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This paper proposes a Bayesian hierarchical model to characterize therelationship between birth weight and maternal pre-eclampsia across gestationat a large maternity hospital in urban Uganda. Key scientific questions weinvestigate include: 1) how pre-eclampsia compares to other maternal-fetalcovariates as a predictor of birth weight; and 2) whether the impact ofpre-eclampsia on birthweight varies across gestation. Our model addressesseveral key statistical challenges: it correctly encodes the prior medicalknowledge that birth weight should vary smoothly and monotonically withgestational age, yet it also avoids assumptions about functional form alongwith assumptions about how birth weight varies with other covariates. Our modelalso accounts for the fact that a high proportion (83%) of birth weights in ourdata set are rounded to the nearest 100 grams. Such extreme data coarsening israre in maternity hospitals in high resource obstetrics settings but common fordata sets collected in low and middle-income countries (LMICs); this introducesa substantial extra layer of uncertainty into the problem and is a major reasonwhy we adopt a Bayesian approach.  Our proposed non-parametric regression model, which we call Projective SmoothBART (psBART), builds upon the highly successful Bayesian Additive RegressionTree (BART) framework. This model captures complex nonlinear relationships andinteractions, induces smoothness and monotonicity in a single target covariate,and provides a full posterior for uncertainty quantification. The results ofour analysis show that pre-eclampsia is a dominant predictor of birth weight inthis urban Ugandan setting, and therefore an important risk factor forperinatal mortality.

Monotone function estimation in the presence of extreme data coarsening: Analysis of preeclampsia and birth weight in urban Uganda