If we got close to a base rate of 50% we are in a very different situation of emergency. Right now NYC is closing schools on a positivity rate of 3% *among those tested*. Unless the bias for tasting is that people with infections are less likely to get tested 50% is very far away. Of course I keep thinking about the fact that the plague kill 25% of the population of Europe over a number of years. The death rate from COVID in North Dakota is 1/1000 and still going up and that’s just a few months.

]]>People over 80 were excluded from the initial study for Pfizer at least, but just like after the initial period with the first group they were allowed to expand to a minimum age of 12, if the data continue to look good they will probably be allowed to expand to older people.

]]>Oh, wow!

Now, there is probably a baseline level of health required to participate in these trials — and I was thinking more of people 85+ in assisted living when I said “very oldest/least healthy” — but that is still *incredibly* good/promising.

]]>Moderna: “Under the assumption of proportional hazards over time and with 1:1 randomization of mRNA-1273 and placebo, a total of 151 COVID-19 cases will provide 90% power to detect a 60% reduction in hazard rate (60% VE), rejecting the null hypothesis H0: VE ≤ 30%, with 2 IAs at 35% and 70% of the target total number of cases using a 1-sided O’Brien-Fleming boundary for efficacy and a log-rank test statistic with a 1-sided false positive error rate of 0.025.”

Pfizer: “Under the assumption of a true VE rate of ≥60%, after the second dose of investigational product, a target of 164 primary-endpoint cases of confirmed COVID-19 due to SARS-CoV-2 occurring at least 7 days following the second dose of the primary series of the candidate vaccine will be sufficient to provide 90% power to conclude true VE >30% with high probability.”

Janssen: “The study TNE is determined using the following assumptions: a VE for molecularly confirmed, moderate to severe/critical SARS-CoV-2 infection of 60%, approximately 90% power to reject a null hypothesis of H0: VE≤30%, type 1 error rate α = 2.5% to evaluate VE of the vaccine regimen (employing the sequential probability ratio test [SPRT] to perform a fully sequential design analysis; detailed in Section 9.5.1), a randomization ratio of 1:1 for active versus placebo. (…) Under the assumptions above, the total TNE to compare the active vaccine versus placebo equals 154, based on events in the active vaccination and placebo group, according to the primary endpoint case definition of moderate to severe/critical COVID-19 (Section 8.1.3.1).”

AstraZeneca: “Approximately 33 000 participants will be screened such that approximately 30 000 participants will be randomized in a 2:1 ratio to receive 2 IM doses of either 5 × 1010 vp (nominal, ± 1.5 × 1010 vp) AZD1222 (the active group, n = approximately 20 000) or saline placebo (the control group, n = approximately 10 000) 4 weeks apart, on Days 1 and 29. The sample size calculations are based on the primary efficacy endpoint and were derived following a modified Poisson regression approach (Zou 2004). (…) For the primary efficacy analysis, approximately 150 events meeting the primary efficacy endpoint definition within the population of participants who are not seropositive at baseline are required across the active and control groups to detect a VE of 60% with > 90% power. These calculations assume an observed attack rate of approximately 0.8% and are based on a 2-sided test, where the lower bound of the 2-sided 95.10% CI for VE is required to be greater than 30% with an observed point estimate of at least 50%.”

AstraZeneca is the only one who mentions the attack rate (percentage of an at-risk population that contracts the disease during a specified time interval). It’s not really used to determine that 150 cases are required, it provides the link between the 150 cases to the 30000 participants.

]]>Carlos: “If you decide you need 200 cases to look at the split vaccine/placebo and be happy with the inference you make…”

But how do they decide they need 200 [or whatever the real number is] cases?

]]>>>What matters is having few/weak antibodies to the spike protein.

For what it’s worth, this may be true in mice for SARS, but not carry over to COVID-19

https://blogs.sciencemag.org/pipeline/archives/2020/11/18/vaccine-possibilities

“one figure to take home is that 90% of the subjects were still seropositive for neutralizing antibodies at the 6 to 8 month time points. The authors point out that in primate studies, even low titers (>1:20) of such neutralizing antibodies were still largely protective, so if humans work similarly, that’s a good sign. An even better sign, though, are the numbers for memory B cells”

If low titers are still protective, the problem may not exist for this disease.

]]>Look, I’m not claiming any special expertise (which I don’t have). But none of those studies that you are quoting really seem to answer the question I was asking: two of them are not in vivo, and the in vivo one may not really demonstrate ADE.

]]>Then what is your explanation for why it hasn’t been done? COVID vaccine efforts are too widespread/decentralized for it to be plausible that everyone is making the same “obvious” mistake.

As for the polio vaccine, I really don’t think problems that happened in *the 1950s* have any relevance. Biological understanding in the 50s was pitifully limited, DNA was just being figured out. That would be like comparing safety of modern aircraft to World War I-era ones.

