# How to understand medical decisions

Evidence-based diagnosis and decisions

Reasoning with uncertainty4

Different ways of estimating degrees of certainty

Reasoning with proportions and their probabilities

Aristotle’s Syllogism and the Probability Syllogism

Bayes rule expressed as triangles and a square

What was actually written in Bayes’ paper in 1763

The ‘Bayesian’ interpretation of ‘Bayes’ Proposition 5’

The importance of combinations of findings

Reasoning with improbable alternatives

A worked example of reasoning with improbable alternatives

Using very low frequencies or probability densities

Different findings with shared lists of differential diagnoses

Evidence for a finding’s role in reasoning with improbable alternatives

Differential likelihood ratios exploit ‘system independence’

Exploiting statistical independence during reasoning with improbable alternatives

The dangers of using false positive rates and overall likelihood ratios

Taking advantage of statistical independence when reasoning with alternative probabilities

Reasoning with numerical test results

Reasoning with improbable alternatives to arrive at ‘stratified’ diagnostic criteria

‘Stratifying’ treatment indication criteria based on the severity of a condition ...

Estimating the probability of a treatment outcome by fitting a mathematical function to the data

Improving treatment selection for patients with better tests

Diagnostic and treatment criteria with shared decision making

An old chestnut: ‘the principle of indifference’ and ‘sampling’

The negative consequences of using inappropriate informal prior probabilities of a true result

The probability of a true proportion lying within a range of possible true results

Should a study be modelled by random sampling?

The probability that a ‘mechanistic’ explanation is ‘true’

The probability of a true result being within a range compared to P values, confidence and credibility intervals

Reasoning with hypotheses and calibrating degrees of certainty

Summary of evidence-based diagnosis and decisions

Proof for the ‘probabilistic elimination’ theorem

Contents of Section 3 for professionals