Concurrent Controls as the Primary Comparison

Why Concurrency Matters

In a platform trial, treatment arms can open, pause, or close at different times. A control group enrolled while a particular treatment is available is usually the most directly comparable control group for that arm: both groups are drawn from people eligible at the same time, under the same trial setting, and are followed under the same contemporaneous procedures. Random assignment then supports a comparison of the assigned groups rather than a comparison of people selected into treatment and control by preference or prognosis.

“Concurrent” is a design and eligibility description, not a guarantee that every observed difference is caused by treatment. The relevant dates, eligibility criteria, allocation scheme, outcome definition, and analysis population must still be specified. In particular, if assignment probabilities vary across randomization strata, a pooled treatment-versus-control mean difference need not represent the average effect in the eligible population. The comparison must respect the randomization scheme.

Definition: For a particular treatment arm, the concurrent comparison window is the set of calendar dates on which (1) that arm is open and available for randomization, (2) the control arm is open and available for randomization, and (3) participants satisfying the prespecified eligibility criteria can be assigned to either group. It is defined on the date of randomization or enrollment, not by the dates on which outcomes are later measured. If availability is interrupted, the window can be a union of separate date intervals.

What the Comparison Estimates

Let \(A=1\) denote assignment to the treatment arm and \(A=0\) assignment to control. Let \(Y(1)\) and \(Y(0)\) be the outcomes that a participant would have under assignment to treatment and control, respectively. For a binary outcome such as response by a fixed time, \(Y(a)\) is 1 for a response under assignment \(a\), and 0 otherwise. The treatment effect for a target population can be expressed as the difference in its average potential outcomes, \(E[Y(1)]-E[Y(0)]\). In a randomized trial, this is an intention-to-treat effect: it compares assignment, regardless of whether participants adhere to the assigned intervention.

The target population here is the eligible population randomized during the specified concurrent window. Concurrency helps make that target population explicit. It also means that treatment and control participants are enrolled under overlapping calendar circumstances, rather than comparing current treatment participants with controls enrolled only in an earlier period. It does not, by itself, establish that the trial’s eligibility criteria stayed constant or that every analysis population is comparable; those features need to be checked in the protocol and data.

A simple marginal interpretation of the group means needs a particular randomization condition. If assignment is independent of the potential outcomes in the whole target population—for example, each eligible participant has the same assignment probability—then randomization supports the marginal comparison of treatment and control means. If randomization is instead conducted within strata, such as disease subtype or risk group, the appropriate basic comparison is conditional on those strata. The overall effect can then be formed by averaging the stratum-specific effects using weights that describe the target population.

Assumptions for a randomized concurrent comparison: (1) Consistency: each participant’s observed outcome equals the potential outcome under the assignment actually received, with treatment and outcome definitions applied consistently. (2) Randomization within the stated design: assignment is independent of potential outcomes conditional on any randomization strata or restrictions. (3) Positivity: within each stratum represented in the target population, both treatment and control have a nonzero probability of assignment. (4) No interference: one participant’s assignment does not change another participant’s outcome. The analysis must also use the stated eligibility criteria, outcome time point, and target population.

Why Stratification Changes the Pooled Comparison

Suppose \(S\) denotes a randomization stratum. Conditional randomization implies that, within a stratum, assigned treatment and control participants represent the same distribution of potential outcomes in expectation. With consistency, this gives

E[Y\mid A=1,S=s]=E[Y(1)\mid S=s],\qquad E[Y\mid A=0,S=s]=E[Y(0)\mid S=s].

Subtracting yields the stratum-specific causal contrast. To obtain an average effect for a target population with stratum proportions \(w_s=P(S=s)\), combine those contrasts using the target-population weights:

\sum_s w_s\left\{E[Y\mid A=1,S=s]-E[Y\mid A=0,S=s]\right\}.

This is not generally the same as subtracting the two pooled group means. If treatment assignment probabilities differ by stratum, the treatment group and control group can have different stratum compositions, even though randomization was correctly conducted within each stratum. A crude pooled difference can therefore combine treatment effects with a composition difference. This is why the assignment scheme and the intended target weights should be stated before interpreting a pooled estimate.

Worked Example: A Continuous Concurrent Window

Consider a hypothetical platform trial in which a new treatment and control are both available from 1 January through 30 June. Eligible participants are randomized during this period, and response is assessed 12 weeks after each participant’s randomization. Suppose the allocation probability is the same for every eligible participant. Among 80 treatment-assigned participants, 48 respond; among 80 control-assigned participants, 36 respond. Assume the same eligibility definition and response assessment apply to both groups, participants are analyzed by assignment, and there is no interference.

