hod (Lambda, mu, sigma) ([@CIT0010]). The world health organization (WHO) Child Growth Standards were used for comparison with the international standards of weight and height ([@CIT0011]).

Confounding factors {#S0002-S20004}
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By mailed questionnaire, the following information on factors that may affect infant growth and maternal vitamin and oxidative stress levels was collected: first weaning month, breastfeeding, mother\'s employment status, secondhand smoke exposure, caregiver (mother or other individual), infant dietary supplementation, hospital admission history, parental education period, and household income.

Statistical analysis {#S0002-S20005}
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Levels of maternal vitamins and oxidative stress were dichotomized into low/high groups at the 25th or 75th percentile as determined by the distribution of serum or urinary concentrations among the entire cohort. The rationale for using different percentiles is that for vitamin A as the 25th percentile, a deficiency effect was important; for vitamins C and E as the 75th percentile, a supplementing effect was important; and for 8-OHdG and MDA as the 75th percentile, an excess effect was important.

Between the two low/high groups, the mean infant weight, height, head circumference, weight percentile, height percentile, and head circumference percentile at birth and at 6, 12, 18, 24, and 36 months were assessed using the PROC Mixed procedure in the Statistical Analysis Systems statistical software package version 9.1 for Windows (SAS Institute, Cary, NC, USA).

The Student\'s *t* test and chi-squared test were conducted to select confounding factors. Finally, we selected the five potential confounding variables that provided valid and precise results.

Results {#S0003}
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General characteristics of the study population {#S0003-S20001}
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A total of 383 infants whose mothers' vitamin and oxidative stress levels were measured were followed up at least once between birth and 