COVID-19 Vaccine Response - III
In the third part, we demonstrate how to refine a model to include more priors and posteriors. We keep enriching the model (from part 1 and 2) by adding more nodes and building a practical case study. We show that prior information on demographics, age, job category or risk level can impact the chances of getting infected and eventually result in more cases. We also add posterior nodes on the severity and contagiousness of an infected person based on these priors and review how these eventually affect the overall cost of care. This simple yet informative scenario can be used by public health policymakers or healthcare insurance to establish the best vaccination strategies. We explore three vaccination strategies and evaluate their respective impact. This is the third of a three parts demo.
Let´s now see how we can expand this model with other hypothesis. We can for example add a prior to exposure based on job category and say that you have three job categories: Home, Office or frontline worker and that impacts your exposure to the virus so you can create a link between job category and exposed. Now you see that the exposed node was updated and you can update the marginal probabilities based on Home, Office or frontline. We can also have a posterior node on the severity and will have now a different type of node called a “discrete node” that will follow a discrete distribution: a simple binomial in the case of not getting the virus or Poisson law with four possible outcome in the case where you catch the virus and the level of severity goes from zero for not being exposed to four for death.
We can now set the “got covid” node to “true” and sample… and we´ll see how the severities go from one to four with one being the most probable obviously and 4 the least probable. And if we set the “got covid” node to “false” as we saw the only severity that we should get is 0 which is the lowest level of severity or not being affected
We can add a prior link between job category and being vaccinated or not in order to guide the policy maker on who should get vaccinated and what their priority should be. if we rearrange the node and add a note for “risk factor” based on comorbidities we´ll see that in this case we have a discrete node as well with three possible outcomes. We limit the number of risk factors to three and we have a Poisson law the same way as before. And we can add for the sake of it age in three categories, low mid high. And we´ll see that age impacts your job category, obviously the fact that you´re vaccinated, but also the amount of people that you can infect. You now have a “contagion” node which is of different nature. This node is a mixture of continuous distribution and that´s why it´s represented with a dashed circle. Based on whether you´re infected or not it will call upon different distribution laws. If you´re not infected obviously you´re not contagious and if you´re infected you can be contagious at different level depending on your job category or your age. Based on this contagion and severity number we can compute a cost for health insurers which ranges from zero to $50,000 based on numbers that we have collected over various reports. We now can test different scenarios of vaccination.
If we have limited vaccines (say enough for 1/3 of the population) and vaccinate everybody with equal probability, what will be the various distribution of covid numbers, contagions, severity, and eventually cost? We obviously made assumptions. Some of them have been picked based on data collected over the internet, other are simple guesses. You can start a model with very basic information and refine it. In this instance, the most likely costs range between 30 and $40,000
we can save the values of this sample for further analysis as we will see later. A CSV file is generated with all samples (10,000 rows) and one column per node where names appear on the top
We can now test a different policy of vaccination. One where we would only vaccinate senior people so people falling in the high age category. If we did this and vaccinated no one but the seniors as you see on the table on the right only the high age group are vaccinated… we can re sample and save that value for further analysis
We now are interested in a different policy where we vaccinate mostly people who are going to be exposed: frontline workers and people in the mid age category who are going to work in the office and we do not vaccinate people who are more likely to stay at home we run a sample …again and save those results for further analysis
Once computed, we represent the distributions of the cost node along with key metrics for the various scenarios that we have computed. On the top left in blue is our baseline case or people randomly selected for vaccination. We see that leads to an average cost for health care of about $46,000. On the top right in orange is the case where we vaccinate seniors as a priority and according to our model it leads to very similar outcome as the first scenario in terms of healthcare cost. On the bottom left in green is the cost distribution for the scenario where we vaccinate people who are the most exposed. It displays a significant drop in healthcare costs down to $37,000 (So about $10,000 less). For better comparison of the risk profiles, we show on the bottom right the comparison of the cumulative distribution function.
Let´s now see how we can expand this model with other hypothesis. We can for example add a prior to exposure based on job category and say that you have three job categories: Home, Office or frontline worker and that impacts your exposure to the virus so you can create a link between job category and exposed. Now you see that the exposed node was updated and you can update the marginal probabilities based on Home, Office or frontline. We can also have a posterior node on the severity and will have now a different type of node called a “discrete node” that will follow a discrete distribution: a simple binomial in the case of not getting the virus or Poisson law with four possible outcome in the case where you catch the virus and the level of severity goes from zero for not being exposed to four for death.
We can now set the “got covid” node to “true” and sample… and we´ll see how the severities go from one to four with one being the most probable obviously and 4 the least probable. And if we set the “got covid” node to “false” as we saw the only severity that we should get is 0 which is the lowest level of severity or not being affected
We can add a prior link between job category and being vaccinated or not in order to guide the policy maker on who should get vaccinated and what their priority should be. if we rearrange the node and add a note for “risk factor” based on comorbidities we´ll see that in this case we have a discrete node as well with three possible outcomes. We limit the number of risk factors to three and we have a Poisson law the same way as before. And we can add for the sake of it age in three categories, low mid high. And we´ll see that age impacts your job category, obviously the fact that you´re vaccinated, but also the amount of people that you can infect. You now have a “contagion” node which is of different nature. This node is a mixture of continuous distribution and that´s why it´s represented with a dashed circle. Based on whether you´re infected or not it will call upon different distribution laws. If you´re not infected obviously you´re not contagious and if you´re infected you can be contagious at different level depending on your job category or your age. Based on this contagion and severity number we can compute a cost for health insurers which ranges from zero to $50,000 based on numbers that we have collected over various reports. We now can test different scenarios of vaccination.
If we have limited vaccines (say enough for 1/3 of the population) and vaccinate everybody with equal probability, what will be the various distribution of covid numbers, contagions, severity, and eventually cost? We obviously made assumptions. Some of them have been picked based on data collected over the internet, other are simple guesses. You can start a model with very basic information and refine it. In this instance, the most likely costs range between 30 and $40,000
we can save the values of this sample for further analysis as we will see later. A CSV file is generated with all samples (10,000 rows) and one column per node where names appear on the top
We can now test a different policy of vaccination. One where we would only vaccinate senior people so people falling in the high age category. If we did this and vaccinated no one but the seniors as you see on the table on the right only the high age group are vaccinated… we can re sample and save that value for further analysis
We now are interested in a different policy where we vaccinate mostly people who are going to be exposed: frontline workers and people in the mid age category who are going to work in the office and we do not vaccinate people who are more likely to stay at home we run a sample …again and save those results for further analysis
Once computed, we represent the distributions of the cost node along with key metrics for the various scenarios that we have computed. On the top left in blue is our baseline case or people randomly selected for vaccination. We see that leads to an average cost for health care of about $46,000. On the top right in orange is the case where we vaccinate seniors as a priority and according to our model it leads to very similar outcome as the first scenario in terms of healthcare cost. On the bottom left in green is the cost distribution for the scenario where we vaccinate people who are the most exposed. It displays a significant drop in healthcare costs down to $37,000 (So about $10,000 less). For better comparison of the risk profiles, we show on the bottom right the comparison of the cumulative distribution function.
Up Next:
