Manipulating a Continuous Instrumental Variable in an Observational Study of Premature Babies: Algorithm, Partial Identification Bounds, and Inference under Randomization and Biased Randomization Assumptions

Regionalization of intensive care for premature babies refers to a triage system of mothers with high-risk pregnancies to hospitals of varied capabilities based on risks faced by infants. Due to the limited capacity of high-level hospitals, which are equipped with advanced expertise to provide critical care, understanding the effect of delivering premature babies at such hospitals on infant mortality for different subgroups of high-risk mothers could facilitate the design of an efficient perinatal regionalization system. Towards answering this question, Baiocchi et al. (2010) proposed to strengthen an excess-travel-time-based, continuous instrumental variable (IV) in an IV-based, matched-pair design by switching focus to a smaller cohort amenable to being paired with a larger separation in the IV dose. Three elements changed with the strengthened IV: the study cohort, compliance rate and latent complier subgroup. Here, we introduce a non-bipartite, template matching algorithm that embeds data into a target, pair-randomized encouragement trial which maintains fidelity to the original study cohort while strengthening the IV. We then study randomization-based and IV-dependent, biased-randomization-based inference of partial identification bounds for the sample average treatment effect (SATE) in an IV-based matched pair design, which deviates from the usual effect ratio estimand in that the SATE is agnostic to the IV and who is matched to whom, although a strengthened IV design could narrow the partial identification bounds. Based on our proposed strengthened-IV design, we found that delivering at a high-level NICU reduced preterm babies' mortality rate compared to a low-level NICU for $81,766 \times 2 = 163,532$ mothers and their preterm babies and the effect appeared to be minimal among non-black, low-risk mothers.