Vitamin A Deficiency

Disease Description

Vitamin A deficiency (VAD) is a lack of vitamin A in blood and tissues. Vitamin A deficiency is considered as one of the most serious public health concerns in developing countries and can contribute directly or indirectly to disability.[1]

GBD 2017 Modeling Strategy

In Global Burden of Disease (GBD) 2017, vitamin A deficiency is defined as having a serum retinol concentration <0·7 μmol/L (<20 μg/dL). Population exposure to vitamin A deficiency is measured by prevalence, i.e. the proportion of the population with serum retinol below 0·7 μmol/L.

The VAD cause is a population attributable fraction (PAF) of 1 cause with the VAD risk factor. That is, 100% of VAD morbidity is attributable to the VAD risk factor. In this particular case, the PAF-of-1 relationship means that the VAD risk and the VAD cause are identical. There is a single VAD model in GBD 2017 (modelable_entity_id=2510) for both the cause and the risk factor, and pulling exposure estimates for the VAD risk factor yields the same data as pulling prevalence outputs from the DisMod model for the VAD cause. 1 [GBD-2017-YLD-Appendix-VAD], [GBD-2017-Risk-Appendix-VAD]

1

Actually, there are numerical differences of up to about 30% between exposure and prevalence in a small fraction of the data points (~0.1% of draw-level values with a relative difference > 5%), but the VAD modeler assured us that these are probably just artifacts of the data processing and that the data sets are intended to be identical.

Vitamin A Deficiency Cause

The VAD cause in GBD 2017 is 100% attributable to the VAD risk factor. The VAD cause in GBD is a YLD-only cause, meaning that it contributes to morbidity, but not mortality.

Modeling Strategy for the Vitamin A Deficiency Cause

Todo

Describe cause in detail

Cause Hierarchy

Health States and Sequela

The sequela associated with the Vitamin A deficiency cause in GBD 2017 include moderate vision impairment loss due to Vitamin A deficiency, severe vision impairment loss due to Vitamin A deficiency, blindness due to Vitamin A deficiency, asymptomatic Vitamin A deficiency, Vitamin A deficiency with mild anemia, Vitamin A deficiency with moderate anemia, Vitamin A deficiency with severe anemia.

Restrictions

GBD 2017 Cause Restrictions

Restriction Type	Value	Notes
Male only	False
Female only	False
YLL only	False
YLD only	True
YLD age group start	Early Neonatal	[0, 7 days), age_group_id = 2
YLD age group end	95 Plus	[95, 125 years), age_group_id = 235

Vitamin A Deficiency Risk Factor

The Vitamin A deficiency risk factor in GBD 2017 is a dichotomous variable . Below is a list of measures and corresponding IDs:

Measures

Measure	ID	Data source
Remission	gbd_id = 2510, measure_id = 7	epi, use get_model_results function
Incidence rate	gbd_id = cid(389)	como, use get_measure
Risk factor exposure	gbd_id = reiid(96)	como, use get_measure

Todo

Address James’s comment about the above table in PR 149:

1. Incidence and remission are measures for the cause.

2. I thought we decided not to use them at all.

Correct, we are not planning to use incidence or remission data, so we should make this clear. E.g. move the first two rows of this table into the Vitamin A Deficiency Cause section and clarify that we’re not planning to use them for the Vivarium model, or just omit them entirely.

Risk Factor Hierarchy

Restrictions

GBD 2017 Risk Restrictions

Restriction Type	Value	Notes
Male only	False
Female only	False
YLL only	False
YLD only	False
YLL age group start	Post Neonatal	[28, 365 days), age_group_id = 4
YLL age group end	1-4 years	[1, 5 years), age_group_id = 5
YLD age group start	Early Neonatal	[0, 7 days), age_group_id = 2
YLD age group end	95 Plus	[95, 125 years), age_group_id = 235

Relative Risks

The causes affected by the Vitamin A Deficiency risk in GBD 2017 include lower respiratory infections, diarrhoeal diseases, and measles. The relative risks for these causes appear in Table 4 on p. 112 of [GBD-2017-Risk-Appendix-VAD], copied here for reference:

Table 4.1: Relative risks for risk-outcome pairs in GBD 2017 [GBD-2017-Risk-Appendix-VAD]

Cause	GBD 2016 RR	GBD 2017 RR	Include in GBD 2017
Diarrhea	1.6 (1.21 - 2.02)	2.35 (2.17 - 2.54)	Yes
Measles	2.4 (1.61 - 3.48)	2.76 (2.01 - 3.78)	Yes
Lower Respiratory Infections (LRI)		1.23 (1.03 - 1.48)	Yes
Meningitis		3.2 (0.69 - 14.75)	No (not significant)
Malaria		3.65 (2.23 - 5.97)	No (only one study)

