The Optimal Control of Child Delivery for Women with Hypertensive Disorders of Pregnancy

Hypertensive disorders of pregnancy (HDP) affect up to 5%-15% of pregnancies around the globe, and form a leading cause of maternal and neonatal morbidity and mortality. HDP are progressive disorders for which the only cure is to deliver the baby. An increasing trend in the prevalence of HDP has been observed in the recent years. This trend is anticipated to continue due to the rise in the prevalence of diseases that strongly influence hypertension such as obesity and metabolic syndrome. In order to lessen the adverse outcomes due to HDP, we need to study (1) the natural progression of HDP, (2) the risks of adverse outcomes associated with these disorders, and (3) the optimal timing of delivery for women with HDP.

In the first study, the natural progression of HDP in the third trimester of pregnancy is modeled with a discrete-time Markov chain (DTMC). The transition probabilities of the DTMC are estimated using clinical data with an order restricted inference model that maximizes the likelihood function subject to a set of order restrictions between the transition probabilities. The results provide useful insights on the progression of HDP, and the estimated transition probabilities are used to parametrize the decision models in the third study.

In the second study, the risks of maternal and neonatal adverse outcomes for women with HDP are quantified with a composite measure of childbirth morbidity, and the estimated risks are compared with respect to type of HDP at delivery, gestational age at delivery, and type of delivery in a retrospective cohort study. Furthermore, the safety of child delivery with respect to the same variables is assessed with a provider survey and technique for order performance by similarity to ideal solution (TOPSIS). The methods and results of this study are used to parametrize the decision models in the third study.

In the third study, the decision problem of timing of delivery for women with HDP is formulated as a discrete-time Markov decision process (MDP) model that minimizes the risks of maternal and neonatal adverse outcomes. We additionally formulate a robust MDP model that gives the worst-case optimal policy when transition probabilities are allowed to vary within their confidence intervals. The results of the decision models are assessed within a probabilistic sensitivity analysis (PSA) that considers the uncertainty in the estimated risk values. In our PSA, the performance of candidate delivery policies is evaluated using a large number of problem instances that are constructed according to the orders between model parameters to incorporate physicians' intuition.