Time-to-Event BOIN (TITE-BOIN) Part 2: Case Study

Introduction

Part 1 introduced the statistical logic behind the Time-to-Event Bayesian Optimal Interval (TITE-BOIN) design. The key problem is straightforward: in a conventional Phase I dose-escalation trial, a patient may require a substantial amount of follow-up before their dose-limiting toxicity (DLT) status is known.

If investigators wait for every patient in a cohort to complete the entire DLT assessment window before enrolling the next cohort, rapidly accruing trials can become unnecessarily slow.

TITE-BOIN addresses this problem by allowing dose decisions to incorporate pending toxicity information. Patients who have not completed their DLT assessment window contribute information according to how much of their observation period has been completed.

This tutorial applies that framework to a complete case study.

The Case Study

Consider a Phase I oncology dose-escalation trial evaluating an investigational agent at five dose levels.

The primary safety endpoint is the occurrence of a dose-limiting toxicity during a prespecified assessment window.

These values create an important operational challenge.

The trial is enrolling approximately two patients per month, but a patient may need three months of observation before their DLT status is completely known.

A traditional design that requires complete assessment of every cohort could therefore spend substantial calendar time waiting for toxicity information.

Trial Design Parameters

The target DLT rate is:

The purpose of dose escalation is therefore to identify the dose whose true DLT probability is sufficiently close to approximately 20%.

BOIN Boundaries for the Target DLT Rate

For a target DLT rate of 20%, the TITE-BOIN decision table is constructed from the underlying BOIN escalation and de-escalation boundaries.

For this case study, the relevant BOIN boundaries are approximately:

and:

The first boundary is associated with escalation and the second with de-escalation.

TITE-BOIN then incorporates pending follow-up information to determine which integer response-count/follow-up combinations correspond to escalation, staying at the current dose, de-escalation, or accrual suspension.

What Is Standardized Total Follow-Up Time?

Suppose a patient has not yet completed the 90-day DLT assessment window.

Let \(t_i\) denote the amount of follow-up accumulated by pending patient \(i\).

The standardized total follow-up time is:

where:

• \(m\) is the number of patients with DLT data pending;
• \(t_i\) is the follow-up time accumulated by pending patient \(i\); and
• \(T\) is the complete DLT assessment window.

For this trial:

Therefore:

A Simple STFT Example

Suppose four patients have pending DLT data and have accumulated:

• 75 days of follow-up;
• 60 days of follow-up;
• 45 days of follow-up; and
• 30 days of follow-up.

The total follow-up is:

Therefore:

Thus, the four pending patients collectively contribute an STFT of approximately:

This is not a probability and should not be interpreted as one.

It is a standardized measure of the amount of follow-up information accumulated among the pending patients.

The TITE-BOIN Decision Table

For a target DLT rate of 20% and a cohort size of three, the TITE-BOIN table contains rules based on:

• Number of patients treated at the current dose;
• Number of observed DLTs;
• Number of patients whose DLT data are pending; and
• STFT of the pending patients.

A simplified portion of the decision structure is shown below.

The complete decision table can be generated for all possible numbers treated at a dose.

Starting the Trial

The first cohort consists of patients 1–3.

They receive the lowest dose, Dose Level 1.

Day 60: Why the Trial Does Not Immediately Escalate

At Day 60, all three patients remain within their 90-day assessment windows.

No DLT has been observed.

At first glance, this might appear to be strong evidence supporting escalation.

However, all three patients still have pending information.

The TITE-BOIN table therefore does not simply treat the absence of an observed DLT as evidence equivalent to three completed non-DLT assessments.

Because the amount of pending information is too large for the prespecified decision rule, the trial temporarily suspends accrual.

Day 120: First Escalation

By Day 120, the first two patients have completed their 90-day assessment windows without experiencing DLTs.

The trial now has enough information to apply the TITE-BOIN decision rule.

With no observed DLTs and sufficient completed follow-up, the design supports escalation.

Patients 4–6 are therefore assigned to Dose Level 2.