The concurrent comparison window is 1 January through 30 June, inclusive. The response proportions are

\hat p_1=\frac{48}{80}=0.600,\qquad \hat p_0=\frac{36}{80}=0.450.

The estimated difference in response proportions is

\hat p_1-\hat p_0=0.600-0.450=0.150.

Thus, in this hypothetical sample, the response proportion was 15.0 percentage points higher in the treatment-assigned group. Under the stated common-probability randomization and outcome assumptions, this difference estimates the treatment-versus-control effect for eligible participants randomized in that window. It is not, on its own, a statement about statistical significance or the size of uncertainty; no standard error or interval has been calculated here.

Derivation: Conditional Randomization Supports the Stratum Contrast

The key justification can be seen directly from the assumptions. Fix a stratum \(S=s\). Conditional randomization makes assignment independent of the potential outcome \(Y(a)\) within that stratum. Therefore, for either \(a=0\) or \(a=1\),

E[Y(a)\mid A=a,S=s]=E[Y(a)\mid S=s].

By consistency, participants assigned \(a\) have observed outcome \(Y=Y(a)\). Substituting this into the left-hand side gives

E[Y\mid A=a,S=s]=E[Y(a)\mid S=s].

Apply this equality once for treatment and once for control, then subtract:

E[Y\mid A=1,S=s]-E[Y\mid A=0,S=s] = E[Y(1)-Y(0)\mid S=s].

The right-hand side is the average assignment effect in stratum \(s\). Averaging these effects with the target population’s stratum proportions gives the population effect for that target. The argument does not imply \(E[Y\mid A=1]=E[Y(1)]\) marginally when assignment probabilities differ across strata; marginal equality requires marginal independence of assignment and potential outcomes, or an analysis that accounts for the strata.

Worked Example: Why the Crude Difference Can Mislead

Consider a hypothetical concurrent trial with two equally prevalent strata, each containing 100 participants. Randomization assigns treatment to 90 participants in stratum A and 10 in stratum B; the remaining participants in each stratum are assigned control. This is a valid illustration of randomization with stratum-specific assignment probabilities, not a common assignment probability. Suppose the observed response proportions are 0.800 for treatment and 0.700 for control in stratum A, and 0.400 for treatment and 0.300 for control in stratum B. Assume assignment is randomized within each stratum, both groups have positive assignment probability in each stratum, and the response definition is common.

The treatment-versus-control response difference is 0.100 in each stratum:

0.800-0.700=0.100,\qquad 0.400-0.300=0.100.

Because the target population has equal proportions in the two strata, the standardized difference is

$$ 0.5(0.100)+0.5(0.100)=0.100. $$

The pooled treatment mean uses 90 participants from A and 10 from B, whereas the pooled control mean uses 10 from A and 90 from B. Their response proportions are

\hat p_1=\frac{90(0.800)+10(0.400)}{100} =\frac{76}{100}=0.760,

\hat p_0=\frac{10(0.700)+90(0.300)}{100} =\frac{34}{100}=0.340.

The crude difference is \(0.760-0.340=0.420\), or 42.0 percentage points, even though the difference is 10.0 percentage points in each stratum. The discrepancy arises because the pooled groups have different stratum compositions. The appropriate target-population contrast in this example is the stratum-weighted 0.100, not the crude 0.420. Concurrency remains useful, but it does not justify ignoring the stratified allocation scheme.

Worked Example: A Window Interrupted by a Pause

In another hypothetical platform trial, a treatment arm and control are both open from 1 February through 31 March. The treatment arm then pauses, while control remains open, and treatment reopens from 16 April through 31 May. Eligible participants can be randomized to either group during the two periods of overlap. Assume the same eligibility criteria and endpoint are used in both periods. The concurrent comparison window is therefore the union of 1 February–31 March and 16 April–31 May; the pause is excluded.

Suppose the response data are as follows: in the first period, 12 of 20 treatment-assigned participants and 10 of 20 control-assigned participants respond; in the second period, 6 of 10 treatment-assigned participants and 5 of 10 control-assigned participants respond. The period-specific differences are

\frac{12}{20}-\frac{10}{20}=0.600-0.500=0.100, \qquad \frac{6}{10}-\frac{5}{10}=0.600-0.500=0.100.

Across the two periods, the treatment proportion is \(18/30=0.600\) and the control proportion is \(15/30=0.500\), giving a pooled difference of \(0.100\), or 10.0 percentage points. Here the period-specific differences agree, and the treatment and control groups have the same proportions from each period, so the pooled difference matches the period-weighted contrast. If those period compositions differed or the period-specific contrasts were not equal, the pooled difference would not automatically represent a chosen target population’s effect. The randomization design and target weights should guide the analysis.

