Liver transplantation is an efficient therapy for patients who have severe liver diseases, and the most common resources of transplanted livers are from deceased donor. Currently the demand for livers is far beyond supply, leading to a pressing shortage in organ resources, an indispensable organ allocation system was subsequently proposed and is now performing the task of organ procurement and allocation by United Network for Organ Sharing (UNOS) via Organ Procurement and Transplantation Network (OPTN).

The allocation system is continuously updated and improved, but there are more space for nowadays researchers to promote a considerably reasonable organ allocation system to achieve a better objective.

In this thesis, we explored the efficiency, equality and utility issues existing in the U.S. liver allocation system. We concentrated on efficiently and equally allocating livers to every subgroups based on disease types, sex and height specifically. In addition, we developed a liver allocation simulation system implemented by the Java programming language which could accurately predict patient disease progression and patient outcomes under certain allocation policy. Lastly, we constructed a fluid model of the liver allocation problem with the objective of maximizing total transplant benefit.

Firstly, we developed the REACH score, which is a priority score based on patients’ medical urgency, in accordance with the principles of organ allocation.We conducted a logistic regression analysis by predicting patient waitlist survival risk by our proposed factors, and derived the score expressed by the proposed covariates. Results indicate that REACH score is an significant index of waitlist survival risk and performs similarly as current MELD allocation score in terms of c-statistic. The REACH score can also provide important information when counseling HCC candidates and families about the expected risk of remaining on the waitlist and the risk of death post-transplant.

In addition, we explored the liver transplant disparity existing between sex and height groups. We identified the LT disparity by observed historical data and proposed several exception score schemes based on the volume of LT disparity. We validated our proposed policies by the authoritative simulation system - Liver Simulated Allocation Model (LSAM). Results suggest that 1- 2 MELD points to the shortest 8\% of liver transplant candidates would improve waitlist outcomes for females with minimal impact on males.

Furthermore, we developed a new liver allocation system (LAS) with consummate modules of patient generator module, liver generator module, patient status update module, ranking algorithm module, offer acceptance module, and patients outcome recorder. Under the collaboration of all modules, we were able to project congruous outcomes with observed data during the same period on the performance of number of transplants, number of death, proportions of transplants and MELD score at transplant. The model includes adequate details to estimate the effects of a wide range of questions regarding liver allocation and policy change.

Lastly, we consider the problem of maximizing the transplant benefit of liver transplants through the redesign of liver allocation priorities. We constructed a fluid model and designed an order of allocation to the disease states based on the marginal gained transplant benefit for the state. Our model provides a theoretical cornerstone for transplant benefit-based liver allocation systems and some interesting results and structural insights are revealed. We provide a choice and consultation to policymakers of potential allocation systems.