Why Recruit Marker Strata Separately?
A biomarker can identify patients for whom treatment effects, prognosis, or both may differ. If the marker-positive group is rare, enrolling participants only through ordinary screening may yield too few marker-positive patients for a useful treatment comparison. A design with separate recruitment cohorts instead sets distinct accrual targets for marker-positive and marker-negative participants. The targets can reflect the information needed in each stratum, rather than requiring the enrolled sample to reproduce the marker prevalence in the wider population.
That flexibility does not change what the trial can claim. The treatment comparison in each stratum must still be based on randomized treatment groups within that stratum. And if the trial aims to make a claim about all eligible patients, the enrolled proportions alone do not define the all-comer effect: the population prevalence and the intended estimand matter.
Design Conditions and Prespecified Targets
The design starts by specifying the marker definition, the target population, and the claims the trial is intended to support. Marker status should be established before treatment assignment using the prespecified assessment procedure. The positive and negative categories should be clearly defined and, for a binary marker, mutually exclusive. The marker assessment must be available in time to determine the participant’s recruitment cohort. If the assay is missing or misclassified, the intended strata may not correspond to the analyzed groups; such issues require explicit handling rather than an assumption that the observed classification is error-free.
A separate target is set for each cohort. For example, the positive cohort may require more participants if its treatment effect is the primary focus, if its clinically relevant effect is smaller, or if its outcome variability is larger. The targets should be based on the estimand, endpoint, desired precision or power, and the error-control plan. A target is not justified merely because it produces convenient cohort sizes.
Within each cohort, treatment groups must remain comparable through random assignment. The design should specify how treatment assignment is conducted and analyzed within the marker stratum; operational details of the allocation procedure should be fixed in advance. Recruitment targets do not themselves provide randomization. If treatment is not randomized within a cohort, observed treatment differences may reflect prognostic differences between people who received different treatments rather than treatment effects.
The usual planning calculations also rely on assumptions about the endpoint and its variability. For a continuous endpoint, a simple calculation may assume independent participant outcomes, a common variance \(\sigma^2\) within a stratum, equal allocation to two treatment groups, and a normal approximation for the treatment-effect estimator. These assumptions are planning approximations: the final analysis may use a more appropriate model, and departures such as clustering, repeated measurements, or substantial non-normality may change the required sample size.
From a Treatment-Effect Target to an Accrual Target
Suppose a trial plans a two-sided test of \(H_0:\Delta_m=0\) in one marker stratum, with a specified marginal significance level \(\alpha\) and power \(1-\beta\) to detect a clinically relevant difference \(\Delta_m\). If there are \(n\) participants per treatment arm in that stratum and the endpoint standard deviation is \(\sigma\), the estimated difference in means has approximate standard error \(\sqrt{2\sigma^2/n}\). Under the assumed alternative, its standardized mean is approximately \(\Delta_m/\sqrt{2\sigma^2/n}\). Requiring this signal to exceed the two-sided critical value by the amount needed for the desired power gives the familiar planning approximation below.
Here \(z_q\) is the \(q\) quantile of the standard normal distribution. The calculation is an approximation under the stated model, not a guarantee of achieved power. When several population claims are confirmatory, the marginal \(\alpha\) used for each calculation must come from the prespecified error-control plan. Using \(\alpha=0.05\) separately for multiple claims does not, by itself, control the overall probability of a false positive at 0.05.
Worked Example: Calculating a Marker-Negative Accrual Target
Consider a hypothetical planning calculation for a continuous outcome in the marker-negative stratum. Suppose the standard deviation is expected to be 12 outcome units, the clinically relevant mean difference is 7 units, and the calculation uses a two-sided marginal \(\alpha=0.05\) with 80% power. Assume independent outcomes, equal allocation, and a normal approximation. The \(\alpha\) value here is for this illustrative single comparison; a design with multiple confirmatory claims must use its prespecified multiplicity plan.
