Why Concurrent Control Sets Are Arm-Specific
In a platform trial, treatment arms can open and close at different times. A control participant enrolled while one arm is recruiting may not be a concurrent control for another arm that has not yet opened or has already closed. The relevant comparison therefore depends on the arm: it is not enough to ask whether a participant was enrolled somewhere in the platform.
This matters because calendar time can coincide with changes in standard care, eligibility, sites, follow-up, or outcome measurement. Randomization can support a fair comparison when treatment and control participants are assigned under the same contemporaneous trial conditions. A control enrolled outside an arm’s recruitment period does not become concurrent merely because that person belongs to the same platform.
The definition is operational, not merely a date filter. For an initial date-based construction, let \(O_j\) be the date arm \(j\) opens and \(C_j\) the date it closes. If the arm is open on the half-open interval \([O_j,C_j)\), and control is available for the relevant participants throughout that interval, the date-based set is
This rule needs refinement if control is unavailable for some dates, sites, or eligibility groups. In that case, include a control participant only if the participant could have been randomized to arm \(j\) or to control under the applicable randomization scheme and protocol at that time. The relevant date is ordinarily the randomization or enrollment date, not the later date on which the outcome is measured. Outcome timing and censoring still need to be handled consistently in the analysis.
Constructing the Sets Carefully
A clear construction begins with the arm’s actual recruitment window, rather than the overall platform’s start and end dates. Then identify when and where that arm could be assigned, and which participants met the arm-specific eligibility rules. This yields the set of controls eligible to contribute to that arm’s randomized comparison.
Record the dates during which the arm was open to randomization. State how boundary dates are treated, and use the same convention for controls and treatment participants.
Confirm that control and arm \(j\) were both available under the trial’s allocation process. A date on which only control was enrolling is not automatically concurrent for that arm.
Check site, eligibility criteria, and protocol version. If these differ across the platform, define the relevant concurrent set within the conditions that apply to arm \(j\).
Keep the rule reproducible. Record why controls outside the arm’s window or applicable conditions are excluded, rather than combining them into a platform-wide pool.
Worked Example: Different Opening Dates
Suppose arm A is open from January 1 through June 30, and arm B is open from March 1 through October 31. Control is available throughout both windows at the same sites, and eligibility and protocol conditions are unchanged. Use intervals that include the opening date and exclude the closing boundary after the last open day.
Arm A’s recruitment interval is January 1 through June 30. Its concurrent control set contains controls randomized during that interval. Arm B’s interval is March 1 through October 31, so its set contains controls randomized during that later interval. Controls enrolled in March through June may belong to both sets; January and February controls are not concurrent for B, and July through October controls are not concurrent for A.
For illustration, suppose A has 60 participants with the outcome among 200 randomized to A, and its concurrent controls have 72 with the outcome among 200 randomized to control. The risk difference, treatment minus control, is
The estimated outcome risk is 6 percentage points lower in A than in its concurrent controls. This is an illustrative randomized comparison, not evidence about a real treatment. It is meaningful as stated only if the outcome definition and follow-up are comparable for the two groups.
Why a Platform-Wide Set Can Mislead
A single platform-wide control set is the union of controls from all calendar periods. Comparing each arm with that same union can quietly introduce controls enrolled when that arm was not available. Those participants may have faced different standard care or trial conditions, so the comparison no longer reflects only the randomized contrast during the arm’s recruitment period.
The issue can be seen directly in a hypothetical example. Suppose arm A recruits January through June. Among its 60 participants, 18 experience the outcome by a fixed follow-up time. There are 60 concurrent controls, 24 of whom experience the outcome. Later, July through October, another 40 platform controls are enrolled, and 10 experience the outcome. Assume the later period has a lower outcome risk because care changed; this example does not assume that the change was caused by treatment.
With concurrent controls, the estimated risk difference is \(-0.10\), or 10 percentage points lower for A. Pooling in the later controls changes the estimate to \(-0.04\), or 4 percentage points lower. The difference arises because the platform-wide comparator includes people enrolled after A closed, during a period with a different underlying risk. The wider set is not automatically more appropriate just because it contains more controls.
This calculation illustrates a potential source of bias; it does not show that every platform-wide analysis is biased by a known amount. If conditions are stable, the numerical impact may be small. But stability is an assumption to justify, not a consequence of pooling.
Here \(g\) indexes the contemporaneous strata used in the comparison, \(\bar{Y}_{jg}\) and \(\bar{Y}_{0g}\) are the observed mean outcomes for arm \(j\) and control in stratum \(g\), and \(q_g\) are common target weights. The justification is that each within-stratum contrast targets the same stratum’s randomized comparison; applying the same weights then defines an average of those contrasts. Arm-specific concurrent sets identify which participants can contribute to these comparisons. The choice of weights determines the target population and should be stated; it is not fixed by the date rule alone.
