Cohort Accrual Decisions Under Delayed DLT Assessment

Why Cohort Timing Is a Design Decision

In dose escalation, a cohort’s dose-limiting toxicity (DLT) outcomes may take weeks to become fully assessable. If the next cohort must wait until every participant in the current cohort completes the assessment window, the trial obtains a clear, complete cohort record before proceeding, but enrollment can be slow. Starting a new cohort while earlier participants are still being assessed can shorten the calendar time to a decision. It also means that the dose decision may depend on information that is incomplete.

This is an operational choice, not a change to the dose-toxicity model itself. The earlier material on TITE-CRM explains how pending follow-up can contribute information to a model update. Here the focus is on the consequences of the schedule: when cohorts start, when their outcomes become fully assessable, and what a time saving does—and does not—tell us about safety.

Definition: A cohort’s assessment window is the protocol-defined period after dosing during which a participant’s DLT outcome is assessed. A participant has pending follow-up when that window is not yet complete and no DLT has been observed to date. A waiting schedule starts the next cohort only after the current cohort’s outcomes are complete. An overlapping schedule starts a later cohort while one or more earlier participants still have pending follow-up.

A pending participant without an observed DLT is not equivalent to a participant who completed the window without a DLT. The former has had less opportunity for a DLT to be observed. A model that incorporates pending follow-up can account for that difference, but it cannot turn incomplete follow-up into complete follow-up. Any schedule that permits overlap therefore needs a pre-specified way to use pending data and to limit decisions while important outcomes remain unresolved.

A Calendar Model for Cohort Accrual

Begin with a simple schedule that makes the timing comparison explicit. Suppose each cohort takes \(C\) days to enroll, and each participant’s assessment window lasts \(W\) days from that participant’s dose. Approximate the cohort’s complete-assessment date as its start date plus \(C+W\): this treats the last participant as dosed at the end of the cohort’s enrollment period. Let \(K\) be the number of cohorts and \(\Delta\) the interval between successive cohort start dates. The start date of cohort \(j\) is \(t_j=(j-1)\Delta\), taking the first cohort’s start as day 0. Thus the final complete-assessment date is:

T_{\mathrm{final}}=(K-1)\Delta+C+W.

Under strict waiting, the next cohort starts after the preceding cohort is fully assessed, so \(\Delta=C+W\). An overlapping schedule uses a shorter interval, \(\Delta<C+W\). Holding \(K\), \(C\), and \(W\) fixed, the calendar time saved relative to strict waiting is:

T_{\mathrm{wait}}-T_{\mathrm{overlap}} =(K-1)\bigl[(C+W)-\Delta\bigr].

Why the Time-Saving Formula Holds

The first cohort starts on day 0 under either schedule. Each of the remaining \(K-1\) start-to-start gaps is \(C+W\) days under strict waiting and \(\Delta\) days under the overlapping schedule. The final cohort has the same \(C+W\) days from its start to complete assessment under both schedules. Therefore, only the \(K-1\) gaps differ:

\begin{aligned} T_{\mathrm{wait}}&=(K-1)(C+W)+C+W,\\ T_{\mathrm{overlap}}&=(K-1)\Delta+C+W,\\ T_{\mathrm{wait}}-T_{\mathrm{overlap}} &=(K-1)\bigl[(C+W)-\Delta\bigr]. \end{aligned}

This is a calendar identity, not a guarantee that an actual trial will finish exactly on that date. It assumes the same number of cohorts and the same cohort-enrollment duration under both schedules, and it ignores pauses, holidays, staffing constraints, dose changes, and additional safety reviews. It also assumes a fixed sequence of cohorts. In an actual trial, pending outcomes can affect dose recommendations, and a safety pause or a different recommendation can change the schedule itself.

Worked Example: Two Cohorts With a Shorter Start Interval

Suppose, hypothetically, that each cohort takes \(C=5\) days to enroll and the assessment window is \(W=40\) days. Compare strict waiting with an overlapping schedule that starts the second cohort 20 days after the first starts.