For these assumptions, \(z_{0.975}=1.960\) and \(z_{0.80}=0.8416\). Substitution gives:
The required integer target is rounded up to 47 participants per arm, or 94 marker-negative participants in total. Rounding down would not meet the calculated requirement. If the target analysis requires a different marginal \(\alpha\), a different variance assumption, or an allowance for missing outcomes, the calculation must be updated rather than treating 94 as universal.
Worked Planning Examples
Worked Example: Translating Separate Targets Into Screening Burden
Suppose a hypothetical trial seeks 160 marker-positive and 320 marker-negative participants. In the screening population, assume marker prevalence is \(p=0.20\), with all screened people classified as either positive or negative. If participants are enrolled consecutively from one screening stream, the expected number screened to accrue 160 positive participants is:
Those 800 screened people would be expected to include \(800(0.80)=640\) marker-negative people. The negative target of 320 would therefore be met before the positive target, with about 320 additional eligible negatives beyond its target if recruitment were not stopped or redirected.
Alternatively, the expected screening burden to identify 320 negatives alone is \(320/0.80=400\) people. These calculations are expectations under the assumed prevalence, not guaranteed counts: actual screening totals vary. A protocol may use additional sites or recruitment routes to meet the positive target, while monitoring whether the negative cohort has reached its own target. It should also account for people who are ineligible, decline participation, or have an unavailable marker result. The key design point is that the planned 160:320 enrolled ratio is not the assumed population ratio of 20:80.
Worked Example: Distinct Targets for Distinct Stratum Effects
Suppose a hypothetical planning team expects the marker-positive stratum to have an outcome standard deviation of 12 units and wants 80% power for a 8-unit difference. For illustration, use the same two-sided marginal \(\alpha=0.05\), equal allocation, and normal approximation as in the preceding calculation. The per-arm requirement is:
Rounding up gives 36 participants per arm, or 72 marker-positive participants. The earlier marker-negative illustration gave 47 per arm, or 94 total, because the targeted difference was smaller there. Thus distinct targets can follow from distinct effect-size goals even when the assumed standard deviation, allocation, power, and marginal significance level are the same. If these are both confirmatory claims, however, the final calculations must use the marginal error levels specified by the trial’s overall testing plan; this illustration alone does not define that plan.
The arithmetic assumes the specified standard deviations and differences are suitable for planning. If the positive-stratum variance is expected to differ from 12, that variance—not the negative-stratum value by default—belongs in the positive-stratum calculation. If missing outcomes are anticipated, enrollment should also be inflated using an explicit retention assumption.
Accrual Mix and Population Claims
Oversampling a rare marker group can make stratum-specific randomized comparisons more informative. It also changes the marker distribution of the enrolled sample. Therefore, a pooled treatment difference calculated by combining all enrolled participants generally describes the trial’s enrolled mix, not automatically the treatment effect in the target population.
For a binary marker with target-population prevalence \(p\), the all-comer mean under treatment assignment \(a\), assuming the two marker strata exhaust the target population, is:
Subtracting the control mean from the treatment mean gives the population-average effect:
This identity is a standardization result: the stratum-specific means are combined using the marker proportions in the target population. It does not say that a sample with a deliberately altered marker mix can be analyzed as if its own mix were the population mix. It also presumes the stratum-specific treatment effects and the target prevalence are relevant to the target population.
Worked Example: Standardizing an All-Comer Effect
Suppose, hypothetically, the marker-positive prevalence in the target population is 0.25. The randomized comparisons estimate a treatment effect of 8 outcome units in the positive stratum and 1 unit in the negative stratum. The all-comer effect under these assumptions is:
The population-standardized estimate is 2.75 units, not the average of 8 and 1 unless the target population has equal marker prevalence. If the trial enrolled equal numbers of positive and negative participants, an unweighted pooled contrast would instead combine the stratum effects using 0.50 and 0.50, yielding \(0.50(8)+0.50(1)=4.5\) units. That number corresponds to the equally mixed sample under the simple model, not to the stated target population. Uncertainty in both the stratum estimates and the prevalence should be reflected when making an inferential population claim.
