Does vaccination help you avoid death if you contract Covid-19?

[RongzongWu]

To answer this question we need to look at the death rate (defined as death per case) among vaccinated people vs. unvaccinated people.

There are several ways to come up with the answer.

One rough (order of magnitude) estimate is to look at the death rate from a country before vaccination begins, and the death rate after majority of the population has been vaccinated. Lets call this Method A. A stands for "Approximation".

The other is to look at more specific data: the death amongst vaccinated cases and death amongst unvaccinated cases. Let's call this Method BG, where B stands for "Best Guest".

[RongzongWu]

Method A (pproximation):

To make this more accurate, we need to look at countries with high vaccination rates. I picked South Korea (85% fully vaccinated) and Israel (66% fully vaccinated) as of 1/21/2022, according to google new:

https://news.google.com/covid19/map?hl=en-US&gl=US&ceid=US%3Aen&mid=%2Fm%2F06qd3 for South Korea https://news.google.com/covid19/map?hl=en-US&gl=US&ceid=US%3Aen&mid=%2Fm%2F03spz for Israel

[RongzongWu]

Let's look at South Korea first:

The vaccination starts about April 1, 2021, and plateaued around November 1, 2021. There were two waves of death:

Around Jan 7, 2021: 7-day average death is 23, this is before the vaccination began, Around Dec 25, 2021: 7-day average death is 75, this is after the vaccination has plateaued.

[RongzongWu]

A case wave should occur about one to two weeks before a death wave. The case waves correspond to the above two death waves should be the ones around Dec 25, 2020, 7-day average case is 1047, and around Dec 18, 2021, with a 7-day average case of 6832.

So the death rate before vaccination is 23/1047 = 2.2%. the death rate after vaccination is 75/6832 = 1.1%.

So the death rate reduced from 2.2% to 1.1%, significant but still within the order of magnitude of each other.

[RongzongWu]

Do the same analysis for Israel and USA, and here is the summary:

[RongzongWu]

In summary, based on Method A, it seems that vaccination helps significantly, but the death rate for a person that has contracted COVID is on the same orders of magnitude regardless of the vaccinated status.

Note that since the vaccination rate is not 100%, the effectiveness of vaccination calculated using Method A is probably less than the truth. So these should be viewed as lower bounds. In other words, we should expect that vaccination to reduce death rate by at least 50%.

[RongzongWu]

In order to do Method B (Best Estimate). Let's see if we can find some number from CDC of the U.S. government.

Here is the page that shows the relevant data:

https://covid.cdc.gov/covid-data-tracker/#rates-by-vaccine-status

There is a link to download the data, see the screenshot below:

A copy of the data I downloaded today (1/23/2022) can be found here in this repo:

https://github.com/RongzongWu/EverydayCovidData/blob/main/Data/Rates_of_COVID-19_Cases_or_Deaths_by_Age_Group_and_Vaccination_Status_Downloaded_20220123.csv

Note that GitHub won't show all the columns. Also note that the data seems to be slightly different between my last download and this download, even for historical data.

[RongzongWu]

After comparing the data in the CSV file against the chart showing on the CDC site, it is clear that the chart is showing the "Age adjusted vax IR", and "Age adjusted unvax IR" columns. "IR" means incident rate, which is incident (either death or COVID case) per 100,000 population.

Here is all the data showing on the chart before splitting into age groups and vaccine type:

