Protocol statistical sections: sample size and randomization

3 Trial Objectives and Associated Estimands

3.1 Primary Objective and Associated Estimand

Primary objective. To show that a single oral 100 mg dose of the SIMDRUG test tablet (T) is bioequivalent to the reference tablet (R) in healthy adults under fasting conditions, in rate (Cmax) and extent (AUC(0-t)) of exposure.

Estimand. The five attributes follow ICH E9(R1):

• Treatment: one 100 mg tablet of T, and one 100 mg tablet of R, each taken fasting, in a 2x2 crossover with a 14-day washout.
• Population: healthy adults who meet the eligibility criteria.
• Variable: Cmax and AUC(0-t) of SIMDRUG in plasma, from actual sampling times, for each participant and period.
• Intercurrent events: emesis within 2 hours of dosing, withdrawal before the second period, and a pre-dose concentration above 5% of that period's Cmax are handled with a hypothetical strategy (exposure had the event not occurred). The handling is set out in section 10.4.1.2 and in the statistical analysis plan.
• Population-level summary: the ratio of geometric means T/R with its two-sided 90% confidence interval. Bioequivalence is concluded for a parameter when the interval lies within 80.00% to 125.00%.

3.2 Secondary Objectives and Associated Estimands

• To compare AUC(0-inf), tmax and the terminal half-life between T and R (supportive, same estimand attributes).
• To describe the safety of single doses of T and R (treatment-emergent adverse events by treatment at onset).

4 Trial Design

4.1 Description of Trial Design

Randomized, open-label, single-center, single-dose, two-period, two-sequence crossover. Participants are randomized 1:1 to the sequence TR or RT and receive one dose on Day 1 and one on Day 15. Plasma is sampled before dosing and at 0.25, 0.5, 1, 1.5, 2, 3, 4, 6, 8, 12, 16, 24, 36 and 48 hours after each dose.

4.2.1 Rationale for Estimand(s)

The question is whether the two formulations deliver the same exposure when each is taken as directed. Events that interfere with absorption or with the comparison (emesis soon after dosing, carry-over, a missing period) do not reflect the formulations, so a hypothetical strategy targets exposure in their absence. A treatment-policy strategy is not used: it would mix formulation differences with events unrelated to them.

6 Trial Intervention and Concomitant Therapy

6.7.2 Randomization

A computer-generated permuted-block schedule assigns sequences TR and RT 1:1. The schedule is generated with a documented seed by a statistician outside the study team and loaded into the randomization system before the first participant is dosed. Following the M11 template, the block size is not stated in the protocol. (This worked example publishes its synthetic schedule and block size on the design page so that the generation and balance check can be inspected.)

10 Statistical Considerations

10.1 General Considerations

Analyses use R (R >= 4.4.0; this example ran on R 4.6.0) with package versions pinned in the study lockfile. Pharmacokinetic parameters are log-transformed (natural log) before inferential analysis. Bioequivalence is tested with two one-sided tests at the 5% level, equivalent to a two-sided 90% confidence interval for the T/R ratio of geometric means.

10.2 Analysis Sets

• Enrolled set: every participant who is randomized.
• Safety set: every participant who receives at least one dose.
• PK concentration set: participants in the safety set with at least one quantifiable post-dose concentration.
• PK parameter set: participants with at least one profile that yields the primary parameters.
• Bioequivalence set: participants with evaluable Cmax and AUC(0-t) after both T and R, after the exclusions in section 10.4.1.2 (ICH M13A: the primary analysis includes every participant with evaluable data for both products).

10.3 Analyses of Demographics and Other Baseline Variables

Demographics and baseline characteristics are summarized by sequence and overall for the safety set. No formal tests are performed.

10.4 Analyses Associated with the Primary Objective

10.4.1.1 Statistical Analysis Method

For each of ln(Cmax) and ln(AUC(0-t)), a general linear model with fixed effects for sequence, period, formulation and participant within sequence is fitted to the bioequivalence set (ICH M13A, Step 4 23 Jul 2024; FDA final 30 Oct 2024; EU effective 25 Jan 2025). The sequence effect is tested against the participant-within-sequence mean square; the other effects are tested against the residual mean square, and all four tests are reported. The T minus R difference in least-squares means and its 90% confidence interval are back-transformed to a ratio. Bioequivalence is concluded when both 90% intervals lie within 80.00% to 125.00%, judged on the unrounded limits. No test for carry-over is performed.

