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Dayesha Rathuwaduge

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✅ SURVIVAL ANALYSIS — FULL EXPLANATION (NON-LATEX)

(from pages 57–60 of the book)

Survival analysis is used when research looks at how long it takes before a particular event happens.

⭐ 1. When do we use survival analysis?

Use these methods when the outcome is:

Time until death
Time until recurrence of a disease
Time until discharge
Time until stroke
Any outcome where time to event matters

These methods are designed to handle censored data:

🔸 What is censorship?

Patients may:

Leave the study
Be lost to follow-up
Not yet experience the event before the study ends

Their data cannot be thrown away — survival analysis includes them as censored cases.

⭐ 2. LIFE TABLES

What is a life table?

A life table shows the proportion of patients surviving at fixed time intervals.

Example: A table showing survival at:

1 month
3 months
6 months
1 year

How life tables work

They divide the follow-up period into chunks (e.g., monthly).

At each time point, they calculate:

How many people are alive
How many died
How many were censored

Usefulness

Life tables give a rough picture of survival but are less precise than Kaplan–Meier because they only update survival at fixed intervals, not whenever a death occurs.

⭐ 3. KAPLAN–MEIER PLOTS (KM curves)

(“product-limit method”)

This is the most commonly used survival method in medical research.

🌟 What makes Kaplan–Meier special?

Recalculates survival every time an event happens
Gives a step-down curve
Shows clearly how survival declines over time

🌟 What the graph looks like

X-axis = time
Y-axis = cumulative survival (%)
Each death → step down
Censored patients → marked with a tiny vertical tick

Example interpretation (from book)

At 20 years, 36% of patients are still alive.
(Shown by the dotted line at 20 years.)

⭐ Comparing two groups

If you plot:

Men vs women
Treatment vs placebo

You get two KM curves.

To see if they are statistically different → use the log-rank test.

⭐ 4. LOG-RANK TEST

Used to compare two or more survival curves.

What does the log-rank test do?

Tests the null hypothesis:

“There is no difference in survival between the groups.”

Gives a P value

P < 0.05 → statistically significant difference
P > 0.05 → survival curves are not different

⭐ 5. COX REGRESSION MODEL (Proportional Hazards Model)

Pages 60–61 in the book.

🌟 When do we use Cox regression?

When you want to know:

“How does a particular factor affect the time until an event?”

Example questions:

Does being male shorten survival?
Does smoking increase risk of heart attack?
Does treatment A reduce risk of death compared to treatment B?

🌟 What Cox regression gives you

Cox regression produces one key number:

► Hazard Ratio (HR)

This is the heart of Cox regression.

⭐ 6. HAZARD RATIO (HR) — THE KEY OUTPUT

💡 What is a hazard?

A hazard is the instantaneous risk of the event happening at a given moment.

💡 Hazard Ratio meaning

HR = 1 → no difference between groups
HR > 1 → higher risk in the first group
HR < 1 → lower risk in the first group

⭐ Example from the book (Rheumatoid arthritis study)

HR for men vs women = 1.91

Meaning:

At any moment in time, men have 1.91 times the risk of death compared with women.

⭐ Confidence interval

Example CI: 1.21 to 3.01

Since it does NOT include 1, the finding is statistically significant.

⭐ 7. How Cox regression is used in real studies

Typical outputs:

Hazard Ratio (HR)
Confidence Interval (usually 95%)
P value
Degrees of freedom (less important clinically)

Clinicians use HR to understand:

Treatment effects
Gender effects
Comorbidity effects
Lifestyle effects (smoking, obesity)

⭐ Cox can adjust for multiple factors

E.g., estimate survival while adjusting for:

Age
Sex
Smoking
Diabetes
Treatment group

This is why Cox is extremely powerful.

⭐ FINAL SUMMARY (EASY TO REMEMBER)

LIFE TABLE

Survival at fixed time intervals
Less commonly used now

KAPLAN–MEIER PLOT

Step-down survival curve
Updates when events occur
Great for visual comparison
Use log-rank test for statistical comparison

COX REGRESSION

Model to explore which factors affect survival
Gives the Hazard Ratio (HR)

HAZARD RATIO

HR = 1 → no difference
HR > 1 → increased hazard (bad)
HR < 1 → decreased hazard (protective)

Forest plot — clear, exam-friendly explanation

A forest plot is a graph used in meta-analysis to show the results of multiple studies and their combined (pooled) effect on one outcome.

What each part means (step-by-step)

1️⃣ Vertical line (Line of no effect)

This is the reference line.
Meaning depends on the measure:

Risk ratio / Odds ratio → line at 1
Mean difference → line at 0

If a study’s result crosses this line, it is not statistically significant.

