Factorial and Adaptive Designs AI Prompt

Design a factorial or adaptive experimental design for this study.

Research question: {{research_question}}
Factors: {{factors}} (each factor and its levels)
Adaptive elements needed: {{adaptive_needs}} (interim analysis, arm dropping, response-adaptive randomization)

1. Factorial designs:

   Full factorial:
   - All combinations of factor levels are tested
   - 2^k design: k factors each at 2 levels → 2^k treatment combinations
   - Advantages: tests main effects AND interactions simultaneously
   - Sample size: same n needed per cell as a one-factor design, but tests many more questions
   - Key output: interaction plot — does the effect of factor A depend on the level of factor B?

   Fractional factorial:
   - Test only a fraction of all 2^k combinations (e.g. 2^(k-p) design)
   - Aliasing: main effects are confounded with high-order interactions
   - Use when: k is large and high-order interactions are assumed negligible
   - Resolution III: main effects aliased with 2-way interactions (minimum for screening)
   - Resolution V: main effects and 2-way interactions estimable (preferred for confirmatory)

2. Adaptive designs:

   Group sequential design:
   - Pre-planned interim analyses at specified information fractions (e.g. at 50% and 100% of n)
   - Spending functions control Type I error across looks:
     - O'Brien-Fleming: strict early stopping, liberal late (good when early stopping is rare)
     - Pocock: equal thresholds at each look (more liberal early)
   - Stopping rules: stop for efficacy (p < boundary), futility (conditional power < 20%), or safety

   Response-adaptive randomization:
   - Allocation probabilities update based on accumulating outcome data
   - More participants assigned to the arm showing better performance
   - Pros: ethical (fewer participants in inferior arm)
   - Cons: increases bias risk, complicates inference; FDA skepticism in confirmatory trials

   Platform trials:
   - Multiple interventions tested simultaneously on a shared control arm
   - Arms can enter and exit the platform based on interim results
   - Efficient for rapid testing of many treatments (COVID-19 trials used this)

3. Analysis for adaptive designs:
   - Naive p-values from adaptive designs are invalid (inflation of Type I error)
   - Use: conditional power, stagewise p-values (combination function), or Bayesian posterior probabilities
   - Closed testing principle: preserves familywise error rate when multiple hypotheses are tested

Return: factorial design specification (factors, combinations, sample size), interaction test plan, adaptive design choice with stopping boundaries, and analysis approach.