Patients 4–6 at Dose Level 2

The next cohort consists of patients 4, 5, and 6.

All three receive Dose Level 2.

The trial continues accruing patients while their DLT outcomes mature.

This is precisely the situation TITE-BOIN was designed to address.

Day 165: A DLT Appears

By the arrival of patient 7, patient 4 has experienced a DLT at Dose Level 2.

Patients 5 and 6 have not experienced a DLT, but their DLT assessments remain incomplete.

Their follow-up is only:

• Patient 5: 1/3 of the assessment window;
• Patient 6: 1/6 of the assessment window.

In terms of days, this corresponds approximately to:

The important point is that one DLT has already been observed among only three patients treated at Dose Level 2.

The TITE-BOIN rule therefore recommends de-escalation.

Why De-escalate Even Though Two Patients Are Pending?

This is one of the most important features of the TITE-BOIN framework.

The design does not necessarily need to wait for every pending patient's final DLT outcome.

When the observed DLT information is already sufficiently concerning, the design can recommend de-escalation immediately.

Waiting for patients 5 and 6 to complete their entire assessment windows could delay the trial without changing the immediate safety decision.

Patients 7–9 Return to Dose Level 1

Patients 7, 8, and 9 are treated at Dose Level 1.

The trial therefore temporarily moves back down the dose ladder:

This is not a permanent declaration that Dose Level 2 is too toxic.

Rather, it is the current dose-assignment decision based on the information available at that point in the trial.

Day 210: Returning to Dose Level 2

By approximately Day 210, three of the six patients treated at Dose Level 1 have completed their DLT assessment without experiencing a DLT.

The accumulated safety information at Dose Level 1 is now sufficiently reassuring to permit escalation again.

The next cohort is therefore returned to Dose Level 2.

Patients 10–12 at Dose Level 2

Patients 10, 11, and 12 receive Dose Level 2.

The trial now has a mixture of completed and pending DLT information at the current dose.

This is where the time-to-event component becomes particularly useful.

Day 255: Patient 13 Is Ready to Enter

At approximately Day 255, one of the six patients previously treated at Dose Level 2 has experienced a DLT.

The design does not automatically escalate simply because the other patients have not yet experienced DLTs.

Instead, the current DLT count and the amount of pending follow-up are evaluated using the TITE-BOIN decision table.

The resulting decision is to remain at Dose Level 2.

Patients 13–15 are therefore also treated at Dose Level 2.

Day 300: Nine Patients at Dose Level 2

By Day 300, nine patients have been treated at Dose Level 2.

One DLT has been observed.

Five patients still have pending DLT information.

The current state can therefore be summarized as:

At this point, the design again encounters a substantial amount of pending information.

Rather than forcing an immediate dose decision, TITE-BOIN suspends accrual.

Why Accrual Is Suspended at Day 300

The suspension is an important safety feature.

The trial has observed only one DLT, but five patients have incomplete DLT follow-up.

The design therefore waits for additional information rather than treating the absence of observed DLTs in those patients as equivalent to completed non-DLT observations.

Day 315: Calculating STFT

Fifteen days later, the pending information has matured enough to calculate the standardized total follow-up time.

The relevant pending patients have accumulated:

The total pending follow-up is:

Because the DLT assessment window is 90 days:

Thus:

Comparing STFT With the Decision Boundary

For this particular state of the TITE-BOIN decision table, the relevant escalation boundary for STFT is approximately:

We have:

Therefore, the accumulated follow-up information supports escalation.

Patients 16–18 at Dose Level 3

Patients 16, 17, and 18 are treated at Dose Level 3.

This is the highest dose reached by the trial at this point.

The dose trajectory has now been:

The path illustrates an important characteristic of model-assisted dose escalation designs: dose movement is data-driven rather than monotonically upward.

Patient 19: A DLT at Dose Level 3

Before patient 19 is enrolled, one DLT has been observed among patients treated at Dose Level 3.

The TITE-BOIN rule therefore calls for de-escalation.

Patients 19–21 are consequently assigned to Dose Level 2.

The Complete Dose-Assignment Timeline

The entire case study can be summarized chronologically.

