Estimating Response-Maximized Decision Rules With Applications to Breastfeeding

To estimate the sequence of actions that optimizes response in a longitudinal setting, it is important to study the actions as part of a set of decision rules rather than in a series of single-action comparisons. We take as our motivating example the estimation of the set of decision rules for the duration of breastfeeding with a view to maximizing infant growth. Breastfeeding has many well-recognized beneficial effects on health and development. However observational evidence has suggested that breastfeeding is associated with reduced infant growth, although the long-term consequences for stature and adiposity remain controversial. The Promotion of Breastfeeding Intervention Trial (PROBIT) recruited 17,046 women in which hospitals and their affiliated polyclinics in Belarus were randomized to a breastfeeding promotion intervention or to standard care. In this article, we propose Structural Mean Models and estimate their parameters using G-estimation to obtain unbiased estimates of the effect of continued breastfeeding on infant growth (weight or length) at one year of age. We also implement a modified version of the G-estimation algorithm that is asymptotically unbiased; this is the first real-data application of the algorithm. Finally, we compare the decision rules implied by the G-estimates with the decision implied by a myopic optimization estimation approach, that is, we compare with decision rules that maximize response in the short-term. The breastfeeding regimes selected by each of the three models are optimal in the sense that specific criteria were optimized; the criteria considered here (maximizing weight or length) were chosen for simplicity, but may not lead to better overall health. We demonstrate in the context of a breastfeeding promotion intervention trial that optimal myopic decision strategies do not coincide with strategies that optimize a longer-term response. Please see the online supplements for a correction to this article.