Table 4.2: Pulled relative risks of GBD 2017

Cause	GBD 2017 RR	Note
Diarrhea	2.44 (2.27 - 2.63)	RR from relative_risk source pulled with rei_id 96 (age 1-5, 1000 draws)
Measles	3.51 (2.53 - 4.67)	RR from relative_risk source pulled with rei_id 96 (age 1-5, 1000 draws)
Lower Respiratory Infections (LRI)	1.33 (1.11 - 1.59)	RR from relative_risk source pulled with rei_id 96 (age 1-5, 1000 draws)

The above relative risks for GBD 2017 can be interpreted as rate ratios for the incidence rates of diarrhea, measles, and LRI. They can also be interpreted as rate ratios for cause-specific mortality rates. The GBD modelers found no statistical difference between RR’s for incidence and RR’s for mortality, so they pooled all data for effect sizes of VAD on incidence and cause-specific mortality to arrive at the estimates in Table 4.

Note

In GBD 2019, the effect on lower respiratory infections (LRI) was dropped due to insufficient evidence of causation found by the network meta-analysis. Moreover, the relative risks for measles and diarrheal diseases were found to be smaller than those in the above table. This should be noted as a limitation in any simulation using the RR’s from GBD 2017.

Todo

Reformat Table 4 (or perhaps make a separate table) to make it more useful for the software engineers, based on James’s comments in PR 149. Namely:

1. We can include the actual data means and uncertainties here if we want, but since we’re planning to use the draw-level RR’s from GBD, we should include the rei_id and cause_id associated with each risk-outcome pair we’re using.

2. Including the interpretations of the RR’s is good. I think you should have the interpretation as a column in the table though. A single risk factor may have different kinds of effects on different outcomes and should be specified pairwise. Also include the numerator and denominator or a link to what rate ratio means (I think we made a glossary in the documentation).

Vivarium Modeling Strategy

We will use an exposure model (or prevalence-only model or propensity model) for a vitamin A deficiency, in which each simulant is initialized with a “propensity” for vitamin A deficiency, and the simulant’s vitamin A status is determined by comparing this propensity to the overall VAD exposure/prevalence in the population. Such propensity/exposure models have been used in Vivarium for other risk factors and risk-attributable causes, such as child stunting, child wasting/PEM, and iron deficiency anemia.

Todo

Reword the above to make it clear that an exposure model is the standard strategy used for risk factors, and that it is infrequently used for cause models because we usually trust the dynamic disease parameters more or we care about counting cases. We should eventually have a description of what “exposure model” means in the general risk factor documentation.

Standardize the terminology above and below to use “exposure model” throughout, since this applies to all risk factors.

Proposal: What about using “exposure propensity model,” because each simulant has a fixed propensity for exposure to the risk? This highlights the fact that we are not only using standard inverse transform sampling to sample from the exposure distribution, but that we do this at each time step without changing the simulants’ percentile ranks, which we conceptualize as fixed propensities for exposure. The same conceptual framework of “propensity” would still apply even if we come up with a way to dynamically change simulants’ percentile ranks over the course of the simulation.

In more detail, the basic strategy is to initialize each simulant with a propensity score distributed uniformly in [0,1], then compare this propensity score with the (location/age/sex/year/intervention-status)-dependent prevalence of vitamin A deficiency at each time step to determine whether the simulant has VAD during that time step. (More precisely, the propensity score is the simulant’s quantile rank in the VAD exposure distribution, and their vitamin A status will be the corresponding quantile.) Each simulant’s propensity is assigned only once, but the underlying prevalence of vitamin A deficiency (i.e. the exposure distribution) can change throughout the course of the simulation, which may result in a change in the simulant’s vitamin A status. The precise algorithm is described below.

In particular, our modeling strategy will not explicitly use incidence or remission data for vitamin A deficiency, but only prevalence (which is the same as the exposure data for the VAD risk factor). The rationale for this approach is twofold:

1. We want to guarantee that the simulated baseline prevalence of vitamin A deficiency matches the prevalence data from GBD (1 - 5 age group), which is likely more trustworthy than incidence and remission data.

2. Relative risks from the literature about the effects of vitamin A supplementation or fortification on vitamin A status are best interpreted as risk ratios for prevalence of vitamin A deficiency. The exposure model provides a way to directly model these effect sizes in a way that preserves this interpretation.

