Replacing Patients With Incomplete DLT Follow-Up

Why Replacement Rules Need Two Separate Decisions

In a dose-escalation trial, a patient may stop treatment or leave observation before the dose-limiting-toxicity (DLT) assessment window is complete. The trial team then faces two related but distinct questions: does this patient count toward the protocol’s planned number of evaluable patients, and how should the available follow-up enter the model? Treating those as one question can either leave a dose level with too few assessable patients or discard useful information.

The first decision is operational. It determines whether another patient may be enrolled to meet a planned evaluable-patient target. The second is statistical. It determines how the original patient’s observed DLT status and time at risk contribute to the dose-toxicity analysis. A patient can be eligible for replacement while still contributing partial follow-up to the model. Replacement does not erase the original patient or convert their incomplete record into a completed non-DLT outcome.

The exact rule must be specified in the protocol. There is no universal minimum follow-up duration that makes a patient evaluable, and a model that can use partial follow-up does not by itself define who is eligible for replacement.

Specify the Rule Before Enrollment

A workable replacement policy needs to state the assessment window \(W\), the event that qualifies as a DLT, what makes an outcome evaluable, and which incomplete outcomes permit replacement. It should also say whether the replacement is assigned to the same dose or to a dose selected under the trial’s current escalation rules. Replacement is not an exception to dose-assignment or safety constraints.

A simple policy might count a patient as evaluable if they experience a protocol-defined DLT during the window or complete the window without a DLT. Under that policy, a patient who stops follow-up early without a DLT is not evaluable and may be replaced. But the protocol might instead define a minimum adequate follow-up duration, or specify how particular events such as progression, death, or withdrawal affect evaluability. Those decisions depend on the trial’s endpoint and must be settled prospectively.

The reason for incomplete follow-up matters for classification, but it should not invite ad hoc decisions. For example, an early stop due to suspected treatment-related toxicity requires review under the protocol’s DLT definition; it must not automatically be treated as a non-DLT dropout. Conversely, an unrelated event is not automatically a DLT merely because it prevents further assessment. Apply the endpoint and attribution rules consistently.

Partial Follow-Up Is Not the Same as a Completed Non-DLT Outcome

Let \(p_d\) denote the probability of a DLT by the end of window \(W\) at dose \(d\). A patient with no DLT observed through time \(t<W\) has not necessarily completed a DLT-free window. The model should therefore use the information actually observed, according to its specified likelihood or partial-follow-up method.

For a compact illustration, suppose the model assumes that, conditional on a DLT occurring by \(W\), its time is uniform over the window. This is a simplifying time-to-event assumption, not a general property of DLTs. For a patient with no DLT observed by time \(t\), the probability of remaining DLT-free through \(t\) is the probability of no DLT in the full window plus the probability of a DLT whose event time is after \(t\):

At \(t=0\), this likelihood contribution is 1: no DLT-free follow-up has been observed. At \(t=W\), it is \(1-p_d\): the patient has completed the window without a DLT. For intermediate \(t\), the observation provides evidence, but less than a completed DLT-free window. Other time-to-event models use their own event-time distribution and likelihood. TITE-CRM methods likewise use the model’s specified partial-follow-up treatment; the expression above should not be substituted for a different model’s likelihood.

Worked Decisions at the Boundary

Justification: Why Keep Both Decisions Separate?

The separation follows from the different purposes of the two rules. The evaluability rule controls whether the planned count of assessable outcomes has been met. The likelihood describes how compatible the observed data are with possible dose-toxicity risks. A patient can fail the first criterion yet provide data for the second.

In the illustrative model, the likelihood of remaining event-free through \(t\) is \(L(p_d;t)=1-p_dt/W\). For \(0<t<W\), this lies between the likelihood at enrollment and the likelihood after a completed DLT-free window:

The inequalities hold because \(0\leq t/W\leq 1\) and \(p_d\geq 0\). Thus partial follow-up is not empty, but it is not the same observation as a completed window. This reasoning depends on the stated model assumptions; a different time-to-event model may produce a different partial-follow-up likelihood. In all cases, replacement must not be used as a reason to remove observed data from the analysis.

Diagnostics, Alternatives, and Common Pitfalls

Operational review should compare replacement counts with the reasons and timing of incomplete follow-up. Unexpectedly frequent replacement at one dose, repeated early exits, or inconsistencies in DLT adjudication can signal a protocol, data-collection, or safety issue. Monitor pending follow-up explicitly: a patient who is still within the window is not the same as a patient whose follow-up has ended prematurely. Track each patient’s dose, window start, last observed day, DLT status and date, reason observation ended, evaluability classification, replacement status, and model-data status.

The main alternative to replacing incomplete patients is to enroll without a fixed evaluable-patient target and let the model use all available follow-up. That can avoid replacement enrollment, but may leave less mature information at a decision point and requires a model appropriate for pending outcomes. A hybrid policy can specify a target number of evaluable patients while also retaining partial observations in the model. Neither approach removes the need for a clear follow-up and dose-assignment policy.

• Mistake: “The model can use partial follow-up, so no replacement is needed.” Correction: model contribution and the protocol’s planned evaluable-patient count answer different questions. A trial may permit partial information in the model and still require replacement to meet its target.
• Mistake: “The patient was replaced, so their data should be dropped.” Correction: replacement adds a patient; it does not undo the original observation. Retain the original event and follow-up information using the specified model.
• Mistake: “No DLT was observed, therefore this was a non-DLT.” Correction: that conclusion is justified for the window only when the endpoint and follow-up rule support it. No event observed during incomplete follow-up is not automatically a completed-window non-DLT.
• Mistake: “A DLT caused early discontinuation, so the patient is not evaluable.” Correction: if the protocol-defined DLT occurred, the relevant endpoint may already be observed. Apply the protocol’s evaluability and adjudication rules rather than using window completion as a blanket requirement.

Replacement can also increase the number of patients exposed and affect how quickly dose recommendations are made. The policy should therefore be reviewed alongside accrual, safety monitoring, and the model’s handling of pending outcomes. It is not a statistical correction for selection bias if patients are classified differently based on whether their outcomes are convenient or informative.