If ADE was likely to be a real problem with COVID, we’d see a lot more trouble with natural reinfection than we do.

]]>Many thanks!

]]>rstan::extract() and arm::invlogit()

]]>https://www.google.com/amp/s/www.bbc.com/news/amp/health-54986208

]]>I read today that the efficacy was 94% for people over 65.

]]>Are you aware of what happened last time hysteria caused a rushed vaccine?

It was only stopped when one of the main proponents publicly vaccinated his grandchildren, one died and the other was paralyzed:

https://www.nytimes.com/1955/05/05/archives/bulbar-polio-kills-doctors-grandson.html

Will the politicians, bill gates, and pharma executives/scientists publicly vaccinate their at risk relatives?

]]>Yes, it only quotes one of the many in vivo studies.

]]>It seems to me to be pretty likely that that’s not been done because it in fact would not be relevant/useful.

It was always considered relevant/useful before covid. And doesnt cost much to do the study given the money being thrown around.

]]>It’s even less useful than that, since the proportion of infected people in a vaccine trial is unlikely to be comparable to the entire population — people who sign up for vaccine trials will be those who take COVID seriously.

]]>So would they still need 151 since the efficacy seems much higher than 60%?

If the efficacy is really 90%+, then you could rule out the “below 50%” that would prevent FDA approval with smaller sample size, couldn’t you?

]]>Press releases aren’t necessarily peer reviewed…

]]>It seems to me to be pretty likely that that’s not been done because it in fact would not be relevant/useful.

Otherwise one would have to assume that many research groups in many different countries are all making the exact same errors.

IE – if this is obvious to you, why isn’t it obvious to them?

I complain a lot about US drug development/approval issues, but those are fairly specific to the way the FDA does things – a single nation with a specific regulatory structure that creates incentives (not always positive ones). In this case many nations with different structures are involved.

]]>Am I reading something wrong? The first and third of those *do* seem to be in vitro (cell line) studies.

The second one is in mice, granted, but I am not sure “the vaccine failed to protect aged animals in which augmented immune pathology was also observed, indicating the possibility of the animals being harmed because of the vaccination” is equivalent to “antibody-dependent enhancement did in fact happen”, much less that it would happen in humans.

]]>Thanks for sharing! Out of curiosity, which package houses the extract() function you’re using here? I couldn’t seem to get it to work loading just rstanarm.

]]>Yeah I wasn’t really clear what the “time base” parameter is supposed to do. I guess it only matters if the two measurements are measured differently?

]]>You guys are right. I just realized I got the direction flipped.

]]>I don’t follow you. Forget the interim analysis. If you decide you need 200 cases to look at the split vaccine/placebo and be happy with the inference you make about the vaccine efficiency, why does it matter whether you get those 200 cases in six weeks or six months [1]? Why would you require more cases if 200 are enough? It’s also possible that I have misundestood your previous comment entirely.

[1] Apart from the insight you may get about duration.

]]>In the design phase, how do they come up with N total cases? Is that a function of the assumed baseline case rate?

]]>Isn’t the design just “go until we get N total cases across both arms”… in which case the base rate is just to estimate how many people are needed to get N cases in a reasonable time?

I think this is the same thing Carlos said, so obviously I’m not following. If you could elaborate a little I’d appreciate.

]]>In classical design (no interim analysis), the closer the base rate is to 50%, the higher the required sample size – so when multiplied by a higher base rate, the # of cases would have been higher, not lower.

]]>Why? What you need is a sufficient number of cases. If incidence is higher than expected and you can get there in six week rather than six months you are happy to have your results earlier. If they had assumed a higher base rate maybe they would have enrolled less people in the trial (on the other hand you need lots of people for the safety endpoints anyway, whatever the incidence).

]]>One thing that’s clear is that the baseline case rate assumed when designing the trial is way too low. In the Moderna and Astrazenaca protocols, the base rate is assumed to be ~0.7% over six months. It’s pretty clear they are seeing that level over just a few weeks so the base rate is off by a huge margin. If they had assumed say 5% base rate in the design, wouldn’t the interim analysis require more cases?

]]>All Ive ever said since Feb is repeat the exact same experiments done for SARS and see. Its now mid nov and still no.

]]>Basically the only thing they have in common is they are both respiratory viruses. Otherwise, the biology and vaccine are completely different.

]]>For this dataset, we can run the following regression to estimate the “effectiveness”:

y1=c(rep(1,5),rep(0,1e4)) # control x1=y1*0 y2=c(rep(1,90),rep(0,1e4)) # treatment x2=y2*0+1 y=c(y1,y2) x=c(x1,x2) library(rstanarm) fit=stan_glm(y~x,family = binomial(link = "logit")) print(fit) stan_fit= extract(fit$stanfit) mean( 1- invlogit(stan_fit$alpha +stan_fit$beta)/invlogit(stan_fit$alpha)) quantile( 1- invlogit(stan_fit$alpha +stan_fit$beta)/invlogit(stan_fit$alpha), c(0.025,0.975))

I am using default prior here but presumably we can do better. The outcome is 94.0%, with its 95 confidence interval to be (87%, 98%). So I guess the final number would not “be a lot lower than 95%” based on such evidence.

