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My question is related to Covid-19 specifically, but it can be generalized to any infectious disease. I am asking this since I am reading a lot of information on several Social Media regarding one specific vaccine which is widely used in my home country.

Suppose 4 weeks ago a country decides to go into lockdown; suppose also that at the same time the same country starts vaccinating the citizens with a vaccine. If now (4 weeks later), we see a drastic reduction of positive cases and hospitalizations, how can we attribute that to the effectiveness of the vaccine or the obvious effects of a lockdown? Is it even possible?

wrong_path
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    It depends on many factors. You have to know the population spread of the virus before the lockdown, in combination with that you have to know how efficient is the countries monitoring of the virus, i.e. the amount of COVID test conducting are such in order to tell you something about the population virus spread. Also, you have to know the strictness of the lockdown in oder to be able to measure the movement of individuals that can spread the virus. So, you can know what helped to the reduction of COVID cases if you have the whole information, or at least some sufficient information – Fiodor1234 May 13 '21 at 11:54
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    If you can know whether the cases occurred in vaccinated individuals or in unvaccinated individuals this is a good starting point. You could look at the changes in case rates between the two groups. – Dan Phillips May 13 '21 at 12:06
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    The best way to do this is to measure case rates among those who have been vaccinated and those not: the first rate might reduce due to lockdown and vaccinations, the second just due to lockdown. If that information is not available, then a proxy might be to note vaccinations often started in older age-groups, and different age groups may have had different changes in case rates, with vaccinations contributing to this. – Henry May 13 '21 at 13:43

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If two interventions are rolled out concurrently with no control condition, I can't see how you could dissect the effect of each on a distal outcome. There might be subtle ways of teasing this out if the two interventions had regional differences in extent or speed of rollout or compliance. Or if you could link local or temporal differences in the outcome to differences in the modes of action of these two interventions.

Which brings us to your overall question - can you distinguish these two interventions in general. So some extent we would expect to be able to. A lockdown decreases the number of contacts each person has, and therefore that any new case will have. A drop in close contacts should be a mediator of the effect of restrictions on movement. Vaccines might actually be associated with an increase in contacts, but their mode of action is (depending on the vaccine I suppose) to reduce infectivity, and thereby reduce transmissions. If a vaccine is affecting incidence, we should observe a lower proportion of close contacts who then test positive.

R Segurado
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The first question that needs to be asked is: have you been able to detect any impact from lockdowns before vaccines were ever even rolled out? I have come across ~30 odd published papers/journals that have concluded that lockdowns do not have any positive impact in delivering any reduction in number of deaths due to the virus, number of hospitalisations, number of infections etc. What I have observed in official government data (depending on which country we're referring to) is the strategic implementation of lockdowns whenever the curves were already naturally dropping down again and subsequently using those observed reductions in the numbers as a means of justifying the lockdowns.

I am going to guess that we also won't be able to detect any major difference in the number of overall deaths due to the rollout of the vaccine. The vaccines might be effective, but since the people who are prone to dying from COVID are also very prone to dying from any other infection and/or natural causes, this claim can be backed up by looking at the QALYs lost for those who died from COVID. The average age of death for COVID deaths are in almost all instances approximately 1 year above that of the country's life expectancy.

Rstew
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