Week	Age adjusted vax case IR	Age adjusted unvax case IR	Age adjusted vax death IR	Age adjusted unvax death IR
202114	21.02451063	203.9323319	0.14802466	2.842742135
202115	18.52872443	203.3859786	0.159363074	2.993971489
202116	16.66126192	175.4118045	0.132634061	2.943645475
202117	15.98967457	159.6048127	0.135112389	2.588312523
202118	11.46537228	136.1643299	0.121080928	2.467597783
202119	8.574761325	116.5863226	0.089706092	2.003318512
202120	7.292606748	90.22434023	0.087131345	1.673362986
202121	5.736668205	68.46282246	0.070741957	1.43467003
202122	5.141028089	55.5179887	0.070511	1.227541079
202123	5.19057167	50.72798976	0.06595192	1.175770354
202124	5.438432335	49.18168573	0.075719921	1.16947474
202125	7.220768436	54.56028842	0.09677206	1.362497124
202126	11.04556018	72.5216213	0.101019844	1.738044504
202127	18.48788738	109.0548874	0.170868479	2.738782493
202128	33.63993835	172.8768935	0.295105522	4.075500579
202129	58.39782885	283.7455799	0.473397441	7.225968495
202130	88.29428495	424.1256506	0.755289571	11.02238333
202131	112.1479814	530.772165	0.934321269	14.59533223
202132	122.7498664	607.8844795	1.124302436	17.04765669
202133	128.3088508	657.1131485	1.119929796	18.16471288
202134	132.0615953	682.8966736	1.055002165	17.35325648
202135	125.4784082	658.8965665	0.987623263	16.64901073
202136	113.1012979	595.1731908	0.939754274	14.43491032
202137	102.4493681	533.0887034	0.809496229	12.39061186
202138	87.84098312	454.9216632	0.710131159	10.2544866
202139	82.97084161	408.3782701	0.591209942	8.676893667
202140	77.66425169	373.4160667	0.533698312	7.709436743
202141	69.32257568	329.4917907	0.50222873	7.116481256
202142	65.30913674	305.4796871	0.467174931	6.431453612
202143	68.7723518	318.0736112	0.455656623	6.301405512
202144	78.34089861	337.1566391	0.461489254	6.882448207
202145	85.36868555	377.6721347	0.484333139	7.471984836
202146	92.34663458	418.2837514	0.509388337	8.39450078
202147	82.89861928	375.3168955	0.510981089	7.770561558
202148	123.852306	559.0325355	0.465690889	9.197037038
202149	113.359997	528.5697208
202150	207.1574417	639.8792063
202151	443.6895645	1006.387219

[RongzongWu]

To calculate the death rate, just divide the death incident rate (IR) by the case incident rate. For example, for the week of 202114 (week 14 of year 2021), the death rate for vaccinated people is 0.14802466/21.02451063 = 0.7%, and for unvaccinated people this is: 2.842742135/203.9323319 = 1.4%. This means a reduction in death rate of 50%.

Week	Vaxed Death Rate (%)	Unvaxed Death Rate (%)	Reduction in Death Rate (%)
4/10/2021	0.7	1.4	49.5
4/17/2021	0.9	1.5	41.6
4/24/2021	0.8	1.7	52.6
5/1/2021	0.8	1.6	47.9
5/8/2021	1.1	1.8	41.7
5/15/2021	1.0	1.7	39.1
5/22/2021	1.2	1.9	35.6
5/29/2021	1.2	2.1	41.2
6/5/2021	1.4	2.2	38.0
6/12/2021	1.3	2.3	45.2
6/19/2021	1.4	2.4	41.4
6/26/2021	1.3	2.5	46.3
7/3/2021	0.9	2.4	61.8
7/10/2021	0.9	2.5	63.2
7/17/2021	0.9	2.4	62.8
7/24/2021	0.8	2.5	68.2
7/31/2021	0.9	2.6	67.1
8/7/2021	0.8	2.7	69.7
8/14/2021	0.9	2.8	67.3
8/21/2021	0.9	2.8	68.4
8/28/2021	0.8	2.5	68.6
9/4/2021	0.8	2.5	68.9
9/11/2021	0.8	2.4	65.7
9/18/2021	0.8	2.3	66.0
9/25/2021	0.8	2.3	64.1
10/2/2021	0.7	2.1	66.5
10/9/2021	0.7	2.1	66.7
10/16/2021	0.7	2.2	66.5
10/23/2021	0.7	2.1	66.0
10/30/2021	0.7	2.0	66.6
11/6/2021	0.6	2.0	71.1
11/13/2021	0.6	2.0	71.3
11/20/2021	0.6	2.0	72.5
11/27/2021	0.6	2.1	70.2
12/4/2021	0.4	1.6	77.1

[RongzongWu]

The death rate per COVID cases is shown in the following chart for vaccinated and un-vaccinated populations respectively. It seems that the death rate changes a lot, not sure why. Overall the numbers are in the same order of magnitude as the ones calculated through Method A.

[RongzongWu]

The reduction in death rate is plotted below:

[RongzongWu]

It seems that vaccination initially only reduce death rate by about 40% then increased to about 60-70%, with a sudden jump occurring around end of June and beginning of July 2021. This seems to coincide with the time when the vaccination rate plateaued.

The 60-70% reduction rate is consistent with the numbers we got from Method A (which provides a lower bound estimate of 50%).

With a 70% reduction, we are looking at 2 out of 3 people that can be saved by vaccination from death, if contracted COVID.

I believe this is significant. However, vaccination is far from being a silver bullet, it does NOT eliminate death, only 70% of it. To say all COVID death is avoidable is wrong.