For strict waiting, the gap between cohort starts is \(C+W=5+40=45\) days. The first cohort starts on day 0 and is fully assessed on day \(0+45=45\); the second starts on day 45 and is fully assessed on day \(45+45=90\). Thus \(T_{\mathrm{wait}}=90\) days.

With overlap, \(\Delta=20\) days. The second cohort starts on day 20 and completes assessment on day \(20+45=65\), so \(T_{\mathrm{overlap}}=65\) days. The time saved is \(90-65=25\) days. The formula gives the same result: \((2-1)[45-20]=25\) days.

The comparison concerns the date when both cohorts’ outcomes are complete. It does not imply that the second cohort’s dose decision on day 20 is based on complete outcomes from the first cohort.

Using Pending Outcomes Without Treating Them as Complete

An overlapping schedule is meaningful only in conjunction with a decision rule. At a planned decision time, the team needs to know which participants have complete assessment, which have pending follow-up, and whether any DLTs have already been observed. If the design uses TITE-CRM, pending follow-up may contribute partial information according to its specified weighting approach. The model update and the protocol’s dose-assignment and safety constraints—not the calendar arithmetic—determine whether another cohort may start and at what dose.

A protocol should state in advance how pending participants are handled, what information is required before a dose assignment, and what findings require a hold or review. These details depend on the design and trial context; there is no universal minimum follow-up fraction that makes overlap safe. In particular, an observed DLT during pending follow-up remains clinically relevant, and an accrual plan should not mechanically proceed merely because a cohort start date has arrived.

Worked Example: Four Cohorts and the Effect of Enrollment Duration

Consider a hypothetical four-cohort schedule with \(C=7\) days of enrollment per cohort and \(W=28\) days of follow-up. Compare strict waiting with a planned overlapping start interval of \(\Delta=14\) days.

For strict waiting, each start gap is \(C+W=7+28=35\) days. The cohort start dates are days 0, 35, 70, and 105. The fourth cohort completes assessment on day \(105+35=140\).

For the overlapping schedule, the start dates are days 0, 14, 28, and 42. The fourth cohort completes assessment on day \(42+35=77\). The saving is \(140-77=63\) days. Equivalently, there are \(K-1=3\) shortened gaps, each by \(35-14=21\) days, giving \(3\times21=63\) days.

The seven enrollment days matter. Using \(W=28\) as the strict-wait start interval would incorrectly assume that the entire cohort is dosed at once and would start the next cohort before the final participant’s 28-day window is complete. If enrollment is staggered differently, the assessment completion date should be calculated from the last participant’s actual dose rather than from this approximation.

Compare Policies at the Same Decision Point

A useful comparison distinguishes the time to an interim decision from the time to complete assessment. An overlap policy may allow a new cohort to begin at an interim decision point, while complete follow-up for the earlier cohort arrives later. If the question is “When can the next cohort start?”, use the specified decision and accrual rules. If the question is “When are all outcomes from these cohorts complete?”, use the assessment dates. These are different endpoints.

For example, suppose a hypothetical cohort begins on day 0, enrolls over days 0–5, and has a 30-day assessment window. Under the scheduling approximation above, complete assessment is expected on day \(5+30=35\). An overlapping policy plans the next cohort to start on day 14. At that time, the first cohort’s follow-up is still pending for some participants. Assume, solely for illustration, that the protocol permits a model update using pending follow-up and that the pre-specified dose constraints allow enrollment at the recommended dose. The next cohort can then start on day 14, but the first cohort is not fully assessed until day 35. The planned start is 21 days before complete assessment: \(35-14=21\). That difference quantifies the overlap; it is not evidence that the risk assessment is as certain on day 14 as it is on day 35.

If instead the protocol requires complete assessment before a new cohort can start, the next start is no earlier than day 35. If the interim update does not satisfy the protocol’s safety conditions, the planned day-14 start is postponed. Thus a schedule’s nominal \(\Delta\) is not a substitute for its actual decision rule.

Worked Example: A Planned Start Is Delayed by a Safety Hold

Suppose, hypothetically, three cohorts each take \(C=4\) days to enroll, with \(W=24\) days of follow-up. A waiting schedule has start gaps of \(4+24=28\) days, giving starts on days 0, 28, and 56; the third cohort completes assessment on day \(56+28=84\).

