Cumulative Incidence - A Detailed Explanation

Definition

• Incidence proportion
• Attack rate (in outbreak settings)
• Risk (in clinical settings)
• Probability of getting disease

The Formula

• It is a dimensionless proportion - ranges from 0 to 1 (or 0% to 100%)
• Always tied to a specific time period (it is meaningless without one)
• The denominator must include only disease-free individuals at the start
• Everyone in the denominator must have been followed for the entire period

Step-by-Step Example 1: Flu Vaccine Study

Step-by-Step Example 2: Diabetes Death Study (from CDC)

Step-by-Step Example 3: Global Blindness (Real-World Scale)

• Global population in 2000: ~6,000 million
• Existing cases of blindness (prevalent): ~50 million
• Population at risk = 6,000 - 50 = 5,950 million
• New cases of blindness per year: ~7 million

Key Concepts to Understand CI Deeply

1. The Time Dimension is Mandatory

• "Risk of lung cancer = 5%" tells you nothing
• "Risk of lung cancer over 10 years among heavy smokers = 5%" is clinically useful

2. Assumptions of CI

• All individuals in the denominator were followed for the entire period
• No one was lost to follow-up (censored)
• No competing risks (dying of something else before getting the disease)

3. Cumulative Incidence vs. Incidence Rate

4. Cumulative Incidence vs. Prevalence

Clinical Use Cases

1. Informing patients: "You have a 20% risk of a second heart attack in the next 5 years" - this is a cumulative incidence statement.
2. Vaccine trials: "The cumulative incidence of infection was 1.8% in the vaccine group vs. 7.2% in placebo over 12 months" - basis for calculating vaccine efficacy.
3. Outbreak investigations: "Attack rate (CI) of food poisoning among cruise ship passengers = 35% over 7 days."
4. Cancer screening: "10-year cumulative incidence of breast cancer among BRCA1 carriers."

Outbreak Example in Detail (Food Poisoning)

• Among chicken-salad eaters: 30 got sick → CI = 30/60 = 50%
• Among non-eaters: 2 got sick → CI = 2/20 = 10%

Summary

Denominator: "People at Risk at Start" vs. "Total Person-Time at Risk"

Part 1 - The Core Difference with a Simple Analogy

• Count-based (CI denominator): Count how many runners started - assume they all ran the full 5 years.
• Time-based (Incidence Rate denominator): Measure the actual metres each runner covered before they stopped.

Part 2 - Side-by-Side Illustrated Example

The Setup

Method 1: "People at Risk at Start" (Cumulative Incidence Denominator)

• Everyone is followed for the same fixed period
• No one drops out (no loss to follow-up)
• No competing deaths (no one dies of something else)

Method 2: "Total Person-Time at Risk" (Incidence Rate Denominator)

Part 3 - How to Decide "Who is People at Risk at Start"?

"have the potential to get the disease and be included in the numerator"

The 3 Criteria for Being "At Risk":

• Someone already diagnosed with diabetes on Day 1 is NOT at risk of "getting" diabetes - they already have it.
• They go in neither numerator nor denominator.

• Studying ovarian cancer? Denominator = women only (men have no ovaries, so they cannot get it - they are not at risk)
• Studying prostate cancer? Denominator = men only
• Studying cervical cancer? Exclude women who had hysterectomy (no cervix = not at risk)
• Studying post-partum depression? Denominator = women who just gave birth

• At a dinner party food poisoning investigation: only people who attended the dinner are at risk - not the whole town
• Only those who ate the specific food are at risk for that food-borne illness

Decision Table

Part 4 - Visual Timeline (What Person-Time Looks Like)

Year:     0    1    2    3    4    5
Person A: [====|====|====|====|====]  → 5 years
Person B: [====|====|====X          ]  → 3 years (X = got disease)
Person C: [====|====L               ]  → 2 years (L = lost to follow-up)
Person D: [====†                    ]  → 1 year  († = died, unrelated)
Person E: [====|====|====|====|====]  → 5 years
                                        Total = 16 person-years

Part 5 - When to Use Which Denominator

Summary in One Sentence Each

• "People at risk at start" = a simple headcount of disease-free individuals on Day 1. Assumes everyone contributed equally. Clean but fragile - fails when people drop out.
• "Total person-time at risk" = the sum of each individual's actual observed at-risk time. Accounts for dropouts, competing deaths, and unequal follow-up. More accurate but requires tracking each person's timeline.

Cumulative Incidence Ratio (CIR)

What It Is

The Formula

• CI (exposed) = a / (a+b)
• CI (unexposed) = c / (c+d)
• CIR = [a/(a+b)] ÷ [c/(c+d)]

How to Interpret CIR

Example 1 - Smoking and Lung Cancer (Classic)

• Smokers who developed lung cancer: 17 out of 100 → CI = 17%
• Non-smokers who developed lung cancer: 1 out of 100 → CI = 1%

Example 2 - Factory Workers and Lung Disease

• CI (exposed) = 800/1,000 = 80%
• CI (unexposed) = 40/2,000 = 2%

Example 3 - Statin Drug Trial (Protective Exposure)

• CI (Pravastatin) = 32/3,302 = 0.0097 (0.97%)
• CI (Placebo) = 41/3,293 = 0.01245 (1.24%)

CIR and Its Related Measures

Applying all to the Statin Example:

• CIR = 0.78 (22% lower risk with statin)
• RRR = 1 - 0.78 = 0.22 = 22% (statin reduced relative risk by 22%)
• ARR = 1.24% - 0.97% = 0.27% (only 0.27 percentage points absolute difference)
• NNT = 1/0.0027 = ~370 (you need to treat 370 people for 5 years to prevent 1 death)

Important Limitations of CIR

• CIR requires that you directly measure CI in both exposed and unexposed groups from the start.
• In case-control studies, you cannot calculate CI (you sampled by disease status, not exposure status), so you use the Odds Ratio (OR) instead.

• OR always overestimates the strength of association compared to CIR when the outcome is common (>10%).
• For rare diseases, OR ≈ CIR (the "rare disease assumption").
• For common outcomes, always prefer CIR over OR when possible.

• CIR is based on CI, which assumes everyone was followed for the full period (as discussed previously). If there's heavy loss to follow-up, use Incidence Rate Ratio (IRR) instead.

CIR vs. IRR - Quick Distinction

Summary

CIR = CI (Exposed)
      ─────────────────
      CI (Unexposed)

CIR = 1   → No difference
CIR > 1   → Exposure causes harm
CIR < 1   → Exposure is protective