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By Statistical Consultancy Team
August 23, 2024

Bayesian Optimal Interval (BOIN) designs are an increasingly popular fit-for-purpose approach to designing phase I clinical trials. The flexibility of the BOIN design means that its utility can be extended to a multitude of complex trial types. Within this guide we will provide an overview of everything you need to know about the BOIN design for clinical trials, and we will discuss several recent extensions to the standard framework.

## What is BOIN Design?

Early phase dose-finding trials play a pivotal role in clinical drug development. A well-designed phase I trial needs to accurately and efficiently target the maximum tolerated dose (MTD) in order to maximise the chance of success in later-stage trials. The Bayesian Optimal Interval (BOIN) design offers a novel approach to early-phase trial design that performs better than the traditional 3+3 design and is comparable or superior to many model-based designs in terms of MTD selection accuracy. The BOIN design is a simple-to-implement model-assisted approach that evaluates dose-limiting toxicity data against a pre-specified toxicity probability interval to inform dosing decisions for each cohort of patients. The toxicity probability interval is established within a Bayesian framework such that the probability of incorrect dosing decisions is minimised with respect to a pre-selected target toxicity rate. Within this guide, I will provide an overview of everything you need to know about the BOIN design and discuss several recent extensions to the standard framework.

## Understanding the Standard BOIN Study Design

The standard BOIN design is a model-assisted approach for determining the maximum tolerated dose (MTD) of a single therapeutic agent in relation to a single binary toxicity endpoint. The first step in BOIN design is to specify a target toxicity rate, φ, along with two alternative toxicity rates, φ1 and φ2, that would warrant dose escalation and de-escalation respectively (default values of φ = 0.33, φ1 = 0.6φ and φ2 = 1.4φ are often assigned). Under a Bayesian framework, these pre-specified toxicity rates are used to calculate escalation and de-escalation boundaries, λe and λd, that aim to minimize the probability of incorrect dosing decisions. BOIN's implementation is then simple. It uses the observed dose-limiting toxicity (DLT) rate at each dose level, j, to inform decisions to escalate, de-escalate or maintain the dose for the next cohort of patients. If j ≤ λe then the next cohort receives a higher dose, if j > λd then the next cohort receives a lower dose, and if λe < j ≤ λd then the dose remains the same for the next cohort. The BOIN design also incorporates a dose elimination rule to enhance safety. If the posterior probability that the true DLT rate exceeds a pre-specified cut-off is greater than 0.95 then the current dose and all higher doses are eliminated from the trial. The trial concludes when the maximum pre-specified sample size is reached, or the initial dose level is found to be too toxic according to the dose elimination rule. Isotonic regression is then used to smooth the observed DLT rates at each dose level so that they increase monotonically. The MTD is selected as the dose with a smoothed DLT rate that is closest to the target toxicity rate.

Tools like the sample size calculator developed by MD Anderson provide invaluable support in planning BOIN-based trials. These tools help researchers determine the optimal number of participants needed to achieve statistical significance without over-enrolling, which is critical for maintaining ethical standards and resource efficiency.

## Comparison with the Traditional 3+3 Design Methods

The 3+3 design has long been the accepted best practice of early-phase dose-finding studies in clinical trials. Characterised by its simplicity, this method involves treating successive cohorts of three patients with increasing doses until the occurrence of DLTs. The decision to escalate, de-escalate, or maintain the dose depends strictly on the number of patients experiencing DLTs within each cohort. However, the traditional 3+3 design has faced criticism for its inefficiency, being overly cautious with escalations and its somewhat arbitrary nature, often leading to inaccurate MTD estimations. This can lead to ineffective doses being recommended, and failures later in the drug development cycle, wasting both time and resources.

In contrast, the BOIN design offers a more dynamic and statistically nuanced approach. Unlike the 3+3 method, BOIN utilises a decision-making framework based on predefined toxicity probability intervals that adjust the dose based on accumulating patient response data. This adaptability allows for a more precise alignment with the trial's therapeutic goals, actively minimising the risks associated with over- or under-dosing. Studies have demonstrated that BOIN design significantly reduces the likelihood of under-dosing compared to the 3+3 design, with minimal increase in the risk of recommending a dose with a true DLT rate that exceeds the target DLT rate.

