Multiple imputation (MI) was proposed by Rubin (1986) as a method to address the missing information or data absence. Briefly, the strategy consists of generating a different value number for each missing data to maintain the population variability and maintain the relationship between variables. The theoretical foundation of MI is based on Bayesian methods [28, 29].

A multiple imputation process by chained equations (MICE) was carried out for this study, where it was considered that the information loss pattern was not completely random [2830]. Children whose caretakers did not present the VC at the survey time were defined as missing data in the DV, as well as the covariates were those without values.

Imputation model (1) was adjusted by the independent variables described above and survey design. Then, internal validation tests were performed using Bootstrap techniques [31, 32] and two variants of the number of database replications (m) [33].


f(Q|Yobs): Final distribution of parameter Q given the observed data.

Q: Proportion.

f(Q|Yobs, Ymis): Distribution of parameter Q given the complete data.

f(Ymis|Yobs): Distribution of missing data given observed data.

∫dYmis: Integral regarding the distribution of missing data.

Then, the estimator and associated variance (T) were obtained from the model with the best performance and considering the following Rubin rules:

Where this total variance (T) constitutes the variability within (U¯) and between (B) the m replications preformed:

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