Prevalence of Vitamin A deficiency in GBD 2017

Source	Exposure source using rei_id 96	Como
Nigeria	0.232 (0.184 - 0.288)	0.232 (0.184 - 0.288)
India	0.25 (0.205 - 0.303)	0.25 (0.205 - 0.304)
Ethiopia	0.315 (0.252 - 0.379)	0.315 (0.253 - 0.38)

Todo

Be more clear about what we mean in point 1. above. E.g. it looks like using GBD’s incidence and remission data will cause most of the population to get VAD over the course of a 5-year simulation, which may not be realistic. See Assumptions and Limitations.

In PR 149, James commented about the above rationale:

We are only doing this because of option 2. We expect the cause version of the model to get incidence and remission correct in addition to getting prevalence correct.

However, it is more important for us to use the intervention data correctly than it is to get the dynamic parameters of the disease correct. Details about the limitations and the expected impact to be found in .

Following is a more detailed description of how the exposure model for VAD should work.

Determining Vitamin A Status

At each time step, Vivarium needs to determine whether each simulant has vitamin A deficiency. To do so, follow these steps:

1. Initialize: When simulant \(i\) enters the simulation (e.g. at the start of the simulation or at the time step when the simulant is born), assign the simulant a random number \(v_i \sim \operatorname{Uniform}([0,1])\), which we call the VAD propensity score for simulant \(i\).

2. Update: On each time step \(t\):

   1. If simulant \(i\) survives, update any of simulant \(i\)’s variables that determine which subpopulation the simulant belongs to. For example, they may move into the next age group, or they may begin receiving or stop receiving an intervention. Call this new subpopulation \(\text{subpop}(i,t)\).

   2. Look up or compute the prevalence \(p_\text{VAD}(\text{subpop}(i,t))\) of vitamin A deficiency for the simulant’s updated subpopulation.

   3. If \(v_i < p_\text{VAD}(\text{subpop}(i,t))\), the simulant has vitamin A deficiency on the next time step; otherwise, they don’t.

In the above algorithm, note that each simulant’s propensity score is assigned only once, and that the simulant’s vitamin A status can change only if the simulant moves into a new subpopulation with a different VAD prevalence. Even then, only simulants with propensity scores in the interval between the old prevalence and the new prevalence will change status.

The different possible subpopulations a simulant can belong to will depend on the particulars of the simulation, and hence so will the determination of the prevalence \(p_\text{VAD}\). For the standard baseline model with no interventions, the stratification into subpopulations should match GBD 2017: Each location, age, sex, and year determines a subpopulation, and the corresponding prevalence \(p_\text{VAD}\) will be the prevalence of vitamin A deficiency pulled from the VAD model in GBD 2017.

To address a point of potential confusion in the above algorithm, note that a lower propensity score \(v_i\) corresponds to a higher propensity for vitamin A deficiency. This is why we called \(v_i\) the “propensity score” rather than just the “propensity.” We could additionally define the propensity for VAD to be \(1-v_i\), but we don’t actually need this number.

Todo

Revise the above algorithm to take into account James’ comments in PR 149:

I think we should standardize the notation for these things. I follow scipy conventions in the code and I think they’re reasonable:

x_i - the random variable (the exposure)

q_i - the percentile or propensity of the exposure x_i in the distribution

(called q because the inverse cdf is the quantile function, though also

called the percent point function).

Initialize should also describe how we actually get x_i.

Actually, as noted above, the propensity score is not the percentile (or quantile), but the quantile rank. Perhaps it would be better to use p_i instead of q_i (I used v_i above)?

In this case x_i would be a binary variable, “has VAD” / “does not have VAD”. How would you initialize this before following the procedure in the “Update” step?

The procedure is the same as in update, but it has to happen before a time step takes place. The value of other attributes the simulant is initialized with (e.g. whether or not they are receiving vitamin a fortification) may be dependent on their initial vitamin a deficiency status. This is a fencepost error. All attributes of a simulant must be assigned an initial value before the first time step starts or you introduce extremely hairy issues into the order you must update simulant state each time step.

Here’s the procedure:

1. Initialization:

   • Sample propensity and store it for all time.

   • Use attributes initial distribution is conditional on (age, sex, year) to construct probability mass function

   • Use propensity to sample pmf and assign initial status.

2. Update:

   • Your procedure looks good here.

