Causal analysis of food insecurity and type 2 diabetes
Food insecurity and type 2 diabetes are associated in observational data. A causal question is harder because the data must establish a defensible time order and support the assumptions required for identification.
This project examined what could be learned from three cycles of the National Health and Nutrition Examination Survey. The estimated effect of food insecurity on subsequent type 2 diabetes was close to zero and not statistically significant across the specifications we considered.
The more important result was methodological. The study makes clear which parts of the causal question NHANES can support, which assumptions remain weak, and why a second planned question could not be identified from the available data.
Defining a causal question from cross-sectional data
The target was the average treatment effect of experiencing food insecurity on the subsequent development of type 2 diabetes.
Food insecurity cannot be assigned experimentally, so the effect has to be estimated from observational data under explicit assumptions.
NHANES is primarily cross-sectional. Each respondent is interviewed and examined once. Exposure and outcome are therefore usually observed at the same point in time, which makes temporal ordering difficult.
For this question, the survey instrument provided a partial way around that problem.
NHANES asks whether a respondent had glycohemoglobin measured by a clinician during the previous twelve months and asks for the recalled value. It also measures glycohemoglobin directly at the examination.
A respondent who reports a prior non-diabetic value and presents with a diabetic value at examination can therefore be treated, within the limits of the survey, as having developed diabetes during the interval.
The food-insecurity questions refer to the same twelve-month period.
This construction creates a usable time ordering within a single-visit survey. It also reduces the sample substantially because respondents need both the recalled prior measurement and the examination measurement. After pooling three cycles, the resulting analytic sample contained only a few hundred people.
That limitation is central to the precision of the estimates.
The identification assumptions
Five assumptions were considered explicitly before interpreting the estimate as causal.
| Assumption | Status |
|---|---|
| Positivity | Satisfied. Every covariate stratum contains both exposed and unexposed respondents. |
| Conditional exchangeability | Partially satisfied. Age, sex, race and ethnicity, educational attainment, and survey cycle were adjusted for. Dietary intake, physical activity, and family history were not measured in a usable form and remain unmeasured confounders. |
| No reverse causation | Assumed, not established. The construction places the exposure window before the outcome window, but food insecurity is treated as persistent over the interval, and diabetes can itself contribute to food insecurity through medical cost. |
| SUTVA | Reasonable. One respondent's food-security status is unlikely to alter another respondent's diabetes risk within this sampling frame. |
| Accurate measurement | Weak. The earlier glycohemoglobin value is recalled from a clinical encounter up to one year earlier, and food insecurity is self-reported. Both are subject to measurement error. |
The last two substantive weaknesses cannot be repaired by a more sophisticated estimator.
Unmeasured confounding remains possible, and the temporal construction is imperfect. Measurement error in both exposure and prior outcome history also tends to attenuate associations.
These limits have to remain part of the interpretation.
Why use a doubly robust estimator
With measured confounders, one approach is to model the outcome given treatment and covariates and average the resulting contrast. This is g-computation.
Another is to model the probability of treatment given covariates and use the estimated propensity score to reweight observations. This is inverse probability weighting.
Each method depends on its own nuisance model.
Augmented inverse probability weighting combines the two.
E[ µ1(X) − µ0(X) + A{Y − µ1(X)} / π(X) − (1−A){Y − µ0(X)} / {1 − π(X)} ]
Here π(X) is the propensity score and µa(X) is the expected outcome under treatment level a.
AIPW is doubly robust. The estimator remains consistent if either the outcome model or the propensity model is correctly specified, provided the other regularity conditions hold.
That does not make it robust to all misspecification. If both nuisance models are wrong, the protection is lost.
Double robustness, demonstrated
The browser simulation generates two hundred datasets of 1,000 observations from a known data-generating process with a true treatment effect of 2.
Each dataset is analyzed with g-computation, inverse probability weighting, and AIPW. When either the propensity model or outcome model is misspecified, its corresponding single-model estimator moves away from the truth while AIPW remains centered near the target. When both are misspecified, AIPW moves as well.
The simulation also shows a small finite-sample bias in inverse probability weighting when estimated propensities approach zero. This is one practical reason to prefer the augmented estimator over weighting alone.
In the NHANES analysis, AIPW was fit with the AIPW package. G-computation from RobinCar was used as a comparison.
We examined a nested sequence of adjustment sets. Covariates were added in the order survey cycle, age, race and ethnicity, sex, and educational attainment.
Looking across several specifications makes it easier to see whether the estimate is sensitive to the adjustment set rather than treating one model as uniquely authoritative.
What the analysis returned
The estimated average treatment effect of food insecurity on developing diabetes remained close to zero across the covariate sets we examined.
No specification reached statistical significance at the five percent level.
AIPW and g-computation also agreed closely. That consistency is reassuring about the mechanics of the analysis, but it does not resolve the identification problems described above.
The null result should therefore be read narrowly.
The sample was small. The outcome was uncommon. Food insecurity was self-reported, and prior glycohemoglobin was recalled. Both forms of measurement error can push estimates toward zero.
The data are compatible with no effect. They are also compatible with a real effect that this design had too little power or too much measurement error to detect.
The estimate should not be treated as evidence that food insecurity has no causal effect on diabetes risk.
The question we could not identify
A second planned question concerned the effect of vitamin D deficiency on type 2 diabetes.
That analysis was abandoned.
Serum vitamin D is measured only at the NHANES examination. Because each survey cycle draws a new cross-sectional sample, there is no earlier vitamin D measurement for the same respondent. Exposure and outcome are therefore observed at the same time.
The temporal construction used for glycohemoglobin is not available.
We also considered an instrumental-variable strategy. Regional sunlight exposure was one candidate.
It was rejected because the exclusion restriction was not credible. Geography and sunlight can influence diabetes risk through physical activity, diet, socioeconomic conditions, and other pathways that do not operate through vitamin D.
An invalid instrument does not merely make an estimate less precise. It undermines identification.
The appropriate result for that question was therefore that the effect could not be estimated credibly from these data.
What would make the question answerable
The main constraint is the cross-sectional design rather than the overall scale of NHANES.
A follow-up component would change that.
NHANES has historical precedent for this approach. The NHANES Epidemiologic Follow-up Study re-interviewed participants from an earlier wave and created longitudinal data that supported later causal analyses.
A similar follow-up structure attached to the modern continuous survey would make it possible to establish temporal ordering directly rather than reconstruct it from recalled measurements.
That is why the null finding was still useful. The project identified where the available data support a causal analysis, where the assumptions remain weak, and what additional data would be needed to answer related questions more credibly.
The manuscript itself is not circulated publicly, at the authors' request. This page describes the design, estimator, and methodological conclusions. The simulation above is an independent illustration of double robustness and uses no study data.