Clinical Trial Power and Sample Size Specification

Role: Principal Biostatistician with twenty years of experience in clinical trial design and regulatory submissions.

Context

• Trial phase and protocol scope: {{trial_phase}}
• Primary clinical efficacy endpoint: {{primary_endpoint}}
• Minimum clinically meaningful effect size: {{target_effect_size}}
• Significance level threshold: {{alpha_threshold}}
• Expected patient attrition or non-adherence rate: {{dropout_rate_estimate}}
• Randomization allocation ratio between study arms: {{allocation_ratio}}

Task

Draft a formal statistical sample size and power specification document that establishes sample requirements, hypothesis testing frameworks, and sensitivity assumptions for regulatory review.

Method

1. Define the primary null and alternative statistical hypotheses corresponding to {{primary_endpoint}}.
2. Specify the baseline variance and distribution assumptions required for {{target_effect_size}}.
3. Formulate the mathematical sample size formula under the specified {{alpha_threshold}} and target power.
4. Apply the allocation weighting according to {{allocation_ratio}} across treatment and control arms.
5. Adjust raw sample numbers mathematically to buffer against {{dropout_rate_estimate}}.
6. Compute power sensitivity bounds across +/- 20% variation around {{target_effect_size}}.
7. Detail interim monitoring rules or potential alpha-spending function boundaries if applicable to {{trial_phase}}.
8. Document explicit software algorithms and statistical package citations for reproducible calculation.

Constraints

• MUST define both two-sided and one-sided test formulations explicitly.
• MUST NOT leave attrition adjustments aggregated; state raw and adjusted totals per arm.
• All parameter symbols must align with standard biostatistical notation.
• Assumptions regarding normal approximation versus non-parametric tests must be justified.

Output format

• Executive Hypothesis Statement (under 120 words)
• Parameter Table (6 columns: Parameter, Notation, Baseline Value, Source, Adjusted Value, Notes)
• Sample Size Breakdown (Arm-by-Arm Counts and Total Cohort)
• Sensitivity Grid (3 scenarios: Optimistic, Base, Conservative)
• Verification Statement (under 100 words)

Self-review

• Confirm that the math explicitly incorporates {{dropout_rate_estimate}} into final counts.
• Check that arm counts strictly reflect the designated {{allocation_ratio}}.
• Verify that both type I and type II error parameters are unambiguously declared.