## Key Advantages of Implementing the BOIN Design

As highlighted above, one of the primary benefits of employing the BOIN design in clinical trials is its ability to accurately determine the MTD by adjusting the dose based on real-time data regarding the occurrence of DLTs. This adaptability allows for more nuanced and efficient decision-making compared to traditional models like the 3+3 design.

Another advantage of the BOIN design is its operational simplicity and computational efficiency. Despite its sophisticated Bayesian elements, BOIN is straightforward to implement. It does not require complex programming or extensive simulation studies, which are often barriers to the adoption of more advanced statistical methods in clinical trials. This ease of use not only saves time and resources but also makes it accessible to a broader range of researchers and institutions.

The BOIN design also offers a flexible framework (see Recent Extensions to the Standard BOIN Design) that can be customised to various therapeutic areas and specific trial requirements. Its flexibility is particularly beneficial in trials involving novel or high-risk treatments, where traditional methods may not adequately address complex dosing requirements. By providing a more tailored approach to dose escalation, BOIN ensures that clinical trials can more effectively balance the dual objectives of determining efficacy and ensuring patient safety. For example, a BOIN study do not have to have cohorts of 3 patients, whilst some designs, such as 3+3, can only recruit in set cohort sizes. This can be especially useful in scenarios where we don’t use a target toxicity rate of 1/3 (for example, a treatment with φ = 0.25 would be easier to interpret with cohorts of 4 patients).

In summary, the BOIN design enhances clinical trial outcomes through its precise dose-finding capabilities, risk minimisation, ease of implementation, and adaptability. These characteristics make it an increasingly preferred choice among clinical researchers seeking to improve the efficiency and ethical standards of Early Phase dose-finding studies.

## Institutional Adoption and Regulatory Recognition

The growing adoption of the BOIN design by leading institutions and its recognition by regulatory bodies highlight its increasing prominence in clinical trial methodologies. Regulatory bodies, including the U.S. Food and Drug Administration (FDA), have acknowledged the BOIN design's potential. The FDA has recognised BOIN as a fit-for-purpose methodology under certain conditions, emphasising its reliability and applicability in Early Phase dose-finding clinical trials. This recognition is crucial as it validates the methodological rigor of BOIN and encourages its broader adoption across the clinical research community.

The European Medicines Agency (EMA) and other international regulatory agencies have similarly provided guidelines that support the use of adaptive designs like BOIN in clinical trials. These guidelines reflect a growing consensus on the need for flexible, data-driven approaches that enhance the ethical and scientific standards of clinical research.

The regulatory recognition of BOIN design not only facilitates its implementation in clinical trials but also aligns the trial design with the highest standards of patient safety and data integrity. This alignment is essential for ensuring that new therapies are developed efficiently and ethically, ultimately benefiting patients by bringing effective treatments to market more swiftly and safely.

## Case study – A UK Oncology Specialist

Quanticate recently partnered with a UK specialist oncology client to provide statistical support to help design a phase I study, with Quanticate leading the study design discussion and the statistical sections of the study protocol.

Adaptations we made from standard BOIN design study to fit the client brief included:

• Rather than specifying a target toxicity rate and using this to define escalation and de-escalation boundaries, the client instead provided a de-escalation boundary of 33.3%. We were able to reverse engineer this to determine that φ=28% and λe=22.1%.
• We included both early stopping rules if the number of participants receiving a dose level reached a set limit (to save time and resources), and rules to include an intermediate dose if one dose level was deemed safe, but the next dose level above was deem too toxic at the discretion of the Sponsor (to potentially find an optimal dose dosage not originally specified)
• If we investigated a dose and there was a 95% probability that dose had a DLT rate of at least our maximum DLT rate, that dose would be de-escalated from, and that dose (and higher levels) would not be considered for any further investigations)

Using the BOIN criteria, and the adaptations above, a simple decision criteria chart was created, which shows what our decision would be based on the number of DLTs observed at a dose (considering all patients in the study treated at that dose):

The client was delighted at both the user-friendly outputs created to be able to easily display the decision making criteria/how decisions would be made, and the speed at which they were produced. The protocol passed review with no amendments to the study design required.

