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eduKateSG · Why Mathematics? · Platform Trials: Concurrent Controls, Calendar Time and Treatment Entry or Exit
Start with the question, audit the worked example, or jump to the assumptions and practice. Every chapter stays open for uninterrupted reading.
Understand the question
Define the quantity and follow the mechanism.Route 2 · Chapters 8–14
Reproduce the example
Audit the numbers one step at a time.Route 3 · Chapters 15–21
Check assumptions
See where design and calibration matter.Route 4 · Chapters 22–28
Explore applications
Connect the method to a concrete investigation.Route 5 · Chapters 29–42
Study and verify
Practise, inspect failure cases and read further.
Full chapter index · Practice and checking · Mathematics Learning Hub
Why is mathematics important when treatments enter and leave an ongoing trial? Platform trials reuse infrastructure and may share controls, but each comparison must respect eligibility, calendar time, changing standard of care, multiplicity and the treatment-specific estimand.
Did You Know? A participant assigned to control before a new arm opened could not have been randomised to that arm. FDA’s 2026 revised draft master-protocol guidance generally recommends primary comparisons use concurrently randomised, eligible controls rather than automatically borrowing earlier controls.
Full chapter index
Chapters 1–7 · Understand the question
Chapters 8–14 · Reproduce the example
Chapters 15–21 · Check assumptions
Chapters 22–28 · Explore applications
Chapters 29–42 · Study and verify
- Communication
- A spreadsheet workflow
- A coding workflow
- Applications and careers
- A student investigation
- Common misconceptions
- Connection to recent mathematics articles
- Guidance for students and parents
- Practice questions
- Frequently asked questions
- A reporting checklist
- The calendar is part of the design
- A final platform audit
- Useful next reading
A platform is an ongoing master protocol under which treatment substudies can enter or exit over time. Shared sites, governance, data systems and controls can reduce repeated start-up work.
Suppose arm A recruits in months 1–12 and arm B enters in month 7 and continues to month 18. Their eligible calendar windows differ.
Arm A can compare with eligible control participants in months 1–12. Arm B’s primary concurrent controls come from months 7–18, when participants could have been randomised to B.
Control participants from months 1–6 precede arm B. Including them without strong justification risks bias from changes in population, care, sites or measurement.
If arm B has 120 concurrent controls in months 7–18 and 60 earlier controls, the primary comparison may use 120. The earlier 60 may support a carefully labelled sensitivity analysis.
| Arm | Open months | Eligible concurrent control months |
|---|---|---|
| A | 1-12 | 1-12 |
| B | 7-18 | 7-18 |
Model periods fine enough to capture important change but not so fine that estimates become unstable. Randomisation within concurrent windows remains the strongest protection.
FDA’s *Master Protocols for Drug and Biological Product Development* is a revised draft issued June 2026 and explicitly says it is not for implementation. Read the status page.
| Control data | Count | Primary use |
|---|---|---|
| Months 7-18 concurrent | 120 | Primary comparison |
| Months 1-6 nonconcurrent | 60 | Excluded or sensitivity only |
The associated FDA recap says primary platform comparisons generally should include concurrently randomised participants who were eligible for the drug, because nonconcurrent controls can differ over time. Read the FDA recap.
A biomarker, age range or contraindication can make some control participants ineligible for an arm. Shared does not mean every control belongs to every contrast.
When arms enter or exit, probabilities change. Store the eligible set and probability vector for every participant so inference and audit reflect the actual design.
An arm may meet a prespecified efficacy rule and leave the platform. Final estimation must respect selection, stopping and the relevant concurrent-control data.
An arm can stop for futility, harm or feasibility. These conclusions are different and should be recorded with the exact boundary and evidence.
A new substudy needs approved objectives, dose, eligibility, control, error strategy and operational readiness. The platform label does not permit informal experimentation.
A control treatment can evolve during a long platform. The estimand and protocol must say which control applies and how transitions are handled.
Multiple treatments, populations, endpoints and repeated looks create a family of potential errors. The required error strategy depends on whether claims belong to one confirmatory family or distinct substudies.
Different schedules or routes make full blinding difficult. Multiple-dummy or substudy-specific blinding can reduce bias, but every approach has operational costs.
Two treatment estimates using overlapping controls are correlated. Joint reporting and multiplicity calculations should recognise that dependence.
Bayesian dynamic borrowing, commensurate priors and regression adjustments can use earlier controls under assumptions. They do not recreate randomisation across time.
