Due to the surge in COVID-19 cases, hospitals have had to receive many more patients than before, which has brought unprecedented pressure to the hospital system. Therefore, the emphasis of medical decision-making has shifted from reaching the best treatment effect to prioritizing the treatment of COVID-19 patients by hospitals, which is key to relieving the pressure on the hospital system and reducing the overall mortality rate of COVID-19. There is no doubt that establishing the prioritization of COVID-19 cases is fundamental and pivotal for hospitals to achieve the shift in medical decision-making. Prioritization of COVID-19 cases in previous studies was mostly based on one patient characteristic, mainly including age, health conditions, and gender. This paper focuses on two patient characteristics at the same time. The probability that a COVID-19 patient who died had a given health condition in a given age group is calculated using the matrix completion technique based on the high-rank assumption of Bayesian matrices and the properties of Markov matrices. The calculated results show that doctors should give patients over 55 with respiratory diseases, patients over 65 with circulatory diseases, and patients over 65 with diabetes a higher prioritization in COVID-19 treatment.