Why Map the Selection Pathway?
In a time-to-event MAMS trial, an intermediate outcome can be available before enough follow-up has accrued to assess the final event endpoint. It may therefore be used to decide which experimental arm continues. The decision is operational: it is a rule applied to interim data. The scientific question is broader: how, if at all, does treatment affect the intermediate outcome and the final event endpoint, and what relationship connects those outcomes?
Mapping the pathway keeps these questions separate. A rule that ranks arms by an intermediate measure relies on the treatment-to-intermediate link and on the data used to estimate that link. It does not automatically rely on, or establish, a link from the intermediate outcome to the final endpoint. Nor does it necessarily use the treatment-to-final-endpoint link. These distinctions matter when explaining what a selection decision means.
Representing the Links
A useful map starts with the order in which information is generated. Randomization assigns \(Z\). The intermediate outcome \(M\) is measured at its prespecified time or assessment window. The selection rule is then applied to the available interim data. The final endpoint is assessed over follow-up, often after the selection decision. The endpoint may be represented as an event time \(T\), or as an event indicator \(Y(\tau)\) at a fixed horizon.
Here \(L\) represents baseline characteristics that may be related to both outcomes. The arrow from \(M\) to \(Y(\tau)\) is a candidate causal link, not something established merely because the outcomes are associated. The arrows from \(Z\) indicate possible treatment effects on the outcomes. Randomization supports comparisons between assigned arms, subject to appropriate handling of missing outcomes and follow-up; it does not by itself establish that changing \(M\) would change the final endpoint.
The selection rule is a separate part of the map. For example, let \(D_M\) denote all intermediate-outcome data available at the decision time, including the relevant arm assignments and observed measurements. A rule that selects the arm with the largest favorable-oriented intermediate statistic can be written as \(S=g(D_M)\), where \(S\) is the selected arm and \(g\) is the prespecified rule. The rule relies directly on \(D_M\). If final-endpoint data are not inputs to \(g\), the rule does not directly rely on those data, even though the final endpoint remains the trial's principal clinical outcome.
This description assumes that assignment is implemented as randomized, the intermediate measure is defined consistently across arms, and the measurement used for selection is available before the decision. It also assumes that the written rule accurately represents the procedure actually used. If measurements are missing, delayed, or gathered differently by arm, the map must include those features: the selection input is the data that were actually available under the prespecified handling rules, not an idealized complete data set.
When Does the Rule Depend on the Intermediate Outcome?
A simple derivation makes the distinction between an outcome pathway and a decision rule precise. Suppose \(D_M\) can take a finite set of possible values and the rule selects arm \(j\) exactly when \(g(D_M)=j\). Then the probability that arm \(j\) is selected is the sum of the probabilities of all intermediate-data configurations that lead to that decision:
Thus, when the rule uses only \(D_M\), its selection probability is determined by the distribution of the intermediate data and the rule \(g\). The final endpoint does not appear as a decision input in this expression. This does not mean that final outcomes are irrelevant to the trial's scientific conclusions; it means only that they do not directly determine this particular selection decision.
If a rule uses final-endpoint data as well—for example, as a tie-breaker—then the decision is instead a function of both data sets, \(S=g(D_M,D_Y)\), where \(D_Y\) denotes the endpoint data available at selection. In that case, the endpoint is a direct input to the rule. This audit is about what the algorithm uses, not about whether a particular input is a good choice or whether it predicts eventual clinical benefit.
Worked Example: Selection Uses the Intermediate Measure
Consider a hypothetical trial with control and two experimental arms. At an interim decision, 100 participants per arm have an observed binary response, where response is the intermediate outcome. The prespecified rule selects the experimental arm with the larger response-rate difference from control. Suppose there are 40 responses in control, 62 in arm A, and 54 in arm B.
The observed response proportions are \(40/100=0.400\) in control, \(62/100=0.620\) in A, and \(54/100=0.540\) in B. The arm-versus-control differences are
Because \(0.220>0.140\), the rule selects arm A. The calculation uses the intermediate response counts and the rule's comparison with control. It does not use any final event counts.
Suppose final-endpoint data are later observed: by a specified follow-up horizon, there are 30 events among the 100 control participants, 24 among the 100 in A, and 26 among the 100 in B. Those data may inform final-endpoint comparisons, but they did not produce the earlier selection if they were unavailable to, and not included in, the rule. The map therefore includes \(Z\) to \(M\) as the link directly assessed by the selection statistic; it does not make the intermediate outcome a demonstrated cause or substitute for \(Y(\tau)\).
Mapping the Rule in Practice
An audit should begin with the decision specification, not with a diagram drawn from memory. State what is measured, when it is measured, how it is summarized, and how those summaries determine the decision. Then mark whether final-endpoint observations enter the rule. This identifies the decision pathway while keeping it distinct from the broader scientific pathway between outcomes.
Define the intermediate measure, its assessment time, the final event, and any fixed horizon used to summarize that event.
Specify the participants, measurements, follow-up, and any missing-data handling that contribute to the interim data set.
Identify which summaries, comparisons, thresholds, and tie-breakers determine the selected arm.
Mark the randomized assignment-to-intermediate link and any other links needed to produce the quantities in the rule.
Record whether final-endpoint data enter the rule, and do not interpret selection on \(M\) alone as evidence that an arm improves \(Y(\tau)\).
Worked Example: A Tie-Breaker Adds an Endpoint Input
In a second hypothetical trial, arm A and arm B each have 52 responses among 100 participants at the interim assessment. The rule first selects the arm with the larger response proportion; if the proportions tie, it selects the arm with fewer observed final events by that decision time. Suppose there are 18 observed events in A and 13 in B.