## Recent Extensions to the Standard BOIN Design

In its standard formulation, the scope of the BOIN design is limited to monotherapies and single binary toxicity endpoints. Due to the continuous evolution and adaptation of the BOIN design however, advanced strategies now exist that extend its utility to accommodate the increasing complexities of modern trials. Extensions to the BOIN design enable it to additionally accommodate combination therapies and therapies that are associated with multiple toxicity types, non-binary toxicity endpoints and late-onset toxicities. It is also possible to consider efficacy data and to use data across all dose levels rather than just the current dose level to inform dosing decisions. The rest of this guide will focus on several key extensions to the standard BOIN design and highlight the advantages and disadvantages of each.

## BOIN Design for Multiple Toxicity Types

The Multiple Toxicity BOIN (MT-BOIN) design is an extension to the standard BOIN design that can accommodate multiple toxicity types and grades. This design is particularly useful in scenarios where different types of toxicities need to be considered simultaneously in dose-finding decisions. MT-BOIN can handle both nested and non-nested toxicity outcomes, making it versatile for use in various clinical trial settings. Multiple non-nested toxicity outcomes are treated marginally.

When dealing with multiple non-nested toxicity types, specification of target toxicity rates and subsequent computation of escalation and de-escalation boundaries is done separately for each type. If the observed DLTs for each toxicity type are all less than or equal to their respective escalation boundaries, then the decision is to escalate the dose for the next cohort. If one of the observed DLTs is greater than its respective de-escalation boundary, then the decision is to de-escalate the dose for the next cohort. Otherwise, the decision is to maintain the dose for the next cohort. At the trial's conclusion, MT-BOIN uses isotonic regression to smooth the observed DLT rates for each separate toxicity type at each dose level so that they increase monotonically. For each toxicity type, the most appropriate dose is selected as the dose where the smoothed DLT rate is closest to the target toxicity rate. The overall MTD is then determined as the smallest of these doses.

MT-BOIN offers several advantages over other designs. It is simple to implement and has comparable operating characteristics to model-based designs that account for multiple toxicity constraints, such as MC-CRM. It is also more robust than model-based designs as it doesn't rely on parametric dose-response assumptions. Additionally, MT-BOIN can be adapted to handle drug combinations, further extending its utility. However, like the standard BOIN, MT-BOIN does not consider late-onset toxicities or efficacy responses. This limitation may be significant in certain trials where delayed toxicities or early efficacy signals are important considerations.

## BOIN Design for Non-Binary Toxicity Endpoints

The generalised BOIN (gBOIN) design is a versatile extension of the BOIN framework that is capable of handling a wider range of toxicity endpoints. Unlike the standard BOIN, which is limited to binary DLT outcomes, gBOIN can accommodate continuous endpoints (such as total toxicity burden or toxicity burden score), quasi-binary endpoints (like normalised equivalent toxicity score), and binary endpoints. In gBOIN, the sample mean of the toxicity endpoint at the current dose is used for decision-making, replacing the observed DLT rate in the standard BOIN. The design uses pre-calculated dose escalation and de-escalation boundaries for various types of endpoints, allowing for flexible implementation across different toxicity measures.

As for standard BOIN design, a pre-specified target value is specified for the toxicity endpoint along with alternative values that would warrant escalation or de-escalation. Under a Bayesian framework, these pre-specified values are then used to calculate escalation and de-escalation boundaries that minimise the probability of making an incorrect decision. The dosing algorithm in gBOIN follows a similar structure to the standard BOIN, comparing the observed toxicity value to the escalation and de-escalation boundaries to inform dosing decisions for the next cohort. At the trial's conclusion, isotonic regression is applied to the observed toxicity values, and the MTD is selected based on the smoothed value that is closest to the pre-specified target value.

gBOIN offers several advantages over existing designs. It demonstrates good statistical operating characteristics compared to designs that handle toxicity grades, such as the quasi-CRM design. Its implementation is straightforward, involving simple comparisons of sample means with pre-specified boundaries, without the need for complex model fitting. Unlike some model-based designs, gBOIN doesn't require a lead-in phase, allowing its decision rules to be applied throughout the trial. However, gBOIN does have some limitations. The use of toxicity scores as an endpoint requires the elicitation of weights and targets, which can be a time-consuming process requiring collaboration between clinicians and biostatisticians. Additionally, like other BOIN variants, gBOIN does not consider late-onset toxicities or efficacy responses, which may limit its applicability in certain trials.

