Optimizing decisions in prenatal screening for Down syndrome and capacity allocation in a school-based asthma care model
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This thesis consists of three decision making topics in two healthcare applications using operations research methodologies. The first application is prenatal screening for Down syndrome (DS) which is a common type of chromosomal abnormality. Prenatal screening for pregnant women, based on multiple serum and ultrasound markers, is non-invasive and used to assess the risk of having a DS baby. A woman with a risk higher than a predefined risk-cutoff value of prenatal screening, i.e., a positive screening result, typically undergoes an invasive diagnostic test, such as amniocentesis, as a follow-up procedure to confirm that her fetus is affected. The risk-cutoff value of DS prenatal screening plays an important role. On one hand, a lower risk-cutoff value elevates the risk of false positives, and on the other hand, a higher risk-cutoff value increases the risk of false negatives. In practice, a one-size-fits-all type of risk-cutoff value of 1 in 270 is usually used for prenatal-integrated screening for DS. The objective of this application is to determine the optimal risk-cutoff values from the individual and population's perspectives. The first topic focuses on the individual perspective. Women considering DS screening usually face two major adverse outcomes: undetected DS live births due to false negatives, and euploid procedure-related fetal losses due to false positives. Evidence shows that women perceive the two outcomes very differently. However, no guidelines exist for setting an appropriate risk-cutoff value based on women's different preferences. We capture the relative preferences using a ratio of weights (penalties), and formulate an optimization model to minimize the weighted sum of the two adverse pregnancy outcomes. The second topic is from the population's perspective. Although using an appropriate one-size-fits-all cutoff value can achieve a high overall detection rate, it usually also brings in undesirably high false positive rates in older ages. Therefore, we explicitly add an upper-bound constraint to every single age for fairness and maximize the overall detection rate with those constraints. The solution methodologies in this application combine the techniques of integer programming and Monte Carlo simulations. We find the preference-sensitive and age-specific risk-cutoff values have the potential to improve pregnancy outcomes and patient satisfaction. Our framework for DS prenatal screening can shed some lights on the optimal decisions in similar settings with a risk-cutoff value to designate positive or negative results. The second application focuses on a capacity allocation problem in a school-based asthma care model, which is faced by Children's Healthcare of Atlanta to improve the health outcomes of pediatric asthma patients within metro Atlanta. In particular, the objective is to maximize the effectiveness of a school-based asthma program by deciding dynamically: (i) which schools to visit, and (ii) if a school is visited, which group of patients in this school to schedule for a limited number of clinical appointment slots. For this purpose, we propose a finite-horizon dynamic programming model which combines a clinic disease model of childhood asthma with operational decisions. We formulate a mixed-integer programming (MIP) for solving this model and propose two computationally-efficient and competitive heuristic solutions based on this MIP formulation. We parameterize our proposed models using data of a local public school district (Atlanta Public Schools district) and quantify the percentages of capacity allocated between patients in the worst illness states (treatment-prioritized capacity allocation) and patients in the moderate illness states (prevention-prioritized centered capacity allocation). We establish the following findings: (1) as capacity increases and planning horizon extends, more patients will be able to end up in the best illness states, (2) our index-based heuristic consistently has a small gap compared to the optimal solution and it usually allocates more capacity to sickest patients, while the optimal solution usually has a smarter balance of allocating capacity between treating the sickest patients and preventing moderately sick patients from deteriorating, (3) capacity allocation are widely spread out among the public schools and driven by larger sizes of asthma patients who are sicker. We further quantify the value of these decisions, which may help decision-makers in daily operations.