Why This Timeline Matters

The timeline demonstrates that TITE-BOIN is not simply "BOIN with incomplete data."

The timing of patient enrollment becomes part of the statistical decision process because the amount of follow-up available at each decision point changes continuously.

Two otherwise identical sets of DLT outcomes can lead to different decisions if the pending patients have accumulated different amounts of follow-up.

Why Patient 5 and Patient 6 Matter

Return to the Day 165 decision.

Patient 4 has experienced a DLT.

Patients 5 and 6 have not experienced a DLT, but their follow-up is incomplete.

A conventional analysis might be tempted to code them temporarily as non-DLTs.

That would be problematic because "no DLT observed yet" is not equivalent to "completed the assessment window without DLT."

A patient who has been followed for only 15 days has not provided the same information as a patient who has completed all 90 days.

TITE-BOIN explicitly recognizes this distinction.

Pending Does Not Mean Missing

This distinction is fundamental.

A pending patient has partial information.

A missing patient may have no usable information for the relevant endpoint.

TITE-BOIN is designed for the former situation.

The Role of the Assessment Window

The DLT assessment window in this example is 3 months.

In days:

A patient who has completed 45 days without DLT has contributed half of the assessment window.

A patient followed for 75 days has contributed:

The STFT combines these contributions across all pending patients.

Why Standardization Is Useful

The STFT is divided by the length of the assessment window.

Therefore, the decision framework can be expressed on a standardized scale rather than requiring an entirely different table for every possible assessment-window length.

For example, a pending patient followed for half of a 60-day window and a pending patient followed for half of a 90-day window each contribute:

to the standardized follow-up measure.

Why the Trial Can Move Up and Down

The dose trajectory in this example is:

This is not a flaw.

Dose-finding designs are deliberately designed to react to accumulating toxicity information.

An escalation followed by a de-escalation simply means that the information available at later decision points changed the evidence about the current dose.

What Happens at the End of the Trial?

The trial continues until the prespecified maximum sample size is reached, unless another prespecified stopping rule terminates the study earlier.

At the end, the MTD is selected using the accumulated toxicity information.

The original TITE-BOIN framework uses isotonic regression to obtain a monotonically non-decreasing estimate of the DLT probability across dose levels.

The selected MTD is the dose whose isotonic-regression estimate is closest to the target DLT probability:

where \(\phi=0.20\) in this case study.

Final Results of the Case Study

At the conclusion of the trial, Dose Level 2 is selected as the MTD.

A total of 21 patients were treated at Dose Level 2, of whom four experienced DLTs.

The observed DLT rate at Dose Level 2 is therefore:

or approximately:

This is very close to the target DLT probability of 20%.

How Long Did the Trial Take?

The entire TITE-BOIN case study takes approximately:

or:

The published example describes this as approximately 20.5 months.

For comparison, a traditional approach that required complete DLT assessment before moving to the next cohort would take approximately 1,200 days, or about 40 months, under the assumptions used in the case study.

Traditional Approach vs. TITE-BOIN

The Most Important Day in the Case Study: Day 315

The Day 315 decision is arguably the clearest illustration of why TITE-BOIN exists.

At Dose Level 2:

• One DLT had been observed;
• several patients had completed follow-up without DLT;
• four patients remained pending; and
• those pending patients had accumulated 210 days of total follow-up.

The standardized total follow-up time was:

The relevant escalation threshold was approximately:

Because:

the trial could escalate without waiting for every pending patient to finish the entire 90-day assessment window.

What Would Happen Without TITE-BOIN?

Under a design requiring complete assessment of each cohort, the trial would have to wait until the DLT status of the relevant patients was known before assigning the next cohort.

That creates a substantial delay when:

• the assessment window is long;
• DLTs occur late;
• patient accrual is rapid; or
• multiple cohorts would otherwise be able to enroll during the waiting period.

In this case study, the assessment window is three months while patients are arriving at approximately two per month.

The mismatch between those two time scales is exactly what creates the opportunity for TITE-BOIN.

