Introduction

The design and conduct of phase I clinical trials have long been rooted in the era of cytotoxic chemotherapies, where toxicities were typically acute and could be readily observed within the first cycle of therapy. However, with the advent of non-cytotoxic agents such as molecularly targeted therapies and immunotherapies, toxicities may take weeks or even months to manifest. This shift has necessitated a reevaluation of traditional phase I trial designs, particularly when it comes to accurately determining the Maximum Tolerated Dose (MTD) of new therapeutic agents.

The traditional 3+3 design, long used for dose escalation in phase I trials, has several limitations, particularly when dealing with late-onset toxicities. Delays in dose-escalation decisions can complicate trial logistics, especially when the accrual rate is rapid. To address these challenges, the Time-to-Event Bayesian Optimal Interval (TITE-BOIN) design was proposed, offering a more flexible and accurate approach to dose finding in phase I trials.

Overview of the TITE-BOIN Design

The Problem with Late-Onset Toxicities

Late-onset toxicity presents a significant challenge in phase I clinical trials. Traditional trial designs assume that toxicities manifest quickly, allowing for prompt dose-escalation decisions. However, with newer therapies, toxicities may take weeks or months to become apparent. This delay complicates dose-escalation decisions, particularly when the accrual rate is rapid.

Jin et al. introduced the concept of the Logistic Difficulty Index (LDI), calculated as the product of the accrual rate and the length of the DLT assessment window. An LDI ≤ 1 indicates minimal logistic difficulty, while an LDI > 1 indicates increasing logistic difficulty, making dose-escalation decisions more complex.

Existing Solutions and Their Limitations

Rolling Six (R6) Design

The Rolling Six (R6) design extends the traditional 3+3 design by allowing for continuous patient accrual while some patients' DLT outcomes are still pending. However, it has several limitations:

**Low Accuracy in Identifying the MTD:**The R6 design tends to be conservative, often leading to the selection of a lower dose as the MTD.**Potential for Underdosing:**It may result in a large proportion of patients being treated at subtherapeutic doses.**Inflexibility in Targeting a Specific DLT Rate:**The R6 design does not allow for targeting a specific DLT rate, which is critical for accurately identifying the MTD.

Time-to-Event Continuous Reassessment Method (TITE-CRM)

The TITE-CRM is a model-based design that allows for continuous accrual and dose-escalation decisions while some patients’ DLT data are still pending. While TITE-CRM offers better accuracy in identifying the MTD compared to the R6 design, it also has its drawbacks:

**Complexity:**TITE-CRM requires repeated and complex model fitting after each patient is treated, which can be computationally intensive and challenging to implement in practice.**Aggressive Dose Escalation:**TITE-CRM tends to be more aggressive in dose escalation, which can increase the risk of overdosing patients.**Limited Practical Application:**Due to its complexity, TITE-CRM is not widely adopted in practice.

Introduction to TITE-BOIN Design

The TITE-BOIN design was developed to address the limitations of both the R6 design and the TITE-CRM. It is a model-assisted approach that combines the simplicity and transparency of the R6 design with the accuracy and flexibility of the TITE-CRM. The TITE-BOIN design allows for continuous patient accrual and real-time dose-escalation decisions, even when some patients’ DLT data are still pending. This is achieved through the use of imputation methods to estimate the DLT outcomes of pending patients, allowing for timely and accurate dose-escalation decisions.

The Mechanics of TITE-BOIN Design

The BOIN Framework

The Bayesian Optimal Interval (BOIN) design is an adaptive dose-escalation method that determines dose-escalation and de-escalation decisions based on the observed DLT rate at the current dose level. The key idea behind BOIN is to compare the observed DLT rate with a pair of pre-determined escalation and de-escalation boundaries.

Let \(\hat{p}\) represent the observed DLT rate at the current dose level, defined as:

\(\hat{p} = \frac{n_{\text{DLT}}}{n}\)

Where:

\(n_{\text{DLT}}\) is the number of patients who have experienced DLT at the current dose level.

\(n\) is the total number of patients treated at the current dose level.

The BOIN design uses the following decision rules:

**Escalate the dose:**If \(\hat{p} \leq \lambda_e\) , where \(\lambda_e\) is the escalation boundary.**De-escalate the dose:**If \(\hat{p} \geq \lambda_d\) , where \(\lambda_d\) is the de-escalation boundary.**Retain the current dose:**If \(\lambda_e < \hat{p} < \lambda_d\) .

The boundaries \(\lambda_e\) and \(\lambda_d\) are determined based on the target DLT rate, and they are typically chosen to optimize the accuracy of MTD identification while controlling the risk of overdosing patients.

