Problem: Consider the following scenario in early 2020. William is a supermarket worker. He lives and works in a Sydney suburb where COVID-19 cases are increasing rapidly due to the current Delta variant outbreak. There has been a significant number of community transmitted infections in the suburb. William is concerned about the current COVID-19 situation, especially since he needs to work in the local supermarket five days a week.
William wants to get vaccinated sooner rather than later. He understands that while vaccination does not completely eliminate the risk for COVID-19 infection, it will help protect people by significantly reducing the chances of infection, hospitalization, and death. William hears that the effectiveness of the different brands of vaccines is similar-recent statistics show that fully vaccinated people (with any brand of vaccine for COVID-19,e.g.,AstraZeneca,Pfizerand Moderna)only have 1/8 chances to have an infection and 1/25 chances to die from COVID-19 infection compared to those who are unvaccinated.
However, William hears that different brands of vaccines may have different side effects (or adverse effects).William does not worry about mild adverse effects (e.g., redness or swelling at the injection site, headaches, and fever).He is only concerned about the very rare but serious risks that could lead to death.
As Australia currently has a very low vaccination rate, William searches for COVID-19 vaccine side effects statistics in other countries where more doses of COVID-19 vaccines have been administered. William notices that the European Medicines Agency (EMA)'s safety committee reported in April that unusual blood clots should be listed as a very rare side effect of the AstraZeneca vaccine for COVID-19. The committee found 18 fatal cases reported in Europe, where around 25 million people had received the AstraZeneca vaccine. The EMA's analysis also found that the Moderna vaccine for COVID-19 could also have some extremely rare but serious adverse effects (e.q.. myocarditis and pericarditis) that could lead to death. Five deaths were reported out of 20 million people who received the Moderna vaccine
Based on these statistics, William prefers the Moderna vaccine to the AstraZeneca vaccine (note: he is not eligible to receive the Pfizer vaccine). However, while the AstraZeneca vaccine is currently available in Australia, the first 1 million doses of the Moderna vaccine are not currently available and are expected to arrive in Australia next month
The current COVID-19 situation in William's suburb is rapidly deteriorating. William believes that if he waited for a month for the Moderna vaccine, there would be a 2% chance that he would get infected with COVID-19 before he gets vaccinated (given the nature of his supermarket job). William's family doctor advises him that the risk of death for people in his age group after contracting COVID-19 is around 1%.
William's objective is to minimize the likelihood of death. William wants to know if he should get the AstraZeneca vaccine today or wait for the Moderna vaccine. [Assumption: A person only needs to receive one shot to get fully vaccinated if William got infected while waiting for the Moderna vaccine, he would not be eligible to receive the vaccine.
Based on these statistics, William prefers the Moderna vaccine to the AstraZeneca vaccine (note: he is not eligible to receive the Pfizer vaccine). However, while the AstraZeneca vaccine is currently available in Australia, the first 1 million doses of the Moderna vaccine are not currently available and are expected to arrive in Australia next month
The current COVID-19 situation in William's suburb is rapidly deteriorating. William believes that if he waited for a month for the Moderna vaccine, there would be a 2% chance that he would get infected with COVID-19 before he gets vaccinated (given the nature of his supermarket job).William's family doctor advises him that the risk of death for people in his age group after contracting COVID-19 is around 1%.
William's objective is to minimize the likelihood of death. William wants to know if he should get the AstraZeneca vaccine today or wait for the Moderna vaccine. [Assumption: A person only needs to receive one shot to get fully vaccinated. If William got infected while waiting for the Moderna vaccine, he would not be eligible to receive the vaccine.]
a) Develop a decision tree for William showing full details. Assumptions need to be stated clearly. Show your workings (e.g., include a Chance Table and Consequence Table), which allow the marker to award you partial marks appropriately.
b) Solve the decision tree by folding back the tree. Clearly show your calculations. Describe in words the optimal decision strategy.
c) Do you think William's decision model in a) is a requisite decision model? What other decision elements would you consider if you were William? Discuss.