NOTE: The prior post on this topic is here.
UPDATE: An edit made after first publishing this has lowered the benchmark SIDS death rate by a small amount (from 225 per million down to 221 per million).
Because death has a normative aspect to it, efforts should be undertaken in order to minimize deaths whenever and wherever possible. But simple descriptive statistics which tell you how many deaths have been occurring lately are insufficient. This is similar to the debate between legal positivists and natural law theorists.
Legal positivists will tell you that law is that which has been written down on paper and signed by an authoritative person. But natural law theorists do not simply accept every single law which has ever been written by fallible human beings. Instead, they will tell you that law has a normative aspect, not merely a historical one.
This means that there are “good laws” and there are “bad laws” (and the bad laws “don’t count" or at least “do not count as much”). In the same vein, there are good death rates (low death rates) and there are bad death rates (high death rates). But in order to know if you are low or high, you need a benchmark.
An article by the CDC provides an excellent example:
[click image to enlarge]
The highlighted part above states that, if you want to know if deaths are low, then you can look at the best-three states out of 50 states in order to find out. When wanting to know if you have a high or low rate of cancer death, compare yourself to the best 3 states. Here is how you would find out if your state has a high or low cancer death rate:
For age 60-69, for example, the best 3 states were Utah, Hawaii, and Colorado — having an average yearly cancer death rate of 352.7 per 100,000. The logic behind this is that the age-specific death rates found in the best places are presumed to be where you have the least environmental insults. The “best” rates are more “natural” ones.
This same method was applied to SIDS (sudden infant death syndrome) below, but let’s first check the national average death rate from two ICD-10 codes: SIDS along with Accidental Suffocation and Strangulation in Bed (ASSB):
The years of 2017-2019 were chosen to obtain a benchmark yearly rate for SIDS. Here is an example search page (both SIDS and ASSB are involved in the numbers below):
New York is highlighted at bottom because after examining all 3 years, New York made the cut and was found to have one of the 3 best rates. After picking every state which had an annual rate (for at least one of the 3 years) at 40.0 per 100,000 or below, the deaths were combined into a 3-year sum, and a weighted annual rate was formed:
The top 10 states meeting the condition of having at least one year with a rate of 40.0 per 100,000 or below were then analyzed further, narrowing it down to the best 3 of them (yellow highlighted). Then those best 3 rates were pooled together and the average was taken from the aggregated whole (treated as a composite group).
The benchmark SIDS death rate is 22.1 yearly SIDS per 100,000 — equivalent to 221 yearly SIDS per million. When wanting to discover if a vaccine increases SIDS risk, then the expected daily rate is 0.605 (221/365.25) daily SIDS per million. In long form, here is that daily probability of SIDS: 0.000000605.
Hypothetical Example
If a million infants got vaccinated, and there had been 1 SIDS death on Day 0, 2 SIDS deaths on Day 1, 3 SIDS deaths on Day 2, 2 SIDS deaths on Day 3, and 1 SIDS death on Day 4 — then those 9 deaths in those 5 days would be highly significant. That’s because, in every 5 days, only 3.025 (5 * 0.605) SIDS deaths are expected from a million infants.
Finding 9 SIDS deaths from a million infants over the course of 5 days would be three times what was expected. Here is the Poisson analysis with a mean rate of 3.025 on an event count of 9, an analysis that begins with one less event than you are evaluating (mean = 3.025; X = 8):
The top decimal (0.995 …) shows the probability of witnessing 8 or less SIDS deaths in 5 days when 3.025 per 5 days was expected to occur. The second line shows the probability of getting 9 or more SIDS deaths in those 5 days of observation — i.e., 0.004, or about 4 chances in a thousand (a low probability).
In this hypothetical, 9 SIDS deaths in 5 million infant-days (1.8 daily SIDS deaths per million) would be enough to call into question the safety of the vaccine — being 3x higher than what would be expected to occur.
Reference
[to know if your rate is low or high, compare yourself to the best-three rates] — https://www.cdc.gov/mmwr/volumes/68/ss/ss6810a1.htm
[to find the best 3 states for SIDS death rates, from 1999-2020, begin here] — https://wonder.cdc.gov/ucd-icd10.html