From Evidence to an Explicit Transition Probability
A development team may have clinical signals, toxicology findings, and a mechanistic model, yet still need to answer a practical question: given what is known now, how likely is the program to meet the conditions for entering the next stage? The evidence does not usually supply that probability directly. It must be interpreted against a clearly defined transition event, and the interpretation depends on assumptions about the evidence, the decision criteria, and what remains uncertain.
A phase-transition probability is useful only when its conditioning is clear. “The probability of success is 60%” is incomplete if it does not say what counts as success, which transition is being considered, what information is included, and over what period or decision point the assessment applies. The probability should describe uncertainty about a specified event, not confidence in a vague label such as “promising.”
Before eliciting a number, specify the transition event. For example, “advance” might mean that a dose is selected, a safety review permits further dosing, or a trial meets a prespecified decision rule. These are different events and can have different probabilities. State the current stage, the next stage, the decision criteria, the evidence cut-off, and any material operational conditions. The earlier material on conditional versus cumulative probability of success distinguishes a single transition from the probability of success across multiple stages; here, the focus is on constructing the transition probability for one defined move.
A Structured Elicitation Process
Elicitation makes expert judgments explicit rather than treating a probability as something that can always be read off a study result or model output. Experts may supply the probability directly, assess intermediate evidence scenarios, or quantify how evidence changes prior odds. Whichever route is used, record the reasoning that connects the evidence to the event.
Write the transition criteria in operational terms. Avoid combining multiple decisions or leaving “success” undefined.
List the clinical, nonclinical, and mechanistic evidence available at the decision point, including important missing or low-quality evidence.
For each finding, state which part of the event it informs and what assumptions connect the finding to the transition.
Obtain a probability or conditional probabilities for defined scenarios. Use a transparent calculation, such as Bayes’ rule or the law of total probability, where appropriate.
Record sources, judgments, dependencies, and uncertainty. Recalculate under plausible alternatives to identify assumptions that materially determine the result.
A probability can be elicited as a single value for a decision model, but the elicitation record should preserve more than that value. Document who provided each judgment, the question they were asked, the evidence shown to them, the rationale, and any range or alternative scenario considered. If experts disagree, retain the disagreement and investigate its sources before summarizing it. A simple average can conceal different interpretations of the event or different assumptions about evidence quality.
Worked Applications
Worked Example: Updating a Transition Probability With a Clinical Signal
Hypothetical case. A team is considering whether to advance from an early clinical stage to a dose-expansion study. The transition event \(T\) is defined as meeting the protocol’s prespecified activity and tolerability criteria at the decision review. Before reviewing a new biomarker signal, the team assigns \(P(T)=0.30\). It judges that a signal at least as strong as the observed one would occur with probability \(0.70\) if \(T\) were true, and with probability \(0.20\) if \(T\) were false. These likelihoods are elicited judgments, not estimates claimed to come from a real study.
Let \(E\) denote observing the signal. Assuming the prior probability and the two conditional likelihoods refer to the same event and evidence definition, Bayes’ rule gives:
Substitute the elicited values:
Under these assumptions, the signal moves the estimated probability of meeting the defined transition criteria from 0.30 to 0.60. This is not a 60% probability that the biomarker signal is “true”; it is the probability of the specified transition conditional on the signal and the stated inputs. The result depends on the quality of the prior and likelihood judgments. The team should therefore document their rationale and examine how the result changes if either likelihood is less favorable.
Worked Example: Translating a Nonclinical Package Into Scenarios
Hypothetical case. A development team reviews a nonclinical safety package before deciding whether to initiate a clinical study. It groups the package into three mutually exclusive interpretations: an adequate exposure margin, a borderline margin, or an inadequate margin. The team assigns probabilities of 0.65, 0.25, and 0.10 to those interpretations, respectively. Conditional on each interpretation, its elicited probability of meeting the stated safety conditions for transition is 0.85, 0.45, and 0.05.
Because the three interpretations partition the team’s uncertainty about the package, the transition probability is the probability-weighted sum of the conditional probabilities:
Here, \(S_i\) denotes one of the three interpretations. Substitution gives:
The elicited probability of meeting the safety transition conditions is 0.670. This calculation assumes that the scenario probabilities sum to one, that the scenarios are mutually exclusive and collectively exhaustive, and that each conditional probability is interpreted consistently with the same transition event. If the “borderline” category is defined vaguely, or if plausible interpretations have been omitted, the weighted result may give an unwarranted impression of precision.
The calculation above follows from a partition: the event \(T\) can occur under any one of the scenarios \(S_i\), so \(P(T)\) is the sum of \(P(T\cap S_i)\). By the definition of conditional probability, \(P(T\cap S_i)=P(T\mid S_i)P(S_i)\), provided \(P(S_i)>0\). Adding those terms yields the displayed formula. The formula does not establish that the scenario probabilities or conditional judgments are correct; it makes their role in the answer visible.
Worked Example: Converting Mechanistic Model Output Into a Transition Probability
Hypothetical case. A mechanistic model predicts whether the proposed dose is likely to reach a prespecified target-engagement threshold. The team uses parameter-uncertainty scenarios, assigning probabilities of 0.50, 0.30, and 0.20 to high, intermediate, and low target-engagement predictions. After reviewing each scenario alongside the clinical plan and other available evidence, the team elicits probabilities of meeting the defined transition criteria of 0.80, 0.55, and 0.25, respectively.
