Biomarker Prevalence And Recruitment Yield

From Biomarker Prevalence to Recruitment Yield

For a biomarker-defined trial, the number of people who must be screened depends on more than the desired enrollment. Some candidates will not have the biomarker of interest, and some biomarker-positive candidates will not meet the remaining eligibility criteria. Converting these rates into recruitment targets makes the operational consequences of a design explicit.

The calculations are planning expectations, not promises about the number of people who will enroll. They are useful for estimating the scale and duration of recruitment, comparing plausible scenarios, and identifying assumptions that need monitoring. They do not by themselves determine the statistical power or the treatment effect in a subgroup.

The conditional definition of \(e_+\) matters. It does not assume that eligibility is identical for biomarker-positive and biomarker-negative candidates. If eligibility is assessed before biomarker status is known, or eligibility rules are associated with biomarker status, use the appropriate conditional rate for the group being planned.

The basic calculation assumes that screened candidates represent the population to which \(p\) applies, each candidate has the same relevant probabilities, and screening outcomes are independent or close enough for the expected-yield approximation to be useful. The rates should refer to the same sites, time period, and screening population. Changes in referral patterns, eligibility rules, or recruitment practices can make historical rates poor forecasts.

Expected Screening Volume and Accrual Time

Each screened candidate has probability \(q_+\) of being both biomarker-positive and otherwise eligible. If the target is \(m_+\), the expected number of successful candidates required is therefore \(m_+/q_+\). Operationally, a screening target is an integer, so a planning value based on this expectation is rounded upward. Rounding upward does not make the target a guarantee: random variation can still leave the trial short.

If the site network screens candidates at an average rate of \(\lambda\) candidates per unit of time, the expected rate of eligible biomarker-positive recruitment is \(\lambda q_+\). Under stable rates, the expected time to recruit \(m_+\) such participants is approximately \(m_+/(\lambda q_+)\). For a Poisson candidate-arrival process with independent yield probability \(q_+\), this expected-time expression follows exactly from thinning the arrivals.

When Eligibility Differs by Biomarker Status

For an all-comer recruitment plan, it is useful to calculate yields in both biomarker groups. Let \(e_-\) be the probability that a biomarker-negative candidate meets the other eligibility criteria. The expected eligible yields per screened candidate are \(q_+=p e_+\) and \(q_-=(1-p)e_-\). The total eligible yield is their sum. Consequently, the biomarker-positive proportion among eligible participants is generally not the same as prevalence among all candidates screened.

This fraction is a recruitment-composition calculation. It accounts for eligibility selection but does not correct for biomarker misclassification, which is a separate measurement issue. In an actual plan, the definitions of the screened population and eligibility rules must be consistent across the rates being combined.

Planning When Prevalence Is Uncertain

Prevalence estimates may be imprecise, outdated, or drawn from a population that differs from the trial’s likely referrals. A practical response is to show how recruitment changes across a defensible range of prevalence values, while keeping the eligibility rate and other assumptions visible. Such scenarios are transparent planning calculations; they do not assign probabilities to the scenarios unless a probability model is specified.

Expected Yield Is Not a Completion Guarantee

The expectation \(m_+/q_+\) describes the average screening effort over repeated recruitment processes under the model. A particular trial can require more or fewer screenings. For a fixed number \(N\) of independent screenings with constant yield probability \(q_+\), the number of eligible-positive candidates \(X\) follows \(X\sim\mathrm{Binomial}(N,q_+)\). Its mean is \(Nq_+\), and its variance is \(Nq_+(1-q_+)\).

If a plan requires a specified probability of reaching at least \(m_+\) participants by a screening cap, the relevant calculation is the binomial tail, not merely the expected count. The smallest acceptable \(N\) is found by checking

against the chosen completion probability. The value of \(N\) needed for high assurance will generally exceed \(m_+/q_+\). This distinction is important whenever a fixed recruitment cap or deadline makes shortfall costly.

For ongoing planning, compare observed screening yield with the assumed rates, using clearly defined denominators: biomarker-positive among all screened, eligible among positive candidates, and eligible among negative candidates where relevant. Large departures may reflect random fluctuation, a changing referral mix, site differences, or recording problems. Re-estimating operational forecasts can be sensible, but changes to trial eligibility or inferential procedures require separate prespecification and statistical consideration.

Choosing and Checking a Recruitment Calculation

The main alternatives are to plan from an expected yield, to use a conservative scenario, or to set a screening cap that meets a chosen probability of obtaining the required count. They answer different questions. Expected yield describes an average; scenario planning shows sensitivity to uncertain inputs; the binomial-tail approach quantifies completion probability under a specified probability model. None removes the need to check whether the prevalence and eligibility rates apply to the intended candidates.

A common mistake is to say, “The biomarker prevalence is 20%, so screening five people will produce one eligible positive participant.” That reasoning ignores eligibility: if only 75% of positive candidates qualify, the yield is \(0.20(0.75)=0.15\), or an expected one eligible positive per \(1/0.15=6.667\) screenings. Even that is an average, not a guarantee that any particular group of 6.667—or 7—screenings will produce one.

Recruitment calculations are only as useful as their inputs. A prevalence estimate from a referral population enriched for disease may not apply to general clinic referrals; eligibility rates can vary across sites; and a screening rate measured during start-up may not represent mature recruitment. Documenting the source and date of each input makes the forecast interpretable and helps identify which assumption is driving a change in expected duration.