A published review found nonconcurrent-control methods commonly downweight or model earlier data and emphasised noncomparability and bias concerns. Read the PubMed record.
New sites, variants, referral patterns or education cohorts can change baseline risk. Plot outcomes and covariates by arm-opening window and site.
Laboratory assays, assessment forms or endpoint adjudication may change. Calibration and version control are needed before combining periods.
Treatment-specific exposure and follow-up determine safety evidence. A platform’s large total sample does not automatically supply enough safety data for each arm.
Simulate staggered openings, time trends, eligibility, changing ratios, shared controls, arm decisions, missingness and the planned analysis.
A long-running school platform may add tutoring apps each term. Earlier control pupils face different teachers and calendars, so each app needs concurrent eligible comparison.
A standing committee coordinates versions, data access, arm entry, monitoring and public reporting. Decisions must remain traceable across years.
Show timelines, eligibility overlaps, concurrent counts, control outcomes over time, allocation probabilities, arm decisions, error rates and sensitivity analyses.
Reproduce the month windows and 120 versus 60 controls. Simulate no treatment effect with improving calendar outcomes and measure bias from naive borrowing.
A platform cannot make old data current, remove secular change, guarantee faster recruitment or turn heterogeneous substudies into one simple trial.
For every arm, report opening and closing dates, eligible concurrent controls, any borrowed data, time adjustment, stopping rule and estimand.
Build an arm-by-calendar table containing eligibility, randomisation ratios, concurrent control counts, versions, estimates, stopping decisions and borrowed-data flags.
Simulate enrolment as a time process. Unit-test arm availability, eligibility, probability updates, calendar periods, shared-control membership and version changes.
Platform designers, operations researchers, epidemiologists and education evaluators manage ongoing systems where evidence and options change over time.
Create a rising control outcome over 18 months and add arm B at month 7. Compare concurrent, all-control and time-adjusted estimates.
Shared control is not automatically concurrent control, a platform is not one timeless population, and modelling time cannot guarantee exchangeability.
The MAMS guide explains fixed arm sets and stages. The covariate-adaptive guide explains baseline balance.
Students should draw a calendar and mark which controls overlap each arm. Parents can ask whether an education comparison spans different school terms or policies.
- Mark concurrent windows.
- Count eligible controls.
- Add a time trend.
- Change randomisation ratios.
- Compare borrowing methods.
### Can earlier controls always be reused? No.
### Why concurrent controls? They preserve randomised comparability in the same period.
### Can arms enter later? Yes, with a governed substudy.
### Is FDA 2026 guidance final? No; the cited document is revised draft guidance.
Report master-protocol version, arm dates, eligibility, randomisation, concurrent controls, borrowed data and assumptions, calendar adjustment, multiplicity, stopping, safety and simulations.
Time determines which options were available and which controls are comparable. It is not merely a reporting date.
Confirm each contrast uses the right concurrent eligible controls, every protocol version is traceable and borrowed evidence is separated from randomised evidence.
Continue through the Mathematics Learning Hub. Recalculate the central worked example, identify the assumptions and explain which claim the result can and cannot support.
Extended practice laboratory
Practice case 1: Define platform question
Setup: Start from the article’s platform-trial comparison mechanism for case 1. Task: Change the named quantity, recompute the dependent result and compare with the original.
Check: Preserve the estimand and design, verify the statistical identity, state one diagnostic, record units and compare one defensible alternative with clear reasoning. Show the arithmetic, name the response and predictor units, and separate the numerical result from the claim it supports. Then vary one defensible assumption, calculate again and explain whether the conclusion changed because of the data, the fitted model or the validation purpose. Finish with one compact table or graph that could reveal a failure hidden by the summary.
Practice case 2: Open first arm
Setup: Start from the article’s platform-trial comparison mechanism for case 2. Task: Change the named quantity, recompute the dependent result and compare with the original.
Check: Preserve the estimand and design, verify the statistical identity, state one diagnostic, record units and compare one defensible alternative with clear reasoning. Show the arithmetic, name the response and predictor units, and separate the numerical result from the claim it supports. Then vary one defensible assumption, calculate again and explain whether the conclusion changed because of the data, the fitted model or the validation purpose. Finish with one compact table or graph that could reveal a failure hidden by the summary.
