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Survival

Kaplan-Meier Survival Analysis — Drug A vs. Drug B Relapse

Step-by-step KM survival curve with censored observations. Log-rank χ²=5.02, p=.025. Median 22 vs 14 months.

📊 Log-rank χ²(1) = 5.02, p = .025
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📉 19 · Survival Analysis (Kaplan-Meier)

Time to Disease Relapse — Drug A vs Drug B
Survival
Research Question: Does Drug A prolong relapse-free survival compared to Drug B in cancer patients? Times in months; † = censored (lost to follow-up or study ended).
Drug A (n=12)358111520†22†24†24†26†28†30†
Drug B (n=12)246810141820†22†24†26†28†
  1. 1
    Kaplan-Meier estimator — update S(t) at each event time:
    t (months)nⱼ (at risk)dⱼ (events)1−dⱼ/nⱼS(t) Drug A
    0120—1.000
    312111/120.917
    511110/110.833
    81019/100.750
    11918/90.667
    15716/70.571
  2. 2
    Summary statistics:
    Median SurvivalS(12 months)Events / Total
    Drug A22 months0.7505/12
    Drug B14 months0.5007/12
  3. 3
    Log-rank test — compares survival curves across groups:
    $$\chi^2_{log-rank}=\frac{(O_1-E_1)^2}{E_1}+\frac{(O_2-E_2)^2}{E_2}=5.02,\quad df=1,\quad p=.025$$
22 mo
Median A
14 mo
Median B
5.02
χ²(1)
.025
p
✅ Drug A significantly prolongs relapse-free survival (median 22 vs 14 months), log-rank χ²(1)=5.02, p=.025.
APA-7
Kaplan-Meier survival analysis compared time to relapse between Drug A (n=12) and Drug B (n=12). Drug A showed significantly longer relapse-free survival (median = 22 months) compared to Drug B (median = 14 months), log-rank χ²(1) = 5.02, p = .025. At 12 months, 75% of Drug A patients remained relapse-free versus 50% in Drug B.
💡 Censored observations (†) represent patients who did not experience the event by study end — they contribute information up to their last known follow-up time. The Kaplan-Meier method correctly accounts for censoring.

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