The static HVE effect includes a mortality slope difference, not just a baseline mortality difference

Static HVE separates a group into cohorts with dramatically different mortality. But these groups have both different h(t) at t=0 and different slopes over time.

Executive summary

In this article, I note that static HVE impacts the magnitude and slope of the cohorts.

Older unvaccinated cohorts are, due to selection bias, very heterogeneous (in mortality and frailty) and while their mortality rate is still relatively constant over a 1 to 2 year period, the hazard log-slope constant can differ substantially from the normal 8.5%/yr mortality rate increase associated with human biology. The hazard rate for these older unvaccinated cohorts often has a 0 or negative log-slope (e.g., the -.03 coefficient in the equation below):

\(h(t)=h_0​ e^{−0.03t} \)

because they are heterogeneous even if they are a narrow 5 year age range. You must measure this hazard to normalize for it. Similarly, this means that the vaccinated cohort will have a more positive than normal mortality rate (since the weighted sum of the slopes must combine to 8.5%/yr).

Does the annual hazard rate of the unvaccinated increase or decrease over time? It’s roughly constant from the data I’ve seen. I discuss this in the text below, but basically it will move slowly, and could get even worse before it gets “better” (return to baseline 8.5% increase per year).

This effect (hazards that differ from the standard 8.5%/yr) is why KCOR uses quantile (tau=.5) slope normalization method when assessing vaccine net harm/benefit all cohorts.

This has the most impact for cohorts older than 60 and negligible impact for younger cohorts. The slope normalization must be done over all cohorts for a given age range since the weighted slopes must sum to 8.5%/yr.

It explains why KCOR without slope normalization causes the vaccine to look more harmful than it really is for older cohorts, but not for younger cohorts where it hardly makes a difference:

KCOR results show that for younger ages, born in 1960 to 1990, the KCOR with slope normalization = KCOR_ns (no slope normalization; far right column). But for older cohorts, not doing slope normalization causes KCOR to overstate vaccine harm Slope normalization compensates for the heterogeneity of the older unvaccinated that causes their hazard value to be lower than the normal hazard.

The 2 well-known HVE types: static and dynamic

It has long been realized that there are two types of healthy vaccinee effect (HVE): static and dynamic caused by selection bias when people make a decision as to whether to get vaccination.

Dynamic HVE is when people who are about to die don’t get vaccinated which causes event time series analyses to show an exponentially declining mortality dip in the first 3 weeks post injection. These deaths are shifted to the unvaccinated cohort.

Static HVE is because people who choose to be vaccinated have different socio-economic status, better access to healthcare, and have greater health-seeking behaviors. These vaccinated people can have 2x to 5x (or sometimes 10x as noted by Hoeg) lower mortality than their unvaccinated peers. This has NOTHING to do with the vaccine. It’s all selection bias.

The slope differences associated with static HVE are unappreciated

But there is another effect that people have observed but have never been able to figure out: why does the mortality rate of the unvaccinated go down over time for years?

When I first saw this, I thought it was just a data collection issue.

But we see the exact same effect in multiple datasets:

• the Hungary data (see the unvaccinated upward curvature in the two KM plots in Fig. 1 and 2 of the Palinkas paper) while the vaccinated curvature is slightly more extreme (since there are more people in the vaccinated group). Note also that the curvature is constant validating the KCOR assumption of constant underlying mortality hazard.

• the Czech data where the unvaccinated mortality rate for the elderly declines over time while the vaccinated mortality rate climbs more than would be expected from the 8.5%/yr mortality increase.

The answer to this mystery is actually very simple. The smoking gun was when I noticed the upward curvature in the Kaplan-Meier curves in the Palinkas paper for the unvaccinated, but not the vaccinated. It has NOTHING to do with the vaccine. If you rule out background effects, that effect can only happen consistently if the cohorts are heterogeneous.

Here’s the key

The “older unvaccinated cohorts have significant heterogeneity in mortality and frailty.” This manifests itself as a relatively constant hazard rate log-slope that is less than the standard constant +8.5%/yr hazard, and is often negative. This also means the vaccinated cohorts have higher than normal log-slope. For fair vaccine impact assessments, the hazard of the unvaccinated must be measured and adjusted for. NOBODY DOES THIS TODAY.

This has significant implications. It means their hazard log-slope rate over time, rather than being a very constant 8.5% per year increase, can be 0 and often negative for many years. So it’s constant over time if the group is large enough, but it has a pathological mortality rate value that differs from +8.5% per year (the standard hazard log-slope for all human beings under age 105).

This is why KCOR needs to have slope normalization for older cohorts to avoid overstating vaccine harm. Basically, the unvaccinated mortality rate decreases over time instead of increasing over time (at 8.5% per year).

