Why the Baseline Risk Needs a Precise Question
A clinician may say that “about one in five” patients have an event, or that the risk is “around 15%.” Those statements are not yet a usable baseline-risk judgment for a trial. The probability depends on which patients are meant, what counts as an event, how long patients are followed, and what care they receive in the control arm. If any of those details differ between the question and the trial, the number may refer to a different clinical quantity.
In a randomized trial, the baseline risk is usually the event probability under the control-arm regimen for the population the trial intends to enroll. It is not necessarily the risk for every patient in the clinic, the risk under no treatment, or the event rate in a historical study. The elicitation task is to make the target quantity concrete before asking for a number.
The target population may be the patients eligible for the planned trial, rather than all patients with the disease. The endpoint should specify the event and any rules for counting it, such as whether a composite endpoint includes hospitalization for any cause or only for a specified cause. The follow-up period should have a clear start and end. The control regimen should include relevant background care, not merely a label such as “standard care.” These details define the probability being elicited.
A simple working model treats each eligible patient’s control outcome as binary, with \(Y_{Ci}\sim\operatorname{Bernoulli}(p_C)\). This model is a useful summary when the goal is a population-average risk. It does not require every patient to have identical clinical risk: it says that \(p_C\) represents the marginal event probability for the specified target population. If the trial population differs from the population a clinician has in mind, the two marginal risks can differ even when the subgroup-specific risks are the same.
A Structured Elicitation Question
Before recording a numerical judgment, state the clinical scenario in a form that a clinician can answer without having to guess what “risk” means. A useful prompt identifies:
- Patients: the intended eligibility characteristics, disease severity, setting, and any other features that materially define the target population.
- Endpoint: exactly what counts as an event, including how composite events or repeat events are handled if relevant.
- Follow-up: the period during which the endpoint is assessed, with a defined starting point.
- Control care: the control intervention and important background or rescue care expected during the trial.
- Numerical response: the clinician’s best judgment of the proportion of such patients expected to experience the endpoint.
Asking for a frequency can make the numerical task more concrete: “Out of 100 patients meeting these criteria and receiving this control regimen, how many would you expect to experience this endpoint within 90 days?” If the clinician answers “about 18,” the implied probability is \(18/100=0.18\), or 18%. This is an elicited judgment, not a claim that 18 of 100 observed trial participants had the event. The distinction matters because the number expresses belief about the defined target, not a newly collected data set.
The question should be neutral. It should not imply that the risk is high or low, and it should not build in an assumed treatment effect. If the control regimen is not described, a clinician may silently assume a different mix of background treatments or care than the trial will provide. If the endpoint or follow-up is vague, two people can give different numbers while answering different questions.
Worked Example: Converting a Frequency Judgment to a Baseline Risk
Suppose the planned trial will enroll adults with a specified chronic condition and moderate disease severity. Its control arm provides the current standard regimen, and the primary endpoint is at least one disease-related hospitalization within 180 days of randomization. A clinician is asked to imagine 200 patients meeting those criteria and receiving that regimen. The clinician estimates that 34 would have the endpoint.
The implied probability is the expected number with the endpoint divided by the number imagined:
Thus the elicited baseline risk is 17% over 180 days for the specified population and control regimen. The number 200 is a frequency scale for expressing the judgment; it is not a claim that 200 patients were observed. The elicited value is not automatically a complete prior distribution: it records a numerical judgment about the baseline probability, while uncertainty about that judgment must be represented separately when specifying a prior.
Matching the Judgment to the Endpoint and Time Horizon
A risk is tied to both an endpoint and a time horizon. “Risk of hospitalization” could mean any hospitalization or only disease-related hospitalization. “Within follow-up” could mean 30 days or one year. These are distinct probabilities, not interchangeable phrasings of the same quantity. For a cumulative endpoint assessed in the same population and under the same care, the probability of having the event by 30 days cannot exceed the probability of having it by 90 days: every event occurring by day 30 also occurs by day 90. This logical check does not supply either probability, but it can reveal an inconsistent pair of judgments.
A related issue is whether the endpoint is a single event or a composite. If a trial’s endpoint is “death or hospitalization,” a judgment about hospitalization alone does not directly specify the composite risk. The composite event includes patients with either component, so the risk depends on both components and their overlap. The clinician should be asked about the endpoint as defined in the trial rather than having the analyst silently substitute a related but different outcome.
Worked Example: Separating Two Endpoint Judgments
A hypothetical protocol defines its endpoint as any unplanned hospitalization within 90 days. A clinician initially says, “About 12%,” but on clarification explains that the figure refers only to disease-related admissions. For the protocol’s broader endpoint, the clinician estimates 29 events among 200 similar patients over 90 days.
The initial judgment corresponds to disease-related hospitalization, not to the protocol endpoint. The judgment matching the protocol is:
The analyst should record 14.5% as the clinician’s stated judgment for the protocol endpoint, while retaining the clarification that 12% referred to a narrower endpoint. It would be incorrect to label 12% the baseline risk for “any unplanned hospitalization” merely because it is a hospitalization probability. The endpoint definition changed the quantity being estimated.
