$title =

Biostats_CRVS_C4+Pooled

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$content = [

  • Cohort 3
    • Active: 12
    • Placebo: 4
    • EASI-75: 6 / 12 active (50%)
    • Placebo: 0 / 4
  • Cohort 4
    • Active: 12
    • Placebo: 12

Pooled totals (Cohorts 3 + 4)

  • Active: 24
  • Placebo: 16

C3 is directionally strong, but not ss due to small size.

C4 Scenarios

weak response (25% EASI-75)

Active: 3 / 12 (25%)

Placebo: 2 / 12

Pooled

GroupResponders%
Active9 / 2438%
Placebo2 / 1612.5%
  • Absolute difference: 25.5%
  • Fisher p ≈ 0.045–0.05

Intermediate response

Cohort 4

  • Active: 4 / 12 (33%)
  • Placebo: 2 / 12

Pooled

GroupResponders%
Active10 / 2442%
Placebo2 / 1612.5%
  • Absolute difference: 29.5%
  • Fisher p ≈ 0.025–0.03

strong response

Cohort 4

  • Active: 5 / 12 (42%)
  • Placebo: 2 / 12

Pooled

GroupResponders%
Active11 / 2446%
Placebo2 / 1612.5%
  • Absolute difference: 33.5%
  • Fisher p ≈ 0.01–0.015

Summary:

With Cohort 3 at 50% EASI-75:

Minimum Cohort-4 requirements to keep p < 0.05:

Placebo respondersCohort-4 active needed
2 / 16 (~12.5%)≥3 / 12 (25%)
3 / 16 (~19%)≥4 / 12 (33%)

Robust win:

≥42–50% EASI-75 in Cohort 4, even with ~15% placebo


What if placebo is unusually strong?

Placebo 3/12 = 18.8%

  • need 10 responders to show stat sig

Cohort 4

  • Active: 4 / 12
  • Placebo: 3 / 12

Pooled

GroupResponders%
Active10 / 2442%
Placebo3 / 1618.8%
  • Absolute difference: 23.2%
  • Fisher p ≈ 0.045–0.05

Placebo 4/12 = 25%

  • Need a 7/12 or 58% response to show stat sig.

Cohort 4

  • Active: 7 / 12 (58%)
  • Placebo: 3 / 12

Pooled

GroupResponders%
Active13 / 2454%
Placebo4 / 1625%
  • Absolute difference: 29%
  • Fisher p ≈ 0.03–0.04


MEAN EASI DATA

Sample size (pooled cohorts 3 + 4)

  • Active: 24
    • Cohort 3: 12
    • Cohort 4: 12
  • Placebo: 16
    • Cohort 3: 4
    • Cohort 4: 12

Observed Cohort 3 data (anchor)

  • Active mean EASI reduction: –64.8%
  • Placebo mean EASI reduction: –25%

Weak cohort 4 still hits ss

Cohort 4

  • Active mean: –45%
  • Placebo mean: –25%

Pooled means

GroupMean % EASI reduction
Active (24)–55%
Placebo (16)–25%
Difference–30%
  • Cohen’s d ≈ 1.0
  • p ≈ 0.006–0.01

IF Cohort 4 matches Cohort 3

Cohort 4

  • Active mean: –65%
  • Placebo mean: –25%

Pooled

GroupMean % EASI reduction
Active–65%
Placebo–25%
Difference–40%
  • Cohen’s d ≈ 1.4–1.5
  • p < 0.0005

Strong placebo mean response

Cohort 4

  • Active mean: –55%
  • Placebo mean: –35%

Pooled

GroupMean % EASI reduction
Active–60%
Placebo–35%
Difference–25%
  • p ≈ 0.015–0.03

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