]]>Was ADE shown for SARS-1 in vivo, or only in vitro?

Ive linked direct quotes about this multiple times on here:

]]>“Every other subgroup”?

Yes, follow the links in my post. They included well defined subgroups, and talked about all except the subjects with comorbidities in their press release.

A peer reviewer who failed to ask about that would be incompetent as can be.

]]>I think the issue is if asymptomatic are multiples of symptomatic. If all we do is reduce the number of symptomatic without reducing asymptomatic, then we may not move R very much. The truth is I don’t know the answer and I have no priors on this (the closest I got to medicine was a course on experimental design). But I would have hoped the trials were set up to answer this question.

]]>It doesn’t sound terribly plausible, though I’m not an immunologist — immunity isn’t binary, it would be very strange if it prevented 95% of symptomatic infections without reducing infections or contagiousness at all!

]]>Yeah, I think the efficacy stated is probably “assuming a population of similar composition to the sample group”.

It would make sense to be less effective in the very oldest/least healthy/most immunocompromised, I’d think, as a vaccine requires a certain degree of functionality of the person’s own immune system.

But this still seems extremely good — people were talking about 50-70% efficacy, not 90%+, and the US population isn’t so old as to shift it *that* much!

]]>Yeah, I think this technology is *very* interesting.

But 90%-95% effectiveness really doesn’t seem particularly weird given that I don’t see why we should have a priori expected COVID to be hard to vaccinate against. Most people get over it on their own & develop an immune response, and it doesn’t have the super-high/complex mutation of influenza.

]]>And I’m not sure that vaccine type is that irrelevant. The RSV vaccine issues Daniel Lakeland mentioned on another thread may have been related to that (the paper I saw on it didn’t seem terribly clear, but that may be because it happened in the 60s and the knowledge of the time was not entirely up to par in terms of understanding what happened).

But that might have had some white-blood-cell involvement rather than being “purely” antibody-caused.

I don’t nearly have the expertise to judge this — but I really don’t think this is nearly as certain/solid as you suggest.

]]>I really do not think there is any reason to expect a risk in young/with comorbidities greater than old/without comorbidities.

In fact, there is pretty strong evidence against it: the observed age disparity in COVID deaths in the US is simply far too great, given how common comorbidities – especially obesity and asthma – are in the younger US population.

So even if *you* specifically were concerned with that group, there’s no reason for the vaccine developers to focus on it or even mention it.

]]>Eh… maybe? But I don’t think there is anything like the certainty you are suggesting that ADE will be a thing for SARS-COV-2, much less what the risk factors for it would be.

Was ADE shown for SARS-1 in vivo, or only in vitro?

And future viruses that haven’t even evolved yet are *by definition* unpredictable!

]]>Vaccine efficacy

]]>Just to be clear: That would produce the Frequentist confidence interval for which parameter of interest?

]]>Definitely… but the issue brought up by Brian suggests a scenario in which the vaccine would reduce only symptomatic cases by turning them into asymptomatic cases without reducing the asymptomatic cases that would have occurred as well. So let’s say there would have been 100 asymptomatic cases and 100 symptomatic cases in each group without vaccine. Would the symptomatic cases that the vaccine prevented just be added to the asymptomatic cases such that in the vaccine group we now have 5 symptomatic cases and 195 asymptomatic cases with no reduction in actual infections? If that’s the case, then there certainly would statistical issues. My question is whether we have any reason to believe that is actually the case (or anywhere close to it).

]]>You’re forgetting that masks work for people when they’re pre-symptomatic, i.e. they have no or mild symptoms and haven’t been tested yet.

A lot here depends on access to testing, i.e. at what level of symptoms do people get tested?

But in the end, does it matter?

Even if p(did not get sick from infection) > p(did not transmit to others), as long as the reduced transmissivity pushes the reproduction rate firmly below 1, herd immunity will stop the virus.

Thanks for posting this

]]>Correct, but no need for the 15e3. You can just do

poisson.test(c(5, 90))

]]>Sure, your immune system *could* suppress the virus to the point you dont really notice but you can still transmit it. That is the whole idea behind the asymptomatic people needing to wear a mask.

]]>Is there any reason to believe that asymptomatic cases would be more prevalent in one arm of the trial than the other? Is there any reason to believe that something that prevents symptomatic cases would not also prevent asymptomatic cases?

]]>1-poisson.test(c(5, 90), 15e3)$conf

[1] 0.9823873 0.8654892

]]>