## BOIN Design for Late-Onset Toxicities

The Time-to-Event-BOIN (TITE-BOIN) design is an adaptation of the standard BOIN that addresses the challenges of late-onset toxicities and rapid patient accrual in dose-finding trials. Unlike the standard BOIN, which requires complete DLT data for all patients in a cohort before making dosing decisions, TITE-BOIN allows for decisions to be made even when some patients have pending DLT data. TITE-BOIN incorporates time-to-event information into its decision-making process. It uses a weighted approach to account for the follow-up time of patients with pending DLT data. This allows the trial to proceed more quickly, as it doesn't need to wait for complete DLT information from all patients before enrolling the next cohort.

The initial steps of TITE-BOIN design are identical to that of standard BOIN-design. A target toxicity rate is specified, and escalation and de-escalation bounds are calculated under a Bayesian framework. The only difference is that dosing decisions are not informed solely by the escalation and de-escalation bounds. The decision to escalate, de-escalate or maintain the dose for the next cohort is also informed by the number of patients treated at the current dose, the number of patients for which toxicity data are pending and the standardised total follow-up time (SDFT) for the patients with data pending. SDFT is defined as the total follow-up time (TFT) divided by the length of the DLT assessment window. All the decision-making processes for a given target toxicity rate and cohort size are helpfully captured in decision tables. These tables provide clear guidelines for dose escalation, de-escalation, or dose maintenance. The design incorporates safety measures, such as suspending accrual if more than 50% of patients at the current dose have pending toxicity outcomes. This ensures that decisions are based on sufficient data. When there are no pending DLT data, TITE-BOIN reverts to the standard BOIN design.

TITE-BOIN offers several advantages over other designs. It significantly shortens trial duration compared to designs that require complete DLT data before making decisions. It is more flexible in choosing the target DLT rate and generally provides better overdose control than some other time-to-event designs. It's also easier to implement than more complex model-based time-to-event designs. TITE-BOIN does have some limitations though. It assumes a uniform distribution of time-to-DLT over the assessment window, which may not always reflect the true underlying distribution. While the design is robust to violations of this assumption, using an informative prior on the time-to-DLT distribution could potentially improve efficiency if reliable information is available.

## BOIN Design for Late-Onset Toxicities with Non-Binary Endpoints

The Time-to-Event generalised BOIN (TITE-gBOIN) design combines the features of gBOIN and TITE-BOIN to create a flexible, time-to-event design that can handle various types of toxicity endpoints. This design is particularly useful for trials with late-onset toxicities, rapid accrual, and complex toxicity measures. TITE-gBOIN accounts for both cumulative and pending numeric toxicity scores in its decision-making process.

The initial steps are the same as that of the gBOIN design. Instead of using the observed toxicity rate to make dosing decisions however, the design uses a likelihood-based approach to estimate the toxicity rate when there are pending toxicity data. This estimated rate is then used in the same decision framework as gBOIN to determine dose assignments for subsequent cohorts. Estimated toxicity probabilities are continuously updated until all patients complete their assessments. As with the TITE-BOIN design, this design incorporates safety measures, such as suspending accrual if more than 50% of patients at the current dose have pending toxicity outcomes.

TITE-gBOIN offers several advantages. It is robust and simple to implement, with performance comparable to gBOIN when there are no pending toxicity data. By allowing for pending data, it can significantly reduce trial duration compared to designs that require complete data for each cohort. However, TITE-gBOIN also has some limitations. As with gBOIN, its performance may depend on the appropriate specification of the toxicity endpoint, which requires careful consideration and collaboration between clinicians and biostatisticians. It also doesn't explicitly consider the accrual rate or outcome evaluation period in its model.

## BOIN Design for Determining Optimal Biological Dose

The BOIN Efficacy Toxicity (BOIN-ET) design is an extension of the BOIN framework that incorporates both binary toxicity and binary efficacy outcomes in dose-finding decisions. This phase I/II trial design aims to target what is referred to as the optimal biological dose (OBD) rather than the MDT. The OBD is the lowest dose that provides the highest rate of efficacy while being safely administered. This design is particularly valuable when the relationship between dose and efficacy may not be monotonically increasing, which is sometimes the case for targeted therapies and immunotherapies.

