Stats please help - trials - effectiveness of vaccine

[mids2019]

If 50% of a trial group is given a vaccine and 50% a placebo and if the vaccine is ineffectual we would expect for a group contracting COVID 50% to have had the vaccine and 50% the placebo. We would not say the vaccine is 50% effective.

Can someone do the stats for a trial where 90% of the group had taken the placebo. How does this translate into the chance of an individual getting COVID ?

I reckon around 80%

I don't understand the question you're asking? Why would there be a trial where 90% of participants have had the placebo?

Woops... I meant 90% of the group that finally contracted COVID had taken the placebo

I still don't understand. Is this a way of trying to discredit the vaccine trials?

I suspect it’s significantly* more complicated than that.

(Stats joke)

If 50% of a trial group is given a vaccine and 50% a placebo and if the vaccine is ineffectual we would expect for a group contracting COVID 50% to have had the vaccine and 50% the placebo. We would not say the vaccine is 50% effective.

Well no, if it's ineffective we'd say it's 0% effective. What are you asking OP? The 90% effective will be based on the group that had the vaccine, not the placebo.

It was effective in protecting 9/10 people who were given the vaccine from contracting the virus

93 people among the 44,000 got symptomatic COVID.

85 of them were in the placebo group.
8 of them were in the group that got 2 doses of the vaccine.

85/93 is just above 90%.

Make sense?

Medschoolrat

I suppose the point is how we describe effectiveness.

If 46 people had been from the placebo group and 47 from the vaccine group then we would say that the vaccine hadn't a significant effect (assuming an equal number of people given the placebo and vaccine) as on average we would expect the same number from each group to contract the virus in this instance. We wouldn't say the effectiveness of the virus was 50%.

So if we are talking about the percentage of vaccinated people that would contract COVID compared to the same group without the vaccine it would be around 20% I.e. 80% effective.

I think we would say 50% effective in this case OP. You're just as likely to get the virus with the vaccine as not. 50/50 chance

50% effective would of course mean no point in having the vaccine

Why do you think that? Not being sarcastic- genuinely, do you have some expertise in the area? Because I’d have thought if taking the vaccine made no difference that would be 0% effective.

I don't think it would be reported as 50% effective. That would be meaningless and confusing. But by using the logic the OP has described, and using the same route to get to the effectiveness, OP is correct.

Right, but the OP is calculating efficacy in a crazy way.

I think we would say 50% effective in this case OP. You're just as likely to get the virus with the vaccine as not. 50/50 chance

It wouldn't be reported like that. A vaccine that offered 50% protection would mean that in the population that had been vaccinated, there were only half the cases you would expect.

So if cases were roughly even between the two groups, then the vaccine would be 0% effective, because the difference between the vaccine and the placebo was 0

@HipTightOnions

If of everyone contracting Covid, 50% had vaccine and 50% had placebo, then the number in the control group is 0% lower than the number in the vaccine group so efficiency is 0%. For efficiency to be 90% I’d expect the number of people who contracted Covid after having the placebo to be 90% lower than the number of people who had the vaccine. This is how I understand it.