Operational Checks, Alternatives, and Limitations
A recruitment plan should monitor both cohorts against their own targets. Useful checks include the number screened, the number classified in each stratum, eligibility and consent rates by stratum, accrual rate by site, treatment allocation within each cohort, and missing endpoint rates. A rapid shortfall in one cohort may signal a prevalence assumption that was too optimistic, assay availability problems, or site-specific recruitment differences. If those problems are ignored until the end, the resulting stratum estimate may be too imprecise for its prespecified purpose.
The protocol should also distinguish the population for each claim. A marker-positive-only efficacy claim concerns the positive stratum; it does not establish efficacy in marker-negative patients or all eligible patients. An all-comer claim requires a suitable all-comer estimand and analysis, including the target marker distribution when the sample is deliberately enriched. If recruitment eligibility or follow-up differs by marker status, the analysis should address whether the observed participants represent the intended stratum populations.
| Design approach | Strength | Main limitation |
|---|---|---|
| Separate targets for marker strata | Allows planned information in each stratum despite unequal prevalence. | Needs stratum-specific recruitment monitoring and clarity about population weighting. |
| Consecutive all-comer recruitment without separate targets | Enrollment mix may more closely reflect the screened population when recruitment is representative. | A rare stratum may accrue too few participants for a useful comparison. |
| Marker-positive-only enrichment | Directs resources to the positive stratum when that is the sole intended population claim. | Does not directly support a marker-negative or all-comer treatment claim. |
These approaches answer different design needs. Separate cohorts are not automatically superior: they can require more screening, additional recruitment infrastructure, and careful handling of population-standardized claims. They are useful when the protocol needs adequate information in both marker groups but should not be used to imply that the trial’s enrolled proportions are the target population proportions.
Common Mistake: Treating the Accrued Mix as the Population
A common error is to argue, “We enrolled equal numbers of marker-positive and marker-negative participants, so the pooled result estimates the effect in a population that is 50% positive.” Equal accrual is a design choice; it does not change the prevalence in the target population. The correction is to state the intended estimand and, for an all-comer claim, combine stratum-specific results using the target-population weights, subject to the assumptions of the analysis. A related error is to assume that separate cohort targets guarantee valid treatment comparisons. They do not: each cohort still needs a randomized treatment comparison and an analysis consistent with the prespecified design.
Check Your Understanding
Work through these questions, then compare your reasoning with the brief solutions.
- A target population has marker prevalence 0.10. A trial sets equal recruitment targets for positive and negative participants. Does the enrolled ratio estimate the target population prevalence? What should be considered for an all-comer claim?
- In a stratum, the planning assumptions are equal allocation, \(\sigma=10\), target difference \(\Delta=5\), two-sided \(\alpha=0.05\), and 80% power. Using \(z_{0.975}=1.960\) and \(z_{0.80}=0.8416\), calculate and round up the per-arm target.
- Why is a randomized comparison within each marker cohort needed even when the recruitment targets are prespecified?
- If \(\Delta_+=6\), \(\Delta_-=2\), and target-population marker prevalence is 0.20, calculate the population-standardized treatment effect.
Solutions. (1) No. Equal accrual is an enrollment choice, not an estimate of prevalence. An all-comer claim should use the target prevalence to combine stratum-specific effects, assuming the stratum estimates apply to the target population. (2) \(n\approx 2(10^2)(1.960+0.8416)^2/5^2=200(7.84896256)/25=62.7917\), so round up to 63 participants per arm. (3) Prespecified targets control how many participants are sought, not how treatment groups are made comparable; random assignment within the stratum supports an unbiased treatment comparison under the trial’s assumptions. (4) \(\Delta_{\text{pop}}=0.20(6)+0.80(2)=1.2+1.6=2.8\) outcome units.