The first step in BOIN-ET is to specify target rates for both toxicity and efficacy. These pre-specified target rates are used to numerically compute jointly optimised decision boundaries to inform dosing decisions. Two boundaries are calculated for toxicity, λe and λd, and an additional lower boundary for response rate, η1. The dosing algorithm considers both the observed DLT rate, j, and the observed response rate, j, at the current dose level. If j ≤ λe and j ≤ η1 then the next cohort receives a higher dose, if j > λd then the next cohort receives a lower dose, and if j ≤ λd and j > η1 then the dose remains the same for the next cohort. If λe < j ≤ λd and j ≤ η1 then the decision may be to de-escalate, maintain or escalate the dose due to the possibility of a non-monotonic dose-efficacy relationship. The ultimate decision depends on an algorithm that considers which doses have already been used and the observed response rates of those that have already been used. At the end of the trial, isotonic regression is used to smooth the observed DLT rates at each dose level so that they increase monotonically. Fractional polynomials with 2 degrees of freedom are used to fit the efficacy data, allowing non-monotonic dose response relationships. The MTD is selected as the dose with a smoothed DLT rate that is closest to the target toxicity rate, and the OBD is then selected as the dose with the highest efficacy that is below the MTD.

BOIN-ET offers several advantages over existing designs. It generally selects the OBD more accurately and allocates more patients to the OBD than some model-based designs. It's simpler to implement and provides better overdose control than more complex Bayesian adaptive designs. BOIN-ET does have some limitations however. It tends to allocate more patients to doses higher than the OBD when efficacy is sufficient at lower doses, which can be a concern in some clinical settings. Additionally, the design may not be suitable for solid tumour trials using RECIST criteria, as the efficacy evaluation typically occurs later than the toxicity evaluation, potentially causing delays in dose-finding decisions.

## Single-Stage BOIN Design for Determining OBD Using a Utility Function

The BOIN12 design is a phase I/II design that can handle categorical toxicity and efficacy endpoints to efficiently target the OBD in a single stage using a utility function. Dosing decisions are informed both by pre-specified escalation and de-escalation boundaries in addition to the utility function. The utility function quantifies the desirability of a dose level by combining efficacy and toxicity data into a single measure called the rank-based desirability score (RDS) that takes values 0-100. It is typically defined in collaboration with clinicians to reflect the relative importance of efficacy and tolerability in the specific clinical context. The goal is to find the dose that optimises the risk-benefit trade-off by maximising the RDS.

The initial steps of the BOIN12 design are the same as the standard BOIN design; a target toxicity rate is specified, and decision boundaries are calculated. As with standard BOIN design, if j ≤ λe then the next cohort receives a higher dose, and if j > λd then the next cohort receives a lower dose. If λe < j ≤ λd however, the decision to de-escalate, maintain or escalate the dose is determined by considering the number of patients treated at the current dose in combination with the utility scores of the current dose and the surrounding doses. At the trial's conclusion, BOIN12 applies isotonic regression to the toxicity data to identify the maximum tolerated dose (MTD). The OBD is then selected as the dose with the highest RDS among those not exceeding the MTD.

One of the key advantages of BOIN12 is its simplicity of implementation. The pre-calculated decision tables allow for easy determination of dose assignments without complex real-time calculations. BOIN12 has been shown to select the OBD more accurately and allocate more patients to the OBD compared to some other dose-finding designs. One limitation however, is that the BOIN12 design assumes that both toxicity and efficacy outcomes are available by the time the next cohort needs to be dosed. This may not be realistic in trials where efficacy takes longer to assess than toxicity. Additionally, BOIN12 does not account for late-onset toxicities or responses, which can be important in some oncology trials, particularly those involving immunotherapies.

## Two-Stage BOIN Design for Determining OBD Using a Utility Function

The utility BOIN (U-BOIN) design is a phase I/II design that can handle categorical toxicity and efficacy endpoints to efficiently target the OBD in two stages using a utility function. This design addresses some of the limitations of single-stage designs by incorporating a preliminary toxicity-only stage, which is seamlessly followed by a second stage that considers both toxicity and efficacy data. The use of a toxicity-only stage means that MDT as well as the OBD can be accurately estimated using the U-BOIN design.

