion is below.
In order to account for the high degree of correlation between CGF indicators, GBD used a constrained optimisation method to adjust the observed univariate RRs that come out of the Burden of Proof analysis. Using a joint distribution of stunting, underweight, and wasting, they generated one thousand RR draws for each univariate indicator and severity. Then they altered these univariate RRs for each causes based upon interactions among the CGF indicators. This means that the resulting RRs are independent of other CGF risks.
Vivarium Modeling Strategy
For the nutrition optimization model, there are separate relative risks for the three components of child growth failure: HAZ, WAZ, and WHZ. Relative risks are categorical.
These risk exposures affect four causes: diarrheal diseases, LRIs, malaria, and measles. Additionally, these relative risks vary by simulant age. The age categories are: 1 to 5 months, 6 to 11 months, 12 to 23 months, and 2 to 4 years. Note that for simulants less than one month of age, the risk effects are caused by LBWSG not CGF and so are not included here. Additionally, there are separate relative risks for incidence and mortality.
Therefore, a simulant’s relative risk value is dependent on: the risk exposure variable (e.g., WAZ), the simulant’s risk exposure category (e.g., moderate), the cause (e.g., malaria) and cause metric affected (e.g., incidence), and the simulant’s age (e.g., 6-11 months). Putting this together, a single relative risk might be the RR for WAZ on malaria incidence for a simulant in the moderate exposure category who is 6-11 months old.
For stunting and underweight, relative risk values can be pulled using the following code:
rrs = get_draws(gbd_round_id=7, year_id=2021, gbd_id_type='rei_id', gbd_id=[241,240,94], source='rr', decomp_step='iterative')
Wasting relative risks were generated separately to accomodate the sub-exposures in the MAM (cat2) category in our wasting risk exposure model and can be found in this CSV file.
These values were calculated in this notebook. Notably, CGF PAFs were calculated prior to the implementation of separate relative risks for MAM substates; however, we have investigated that the substate relative risks change PAF estimates very minimally.
In April of 2024, this was updated due to a found bug in the code. The data was aggregated over age and sex, though kept location specific. The data file and notebook were updated accordingly. This change was due to lack of difference in subcategory MAM exposure at the age or sex level, and small counts leading to NaN values and incorrect final data.
The mortality relative risk values will then need to be adjusted. The GBD values are for CSMR, but we will use EMR. To adjust between CSMR and EMR values, you can use this equation:
We have validated this equation in two ways. First, we checked this mathematically.
Using equations for incidence, EMR, and prevalence based on information we knew in the
model, we found an equation for EMR relative risk. We tested this equation and found
that the answer was almost identical to the equation shown above. The math
proof for this can be found in this word doc.
Secondly, we created a nano simulation to test that by using the equation above and applying the EMR and incidence relative risks to the simulated population, that the resulting CSMR relative risk was about what we expected. The notebook validated this approach and was able to reproduce the expected CSMR RR with some noise.
There are some cases where the CSMR RR is less than the incidence RR value. This will then create an EMR RR less than one - or a protective effect from CGF to disease survival. There are also some cases in which the GBD estimate of the incidence RR is less than one. While this is counterintuitive, we are allowing for this case to be in the model. We expect this is due to a lack of statistical significance in creation of RR values which will be accounted for in our monte carlo uncertainty.
PAFs will be calculated separately to account for the correlation between wasting, stunting, and underweight risk exposures as a single joint PAF for CGF. Draw-level PAF values are available below:
Note
There are some draws for which the PAF is negative. This happens because the relative risk values for some draws are less than one. We should use these values regardless as part of our Monte Carlo analysis.
With the RR and PAF values above, the following equations can be used to calculate simulant level incidence and EMR.
Where the relative risk value will depend on the simulant’s age group and risk exposure category.
Note that since the RR values from GBD are independent, we multiply them together here without double counting the CGF relative risks.
Validation and Verification Criteria
Verification and validation criteria from the diarrheal diseases, malaria, mealses and LRI cause models should remain true.
Verification and validation criteria from the child growth failure exposure model should remain true.
Relative risk values should approximately match what is expected for incidence and mortality from each cause.
Assumptions and Limitations
We assume that converting to EMR relative risks from the GBD supplied CSMR relative risks will work for all combinations of RRs, incidences, risk exposures, etc. We believe this is true based on the nano sim and math proof above.
We assume that the duration of illness will be the same for all simulants. It is possible that wasted, stunted, or underweight children might have lower immune function and therefore take longer to recover from an illness. This would lead to a longer duration. We do not include this in our model.
Some EMR RR values might be less than 1 when the CSMR RR is less than the incidence RR. This is counterintuitivebut we allow it in the model since we think this is due to a lack of statistical significance in creation of RR values which will be accounted for in our monte carlo uncertainty.
References
Olofin I, McDonald CM, Ezzati M, et al. Associations of Suboptimal Growth with All‐Cause and Cause‐ Specific Mortality in Children under Five Years: A Pooled Analysis of Ten Prospective Studies. PLOS ONE 2013; 8: e64636