The response proportions are \(52/100=0.520\) in both arms, so the first part of the rule cannot distinguish them. The tie-breaker compares the observed event counts: \(13<18\), so the rule selects B. In this example, the pathway to selection includes both the intermediate outcome and final-endpoint information, but the endpoint enters only in the tie case.
The rule can be written as a function of \(D_M\) and \(D_Y\), not \(D_M\) alone. It would be inaccurate to describe this as selection based exclusively on the intermediate outcome. The timing and maturity of those event counts also matter: the map must specify which follow-up information was available and whether it was included by design. This example describes the rule's inputs; it does not show that the tie-breaker is clinically preferable.
Worked Example: Distinguishing Selection From Final-Endpoint Results
A third hypothetical trial uses the same response-based rule as the first example, but the response counts are 45 of 100 in control, 70 of 100 in A, and 60 of 100 in B. By the later endpoint analysis horizon, event counts are 30 of 100 in control, 32 of 100 in A, and 22 of 100 in B.
The response proportions are 0.450, 0.700, and 0.600. The two differences from control are
The rule therefore selects A. At the endpoint horizon, the observed event proportions are \(30/100=0.300\) in control, \(32/100=0.320\) in A, and \(22/100=0.220\) in B. These observed proportions do not change which arm the response-based rule selected. They do show why the selection decision should not be reported as if it were a conclusion about the final endpoint: the arm ranked highest on the intermediate measure is not necessarily ranked highest on the observed endpoint measure.
These counts are descriptive hypothetical data. Their comparison alone does not establish a causal effect or account for uncertainty, censoring, or differences in follow-up. The point of the example is the pathway: the selection rule used response data, while final-endpoint data address a different question.
Diagnostics and Failure Modes
A pathway map is useful only if it matches the data collection and decision process. Several checks can reveal a mismatch:
- Timing mismatch. Verify that every measurement used in the rule was available before the decision. A measure collected later cannot be described as an interim selection input.
- Outcome-definition mismatch. Check that the intermediate measure has the same definition, assessment window, and direction of benefit across arms. A score whose larger values indicate worse status must not be ranked as though larger were better.
- Unstated tie-breakers. Read the full rule, including thresholds, ties, exclusions, and overrides. An endpoint-based tie-breaker creates a direct endpoint input even if it is rarely activated.
- Availability mismatch. Compare planned and actual data availability by arm. Differential missingness or delayed measurement can alter which information reaches the decision, even if the written formula is unchanged.
- Association mistaken for a causal link. A relationship between \(M\) and \(Y(\tau)\) does not by itself show that treatment effects on \(M\) imply treatment effects on the endpoint. Baseline factors, selection of participants with observed outcomes, or other processes can contribute to an observed association.
- Selection mistaken for confirmation. An arm chosen because its interim statistic is favorable has not thereby passed a final-endpoint test. Selection and endpoint inference are distinct operations.
A useful implementation check is to reconstruct the decision using the recorded inputs and the written rule. If the reconstructed selected arm differs from the actual decision, investigate the discrepancy rather than silently redrawing the pathway. Possible causes include a different data cutoff, a prespecified override, unavailable measurements, or a coding error.
What the Map Can and Cannot Establish
Mapping clarifies what information drives a decision; it does not decide which intermediate outcome should be chosen. An intermediate-only rule can be timely and operationally simple, but it can rank arms differently from a rule based on mature final-endpoint data. A rule based directly on the final endpoint is more directly tied to the clinical outcome, but may require longer follow-up or more events before a decision is possible. A rule that combines inputs inherits the need to specify how each input contributes.
Most importantly, the map is not proof of surrogacy or of a causal mechanism. To argue that effects on \(M\) reliably predict effects on \(Y(\tau)\) requires evidence and assumptions beyond the fact that \(M\) was used to select an arm. The map makes that gap visible: selection may depend on the assignment-to-intermediate link, while a claim about endpoint benefit concerns the assignment-to-final-endpoint link and possibly the relationship between the two outcomes.
Check Your Understanding
Answer each question, then compare your reasoning with the solutions.
- A rule selects the arm with the highest intermediate score. Final event data are collected later but are not inputs to the rule. Which outcome data directly determine selection?
- A rule uses intermediate response to rank arms and final-event counts only to break ties. Does the rule rely exclusively on the intermediate outcome?
- Why does observing an association between an intermediate measure and the final endpoint not establish that changing the intermediate measure would change the endpoint?
- A response measure is defined so that lower values indicate better status, but the software selects the arm with the largest value. What should be checked?
- In a hypothetical trial, control, A, and B have 30, 48, and 42 responses among 100 participants, respectively. A rule selects the experimental arm with the largest response-rate difference from control. Which arm is selected, and what does that decision establish?
Solutions. (1) The intermediate-score data, together with the written ranking rule, directly determine selection; later endpoint data do not directly determine it if they are not rule inputs. (2) No. In tie cases the endpoint counts are direct inputs, so the rule depends on both data sources. (3) The association may reflect baseline factors or other processes, and association alone does not establish a causal effect of intervening on the intermediate measure. (4) Check the outcome coding and direction of benefit, then verify that the software implements the intended ranking; selecting the largest value would reverse the intended preference. (5) The proportions are 0.300, 0.480, and 0.420. The differences from control are \(0.480-0.300=0.180\) for A and \(0.420-0.300=0.120\) for B, so A is selected. This establishes only that A ranks highest under the stated response-based rule in these data, not that A improves the final event endpoint.