Defining and Using the Window in Practice

A useful window specification is arm-specific. For each treatment, record the dates during which it was actually eligible for assignment, the corresponding dates during which control was available, and the eligibility version in force. If one treatment closes while others remain open, each arm can have a different concurrent window. For a treatment paused and later reopened, do not silently treat the gap as concurrent time.

The window concerns when participants enter the randomized comparison. It does not mean that all outcomes must be observed before the window closes. For example, a participant randomized near the final date may have a 12-week outcome measured after enrollment to that arm has stopped. The endpoint’s follow-up and data cutoff still need clear definitions, but they do not change that participant’s randomization date.

When eligibility changes after a protocol amendment, a calendar overlap alone is insufficient if people enrolled before and after the amendment do not belong to the same intended cohort. Specify which eligibility definition determines inclusion and which population the effect is intended to describe. A direct comparison should use participants eligible for the relevant treatment and control assignments under the comparison being defined.

Concurrent controls are the primary direct comparison because treatment and control assignments are made among eligible participants under overlapping trial conditions. A control group enrolled only before the treatment arm opened is not concurrent for that arm. Such observations may be considered for other purposes, but they do not replace the contemporaneous randomized comparison by virtue of being control observations. The introductory material on platform and umbrella trial structures gives the broader setting; here the essential task is to define the arm-specific overlap precisely.

Comparisons, Diagnostics, and Limitations

Comparison approach	What it offers	What to check
Concurrent randomized control	Direct randomized comparison among eligible participants enrolled during overlapping availability.	Confirm overlap, common eligibility and outcome definitions, and analysis consistent with the allocation scheme.
Nonconcurrent or historical control	May provide observations from outside the treatment arm’s open period.	It is not the direct concurrent randomized comparison; do not treat it as interchangeable with contemporaneous randomized control.
Unadjusted pooled comparison across randomization strata	Simple to calculate and may be suitable when the randomization and target population justify it.	Check whether treatment and control have the same stratum composition. If not, the crude contrast can differ from the target-weighted effect.

Practical checks include confirming that both groups could actually be assigned on each included date, verifying that the analysis uses the correct arm-specific eligibility criteria, and tabulating assignment by any randomization strata. A discrepancy between the intended window and the observed enrollment dates, an empty treatment or control cell in a stratum, or a changed endpoint definition is a reason to revisit the comparison before interpreting it. These checks do not prove all assumptions, but they can reveal a mismatched population or an analysis that does not follow the design.

Concurrency has limits. It cannot guarantee that the eligibility definition, follow-up procedures, or outcome measurement were applied identically; it does not correct deviations from the stated randomization; and it does not make an inappropriate pooled analysis appropriate. Nor does it determine how effects should be combined across multiple periods or populations. The window identifies the most direct randomized comparison; the estimand and analysis must still be specified for the question of interest.

Common Mistake

Wrong reasoning: “Treatment and control were concurrent, so their pooled means estimate the overall population means without qualification.”
Correction: Concurrency identifies overlapping enrollment and improves direct comparability, but a pooled equality such as \(E[Y\mid A=1]=E[Y(1)]\) requires marginal independence of assignment and potential outcomes. With stratified randomization, use stratum-specific comparisons and weights for the target population, or another analysis that accounts for the design.
Wrong reasoning: “The concurrent window ends when the last participant’s outcome is measured.”
Correction: The window is defined by dates when both assignments were available for randomization. Outcomes may be measured later according to the prespecified follow-up schedule.

Key takeaway: Define concurrency for each treatment arm as the overlap of treatment availability, control availability, and eligibility for randomization. Use this window to identify the direct randomized comparison, then ensure the analysis respects the allocation scheme and the target population.

Check Your Understanding

Answer each question, then compare your reasoning with the solutions below.

A treatment arm is open from 1 March through 30 September, while control is open all year. What is the arm’s concurrent comparison window if eligibility criteria are unchanged?
Why is an outcome measured after the treatment arm closes not automatically outside the concurrent comparison?
In two equally weighted randomization strata, the treatment-control differences are 0.08 and 0.14. What is the target-weighted difference?
Can a crude pooled comparison be assumed to estimate the target-population effect when treatment assignment probabilities differ by randomization stratum? Explain.

Solutions. (1) The window is 1 March through 30 September, the period when treatment, control, and eligible enrollment overlap. (2) Concurrency is defined by randomization date; a participant enrolled during the window can complete the prespecified outcome follow-up afterward. (3) The weighted difference is \(0.5(0.08)+0.5(0.14)=0.11\), or 11 percentage points. (4) No. Different assignment probabilities can produce different stratum compositions in the pooled groups, so the crude contrast may not equal the target-weighted effect; compare within strata and use the target population’s weights, or otherwise account for the design.