10.4.1.2 Handling of Data in Relation to Primary Estimand

The rules for removing data are pre-specified here and in the statistical analysis plan (ICH M13A 2.2.1 and 2.2.1.1). Two kinds of rule apply at different times:

• Documented before bioanalysis. Withdrawals, emesis and other protocol violations are recorded as they happen, and the decision to exclude is documented at the end of clinical sampling, before any concentration is known (ICH M13A 2.2.1 and 2.2.3.1). A period with emesis within 2 hours of dosing (twice the expected median tmax of 1 hour) is excluded.
• Applied to the bioanalytical results. A period whose pre-dose concentration is above 5% of that period's Cmax is excluded (carry-over, ICH M13A 2.2.3.3). A period whose AUC is below 5% of the geometric mean AUC of that product, calculated without the participant, may be excluded as very low exposure; at most one participant is expected (ICH M13A 2.2.1.1). Both rules need the measured concentrations, so they are applied, as written here, once bioanalysis is complete.

A participant without evaluable data for both products leaves the bioequivalence set but stays in the safety and PK sets.

10.4.1.3 Handling of Missing Data in Relation to Primary Estimand

No values are imputed. Missed samples are omitted from the profile. Concentrations below the lower limit of quantification (0.50 ng/mL) are set to zero in PK calculations wherever they occur, including between two quantifiable concentrations, and are omitted from the estimate of the terminal rate constant (ICH M13A 2.2.2.2).

10.4.1.5 Supplementary Analysis

Two supplementary analyses repeat the primary model: (1) with the periods excluded under section 10.4.1.2 put back, for participants who have both periods; (2) without the participants whose Cmax occurs at the first post-dose sample in either period, because their true Cmax may have been missed (ICH M13A 2.1.8.1). No separate sensitivity analysis is planned.

10.7 Safety Analyses

Treatment-emergent adverse events are summarized by the treatment taken at onset, counting each participant once per row, with the number of participants exposed to that treatment as the denominator.

10.9 Interim Analyses

None.

10.10 Multiplicity Adjustments

Bioequivalence requires both primary parameters to pass, so each is tested at the full 5% level (an intersection-union test) without adjustment.

10.11 Sample Size Determination

No earlier study of this synthetic product exists. The planning within-participant CV of 25% applies to both primary parameters. The simulator behind this example (sim_lifecycle/priors.R) puts occasion-to-occasion variability at 15% on apparent clearance plus an 8% proportional assay error; 25% adds a margin for a formulation that behaves less well than the simulator. The assumed true ratio is 0.95, a conventional allowance for a test product close to the reference (the simulator's true ratio is 1.00).

With two one-sided tests at the 5% level, acceptance limits of 80.00% to 125.00%, CV 25% and a ratio of 0.95, PowerTOST 1.5-7 (exact method) gives 28 evaluable participants for 80% power (achieved 80.7%) and 38 for 90% power (achieved 90.9%). The study plans for 90% power and allows for 5% of participants not being evaluable: 38 / (1 - 0.05), rounded up to an even number, gives 40 participants enrolled (20 per sequence). ICH M13A requires at least 12 evaluable participants; the plan exceeds that.

From pa.ABE(), power stays at or above 80% when one assumption moves while the others stay at plan: a CV up to 29.8%, a ratio down to 0.9232, or as few as 28 evaluable participants. The tables below show the rest of the sensitivity grid.

Evaluable participants needed (80% / 90% power)

Power with the planned 38 evaluable participants

Dropout inflation

Randomization schedule (synthetic)

Generated with blockrand 1.5, seed 2026, permuted blocks of 4 (block size shown here only because the study is synthetic). Balance check:

Files: randomization_schedule.csv, balance_check.csv, sample_size.csv, sensitivity_n.csv, sensitivity_power.csv, dropout_inflation.csv, design_parameters.json. Program: study/01_design/design.R.