Stopping at the Lowest Dose Level

Why the Lowest Dose Creates a Special Decision

In a rule-based escalation study, reaching the excessive-toxicity criterion at a dose usually has a directionally clear consequence: do not escalate to a higher dose. At the lowest tested dose, there is no lower tested dose to select instead. The stopping rule therefore has a distinct consequence: the trial stops dose escalation without selecting an MTD under the standard 3+3 rule.

This is a decision about what the design has established, not a claim that every lower, untested dose would be too toxic. The study has observed unacceptable toxicity at its starting dose according to a prespecified rule; it has not evaluated doses below that starting dose. Clear reporting must preserve that distinction.

Definition: The lowest-dose stopping event occurs when the lowest dose level tested meets the protocol-defined excessive-toxicity criterion. In the standard 3+3 rule, that criterion is at least 2 dose-limiting toxicities (DLTs) among 3 evaluable participants, or at least 2 DLTs among 6 evaluable participants after expansion. If this occurs at the lowest tested dose, escalation stops and the standard rule does not identify an MTD.

Applying the Rule at the Lowest Tested Dose

The standard 3+3 decision depends on the number of DLTs among evaluable participants at a dose. If the first cohort of 3 has 0 DLTs, the design permits escalation, subject to the protocol’s other requirements. If it has 1 DLT, the cohort is expanded to 6. With 0 or 1 DLT among those 6, the design permits escalation; with 2 or more, the dose meets the excessive-toxicity criterion. If the first 3 have 2 or 3 DLTs, the criterion is already met and the dose is not expanded to 6 merely to continue the standard rule.

At a dose above the lowest, a usual 3+3 disposition may select the preceding dose if that dose satisfies the rule. At the lowest dose, there is no preceding tested level available for that disposition. The trial therefore stops without selecting a dose as the MTD. The lowest dose remains the lowest tested dose, not a demonstrated tolerable dose and not an automatically selected treatment dose.

The exact decision must follow the protocol in force. A protocol may define a different trigger, cohort size, evaluability requirement, or permitted action. Apply the written criterion rather than substituting the familiar 3+3 threshold for a different prespecified rule.

Worked Example: Three DLTs in the First Cohort

Hypothetical trial. The starting dose is the only dose tested so far. Three evaluable participants complete the DLT assessment period, and all three experience a DLT. Apply the standard 3+3 rule.

Let \(x\) be the number of DLTs and \(n\) the number of evaluable participants. Here, \(x=3\) and \(n=3\), so the observed DLT proportion is

\hat{p}=\frac{x}{n}=\frac{3}{3}=1.000.

The standard trigger is at least 2 DLTs among the first 3. Since \(3\geq 2\), the lowest dose meets the excessive-toxicity criterion. The trial stops dose escalation; no MTD is identified by this rule. There is no lower tested dose to select, and the trial should not report the starting dose as the MTD merely because it was the only dose studied.

What the Stopping Decision Does—and Does Not—Establish

The logic can be stated directly. The standard 3+3 MTD selection rule can select a dose only when its conditions are met using observed dose levels; in the usual rule, the selected dose is a tested dose with an acceptable DLT count and an adjacent higher dose at which the excessive-toxicity criterion is met. If the lowest tested dose itself reaches that criterion, it cannot be the acceptable dose in such a selection. And because no lower dose was tested, there is no other tested dose that can satisfy the selection rule.

Therefore, the design outcome is no MTD selected, not “the MTD is below the starting dose.” The latter may be a plausible concern, but it is not an observed result: no lower dose’s toxicity has been measured. Nor does this decision establish that no dose could be used safely in any future study. It says that this trial, starting at this level and applying this rule, did not identify an MTD.

This distinction matters because the observed proportion \(x/n\) is a summary of a small number of participants, not a precise estimate of the underlying DLT probability \(p_d\) at that dose. A stopping rule makes a prespecified operational decision from the observed count; it does not prove that \(p_d\) exceeds a particular value or quantify the risk at an untested lower dose.

Worked Example: Two DLTs After Cohort Expansion

Hypothetical trial. At the lowest tested dose, 1 of the first 3 evaluable participants experiences a DLT. The protocol expands the cohort to 6. Among the 3 additional evaluable participants, 1 experiences a DLT. Determine the final decision.

The total is \(x=1+1=2\) DLTs among \(n=3+3=6\) evaluable participants. Thus,

\hat{p}=\frac{x}{n}=\frac{2}{6}=0.3333.

The standard 3+3 criterion is at least 2 DLTs among 6 after expansion. Because \(2\geq 2\), the criterion is met. Since this is the lowest tested dose, the trial stops without selecting an MTD. The observed proportion of 33.33% is a descriptive result for these six evaluable participants; it is not proof that the true DLT probability is exactly 33.33%, and it does not describe an untested dose below the starting level.

A suitable concise record would state that 2 of 6 evaluable participants had a DLT at the lowest tested dose, the protocol’s 2-of-6 criterion was met, and escalation stopped with no MTD identified. It should not imply that the participants were enrolled at a lower dose, or that a lower dose was tested and found acceptable.

