Scientific Background: In developing countries, higher infant mortality is partially caused by poor maternal and fetal nutrition. Clinical trials of micronutrient supplementation are aimed at reducing the risk of infant mortality by increasing birth weight. Because infant mortality is greatest among the low birth weight infants (LBW) (less than or equal to 2500 grams), an effective intervention might be needed to increase birth weight among the smallest babies. Although it has been demonstrated that supplementation increases the birth weight in a trial conducted in Nepal, there is inconclusive evidence that the supplementation improves their survival. It has been hypothesized that a potential benefit of the treatment on survival among the LBW infants is partly compensated by a null or even harmful effects among the largest infants. Exploratory analyses have suggested that the treatment effect on birth weight might vary with respect to the percentiles of the birth weight distribution. Data: The methods in this paper are motivated by a double-blind randomized community trial in rural Nepal (Christian et al. 2003a,b). The investigators implemented an intervention program to evaluate benefits of the following micronutrient supplementations: folic acid and vitamin A (F+A); folic acid, iron, and vitamin A (F+I+A); folic acid, iron, zinc, and vitamin A (F+I+Z+A); multiple nutrients and vitamin A (M+A). Each micronutrient supplement was administered weekly to 1000 pregnant women, who ultimately delivered approximately 800 live-born infants. The team measured the birth weight within 72 hours of delivery and then followed the infants for one year to determine whether or not they survived. In addition, they measured several characteristics of the mother (maternal age, parity, maternal height, arm circumference) and of the infant (weight, length, head and chest circumference).

In this case study we focus on the supplementations F + I + A and M + A as compared to vitamin A only and we address the following scientific questions: 1. Is there an overall effect of the treatments on birth weight? Does this effect vary with the percentiles of the birth weight distribution; in particular, is it largest among the LBW infants? 2. Is there an overall effect of the treatments on survival? Does this effect vary with the percentiles of the birth weight distribution; in particular, is it largest among the LBW infants? 3. Do these percentile-specific effects on birth weight and survival differ by micronutrients? Statistical Approach: The data analysis is challenged by measurement error and informative missing data in birth weight and survival. In community-based interventions in developing countries, most births occur in the home without assistance from trained birth attendants. Approximately 88% of the babies are measured within 72 hours of the delivery. The remaining 12% are measured between the 72 and the 2000 hours approximately. Hence, weights are obtained at varying times following birth and therefore they are imprecise measures of the "true weight at birth". In addition, a high proportion of deaths of young infants occur in the first few hours after birth. If there is a delay in reaching the mother and infant, then many of these infants would be weighed because they have already died. For example in the F +1+ A group, approximately 7% of the birth weight measurements are missing and among this 7%, approximately 34% of the babies have died right within 24 hours of the delivery. These babies are likely to have been of lower birth weight than those who survived to be weighed, and therefore, these missing birth weights due to death are likely to be informative.

In this paper we develop a measurement error model with counterfactual variables that address the scientific questions for this birth weight-mortality case study. Our approach integrates Bayesian methods and data augmentation (Tanner and Wong, 1987; Tanner, 1991; Albert and Chib, 1993; Chib and Greenberg, 1998) with a counterfactual model and principal stratification (Rubin, 1978; Holland, 1986; Frangakis and Rubin, 2002). We calculate marginal posterior distributions of the treatment effects on birth weight and infant mortality that are allowed to vary with the percentiles of the birth weight distributions. We compare our posterior inferences with two simpler approaches. The first still relies on a Bayesian approach but ignores the uncertainty in the imputation and prediction of the birth weight and does account for the mother's covariates. The second is a simpler re-sampling approach that imputes the missing birth weights (Rubin, 1987). Results and Public Health Impact: First we found that both F+I+A and M+A increase birth weight. However, the F+I+A increases birth weight mainly among the LBW infants, whereas M + A increases birth weight across the entire birth weight distribution compared to vitamin A only. The F+I+A reduces the risk of infant mortality, whereas the M+A slightly increases the risk of early infant mortality, especially among the larger infants.

Currently recommendations exist to supplement pregnant women in developing countries. This case study provides critical information toward the evaluation and planning of these public health interventions.


Statistical Models