Treating those scenarios as a partition of the model uncertainty, the overall probability is:
The resulting probability is 0.615, or 61.5%, under the elicited scenario weights and conditional judgments. The model’s target-engagement output is not itself the probability of transition: it is evidence used to define scenarios and inform the judgments within them. The calculation also assumes that the model scenarios capture the relevant uncertainty and that no separate transition requirement has been silently omitted. If safety or operational feasibility is part of \(T\), those considerations must be incorporated into the conditional probabilities or explicitly represented in additional scenarios.
Assumptions, Diagnostics, and Alternatives
A defensible elicitation makes its assumptions inspectable. Clinical findings may be noisy, measured in a selected population, or only indirectly related to the next-stage criteria. Nonclinical evidence may depend on species, exposure, or endpoint translation. A mechanistic model may be sensitive to uncertain parameters or structural choices. For each evidence source, ask what it actually informs, how directly it relates to the transition event, and what uncertainty remains between the measured or predicted quantity and that event.
A useful diagnostic is to ask experts to explain what would make their probability higher or lower. If the answer cannot be tied to observable evidence, a stated assumption, or a defined scenario, the number may be an unsupported impression. Check that scenario probabilities are nonnegative and sum to one, that scenarios do not overlap, and that the conditional probabilities refer to one consistent event. Also compare the elicited result under plausible alternative assumptions. A large change may be decision-relevant even when no single input is clearly “wrong.”
Avoid counting the same evidence twice. For example, a clinical biomarker result and a mechanistic model output may both rely on the same underlying observations. Treating them as independent evidence updates can exaggerate the effect of that information. Even when dependence is not quantified, document shared data and avoid multiplying evidence contributions as though they were independent without justification.
There are several practical approaches, with different strengths:
- Direct expert probability: efficient when the event is clear and experts can make a defensible overall judgment. Its weakness is that it can hide which evidence or assumption drives the number.
- Scenario-weighted elicitation: separates uncertainty about what the evidence means from the probability of transition under each interpretation. It is transparent, but results depend on the scenario definitions and weights.
- Bayesian evidence updating: shows how an evidence result changes a prior probability when conditional evidence probabilities can be specified. It is useful for making evidence strength explicit, but poor or double-counted likelihood judgments can mislead.
- Mechanistic model-based assessment: can connect biology, exposure, and response quantitatively. Its output is only as relevant as the link from model outputs to the defined transition event, and structural uncertainty may remain.
These approaches need not be competing recipes. A team can use a mechanistic model to define informative scenarios, elicit conditional judgments about the actual transition, and use a Bayesian update when evidence likelihoods are sufficiently well specified. The selected probability should remain conditional on the evidence set and assumptions, rather than being presented as an objective property of the compound.
Common Pitfalls and Practical Limits
- Undefined success: “The chance of advancing” is not meaningful without criteria. Specify the decision and the conditions for satisfying it.
- False precision: Reporting 0.615 does not mean the elicitation is accurate to three decimal places. Retain sensible precision in the final report and show important ranges or scenario sensitivity.
- Evidence treated as a probability: A target-engagement prediction or safety margin is an input to the reasoning, not automatically the probability of transition.
- Hidden judgment: A number produced by a spreadsheet may still depend on elicited weights, assumptions, or expert interpretations. Label them rather than presenting the output as purely data-driven.
- Overconfident consensus: A single group estimate can mask disagreement. Record materially different judgments and clarify whether they reflect evidence interpretation, event definition, or risk tolerance.
Elicitation cannot remove uncertainty, guarantee that experts are calibrated, or make incomplete evidence complete. Its value is disciplined transparency: the probability can be challenged, updated when new evidence arrives, and compared across scenarios without obscuring how the conclusion was reached.
Check Your Understanding
Answer each question, then compare your reasoning with the solutions below.
- A transition has prior probability 0.25. For evidence \(E\), suppose \(P(E\mid T)=0.80\) and \(P(E\mid \neg T)=0.30\). What is \(P(T\mid E)\)?
- Three mutually exclusive evidence scenarios have probabilities 0.40, 0.40, and 0.20. Their conditional transition probabilities are 0.90, 0.50, and 0.10. Calculate the overall probability.
- A transition requires both a clinical criterion and a safety criterion. Their marginal probabilities are 0.70 and 0.60. What joint probability follows if independence is assumed? What is the possible range without that assumption?
- Name two details that must be documented before an elicited transition probability can be interpreted.
Solutions. (1) \(P(T\mid E)=0.80(0.25)/[0.80(0.25)+0.30(0.75)]=0.20/0.425=0.471\). (2) \(0.40(0.90)+0.40(0.50)+0.20(0.10)=0.36+0.20+0.02=0.580\). (3) Under independence, the joint probability is \(0.70(0.60)=0.420\). Without an assumption about dependence, the joint probability can range from \(\max(0,0.70+0.60-1)=0.30\) to \(\min(0.70,0.60)=0.60\). (4) Any two of: the defined transition event and criteria, the evidence cut-off, the assumptions linking evidence to transition, the elicitation method, the experts’ rationale, or the source and interpretation of each evidence item.