Extending BOIN to TITE-BOIN

The TITE-BOIN design extends the BOIN framework to handle late-onset toxicities and rapid accrual. The main challenge in these scenarios is that some patients’ DLT data are still pending, making it difficult to calculate the observed DLT rate accurately. TITE-BOIN addresses this challenge by imputing the pending DLT outcomes based on the available follow-up data.

Let \(\hat{y}_i\) represent the imputed DLT outcome for the \(i\)-th patient, defined as:

\(\hat{y}_i = \frac{t_i}{T}\)

Where:

\(\hat{y}_i\) is the imputed DLT outcome for patient \(i\) .

\(t_i\) is the follow-up time for patient \(i\) .

\(T\) is the length of the DLT assessment window.

This imputed outcome \(\hat{y}_i\) is then used in place of the actual DLT outcome when calculating the observed DLT rate \(\hat{p}\) at the current dose level.

Example: TITE-BOIN Decision Rules in Action

Let’s consider an example to illustrate how the TITE-BOIN design works in practice. Suppose we have a trial with a target DLT rate of 20%, and we are currently evaluating dose level 2. So far, four patients have been treated at this dose level, with one patient having experienced a DLT, two patients having completed the DLT assessment without experiencing a DLT, and one patient whose DLT assessment is still ongoing with a follow-up time of 3 weeks (out of a total 6-week DLT assessment window).

Step 1: Calculate the Observed DLT Rate

For the three patients whose DLT outcomes are known, the observed DLT rate \(\hat{p}\) is:

\(\hat{p} = \frac{1}{3} = 0.33\)

Step 2: Impute the Pending DLT Outcome

For the pending patient with 3 weeks of follow-up, the imputed DLT outcome \(\hat{y}_i\) is:

\(\hat{y}_i = \frac{3}{6} = 0.5\)

Step 3: Calculate the Updated Observed DLT Rate

The updated observed DLT rate, including the imputed DLT outcome, is:

\(\hat{p} = \frac{1 + 0.5}{4} = 0.375\)

Step 4: Apply the BOIN Decision Rules

If the escalation boundary \(\lambda_e = 0.25\) and the de-escalation boundary \(\lambda_d = 0.35\) , the updated observed DLT rate of 0.375 suggests that the dose should be de-escalated.

Performance and Practical Considerations

The TITE-BOIN design has been shown to outperform traditional designs like the 3+3 and R6 designs in terms of accuracy in identifying the MTD, patient safety, and efficiency. Several simulation studies have demonstrated that TITE-BOIN has a higher probability of correctly identifying the MTD and a lower probability of treating patients at overly toxic doses.

Advantages

**Accuracy in MTD Identification:**TITE-BOIN improves the accuracy of MTD identification by incorporating information from all available patients, including those with pending DLT data.**Flexibility:**The design allows for continuous accrual, making it well-suited for trials with rapid accrual and/or late-onset toxicities.**Patient Safety:**TITE-BOIN controls the risk of overdosing by using conservative imputation methods and pre-determined escalation/de-escalation boundaries.

Limitations

**Complexity:**While TITE-BOIN is less complex than TITE-CRM, it is still more complex than the traditional 3+3 or R6 designs, requiring careful planning and implementation.**Dependence on Accurate Imputation:**The accuracy of the TITE-BOIN design depends on the accuracy of the imputation method used to estimate pending DLT outcomes. Poor imputation can lead to incorrect dose-escalation decisions.

Practical Implementation

Implementing the TITE-BOIN design in a real-world trial requires careful planning and consideration of several factors, including:

**Choosing the Target DLT Rate:**The target DLT rate should reflect the acceptable level of toxicity for the patient population and therapeutic area.**Determining the Escalation/De-escalation Boundaries:**The boundaries \(\lambda_e\) and \(\lambda_d\) should be carefully chosen based on the target DLT rate and the desired level of conservatism in dose-escalation decisions.**Monitoring Accrual Rates and Follow-up Times:**The accrual rate and follow-up times should be closely monitored throughout the trial to ensure that the TITE-BOIN design is applied correctly.

Conclusion

The TITE-BOIN design represents a significant advancement in the design of phase I clinical trials, particularly for therapies with late-onset toxicities or rapid accrual rates. By combining the simplicity of traditional interval-based designs with the accuracy and flexibility of model-based approaches, TITE-BOIN offers a powerful tool for identifying the MTD while maintaining patient safety and trial efficiency. Its ability to handle pending DLT data in real-time makes it a valuable asset in the modern era of clinical research, where the pace of therapeutic development continues to accelerate.

While the TITE-BOIN design is not without its challenges, its advantages in terms of accuracy, flexibility, and patient safety make it a strong candidate for consideration in phase I trials. As with any trial design, careful planning and execution are key to realizing its full potential, but when done correctly, TITE-BOIN can provide a more reliable and efficient pathway to identifying the optimal dose of new therapies.