Standardizing to the Trial’s Patient Population
Clinicians often base a judgment on a familiar mix of patients, while the planned trial may enroll a different mix. When clinically relevant subgroups have different event risks, a population-average risk depends on the proportion of patients in each subgroup. This is why the target population must be stated before recording a numerical judgment.
For two mutually exclusive subgroups, let \(w_1\) and \(w_2\) be their proportions in the target population, and let \(p_1\) and \(p_2\) be their control-arm event probabilities over the specified period. Since the subgroups partition the population, the overall probability is the weighted average of their risks:
where \(G\) identifies subgroup membership and \(w_1+w_2=1\). This identity follows by splitting the event into the mutually exclusive cases \(G=1\) and \(G=2\), then adding their probabilities. It applies when the subgroup risks refer to the same endpoint, follow-up, and control regimen.
Worked Example: Adjusting for the Trial’s Subgroup Mix
Suppose a clinician’s usual population is 50% lower-risk patients and 50% higher-risk patients. For a defined 90-day endpoint under the control regimen, the clinician judges the subgroup risks to be 10% and 30%, respectively. The planned trial, however, is expected to enroll 70% lower-risk and 30% higher-risk patients. Assume the subgroup definitions and care are otherwise the same.
The clinician’s usual population has an average risk of:
That 20% judgment describes the clinician’s 50:50 patient mix. For the planned trial’s mix, the corresponding standardized risk is:
The target-population judgment is therefore 16%, not 20%, under the stated assumptions. The change is due to the different subgroup proportions, not a change in either subgroup’s risk. If the clinician cannot judge subgroup risks, do not manufacture them from the overall 20% figure; instead, clarify how closely the clinician’s usual population resembles the planned trial population and record that limitation.
Assumptions, Diagnostics, and Common Pitfalls
An elicited risk is most useful when the clinical scenario is plausible and sufficiently specified for the clinician to judge. The clinician should be able to relate the target population to relevant experience or evidence, and the assumed control care should be realistic for the trial setting. If the endpoint is difficult to ascertain, the stated probability may implicitly refer to a different measurement process than the protocol’s. A precise elicitation prompt cannot remove genuine uncertainty or guarantee that a judgment is well calibrated.
Before using the number, check the following:
- Definition check: Can the clinician restate who is included, what event counts, and when it is assessed?
- Scale check: Does the reported percentage agree with the frequency response? For example, 34 of 200 is 17%, not 34%.
- Population check: Is the clinician imagining the planned eligibility criteria and patient mix, or a broader clinical population?
- Care check: Does the imagined control regimen include the same background treatment and care expected in the trial?
- Time check: Is the judgment for the stated follow-up period, rather than a familiar but different duration?
- Endpoint check: Does the judgment cover the protocol endpoint, rather than a single component or a related outcome?
A common mistake is to record “the risk is 20%” without recording the conditions attached to that statement. The mistaken reasoning is that event probabilities are fixed properties of a disease. In fact, the probability is conditional on the population, endpoint, follow-up, and care being considered. The correction is to record the number together with those defining features and to ask for clarification when any are ambiguous.
How This Approach Differs From Other Sources
A clinician’s elicited judgment is one way to describe a baseline risk; it is not the only one. Historical control data can provide observed event proportions in a previous population, while a clinician’s judgment summarizes belief about a specified future trial population. Historical data may be more directly empirical, but differences in eligibility, calendar time, endpoint definitions, and care can make their risk a poor match. Clinician judgment can incorporate current practice and the planned population, but it may be imprecise or dependent on what cases are most familiar.
Scenario elicitation for a treatment effect asks a different question: how outcomes are expected to differ between treatment and control. Baseline-risk elicitation asks for the control-arm probability itself. A treatment-effect judgment does not by itself determine the control risk; the baseline and treatment contrast are distinct quantities. Using both types of judgment requires keeping their meanings and reference conditions clear.
These approaches can be compared, but they should not be treated as interchangeable numbers. A historical proportion is calculated from observed data; an elicited probability is a clinician’s judgment. Both need to match the target population and endpoint before they can inform a trial prior. A baseline point judgment also does not settle how much uncertainty to assign to the underlying probability.
Check Your Understanding
Try each question, then compare your reasoning with the solutions below.
- A clinician expects 27 events among 150 patients matching a specified control-arm scenario. What baseline probability does this imply?
- Why is a risk of disease-related hospitalization not automatically the risk for an endpoint defined as any hospitalization?
- A population is 40% subgroup A and 60% subgroup B. Their control risks are 5% and 20%. Calculate the population-average risk.
- A clinician gives a risk for 30 days, but the trial endpoint is assessed over 180 days. What should the elicitor do before recording that number as the trial baseline risk?
Solutions. (1) \(27/150=0.18\), so the implied judgment is 18% for the stated scenario. (2) The endpoints differ: any hospitalization includes events outside the disease-related category, so the narrower probability does not specify the broader endpoint probability. (3) The weighted risk is \((0.40)(0.05)+(0.60)(0.20)=0.02+0.12=0.14\), or 14%. (4) Clarify the judgment for the protocol’s 180-day follow-up; the 30-day number answers a different time-specific question and should not be substituted without justification.