TITE-BOIN Does Not Ignore Safety

It is important not to interpret the shorter trial duration as meaning that TITE-BOIN accepts more uncertainty about toxicity.

The design instead uses the available follow-up information in a structured, prespecified manner.

For example, if an observed DLT already provides sufficient evidence for de-escalation, the design does not require investigators to wait simply because other patients are still pending.

Conversely, if too much information remains pending to make a reliable decision, the design can suspend accrual.

Thus the design contains both mechanisms:

Understanding Accrual Suspension

Accrual suspension is not a failure of the TITE-BOIN design.

It is part of the design.

A common misconception is that a time-to-event design should always permit continuous enrollment.

That is not the objective.

The objective is to permit enrollment when the available information supports a prespecified decision, while avoiding unnecessary waiting when sufficient information is already available.

Three Possible TITE-BOIN Decisions

At a given dose, the design may effectively produce three operational outcomes:

Some rules may additionally eliminate a dose when the observed toxicity is sufficiently high.

Dose Elimination

TITE-BOIN can incorporate dose-elimination rules for doses that appear unacceptably toxic.

For example, the decision table may specify a rule such as:

Once a dose is eliminated, subsequent patients should not be assigned to that dose under the prespecified design.

Why the Final MTD Is Not Simply the Last Dose Used

The highest dose administered during a trial is not automatically the MTD.

In this case, Dose Level 3 was reached.

But the final MTD was Dose Level 2.

That is appropriate because the MTD is selected from the accumulated evidence, not from the highest dose reached during the escalation sequence.

The Final Data Structure

At the end of a TITE-BOIN trial, investigators have information across all dose levels.

Conceptually:

The observed rates are not necessarily used completely raw.

Isotonic regression can be used to enforce the clinically natural assumption that toxicity probability does not decrease as dose increases.

Why Isotonic Regression Is Needed?

Suppose raw observed DLT rates were:

These are already monotonically increasing.

But random sampling can produce an unusual pattern such as:

It would be undesirable for the estimated toxicity probability to decrease when moving from Dose Level 2 to Dose Level 3.

Isotonic regression produces a monotonic estimate:

The MTD is then selected by comparing these estimates with the target DLT probability.

R: Calculating Standardized Total Follow-Up Time

The STFT calculation is straightforward.

follow_up <- c(75, 60, 45, 30)

assessment_window <- 90

stft <- sum(follow_up) / assessment_window

stft

The result is:

2.333333

Thus:

R: Expressing Follow-Up as Fractions of the Window

The same calculation can be performed using fractions of the 90-day window.

follow_up_fraction <- c(
  75 / 90,
  60 / 90,
  45 / 90,
  30 / 90
)

sum(follow_up_fraction)

which again gives:

2.333333

This makes the interpretation particularly intuitive:

R: A Simple Trial-State Representation

For an implementation, it is useful to represent the current state of the trial explicitly.

trial_state <- list(
  dose = 2,
  n_treated = 9,
  n_dlt = 1,
  n_pending = 5,
  assessment_window = 90
)

trial_state

The actual decision engine would additionally require the individual follow-up times of the pending patients.

pending_followup <- c(
  75,
  60,
  45,
  30
)

stft <- sum(pending_followup) /
  trial_state$assessment_window

stft

R: A Generic STFT Function

calculate_stft <- function(
  follow_up,
  assessment_window
) {

  sum(follow_up) /
    assessment_window
}

calculate_stft(
  c(75, 60, 45, 30),
  90
)

This returns the standardized total follow-up time for the pending patients.

R: A Generic Dose-Decision Skeleton

A practical implementation would first generate the complete TITE-BOIN decision table.

The trial database can then be evaluated against that table.

tite_boin_decision <- function(
  n_treated,
  n_dlt,
  n_pending,
  stft,
  decision_table
) {

  row <- subset(
    decision_table,
    treated == n_treated &
    dlt == n_dlt &
    pending == n_pending
  )

  if (nrow(row) == 0) {
    return("No prespecified rule found")
  }

  if (n_pending > 0 && !is.na(row$stft_min)) {

    if (stft >= row$stft_min) {
      return(row$decision_high_stft)
    }

    return(row$decision_low_stft)
  }

  row$decision
}

The exact implementation depends on how the complete decision table is generated and stored.