In the first stage, U-BOIN operates in the same way as the standard BOIN design, terminating once a pre-specified number of patients have been treated at one dose level. At this point, the trial seamlessly transitions to the second stage, which uses both efficacy and toxicity data to guide dose selection. The set of admissible doses in stage two of the trial are determined by marginal toxicity and efficacy criteria in order to eliminate doses with excessive toxicity or insufficient efficacy. If there are no admissible doses, then the trial should be terminated as there is no OBD. The next cohort of patients is given the dose with the highest posterior mean utility among the admissible doses. The process of determining the admissible doses and calculating posterior mean utility functions is repeated until either a pre-specified maximum sample size is reached or until the maximum number of patients have been treated at one dose. At this point, the OBD is the admissible dose that has the highest utility value.

One of the main advantages of U-BOIN is its simplicity of implementation. Despite its sophisticated underlying framework, it can be executed using pre-determined decision tables, avoiding the need for complex real-time model fitting. U-BOIN has been shown to identify the OBD more accurately and robustly than some model-based designs. A downside of the U-BOIN design is that it typically requires a larger sample size than toxicity-only designs to ensure desirable performance, which may be a concern in some clinical settings. Additionally, by modelling efficacy and toxicity independently at each dose, there's a potential for some loss of efficiency compared to designs that model these outcomes jointly across doses.

## BOIN Design for Determining OBD with Non-Binary Toxicity Endpoints

The generalised BOIN Efficacy Toxicity (gBOIN-ET) design is an extension of the BOIN-ET framework that accommodates ordinal graded efficacy and toxicity outcomes. This design is particularly useful for calculating OBD when binary endpoints may not capture the full spectrum of treatment effects. gBOIN-ET uses quasi-Bernoulli endpoints for both toxicity and efficacy, allowing for a more nuanced assessment of treatment outcomes. These endpoints are derived by assigning weights to different grades of toxicity and efficacy, typically through collaboration between clinicians and biostatisticians.

The design employs a similar decision-making framework to BOIN-ET, but replaces the observed binary rates with quasi-Bernoulli probabilities. These probabilities are estimated using a quasi-likelihood approach. The dosing algorithm compares these estimated probabilities to pre-specified boundaries to determine whether to escalate, de-escalate, or maintain the current dose. As for BOIN-ET, at the trial's conclusion gBOIN-ET applies isotonic regression to the toxicity data and uses fractional polynomials to model the efficacy data. This allows for flexible modelling of the dose-efficacy relationship, accommodating potential non-monotonicity.

gBOIN-ET offers several advantages over other designs. It's relatively simple to implement and has shown superior performance in simulations, particularly in terms of correctly selecting the optimal biological dose (OBD) and allocating patients to the OBD. It also demonstrates good performance in avoiding selection of overly toxic doses. The performance of gBOIN-ET can however be sensitive to the specification of the quasi-Bernoulli endpoints. This requires careful consideration and potentially time-consuming collaboration between clinicians and statisticians to accurately derive these endpoints. Additionally, like many other designs, gBOIN-ET does not explicitly account for factors such as accrual rate, outcome evaluation period, or late-onset outcomes, which may be important in some clinical trial settings.

## BOIN Design for Determining OBD with Late-Onset Toxicities

The Time-to-Event BOIN Efficacy Toxicity (TITE-BOIN-ET) design is an extension of BOIN-ET that addresses challenges associated with late-onset toxicities and efficacy responses, as well as rapid patient accrual. This design is particularly valuable in trials where the assessment periods for toxicity and efficacy may differ or where outcomes may not be immediately observable.

TITE-BOIN-ET incorporates time-to-event information for both toxicity and efficacy outcomes. It uses a weighted approach to account for patients with pending data, allowing the trial to proceed even when complete information is not available for all patients. This is achieved by calculating "effective sample sizes" for both toxicity and efficacy, which take into account the follow-up time for patients with pending outcomes. The design uses a decision table similar to BOIN-ET, but with the observed rates replaced by estimated rates based on the available data and follow-up times. This allows for continuous updating of toxicity and efficacy estimates even as new patients are enrolled. TITE-BOIN-ET also includes safety measures, such as rules for suspending accrual if there's insufficient information at the current dose level. At the trial's conclusion, it uses isotonic regression for toxicity data and fractional polynomials for efficacy data to determine the optimal biological dose (OBD).

