Analysis of data from a national micronutrient survey with a linear mixed model: estimates, predictions and lessons...

Because micronutrient deficiencies affect public health, countries monitor population status by national-scale, multi-stage, micronutrient surveys (MNS). In design-based surveys, inclusion probabilities are specified for sample units and the corresponding sample weights allow design-unbiased estimates to be made of population parameters. Corrections may be possible on departures from the design; an alternative is to use linear mixed models (LMM), with an estimated covariance structure reflecting the sampling design, to obtain model-based estimates.

The Ethiopia National Micronutrient Survey (2016) specified inclusion probabilities at enumeration area (EA) and household (HH) levels, and sample weights are provided. However, the design was not followed as it would have resulted in insufficient sampling from women of reproductive age.

Having found no evidence that sample weights were informative for target serum micronutrient concentrations (Zn), we estimated LMM parameters, with Regions as fixed effects, and the variation of individuals nested within households, households within EA, and EA within regions, random effects. We obtained LMM standard errors, Best Linear Unbiased Estimates (BLUEs) of regional means, and empirical Best Linear Unbiased Predictions for sampled/unsampled EA and HH. The probability that each true regional mean exceeded the sufficiency threshold $\left(65\mu g{\mathrm{dL}}^{-1}\right)$ was evaluated. The variances of BLUEs of regional means, under alternative sampling designs, were bootstrapped from LMM variance components.

We demonstrate use of LMM to obtain model-unbiased estimates and predictions when surveys deviate from the original design; and the use of LMM variance components to evaluate alternative designs for further sampling, or for sampling comparable populations.