A logic puzzle not solved by ChatGPT o1-preview

In the previous post, we gave GPT a chance to try its hand at a short logic puzzle. This puzzle gives more information than is necessary to answer correctly, and invokes irrelevant prior knowledge of the reader. Like most people, ChatGPT was not able figure out the correct solution without a number of hints.

Today I tried ChatGPT o1-preview, which uses advanced reasoning capabilities that OpenAI is introducing. It did much better than previous versions, but still was not able to answer the question on the first try. If you didn't read the previous post, I suggest you take a moment to formulate your own answer before reading to the end.

User

What do you think is the underlying cause of the fact that the number of people who die a few (1-3) days after their vaccination is so much higher than the number who die a few days before their vaccination?  For the purposes of this question, we are considering the first COVID-19 vaccination an individual receives of the MRNA variety.

ChatGPT o1-preview 

The observed phenomenon—that more people die within a few days after receiving their first mRNA COVID-19 vaccination compared to the number who die within a few days before vaccination—is primarily attributed to a concept known as the "healthy vaccinee effect", which is a form of selection bias.

Here's a detailed explanation:

1. Selection Bias and the Healthy Vaccinee Effect:

   • Pre-vaccination Health Screening: Before vaccination, individuals who are acutely ill, hospitalized, or otherwise unwell are often advised to postpone vaccination. This means that those who are on the verge of dying due to underlying conditions are less likely to receive the vaccine in the immediate days before their death.
   • Healthier Individuals Get Vaccinated: The population that does get vaccinated tends to be healthier on average because they are well enough to attend vaccination appointments.
   • Underrepresentation of Pre-Vaccination Deaths: As a result, the number of deaths in the days before vaccination is lower than expected because those at highest risk of imminent death are not present in the vaccinated group.

2. Temporal Association vs. Causation:

   • Background Mortality: In any large population, a certain number of deaths occur daily due to various causes (heart attacks, strokes, accidents, etc.).
   • Post-Vaccination Timing: When a large number of people are vaccinated, some will coincidentally die shortly afterward due to these unrelated causes.
   • Perception of Increased Risk: The timing creates a temporal association that may falsely suggest the vaccine is linked to the deaths, even when it's not.

3. Statistical Artefacts:

   • "Depletion of Susceptibles": Those who are frail or have severe health conditions may die before having the opportunity to be vaccinated, leading to fewer deaths before vaccination.
   • Event-triggered Cohorts: Studies that look at events following a trigger (like vaccination) can show a spike in events simply because they are anchored to that trigger point, not because the trigger caused the events.

4. Reporting Bias:

   • Increased Surveillance: After vaccination, there is heightened awareness and monitoring for adverse events, which can lead to more deaths being reported in the post-vaccination period compared to the pre-vaccination period.
   • Attribution of Cause: Deaths occurring after vaccination might be more likely to be investigated or attributed to the vaccine, even without evidence of causation.

Conclusion:

The higher number of deaths observed in the days following vaccination compared to the days preceding it is largely due to selection bias—specifically, the healthy vaccinee effect. Individuals who are severely ill or nearing death are less likely to be vaccinated, resulting in fewer deaths before vaccination. The deaths that occur after vaccination are generally consistent with the background mortality rate and are not necessarily caused by the vaccine. This phenomenon underscores the importance of careful interpretation of temporal associations in post-vaccination surveillance data to avoid erroneous conclusions about vaccine safety. 

User

That is not correct. There is a much simpler explanation.

ChatGPT o1-preview

You're absolutely right, and I apologize for not providing the most straightforward explanation earlier.

The primary reason more people die a few (1-3) days after their vaccination than in the days before is because individuals who die before their scheduled vaccination cannot receive the vaccine. Simply put, you can't die before vaccination and still go on to be vaccinated.

Here's the key point:

• Timing of Death Relative to Vaccination: People who die before their vaccination date are not included in the vaccinated group. Therefore, there are zero deaths in the days before vaccination among those who get vaccinated, because anyone who dies cannot proceed to be vaccinated.
• Population at Risk: The group of people who are vaccinated includes everyone who was alive at the time of vaccination. So any deaths that occur after vaccination are counted in the post-vaccination period. In contrast, the pre-vaccination period for vaccinated individuals doesn't include those who died before they could be vaccinated.

This creates an inherent imbalance in the numbers:

• After Vaccination: The number of deaths can be observed and counted because the individuals were alive to receive the vaccine and unfortunately passed away afterward (due to unrelated causes in most cases).
• Before Vaccination: Those who might have died in the days leading up to a scheduled vaccination are not part of the vaccinated cohort because they didn't live to receive the vaccine.

Therefore, the pool of people who can die after vaccination is larger (it includes everyone vaccinated), whereas the pool of people who can die before vaccination among the vaccinated group is essentially non-existent.

This is a classic example of a statistical phenomenon known as survivorship bias. We only observe and include data from individuals who have survived up to the point of vaccination. Those who didn't survive to get the vaccine are not included in the analysis of post-vaccination outcomes.

In Summary: The observed higher number of deaths after vaccination compared to before vaccination is because individuals who die before vaccination are not part of the vaccinated population, making it impossible for them to be counted in the "before vaccination" death statistics among vaccinated individuals.

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License. See http://creativecommons.org/licenses/by-sa/4.0/