2️⃣ Squares (■) = individual studies

Each square = one study’s effect estimate
Position of square → size & direction of effect

Left = favors treatment A
Right = favors treatment B

Size of square → weight of the study

Bigger square = larger sample / more precise study

3️⃣ Horizontal line through square = Confidence Interval (CI)

Usually 95% CI
Long line → less precise
Short line → more precise
If CI crosses the line of no effect → not significant

4️⃣ Diamond (◆) at the bottom = pooled result

Represents the overall combined effect
Center of diamond → pooled estimate
Width of diamond → pooled 95% CI
If the diamond does NOT cross the line of no effect → overall result is statistically significant

How to interpret quickly (exam logic)

✅ All squares on one side + diamond not crossing line

→ Strong evidence for that side

⚠️ Wide CIs + mixed directions

→ High variability / heterogeneity

❌ Diamond crosses line of no effect

→ No significant overall effect

Common measures shown on forest plots

Odds Ratio (OR)
Risk Ratio (RR)
Hazard Ratio (HR)
Mean Difference (MD)
Standardized Mean Difference (SMD)

One-line exam answer 🧠

A forest plot graphically displays individual study effects and their confidence intervals in a meta-analysis, along with a pooled overall effect, allowing visual assessment of effect size, precision, and consistency.

TABLE 1 — SURVIVAL ANALYSIS: WHAT IT IS + WHEN USED + CENSORING

Item	Zero-omission details
What survival analysis studies	How long (time) it takes until an event happens (time-to-event)
Typical “events” (when to use)	Time until death; recurrence; discharge; stroke; any outcome where time to event matters
Why normal methods fail	Because many participants don’t have the event observed during follow-up → you’d lose info if you delete them
Censored data (why it exists)	People may leave the study, be lost to follow-up, or not yet experience the event before study ends
Meaning of “censored”	Event time is unknown beyond a point (we know they survived/event-free up to last contact)
Key rule	Do not throw censored patients away → survival methods incorporate them

TABLE 2 — LIFE TABLES (ACTUARIAL METHOD)

Item	Zero-omission details
What a life table shows	Proportion surviving at fixed time intervals
Example intervals	1 month, 3 months, 6 months, 1 year
How it works (core logic)	Split follow-up into chunks (e.g., monthly). At each interval count: alive, died, censored
Output style	Survival updated only at interval boundaries
Strength	Gives a rough picture of survival over time
Limitation vs KM	Less precise than Kaplan–Meier because it doesn’t update survival at each event, only at fixed intervals
Current use	Less commonly used now (per your summary)

TABLE 3 — KAPLAN–MEIER PLOT (KM CURVE) “PRODUCT-LIMIT METHOD”

Item	Zero-omission details
Other name	Product-limit method
How common	Most commonly used survival method in medical research
What makes KM special	Recalculates survival every time an event happens
Shape	Step-down curve (drops at each event)
Axes	X-axis = time; Y-axis = cumulative survival (%)
Event marking	Each death/event → step down
Censor marking	Censored cases shown as a tiny vertical tick on the curve
Example interpretation (from book)	“At 20 years, 36% are alive” (read off X=20 years → Y=36%)
Comparing groups visually	Plot two (or more) curves (e.g., men vs women; treatment vs placebo)
Statistical test to compare curves	Log-rank test

TABLE 4 — LOG-RANK TEST (COMPARING SURVIVAL CURVES)

Item	Zero-omission details
Purpose	Compare two or more Kaplan–Meier survival curves
Null hypothesis (H₀)	“There is no difference in survival between the groups.”
Output	P value
Interpretation rule	P < 0.05 → statistically significant difference; P > 0.05 → curves not different

TABLE 5 — COX REGRESSION (PROPORTIONAL HAZARDS MODEL)

Item	Zero-omission details
Name	Cox regression model
Also called	Proportional hazards model
When used	When you want to know how a factor affects time until event
Example questions	Does being male shorten survival? Does smoking increase risk of heart attack? Does treatment A vs B change death risk?
Key output	Hazard Ratio (HR) (the “heart” of Cox)
Typical reported outputs	HR, 95% CI, P value, degrees of freedom (less clinically important)
Why powerful	Can adjust for multiple factors simultaneously
Examples of adjustment variables	Age, sex, smoking, diabetes, treatment group
Clinical use	Understand treatment effects, gender effects, comorbidity effects, lifestyle effects (smoking, obesity)

TABLE 6 — HAZARD RATIO (HR): MEANING + INTERPRETATION

Item	Zero-omission details
What “hazard” means	Instantaneous risk of the event happening at a given moment
What HR compares	Hazard in one group vs another at any moment in time
HR = 1	No difference between groups
HR > 1	Higher risk in the first group (worse outcome)
HR < 1	Lower risk in the first group (protective)
Example (book: rheumatoid arthritis study)	HR (men vs women) = 1.91 → at any moment men have 1.91× the risk of death vs women
Confidence interval (CI) role	If CI does NOT include 1 → statistically significant
Example CI given	1.21 to 3.01 → significant because it does not cross 1

TABLE 7 — QUICK “FINAL SUMMARY” (ONE-LOOK EXAM TABLE)

Method/Concept	What it is	Key exam line
Life table	Survival at fixed intervals	Less used now; less precise than KM
Kaplan–Meier	Step-down survival curve; updates at each event	Use log-rank to compare curves
Log-rank test	Statistical test comparing survival curves	Tests “no survival difference” via P value
Cox regression	Model linking predictors to time-to-event	Main output = Hazard Ratio; adjusts for confounders
Hazard ratio	Relative instantaneous risk	1 = same; >1 worse; <1 protective; CI crossing 1 = NS