Skip to content

A Causal Analysis of 'Vaccine Kills' Claim

TL;DR

When analyzing the 'Vaccine kills more than disease', looking only at raw counts is a classic human mistake. Causal counterfactuals make the policy choice clear.

The Puzzle#

You sometimes hear: "Data show more people die from the smallpox vaccine than from smallpox itself, so vaccination should be banned."

This is a misinterpretation of the data if you only compare totals. The mistake is ignoring considering counterfactual reasoning.

Below is a simple, self-contained scenario to illustrate the logic.

The Setup (Hypothetical Data)#

Consider the case of a population of 1,000,000 children and imagine that the vast majority is vaccinated against smallpox:

  • Population: 1,000,000 children
  • Coverage: 99% vaccinated (990,000) and 1% unvaccinated (10,000)

When kids are vaccinated rarely they have a reaction and even more rarely that reaction is fatal:

  • If vaccinated

    • Reaction probability: 1 in 100 (1%)
    • Fatality among reactions: 1 in 100 (1%)

  • If unvaccinated

    • Smallpox probability: 1 in 50 (2%)
    • Smallpox fatality among cases: 1 in 5 (20%)
    • Smallpox is quite contagious and fatal.

What We Observe#

Group Population Event chain Expected events Expected deaths
Vaccinated 990,000 Reaction: 1% → fatality among reactions: 1% 9,900 reactions 99 deaths
Unvaccinated 10,000 Smallpox: 2% → fatality among cases: 20% 200 cases 40 deaths
Total 1,000,000 — — 139 deaths

  • A correct observation is that more deaths from vaccination (99) than from smallpox (40)
  • A misinterpretation: is that "vaccines kill!"

Counterfactuals: the Right Comparison#

Let's create a causal diagram to understand the situation

To decide policy, we need to compare counterfactuals (i.e., create situations based on a different way of doing things and assess their outcomes).

  • Scenario 1: No one vaccinated

    • Infections: \(1,000,000 \times 2\% = 20,000\)
    • Deaths: \(20,000 \times 20\% = 4,000\)

  • Scenario 2: Current mix (99% vaccinated)

    • Deaths: \(99\) (vaccine) \(+ 40\) (disease) \(= 139\)

  • Scenario 3: Everyone vaccinated

    • Reactions: \(1,000,000 \times 1\% = 10,000\)
    • Deaths: \(10,000 \times 1\% = 100\)

From 4,000 deaths (none vaccinated) to 139 deaths (current mix) = 3,861 fewer deaths, a 96.5% reduction in deaths. If everyone were vaccinated, expected deaths would fall further to 100.

The counterfactual reasoning shows us that when vaccinating, although the number of deaths due to vaccine might be larger than the number of death due to smallpox, the alternative on vaccinating increases 40x the death rate.

The conclusion is pretty clear: vaccination is the right policy, and the more vaccination the better.