Practice case 3: Open second arm later
Setup: Start from the article’s platform-trial comparison mechanism for case 3. Task: Change the named quantity, recompute the dependent result and compare with the original.
Check: Preserve the estimand and design, verify the statistical identity, state one diagnostic, record units and compare one defensible alternative with clear reasoning. Show the arithmetic, name the response and predictor units, and separate the numerical result from the claim it supports. Then vary one defensible assumption, calculate again and explain whether the conclusion changed because of the data, the fitted model or the validation purpose. Finish with one compact table or graph that could reveal a failure hidden by the summary.
Practice case 4: Define concurrency window
Setup: Start from the article’s platform-trial comparison mechanism for case 4. Task: Change the named quantity, recompute the dependent result and compare with the original.
Check: Preserve the estimand and design, verify the statistical identity, state one diagnostic, record units and compare one defensible alternative with clear reasoning. Show the arithmetic, name the response and predictor units, and separate the numerical result from the claim it supports. Then vary one defensible assumption, calculate again and explain whether the conclusion changed because of the data, the fitted model or the validation purpose. Finish with one compact table or graph that could reveal a failure hidden by the summary.
Practice case 5: Count concurrent controls
Setup: Start from the article’s platform-trial comparison mechanism for case 5. Task: Change the named quantity, recompute the dependent result and compare with the original.
Check: Preserve the estimand and design, verify the statistical identity, state one diagnostic, record units and compare one defensible alternative with clear reasoning. Show the arithmetic, name the response and predictor units, and separate the numerical result from the claim it supports. Then vary one defensible assumption, calculate again and explain whether the conclusion changed because of the data, the fitted model or the validation purpose. Finish with one compact table or graph that could reveal a failure hidden by the summary.
Practice case 6: Exclude nonconcurrent controls
Setup: Start from the article’s platform-trial comparison mechanism for case 6. Task: Change the named quantity, recompute the dependent result and compare with the original.
Check: Preserve the estimand and design, verify the statistical identity, state one diagnostic, record units and compare one defensible alternative with clear reasoning. Show the arithmetic, name the response and predictor units, and separate the numerical result from the claim it supports. Then vary one defensible assumption, calculate again and explain whether the conclusion changed because of the data, the fitted model or the validation purpose. Finish with one compact table or graph that could reveal a failure hidden by the summary.
Practice case 7: Model calendar period
Setup: Start from the article’s platform-trial comparison mechanism for case 7. Task: Change the named quantity, recompute the dependent result and compare with the original.
Check: Preserve the estimand and design, verify the statistical identity, state one diagnostic, record units and compare one defensible alternative with clear reasoning. Show the arithmetic, name the response and predictor units, and separate the numerical result from the claim it supports. Then vary one defensible assumption, calculate again and explain whether the conclusion changed because of the data, the fitted model or the validation purpose. Finish with one compact table or graph that could reveal a failure hidden by the summary.
Practice case 8: Change randomisation ratio
Setup: Start from the article’s platform-trial comparison mechanism for case 8. Task: Change the named quantity, recompute the dependent result and compare with the original.
Check: Preserve the estimand and design, verify the statistical identity, state one diagnostic, record units and compare one defensible alternative with clear reasoning. Show the arithmetic, name the response and predictor units, and separate the numerical result from the claim it supports. Then vary one defensible assumption, calculate again and explain whether the conclusion changed because of the data, the fitted model or the validation purpose. Finish with one compact table or graph that could reveal a failure hidden by the summary.
Practice case 9: Graduate an arm
Setup: Start from the article’s platform-trial comparison mechanism for case 9. Task: Change the named quantity, recompute the dependent result and compare with the original.
Check: Preserve the estimand and design, verify the statistical identity, state one diagnostic, record units and compare one defensible alternative with clear reasoning. Show the arithmetic, name the response and predictor units, and separate the numerical result from the claim it supports. Then vary one defensible assumption, calculate again and explain whether the conclusion changed because of the data, the fitted model or the validation purpose. Finish with one compact table or graph that could reveal a failure hidden by the summary.
Practice case 10: Drop an arm
Setup: Start from the article’s platform-trial comparison mechanism for case 10. Task: Change the named quantity, recompute the dependent result and compare with the original.
Check: Preserve the estimand and design, verify the statistical identity, state one diagnostic, record units and compare one defensible alternative with clear reasoning. Show the arithmetic, name the response and predictor units, and separate the numerical result from the claim it supports. Then vary one defensible assumption, calculate again and explain whether the conclusion changed because of the data, the fitted model or the validation purpose. Finish with one compact table or graph that could reveal a failure hidden by the summary.