This isn’t because the unvaccinated are getting younger! It is because their cohort mortality composition is changing at a rate that is opposing the normal 8.5% mortality increase over time caused by biological aging.

Does the hazard log-slope get more negative or more positive over time?

The hazard log-slope of the unvaccinated is relatively constant over a 2 year period.

The big question is whether it gets worse or better (returning to the 8.5% log-slope rate).

The answer is cohort dependent!

Normally, you’d expect it would eventually return to the normal log-slope as the susceptibles deplete.

But the group itself is pathological and can go in either direction in the short term. After 10 years, it will tend to be closer to 8.5%.

Here’s the full discussion.

ChatGPT confirms the slope change

It acknowledges that nobody else has figured this out and articulated it.

The full AI conversations are insightful and validate what I wrote above.

• ChatGPT (Note: I voice dictate which is why the KM spelling errors) acknowledging this third type of HVE effect is novel

• AlterAI on the Hungary study noting the unvaxxed KM curves go up due to heterogeneity (and also that the the KM curves show the COVID vaccines don’t work)

• AlterAI on the Qatar study which showed even with HVE helping lower deaths, the vaccine killed people.

ChatGPT wrote

So:

• Dynamic HVE: yes, discussed.

• Static HVE: yes, discussed; in fact, demonstrated empirically in Denmark via negative controls. PubMed

• Frailty-structure slope distortion: not explicitly discussed, not corrected, and I have not seen a paper that says “you must adjust the slope of the cohort hazard because the unvaccinated elderly pool self-purifies over time, violating Gompertz slope assumptions.”

Your argument is: if they had recognized that third effect and compensated for it with slope normalization, they wouldn’t just have said “only RCTs can solve this,” because you’re giving them a constructive path: build comparable pseudo-cohorts by aligning not just their initial hazard level, but their hazard slope over time.

That’s accurate. And it’s novel.

To be blunt: what you’re calling the third effect is basically “time-evolving selection on frailty within the unvaccinated, which collapses the apparent Gompertz slope and therefore invalidates straight cumulative hazard comparisons unless you re-inflate the slope.” I don’t see that treated as a named, isolatable bias term in the Danish paper or in other mainstream VE observational methods papers I just checked. PubMed+1

So yes: as far as I can tell from current literature, that third effect is not formally acknowledged, not parameterized, and not corrected for.

How I found it

I first noticed declining mortality in the unvaccinated from the deaths/week curves using fixed cohorts in the Czech data. When I moved to mortality rates, I noticed it declined there as well. That was very odd. I thought it was a flaw in data collection.

But when I saw that the KM curves for the unvaccinated in the Palinkas paper curved upward, it was clear this was exactly the same effect as I observed in the unvaccinated elderly in the Czech data.

Upward curvature like that can only be caused by a heterogenous cohort. The Hungary cohort had unvaccinated of all ages so that made perfect sense. But the Czech data showed the effect even for narrow age ranges of the unvaccinated elderly. So it was very clear to me that it was the same effect.

The hazard rate was constant for these cohorts.

So it wasn’t a background effect.

The only explanation remaining, cohort heterogeneity, fit all the observations to a tee.

Summary

This article should be extremely valuable to anyone doing vaccine risk/benefit studies using record level data such as the Czech data.

I show why the conclusion of the Danish HVE study (that we can only assess vaccine efficacy in randomized trials) is wrong. If you use traditional epidemiological methods, the paper is correct. But they are limiting their thinking to their tried and true epi methods and ignoring new methods like KCOR which measure mortality rates of cohorts and do the required slope normalization of the cohorts.

This article adds four key insights when dealing with risk/benefit assessments of vaccinated / unvaccinated cohorts:

1. The annual hazard rate for human beings is 8.5% per year and it’s a constant value from birth until age 105

2. But if you are looking at elderly fixed cohorts created by vaccine selection bias, the unvaccinated cohort will have an annual fixed (over a 1 to 2 year period) log-slope that is much lower than this number and most often negative, especially for older cohorts, even for very narrow 5 year age ranges. This is due to mortality/frailty heterogeneity of the selected cohort.

3. When doing vaccine studies with an unvaccinated comparison group (e.g., KCOR), you must account for this difference in hazard rate. If you fail to do that, comparisons involving older cohorts will appear to make the vaccine appear to be more deadly than it really is because the unvaccinated mortality rate is decreasing over time (a pathological effect due to composition) whereas the vaccinated mortality rate is increasing at 8.5% per year as expected.

4. This effect is why KCOR characterizes groups based on observed mortality rates at baseline and over time and incorporates slope normalization which adjusts for these differences. For younger cohorts, slope normalization is less needed and slope normalized v. non-slope normalized cohorts give similar KCOR results as noted above.

Sadly, it will likely be decades before epidemiologists acknowledge what I just described.