What the Case Study Teaches About Pending Data

The case study produces several important lessons.

1. A pending patient is informative. Partial follow-up contains information about the absence of toxicity so far.
2. Pending information is not equivalent to completed information. A patient followed for 15 days does not provide the same evidence as a patient who completed a 90-day window.
3. DLTs are definitive events. Once a DLT occurs, the patient is no longer pending for that endpoint.
4. STFT aggregates partial information. Multiple pending patients can collectively provide enough follow-up to support a dose decision.
5. The design can wait when information is insufficient. Accrual suspension is part of the prespecified design.

What Makes TITE-BOIN Different From TITE-CRM?

Both TITE-BOIN and TITE-CRM are designed to address late-onset toxicity.

The major practical distinction is how dose decisions are generated.

TITE-CRM repeatedly fits a dose-toxicity model as information accumulates.

TITE-BOIN instead uses a model-assisted framework whose practical decision rule can be tabulated before the trial begins.

This transparency is one reason TITE-BOIN can be attractive for practical clinical-trial implementation.

Why This Is Called a Model-Assisted Design

TITE-BOIN is not purely algorithmic in the traditional sense.

The boundaries are derived using a statistical model and optimization criterion, but the resulting dose-assignment rule can be represented as a simple table.

This creates a useful middle ground:

A Critical Distinction: Assessment Time vs. Accrual Time

The case study is particularly useful because it separates two different clocks.

Accrual Clock

Patients are arriving at approximately:

Toxicity Clock

Each patient has a:

DLT assessment window.

Because these clocks operate at different speeds, a conventional design can spend substantial time waiting.

TITE-BOIN is designed specifically for this mismatch.

Calendar Time vs. Patient Information

A crucial conceptual point is that calendar time itself does not determine whether enough information exists to make a dose decision.

Instead, the design asks:

How much relevant toxicity information has accumulated?

This is why the Day 300 and Day 315 decisions differ.

Only 15 calendar days separate those decision points, but those 15 days generate enough additional follow-up to change the TITE-BOIN decision.

Day 300 vs. Day 315

This is the essence of a time-to-event design.

Why TITE-BOIN Can Accelerate Development

The design does not necessarily reduce the number of patients needed to identify an MTD.

Its principal advantage is often calendar time.

When toxicity information arrives gradually, the design can make use of information as it becomes available rather than treating all incomplete patients as completely uninformative.

That can shorten the time required to complete dose escalation.

Safety and Operational Trade-Offs

A TITE-BOIN trial must still be carefully monitored.

Operational planning should address:

• Real-time capture of DLT onset dates;
• Accurate calculation of follow-up time;
• Timely identification of DLTs;
• Accurate identification of pending patients;
• Correct dose-level assignment;
• Accrual suspension procedures;
• Dose-elimination rules;
• Communication between clinical and statistical teams.

The mathematical design can only work as intended if the underlying patient data are updated accurately and promptly.

What Happens if a DLT Occurs?

A DLT is treated differently from a pending observation.

Once a DLT occurs:

• The patient is no longer pending;
• The DLT count increases;
• The patient's follow-up no longer needs to contribute to STFT;
• The dose decision is reevaluated using the appropriate TITE-BOIN rule.

This can lead to immediate de-escalation.

What Happens if a Patient Completes Follow-Up Without DLT?

A patient who completes the entire DLT assessment window without experiencing a DLT is considered to have a completed non-DLT outcome.

That patient no longer contributes to the pending STFT.

Instead, the patient contributes to the observed number of patients without DLT.

Why Follow-Up Time Stops at the Assessment Window

Suppose a patient remains on study for 150 days, but the DLT assessment window is only 90 days.

For the TITE-BOIN DLT calculation, the relevant observation window is 90 days.