Todo

In a separate document, write a description of how Vivarium’s standard risk exposure model works using inverse transform sampling, and explain how the VAD model is a special case of this. The general procedure is described by James in PR 149:

Just leaving notes. I think this section is great. I think we want to pull it out into the general risk model for the standard way to sample from categorical distributions. In order to do so, we have to generalize this section a bit. Technically what we do is start with a distribution

p = [P_1, P_2, …, P_N, 1 - (P_1 + … +P_n)]

where P_j is the probability that an individual is in category j.

We then take the cumulative sum over the distribution

p_cum = [P_1, P_1 + P_2, …, P_1 + …+ P_N, 1]

to form the right bounds of a partition of the interval [0, 1] with each subinterval mapping to a risk exposure category with probability p_cum[right] - p_cum[left].

We then select the exposure category k by arg_max_k (q_i < p_cum[k]) and assign that category as x_i.

This means the interpretation of propensity is dependent on the sort order of the categories.

The default sort order is worst to best.

w/r/t risk effect. We have not had to deal with unordered categorical risks.

Tracking Years Lived with Disability due to Vitamin A Deficiency

Todo

Describe how to calculate YLDs from vitamin A deficiency, using the average disability weight over all 7 sequelae.

Risk Effects

Todo

Describe how to apply the relative risks in Risk Appendix Table 4 to affect the incidence rates of measles, diarrhea, and LRI. The relative risks should be available at the draw level from the VAD risk model in GBD. Presumably the GBD draws of each RR should follow a lognormal distribution whose geometric mean (=median) matches the central estimate and whose 2.5% and 97.5% percentiles match the upper and lower confidence bounds.

Scope

Assumptions and Limitations

Todo

Explain why the prevalence-only model is a reasonable strategy, citing incidence, remission, and prevalence data, as well as expert opinions about VAD. Note Abie’s concern (partially explained below) that using GBD’s incidence and remission data would result in most of the population getting VAD over the course of a 5-year simulation.

In addition to probably not getting incidence and remission of VAD right, this model has a particular implication about who does not get VAD. GBD has estimated that the prevalence of VAD is around 30% and the duration until remission is around 1 year. GBD has not estimated what fraction of the population will have ever had VAD over a time longer than a year, however. Will most kids have experienced VAD by the time they are five? Or are the same 60% cycling in and out of VAD to maintain the 30% prevalence and 1 year duration? Probably something in between these extremes, but we have no data on this yet, and we don’t have guidance from GBD about how to do it. So it is hard to even know how wrong our model is when we don’t get remission right, let alone how much it matters for quantifying the impact of vitamin A fortification or supplementation.

In GBD 2019, the effect on lower respiratory infections (LRI) was dropped due to insufficient evidence of causation found by the network meta-analysis. Moreover, the relative risks for measles and diarrheal diseases were found to be smaller than those in the above table. Clients should be made aware that the relative risks from GBD 2017 do not reflect the most up-to-date data.

Cause Model Diagram

State and Transition Data Tables

Todo

Create tables specifying exactly what data is needed for the model and where to get it.

Validation Criteria

This model should get prevalence and YLDs right (meaning the prevalence and YLDs in the sim should match that in GBD). It will not necessarily get incidence and remission right (see Assumptions and Limitations).

Todo

Try to estimate how wrong we expect incidence and remission to be.

References

1. Amy L. Rice, Keith P. West JR. and Robert E. Black. Comparative quantification of health risks. Chapter 4 Vitamin A deficiency.

GBD-2017-YLD-Appendix-VAD

Pages 305-308 in Supplementary appendix 1 to the GBD 2017 YLD Capstone:

(GBD 2017 YLD Capstone) GBD 2017 Disease and Injury Incidence and Prevalence Collaborators. Global, regional, and national incidence, prevalence, and years lived with disability for 354 diseases and injuries for 195 countries and territories, 1990–2017: a systematic analysis for the Global Burden of Disease Study 2017. Lancet 2018; 392: 1789–858. DOI: https://doi.org/10.1016/S0140-6736(18)32279-7

GBD-2017-Risk-Appendix-VAD(1,2)

Pages 109-114 in Supplementary appendix 1 to the GBD 2017 Risk Capstone:

(GBD 2017 Risk Capstone) GBD 2017 Risk Factor Collaborators. Global, regional, and national comparative risk assessment of 84 behavioural, environmental and occupational, and metabolic risks or clusters of risks for 195 countries and territories, 1990–2017: a systematic analysis for the Global Burden of Disease Study 2017. The Lancet. 8 Nov 2018; 392: 1923-94. doi: http://dx.doi.org/10.1016/S0140-6736(18)32225-6.