Thesis title: Discrete Optimization and Statistical Analysis for Healthcare Applications

Advisor: Pinar Keskinocak, School of Industrial and Systems Engineering, Georgia Tech

Committee members:

Dima Nazzal, School of Industrial and Systems Engineering, Georgia Tech

Matthew C Freeman, School of Public Health, Emory University

Nicoleta Serban, School of Industrial and Systems Engineering, Georgia Tech

David Goldsman, School of Industrial and Systems Engineering, Georgia Tech

Date and time: Monday, December 13th, 2021, at 9:45 AM (EST)

Location: Groseclose 402 or attendee link: https://primetime.bluejeans.com/a2m/live-event/uwxeuugb

Abstract:

Operations Research has been continuously extending into new applications to optimize and explain reality through a methodological and analytical perspective. Healthcare systems are no exception, as they require operational solutions to traditional problems such as scheduling, routing, inventory management, process management, and statistical analysis.

This thesis focuses on two main healthcare applications: patient scheduling problems to treat as many patients as possible while minimizing overtime; and studying factors associated with the success of childhood immunization systems in low- and lower-middle-income countries. Chapter 1 gives an overview of both applications, highlighting the main contributions of this thesis.

In Chapter 2, we study the Multiple Knapsack Problem with Grouped Items inspired by a patient scheduling problem where patients may require multiple therapy sessions during their treatment. The studied problem is NP-hard with no polynomial-time approximation scheme. We relaxed the capacity constraints to work with the Bi-Criteria Multiple Knapsack Problem with Grouped items to design pseudo-polynomial-time approximation algorithms and heuristics that generate good solutions in short computation time. We proved tight approximation guarantees of our approximation algorithms and tested them in an extensive computation experiment of 3000 instances. In 99% of instances, our approximation algorithms ran in less than 19 seconds and exceeded knapsack capacities by at most 16%. Our heuristics obtained capacity-feasible solutions in 95% of instances in less than a minute, and the worst reward received was 21% below the optimal.

Chapter 3 studies economic and financial changes associated with childhood immunization improvements in low-income countries from years 2000 to 2018. We identified financial indicators that were statistically significant predictors of vaccination coverage through cross-country regression models. Government health spending per capita and government health spending per birth on routine immunization were significant positive predictors of vaccination coverage. We compared—through mixed-effects models—the financial trends of two groups of countries: low-income countries with outstanding vaccination coverage (over 90% coverage on the third dose of the diphtheria-tetanus-pertussis vaccine), and other low-income countries with lower coverage. Outstanding low-income countries increased their government health spending per capita by US$0.30 a year, while the other low-income countries decreased by US$0.16 a year. Overall, vaccination coverage success was associated with increasing government health spending, particularly on routine immunization vaccines.

Chapter 4 determines the extent to which childhood immunization is strongly associated with family planning access & education, reproductive & child healthcare access, and woman education & empowerment in Nepal, Senegal, and Zambia. We used ordinal logistic regression models to test strong associations and used bootstrapping methods combined with optimal propensity scores matching to compare children with few or no vaccines with similar fully-vaccinated children. Mothers of fully-vaccinated children were 17–30% more likely than mothers of children with few vaccines to have accessed a health facility at least once in the last year, knew on average 0.7–1.6 more contraceptive methods, and had 12–23% higher literacy rates. Our results suggest that children with few vaccines and their mothers are behind in access to family planning, healthcare, and education; integrated efforts could improve these vulnerabilities altogether.

Lastly, Chapter 5 focuses on a cross-country analysis of low- and lower-middle-income countries to determine country-level risks that are relevant and good predictors of success in childhood immunization systems. We used a combination of statistical and machine learning techniques, using multivariate mixed-effects regression models to determine strongly associated factors while using data imputation and feature importance methods to rank relevant risk variables by importance. Access to healthcare, human conflicts & uprooted people, gender inequality, and governance are relevant factors to consider when improving vaccination systems worldwide. Sanitation, zoonose exposure, and malnutrition in children under 5 were good predictors of vaccine coverage—as children with few vaccinations share similar vulnerabilities. This chapter aims to facilitate future analysis so researchers can study childhood vaccinations and their relationship with other country risks.