The patient is therefore considered to have completed the relevant DLT assessment once the 90-day window is reached.

where \(T\) is the assessment window.

Protocol Language Should Be Precise

A protocol implementing TITE-BOIN should define the following explicitly:

• Target DLT probability;
• DLT definition;
• DLT assessment window;
• Starting dose;
• Available dose levels;
• Cohort size;
• Maximum sample size;
• Escalation boundary;
• De-escalation boundary;
• Decision-table generation method;
• Rules for pending patients;
• STFT calculation;
• Accrual suspension rules;
• Dose-elimination rules;
• MTD selection method;
• Rules for unevaluable patients.

Common Mistakes in a TITE-BOIN Implementation

1. Treating every pending patient as a non-DLT. A pending patient has incomplete information and should not automatically be coded as a completed non-DLT.
2. Ignoring the exact follow-up time. STFT depends on the amount of follow-up accumulated.
3. Using calendar time instead of patient follow-up. The design is based on patient-level toxicity information, not simply the number of days since the trial opened.
4. Failing to suspend accrual when required. If the prespecified table calls for suspension, investigators should not override the rule simply to maintain enrollment momentum.
5. Using a homemade decision table. The table should be generated from the prespecified statistical design.
6. Changing the target DLT rate after seeing data. The target is a design parameter and should be prespecified.
7. Assuming the highest dose reached is the MTD. The MTD is selected using the final accumulated data.
8. Failing to account for late DLTs. The operational system must continue to monitor patients through the entire prespecified assessment window.

A Practical TITE-BOIN Workflow

The Entire Case in One Table

The Key Statistical Calculation

The most important numerical calculation in this case study is the STFT calculation at Day 315.

The relevant escalation threshold is approximately:

Since:

the design permits escalation to Dose Level 3.

This single calculation captures the essential mechanics of TITE-BOIN: pending patients contribute partial information according to how much of the assessment window they have completed.

What the Final Result Means

The selected Dose Level 2 had:

or approximately 19% observed DLTs.

The target was:

Thus the final selected dose has an observed toxicity rate very close to the target.

This illustrates the fundamental objective of a dose-finding study: identify a dose whose toxicity probability is acceptably close to the prespecified target while protecting patients from unnecessarily toxic doses.

Case Study Takeaways

Final Summary

The TITE-BOIN case study demonstrates how a modern Phase I dose-finding design can handle the practical problem of late-onset toxicity.

The trial begins at Dose Level 1 and moves dynamically through the dose levels as DLT information accumulates.

At several points, the trial can make an immediate decision because the observed toxicity information is sufficiently strong.

At other points, accrual is suspended because too much information remains pending.

The most illustrative example occurs at Day 315, when four pending patients have accumulated 210 days of combined follow-up:

Because this exceeds the relevant escalation boundary of approximately 2.15, the trial can escalate to Dose Level 3 without waiting for every pending patient to complete the full DLT assessment window.

Later, a DLT at Dose Level 3 causes the design to de-escalate back to Dose Level 2.

At the end of the trial, Dose Level 2 is selected as the MTD, with four DLTs among 21 treated patients:

which is close to the target DLT rate of 20%.

References

Yuan, Y., Lee, J.J. & Hilsenbeck, S.G. (2018). Time-to-Event Bayesian Optimal Interval Design to Accelerate Phase I Trials. Clinical Cancer Research, 24(20), 4921–4930.
Yuan, Y., et al. (2018). Time-to-Event Bayesian Optimal Interval Design to Accelerate Phase I Trials. Clinical Cancer Research.
Liu, S. & Yuan, Y. (2015). Bayesian Optimal Interval Designs for Phase I Clinical Trials. Journal of the Royal Statistical Society: Series C, 64, 507–523.
Yuan, Y., Lin, R. & Li, Y. (2022). An overview of the BOIN design and its current extensions for novel early-phase oncology trials. Contemporary Clinical Trials.
Yuan, Y., et al. (2025). Practical Considerations for Using the TITE-BOIN Design to Handle Late-onset Toxicity or Fast Accrual in Phase I Trials. Clinical Trials.