Worked Example: A Control Can Be Concurrent for Two Arms
Suppose arm A is open April 1 through September 30, while arm B is open July 1 through December 31. Both arms and control are available at the same sites throughout their respective windows, with no changes in eligibility or protocol. A control participant randomized on August 15 can belong to both \(\mathcal{C}_A\) and \(\mathcal{C}_B\), because both arms were available then. A control participant randomized on May 10 can be in \(\mathcal{C}_A\), but not \(\mathcal{C}_B\).
Now suppose the hypothetical outcome counts are as follows: A has 30 outcomes among 100 participants; its concurrent controls have 36 among 120. B has 20 outcomes among 80 participants; its concurrent controls have 24 among 100. The corresponding crude risk differences are
The estimated difference is 0 percentage points for A and 1 percentage point higher outcome risk for B. These are distinct arm-specific contrasts, each using its own concurrent set. Some control participants may contribute to both contrasts, so the estimates are not necessarily statistically independent. Reusing a participant in two arm-specific comparisons does not justify treating that person as two independent people in a joint analysis.
Assumptions, Diagnostics, and Alternatives
The arm-specific date rule supports a comparison only when it corresponds to the trial’s actual randomization and measurement conditions. At a minimum, verify that the arm and control were jointly available, that participants met the relevant eligibility criteria, and that outcomes are defined and observed on comparable schedules. Randomization within the relevant comparison is central; calendar overlap alone does not repair departures from randomization or inconsistent outcome measurement.
Useful checks include plotting enrollment by arm and control over time, reviewing arm-specific opening and closing logs, and checking availability by site and protocol version. These checks can reveal apparent overlap when an arm was not actually offered at a site, a pause in control recruitment, or a change in eligibility that divides the period into distinct conditions. A date range written in a protocol is not a substitute for checking actual enrollment and assignment records.
The arm-specific set also has limitations. Restricting controls to the arm’s recruitment window may yield a smaller comparison group and wider uncertainty. It does not eliminate all time-related concerns: important changes can occur within the open window, and sites or patient characteristics may differ even among contemporaneous participants. The earlier material on calendar-time adjustment and period-stratified analysis addresses ways to model or stratify temporal variation; the definition of the set remains a design and data-construction decision.
| Approach | What enters the comparison | Main consideration |
|---|---|---|
| Arm-specific concurrent controls | Controls eligible for the arm’s contemporaneous randomized comparison | Preserves the arm’s time-specific comparison; may use fewer controls |
| One platform-wide control set | Controls from multiple arm-opening periods | Can include controls from dates when a particular arm was unavailable |
| Adding nonconcurrent controls | Concurrent controls plus controls from outside the arm’s window | May improve precision, but requires additional assumptions and careful interpretation |
The main practical distinction is between defining the randomized concurrent comparison and choosing whether to supplement it with other information. The concurrent set is the direct reference for the arm-specific randomized contrast. Any use of nonconcurrent participants is a separate analytical choice, not a reason to redefine every platform control as concurrent.
Common Mistakes
- Using the platform’s overall calendar span. The wrong reasoning is that every control enrolled during the platform belongs in every arm’s comparison. Instead, construct a set for each arm using that arm’s actual availability and relevant randomization conditions.
- Checking dates but not availability. A control enrolled during an arm’s nominal dates may still be ineligible for that comparison if the arm was not open at that site or under that protocol version.
- Assuming more controls always improve the comparison. More observations can reduce sampling uncertainty, but controls from a different period can also change the population being compared and introduce temporal differences.
- Assuming concurrent means identical. Calendar overlap does not ensure identical follow-up, measurement, or patient composition. Check these features and define the estimand and analysis accordingly.
Check Your Understanding
Answer each question, then compare your reasoning with the solutions.
- Arm C is open May through August. A control participant is randomized in September while another platform arm remains open. Is this participant concurrent for C? Why?
- Arm D and control are both available from January through June. Eligibility criteria change on April 1. What should be checked before treating all six months of controls as one concurrent set?
- Arm E has 40 outcomes among 160 participants. Its concurrent controls have 30 outcomes among 150. Calculate the crude risk difference in percentage points.
- Explain why one control participant may contribute to the concurrent sets for two different arms, and name one issue this creates for a joint analysis.
Solutions. (1) No. C closed at the end of August, so the September control was not enrolled while C was available. Its enrollment during the platform’s overall operation does not make it concurrent for C. (2) Check which eligibility criteria applied to each participant and whether the arm and control were both available under each version. If the change affects who could enter the comparison, define or analyze the corresponding periods separately rather than assuming one homogeneous set. (3) The treatment risk is \(40/160=0.25\), and the control risk is \(30/150=0.20\). Thus \(\widehat{RD}=0.25-0.20=0.05\), an estimated 5 percentage-point higher outcome risk in E. (4) The participant can be in both sets if randomized during a period when both arms and control were available under the relevant conditions. In a joint analysis, the shared participant induces dependence between the arm-specific estimates and must not be counted as independent in both comparisons.