An overlap plan sets \(\Delta=14\) days, so the planned starts are days 0, 14, and 28. If all planned starts occur, the third cohort completes assessment on day \(28+28=56\), 28 days earlier than under strict waiting. This follows from \((3-1)(28-14)=28\) days.

Now suppose a pre-specified review pauses accrual at day 14 and does not release the hold until day 35. The second cohort’s start moves from day 14 to day 35. If the third cohort then starts 14 days later, on day 49, its complete-assessment date is day \(49+28=77\). The realized saving relative to day 84 is \(84-77=7\) days, not 28. The nominal formula described the no-pause plan; the hold changed the schedule. The dates here are hypothetical and illustrate the arithmetic, not a recommendation to use any particular pause rule.

Diagnostics, Alternatives, and Limitations

Before presenting a calendar-time comparison, check that both schedules use the same definition of the endpoint, cohort size, enrollment duration, assessment window, and number of cohorts. Confirm that the strict-wait interval includes the time needed to enroll the cohort as well as follow-up for its last participant. When actual enrollment is staggered, calculate completion from individual dose dates; a single cohort-level \(C+W\) approximation may not be accurate.

The main alternative to overlap is strict waiting for complete assessment. It is easy to interpret operationally because each new cohort is informed by completed outcomes from the preceding cohort, but it may extend trial duration. Overlap can reduce planned calendar time and may be reasonable when the protocol has a defensible method for updating with pending data and clear safety controls. Its time advantage is conditional: holds, changes in cohort size, or altered dose recommendations can reduce or erase it. Nor does faster accrual itself improve the statistical model or establish that a dose is safe.

A common mistake is to say that overlap saves the full assessment-window length for every added cohort. The saving depends on the difference between the strict-wait gap and the chosen overlapping gap, multiplied by the number of gaps, \(K-1\). Another mistake is to compare different start intervals while calling both schedules “wait for completion.” Under strict waiting in this calendar model, the interval is \(C+W\); if a stated waiting interval is longer or shorter, calculate from the stated interval and do not silently replace it.

Finally, these calculations address timing, not the probability of making a correct dose decision. That probability depends on the model, the observed and pending outcomes, the decision constraints, and the actual toxicity process. A shorter projected trial calendar is therefore an operational benefit to evaluate alongside—not instead of—dose assignment and patient-safety considerations.

Key takeaway: For \(K\) cohorts with enrollment duration \(C\), assessment window \(W\), and fixed start gap \(\Delta\), the approximate final complete-assessment date is \((K-1)\Delta+C+W\). Relative to strict waiting, where \(\Delta=C+W\), the planned time saving is \((K-1)[(C+W)-\Delta]\). Overlap changes when decisions occur; it does not make pending outcomes complete.

Check Your Understanding

Answer each question, then compare your reasoning with the solutions.

Three cohorts have \(C=3\) days of enrollment and \(W=21\) days of follow-up. Under strict waiting, what are the start dates and final complete-assessment date?
For the same three cohorts, an overlap schedule uses \(\Delta=12\) days. What is the final complete-assessment date, and how many days are saved relative to strict waiting?
Two cohorts start 50 days apart, each with \(C+W=45\) days. What is the final complete-assessment date for the second cohort, and how does that differ from strict waiting?
Why is a participant with no observed DLT but incomplete follow-up not the same as a participant who completed the assessment window without a DLT?

Solutions. (1) The strict-wait gap is \(C+W=3+21=24\) days. Starts are days 0, 24, and 48; the final complete-assessment date is \(48+24=72\) days. (2) The starts are days 0, 12, and 24, and the final assessment date is \(24+24=48\) days. The saving is \(72-48=24\) days, also \((3-1)(24-12)=24\). (3) The second cohort completes on day \(50+45=95\). Strict waiting would start it 45 days after the first cohort, so it would complete on day \(45+45=90\). The stated 50-day interval is five days longer than strict waiting, making its final assessment five days later—not an earlier or equivalent waiting schedule. (4) The participant with incomplete follow-up has had less time in which a DLT could be observed. No DLT observed so far does not establish that the assessment window was completed without a DLT.