Checking the Evidence Before Stopping

The rule is only as clear as the data and the protocol details to which it is applied. Before recording a lowest-dose stopping event, verify that the count includes the correct participants and that the outcome classifications are final under the study’s prespecified definitions. The earlier material on classifying ambiguous toxicity outcomes is relevant when an event’s classification is uncertain; do not resolve uncertainty by informally counting an event as a DLT or as a non-DLT to obtain a desired decision.

Also confirm whether each participant has completed the required DLT assessment period and whether the protocol defines any outcomes as unevaluable. The denominator is the number of participants the rule treats as evaluable, not automatically the number enrolled or treated. If outcomes are pending or evaluability is unresolved, report the status accurately and follow the protocol’s specified procedure before declaring the criterion met.

A useful audit is to write down the dose level, evaluable denominator, final DLT count, applicable threshold, and resulting action. In a standard 3+3 design, these records should make it possible to verify whether the trigger was 2 or more among the first 3, or 2 or more among the 6 after expansion. If the protocol differs from the standard rule, document its actual threshold and action instead.

Worked Example: Separating the Observed Result From the Unknown Risk

Hypothetical interpretation. Suppose 2 of 3 evaluable participants at the starting dose have a DLT. The trial stops at that lowest dose. Consider how much the observed count alone says about the unknown DLT probability \(p_d\).

Under a simple binomial model for illustration, assume participants’ DLT outcomes at this dose are independent and each has the same probability \(p_d\). If \(X\) is the number of DLTs among 3 participants, then the chance of meeting the 2-of-3 trigger at a given \(p_d\) is

P(X\geq 2\mid p_d) =\binom{3}{2}p_d^2(1-p_d)+p_d^3 =3p_d^2-2p_d^3.

For example, if \(p_d=0.30\), the chance of triggering the rule is

$$ 3(0.30)^2-2(0.30)^3 =0.270-0.054 =0.216. $$

Thus, under these illustrative assumptions, the trigger would occur with probability 0.216 (21.6%) when the underlying risk is 30%. This calculation does not change the protocol decision after 2 observed DLTs: the rule is met. It shows why the count should not be misreported as certainty about \(p_d\). The calculation also depends on the binomial assumptions and is not a replacement for the protocol’s decision rule.

Reporting and Common Pitfalls

A clear report separates the observed data from the design consequence. It names the dose as the lowest tested dose, gives the number of DLTs and evaluable participants, states the threshold that was reached, and says that escalation stopped with no MTD selected under the rule. If the trial enrolled more participants than were evaluable at the time of the decision, distinguish those counts rather than combining them.

Avoid overstating what the event means. “The lowest tested dose met the stopping criterion” is supported by the rule and data. “The lowest dose is unsafe for all patients,” “the true DLT rate is 67%,” or “the MTD is below the starting dose” are not conclusions established by the observed count alone. Likewise, “no dose is tolerable” is too strong: no lower dose was tested, and the rule has not evaluated every possible dose.

The principal alternative to stopping is not an informal change to the algorithm. A lower dose could be studied only if an applicable protocol already specifies a permitted lower-dose action or if an appropriate prospective protocol change is made and approved. That is distinct from the standard 3+3 disposition, which does not automatically create or evaluate a dose below the starting level.

Wrong: “Two of three had DLTs, so the starting dose is the MTD because no higher dose was tested.” Correction: The dose met the excessive-toxicity criterion; the standard rule stops and does not select it as the MTD.
Wrong: “The trial proves the true DLT probability is \(2/3\).” Correction: \(2/3\) is the observed proportion in that cohort; the underlying probability is not known exactly from the count.
Wrong: “The rule shows that a lower dose would also be too toxic.” Correction: The lower dose was not observed. The trial establishes no such result.
Wrong: “Use the number enrolled as the denominator.” Correction: Use the evaluable denominator specified by the protocol and report enrollment and evaluability separately when relevant.

Key takeaway: If the lowest tested dose meets the protocol’s excessive-toxicity criterion, apply the stopping action and report the observed DLT count and evaluable denominator. Under the standard 3+3 rule, stop without selecting an MTD; do not convert the result into a claim about untested lower doses or certainty about the true toxicity probability.

Check Your Understanding

Answer each question using the standard 3+3 rule unless a different protocol rule is stated.

At the lowest tested dose, 2 of the first 3 evaluable participants have DLTs. What is the decision, and is an MTD selected?
At the lowest tested dose, 1 of the first 3 has a DLT. After expansion, the total is 1 DLT among 6 evaluable participants. Has the excessive-toxicity stopping criterion been met?
At the lowest tested dose, 2 of 6 evaluable participants have DLTs. What should a report say about the observed proportion and the MTD?
Why does stopping at the lowest tested dose not establish that all lower doses are too toxic?

Solutions. (1) The 2-of-3 threshold is met, so stop escalation. Because this is the lowest tested dose, the standard rule selects no MTD. (2) No. The 3+3 trigger after expansion is at least 2 of 6, and the observed count is 1 of 6. (3) Report \(2/6=0.3333\), or 33.33%, as the observed DLT proportion; state that the 2-of-6 criterion was met and that no MTD was identified by the rule. Do not describe 33.33% as the known true DLT probability. (4) No lower dose was administered under the design, so its toxicity outcome is unobserved. The stopping decision concerns the tested starting dose and the rule’s action, not the toxicity of untested doses.