For your trial · regulatory-facing

Take it to your SAP

Describe a randomized trial. Get back the estimand, draft SAP text for a covariate-adjusted primary analysis, the sample size it buys you, simulated operating characteristics, the questions a reviewer will ask, and R code that runs.

Start from an example:

The question

ICH E9(R1) defines an estimand by its population, treatment, endpoint, intercurrent events and summary measure. Fill them in plainly; the SAP text uses your words.

Trial name Product Population Treatment Control Endpoint Timepoint Endpoint type Summary measure

Intercurrent events

Events after randomization that change how the endpoint is read, such as discontinuation, rescue therapy, crossover, or death.

The numbers

The one number that decides the gain is R²: how much of the endpoint's variance your baseline covariates explain. If the endpoint is the follow-up value and its correlation with baseline is r, R² is about r². If the endpoint is change from baseline (with similar variances at both times), R² is only about (1 − r)/2, because the change score has already used part of the baseline.

Effect to detect Outcome SD Control rate Treatment rate Two-sided α Power Allocation (treatment:control) Not evaluable (%)

R² explained by baseline covariates:

Where the R² comes from Baseline covariates Stratification factors

How to size the trial Conservative. Size for the unadjusted analysis and let adjustment buy extra power. FDA (2023) notes this is often the more conservative choice. Bank the gain. Size for the adjusted analysis and enrol fewer patients. Needs a documented, credible R².

Does it hold up?

Simulate the trial you planned, under no effect, under the planned effect, and when the working model misses the true shape. Reviewers ask for exactly this table.

The SAP text

Paste it into your SAP and edit. It updates as you change anything above, and includes the simulation table once you have run it.

What a reviewer will ask

The questions change with your choices. Each answer names its source.

The R script

Base R, no packages. It runs as is on example data with your covariate names; swap in the locked analysis dataset.

Sources: FDA (2023), Adjusting for Covariates in Randomized Clinical Trials for Drugs and Biological Products; ICH (2019), E9(R1) Addendum on Estimands and Sensitivity Analysis; EMA (2015), Guideline on adjustment for baseline covariates; Tsiatis, Davidian, Zhang and Lu (2008); Ye, Shao, Yi and Zhao (2023). Sample sizes use large-sample normal approximations; the simulation summarizes the covariates as one prognostic score. Check both against your own trial before relying on them.