Practice case 11: Add a new arm
Setup: Start from the article’s platform-trial comparison mechanism for case 11. Task: Change the named quantity, recompute the dependent result and compare with the original.
Check: Preserve the estimand and design, verify the statistical identity, state one diagnostic, record units and compare one defensible alternative with clear reasoning. Show the arithmetic, name the response and predictor units, and separate the numerical result from the claim it supports. Then vary one defensible assumption, calculate again and explain whether the conclusion changed because of the data, the fitted model or the validation purpose. Finish with one compact table or graph that could reveal a failure hidden by the summary.
Practice case 12: Update standard of care
Setup: Start from the article’s platform-trial comparison mechanism for case 12. Task: Change the named quantity, recompute the dependent result and compare with the original.
Check: Preserve the estimand and design, verify the statistical identity, state one diagnostic, record units and compare one defensible alternative with clear reasoning. Show the arithmetic, name the response and predictor units, and separate the numerical result from the claim it supports. Then vary one defensible assumption, calculate again and explain whether the conclusion changed because of the data, the fitted model or the validation purpose. Finish with one compact table or graph that could reveal a failure hidden by the summary.
Practice case 13: Protect blinding
Setup: Start from the article’s platform-trial comparison mechanism for case 13. Task: Change the named quantity, recompute the dependent result and compare with the original.
Check: Preserve the estimand and design, verify the statistical identity, state one diagnostic, record units and compare one defensible alternative with clear reasoning. Show the arithmetic, name the response and predictor units, and separate the numerical result from the claim it supports. Then vary one defensible assumption, calculate again and explain whether the conclusion changed because of the data, the fitted model or the validation purpose. Finish with one compact table or graph that could reveal a failure hidden by the summary.
Practice case 14: Protect familywise error
Setup: Start from the article’s platform-trial comparison mechanism for case 14. Task: Change the named quantity, recompute the dependent result and compare with the original.
Check: Preserve the estimand and design, verify the statistical identity, state one diagnostic, record units and compare one defensible alternative with clear reasoning. Show the arithmetic, name the response and predictor units, and separate the numerical result from the claim it supports. Then vary one defensible assumption, calculate again and explain whether the conclusion changed because of the data, the fitted model or the validation purpose. Finish with one compact table or graph that could reveal a failure hidden by the summary.
Practice case 15: Define arm-specific estimand
Setup: Start from the article’s platform-trial comparison mechanism for case 15. Task: Change the named quantity, recompute the dependent result and compare with the original.
Check: Preserve the estimand and design, verify the statistical identity, state one diagnostic, record units and compare one defensible alternative with clear reasoning. Show the arithmetic, name the response and predictor units, and separate the numerical result from the claim it supports. Then vary one defensible assumption, calculate again and explain whether the conclusion changed because of the data, the fitted model or the validation purpose. Finish with one compact table or graph that could reveal a failure hidden by the summary.
Practice case 16: Add eligibility change
Setup: Start from the article’s platform-trial comparison mechanism for case 16. Task: Change the named quantity, recompute the dependent result and compare with the original.
Check: Preserve the estimand and design, verify the statistical identity, state one diagnostic, record units and compare one defensible alternative with clear reasoning. Show the arithmetic, name the response and predictor units, and separate the numerical result from the claim it supports. Then vary one defensible assumption, calculate again and explain whether the conclusion changed because of the data, the fitted model or the validation purpose. Finish with one compact table or graph that could reveal a failure hidden by the summary.
Practice case 17: Add site drift
Setup: Start from the article’s platform-trial comparison mechanism for case 17. Task: Change the named quantity, recompute the dependent result and compare with the original.
Check: Preserve the estimand and design, verify the statistical identity, state one diagnostic, record units and compare one defensible alternative with clear reasoning. Show the arithmetic, name the response and predictor units, and separate the numerical result from the claim it supports. Then vary one defensible assumption, calculate again and explain whether the conclusion changed because of the data, the fitted model or the validation purpose. Finish with one compact table or graph that could reveal a failure hidden by the summary.
Practice case 18: Add outcome drift
Setup: Start from the article’s platform-trial comparison mechanism for case 18. Task: Change the named quantity, recompute the dependent result and compare with the original.
