⭐ 1. RISK RATIO (also called Relative Risk)

From: “Risk Ratio”, pg. 37–39

What is “risk”?

Risk = the probability something will happen.

Examples from the book:

• Giving birth to a boy → 1 out of 2 births → risk = 0.5
• If 1 out of 100 patients get a side-effect → risk = 0.01

What is the Risk Ratio?

Risk Ratio compares the risk in an exposed group with the risk in a control group.

Risk Ratio =risk in exposed group ÷ risk in control group

How to interpret

• RR = 1 → no difference in risk
• RR > 1 → exposure increases risk
• RR < 1 → exposure reduces risk (protective)

Book Example: Football injuries

• 12 broken legs in 1000 footballers

→ risk = 12 ÷ 1000 = 0.012

• 4 broken legs in 1000 non-footballers

→ risk = 4 ÷ 1000 = 0.004

• RR = 0.012 ÷ 0.004 = 3

Meaning:

Footballers had three times the risk of breaking a leg.

BUT: 95% CI included 1 → may be due to chance.

⭐ 2. ODDS RATIO

From: “Odds Ratio”, pg. 40–42

What are “odds”?

Odds = how many times something happens compared to how many times it does NOT happen.

Examples from book:

• Birth of a boy: 1 boy for 1 girl → odds = 1 to 1
• Side effect in 1 out of 100 → odds = 1 to 99 = 0.0101

When we use Odds Ratio

• Used in case–control studies.
• You compare odds of exposure in those WITH the disease vs WITHOUT the disease.

How to interpret

• OR = 1 → no difference
• OR > 1 → exposure associated with higher odds of disease
• OR < 1 → exposure associated with lower odds

Book Example: Skiers & knee injuries

Cases (knee injuries):

• 40 skied, 60 didn’t → odds = 40 ÷ 60 = 0.66

Controls:

• 20 skied, 80 didn’t → odds = 20 ÷ 80 = 0.25

Odds Ratio = 0.66 ÷ 0.25 = 2.64

Meaning:

Skiers had 2.64 times the odds of getting knee injuries.

95% CI did NOT include 1 → statistically significant.

Important point from the book:

For rare events, odds and risk are similar.

For common events, odds and risk become very different.

This is why OR is used mainly in case-control studies only, not cohorts.

⭐ 3. RISK REDUCTION & NNT (Numbers Needed to Treat)

From: “Risk reduction and numbers needed to treat”, pg. 43–47

A. Absolute Risk Reduction (ARR)

ARR = improvement in treatment group minus improvement in control group.

Book Example: Oral antifungal for candida

• 80 improved out of 100 treated → 80%
• 60 improved out of 100 placebo → 60%

ARR = 80% – 60% = 20%

Meaning:

Treatment improves cure rate by 20% in absolute terms.

B. Number Needed to Treat (NNT)

NNT = how many people you must treat for one person to benefit.

NNT = 100 ÷ ARR

(using ARR as a percentage)

Using candida example

ARR = 20%

NNT = 100 ÷ 20 = 5

Meaning:

You must treat 5 women for 1 extra woman to be cured.

The book highlights:

NNT should always be interpreted along with time, side-effects, and cost.

C. Relative Risk Reduction (RRR)

RRR = proportion by which risk is reduced.

Using candida example:

Placebo failure (non-improvement) = 40%

Treatment failure = 20%

RRR =

reduction (20%) ÷ original (40%) = 0.5 = 50%

Meaning:

Treatment “halves” the risk of persistence.

BOOK WARNING

RRR looks very impressive but can be misleading — always check NNT to see real-world impact.

⭐ 4. Comparing RRR vs ARR vs NNT (Book Emphasis)

Example from book: cleverstatin trial

• ARR was only 0.2%
• NNT = 500
• but RRR was 50%

RRR made the drug seem amazing,

but NNT showed almost no real benefit.

⭐ Final Super-Simple Summary (Based on Book)

Risk Ratio

“How much risk changes between two groups.”

Used in cohort studies.

Odds Ratio

“How much the odds change between cases and controls.”

Used in case–control studies.

Absolute Risk Reduction (ARR)

“How much better is the treatment in real numbers?”

Relative Risk Reduction (RRR)

“What percentage change compared to the original risk?”

NNT

“How many you must treat to help one patient?”

Lower NNT = better.

What is Standard Error of the Mean?

SEM tells you how precise your sample mean is as an estimate of the true population mean.

• Small SEM → sample mean is very close to the true mean
• Large SEM → sample mean is less reliable

👉 Exam logic:

SD = variability of data

SEM = variability of the mean

Formula (written normally)

Standard Error of Mean =

Standard Deviation ÷ Square root of sample size

In words:

SEM = SD / √n

Where:

• SD = standard deviation of the sample
• n = number of observations

Step-by-step calculation

Example

Given:

• Standard deviation = 10
• Sample size = 25

Steps:

1. Square root of sample size

√25 = 5

2. Divide SD by √n

10 ÷ 5 = 2

✅ SEM = 2

Another quick example

SD = 12

n = 36

√36 = 6

SEM = 12 ÷ 6 = 2

Key exam points (very high yield)

• SEM decreases when sample size increases
• SEM is always smaller than SD (unless n = 1)
• Large studies → small SEM → more precise mean
• Used in:
• Confidence intervals
• Error bars in graphs
• Comparing means

SD vs SEM (must not mix up)

• Standard Deviation

→ spread of individual data points

• Standard Error of Mean

→ spread of the sample mean

👉 Exam trap:

SD describes data

SEM describes the mean

One-line memory hook

SEM = SD divided by square root of n → precision of the mean