Check: Preserve the estimand and design, verify the statistical identity, state one diagnostic, record units and compare one defensible alternative with clear reasoning. Show the arithmetic, name the response and predictor units, and separate the numerical result from the claim it supports. Then vary one defensible assumption, calculate again and explain whether the conclusion changed because of the data, the fitted model or the validation purpose. Finish with one compact table or graph that could reveal a failure hidden by the summary.
Practice case 19: Handle shared controls
Setup: Start from the article’s platform-trial comparison mechanism for case 19. Task: Change the named quantity, recompute the dependent result and compare with the original.
Check: Preserve the estimand and design, verify the statistical identity, state one diagnostic, record units and compare one defensible alternative with clear reasoning. Show the arithmetic, name the response and predictor units, and separate the numerical result from the claim it supports. Then vary one defensible assumption, calculate again and explain whether the conclusion changed because of the data, the fitted model or the validation purpose. Finish with one compact table or graph that could reveal a failure hidden by the summary.
Practice case 20: Estimate treatment effect
Setup: Start from the article’s platform-trial comparison mechanism for case 20. Task: Change the named quantity, recompute the dependent result and compare with the original.
Check: Preserve the estimand and design, verify the statistical identity, state one diagnostic, record units and compare one defensible alternative with clear reasoning. Show the arithmetic, name the response and predictor units, and separate the numerical result from the claim it supports. Then vary one defensible assumption, calculate again and explain whether the conclusion changed because of the data, the fitted model or the validation purpose. Finish with one compact table or graph that could reveal a failure hidden by the summary.
Practice case 21: Simulate time trends
Setup: Start from the article’s platform-trial comparison mechanism for case 21. Task: Change the named quantity, recompute the dependent result and compare with the original.
Check: Preserve the estimand and design, verify the statistical identity, state one diagnostic, record units and compare one defensible alternative with clear reasoning. Show the arithmetic, name the response and predictor units, and separate the numerical result from the claim it supports. Then vary one defensible assumption, calculate again and explain whether the conclusion changed because of the data, the fitted model or the validation purpose. Finish with one compact table or graph that could reveal a failure hidden by the summary.
Practice case 22: Simulate staggered entry
Setup: Start from the article’s platform-trial comparison mechanism for case 22. Task: Change the named quantity, recompute the dependent result and compare with the original.
Check: Preserve the estimand and design, verify the statistical identity, state one diagnostic, record units and compare one defensible alternative with clear reasoning. Show the arithmetic, name the response and predictor units, and separate the numerical result from the claim it supports. Then vary one defensible assumption, calculate again and explain whether the conclusion changed because of the data, the fitted model or the validation purpose. Finish with one compact table or graph that could reveal a failure hidden by the summary.
Practice case 23: Audit governance
Setup: Start from the article’s platform-trial comparison mechanism for case 23. Task: Change the named quantity, recompute the dependent result and compare with the original.
Check: Preserve the estimand and design, verify the statistical identity, state one diagnostic, record units and compare one defensible alternative with clear reasoning. Show the arithmetic, name the response and predictor units, and separate the numerical result from the claim it supports. Then vary one defensible assumption, calculate again and explain whether the conclusion changed because of the data, the fitted model or the validation purpose. Finish with one compact table or graph that could reveal a failure hidden by the summary.
Practice case 24: Name limits
Setup: Start from the article’s platform-trial comparison mechanism for case 24. Task: Change the named quantity, recompute the dependent result and compare with the original.
Check: Preserve the estimand and design, verify the statistical identity, state one diagnostic, record units and compare one defensible alternative with clear reasoning. Show the arithmetic, name the response and predictor units, and separate the numerical result from the claim it supports. Then vary one defensible assumption, calculate again and explain whether the conclusion changed because of the data, the fitted model or the validation purpose. Finish with one compact table or graph that could reveal a failure hidden by the summary.
Practice case 25: Write conclusion
Setup: Start from the article’s platform-trial comparison mechanism for case 25. Task: Change the named quantity, recompute the dependent result and compare with the original.
Check: Preserve the estimand and design, verify the statistical identity, state one diagnostic, record units and compare one defensible alternative with clear reasoning. Show the arithmetic, name the response and predictor units, and separate the numerical result from the claim it supports. Then vary one defensible assumption, calculate again and explain whether the conclusion changed because of the data, the fitted model or the validation purpose. Finish with one compact table or graph that could reveal a failure hidden by the summary.