One of the main advantages of TITE-BOIN-ET is its ability to significantly shorten trial duration compared to designs that require complete data before making decisions. Simulation studies have shown that it selects the OBD more accurately and allocates more patients to the OBD than some model-based approaches. TITE-BOIN-ET does however share a limitation with BOIN-ET in that it may allocate more patients to doses higher than the OBD when efficacy is sufficient at lower doses. Additionally, in scenarios with very rapid accrual relative to outcome evaluation times, additional suspension rules may be necessary to ensure sufficient information for decision-making.

## BOIN Design for Determining OBD with Late-Onset Toxicities Using a Utility Function

The Time-to-Event BOIN12 (TITE-BOIN12) design is an extension of BOIN12 that addresses the challenges of late-onset toxicities and responses in phase I/II trials. This utility-based design allows for continuous patient accrual and dose-finding decisions even when some patients have pending outcomes for toxicity or efficacy.

TITE-BOIN12 employs either Bayesian data augmentation or an approximated likelihood method to estimate toxicity and efficacy probabilities when there are pending outcomes. This allows the design to use a similar dose-finding algorithm to BOIN12, but with estimated probabilities replacing observed rates. The design incorporates a utility function that quantifies the desirability of each dose based on its estimated toxicity and efficacy profile. At each interim analysis, TITE-BOIN12 updates the estimates for all doses and selects the dose with the highest utility for the next cohort, subject to safety constraints. TITE-BOIN12 also includes an accrual suspension rule to ensure patient safety: if more than 50% of patients at the current dose have pending outcomes, the trial is suspended until more data become available.

One of the key advantages of TITE-BOIN12 is its ability to allow continuous accrual while maintaining patient safety and accuracy in identifying the optimal biological dose (OBD). Simulation studies have shown that it often provides better overdose control and higher accuracy in OBD identification compared to some model-based designs. In addition, TITE-BOIN12 is flexible in accommodating different shapes of dose-efficacy curves and incorporates risk-benefit trade-offs based on clinician input. It can significantly shorten trial duration compared to designs that require complete data before making decisions. One limitation of TITE-BOIN12 is that it assumes that the time to toxicity and efficacy events are uniformly distributed over the assessment window. While the design is generally robust to violations of this assumption, using an informative prior on the time-to-event distribution could potentially improve efficiency if reliable information is available. Unlike BOIN12, TITE-BOIN12 cannot use a pre-generated decision table due to the continuous nature of the time-to-event data. However, dose desirability can be easily calculated using available software, allowing for straightforward implementation in practice.

## BOIN Design for Determining a Single MDT for Combination Therapies

The BOIN combination (BOIN comb) design extends the BOIN framework to drug combination trials, allowing for dose finding in two dimensions. This design is crucial for identifying the maximum tolerated dose (MTD) in combined therapies, which are becoming increasingly important in oncology for achieving synergistic effects and overcoming resistance to monotherapy. The design considers a matrix of dose combinations, where each axis represents the doses of one drug. The toxicity probabilities in this matrix are only partially ordered, adding complexity to the dose-finding process.

The BOIN Combination design uses a similar framework to the standard BOIN, with pre-specified boundaries λe and λd for dose escalation and de-escalation. The dosing algorithm considers the observed DLT rate at the current dose combination and compares it to these boundaries. However, when escalating or de-escalating, the design also considers the probability of the DLT rate falling within the target interval for neighbouring dose combinations. This is done using a desirability score, which allows for more informed decisions in the two-dimensional dose space. The design also incorporates safety measures, including rules for dose elimination due to excessive toxicity. At the trial's conclusion, two-dimensional isotonic regression is applied to the observed DLT rates to ensure monotonicity, and the MTD is selected as the dose combination with the smoothed DLT rate closest to the target rate.

One of the main advantages of the BOIN Combination design is its ease of implementation, using decision tables similar to the standard BOIN with an additional desirability score table. It offers comparable performance to more complex model-based designs for drug combinations, such as the partial ordering CRM and copula-type regression method. However, like other BOIN designs, it considers only toxicity in its decision-making, which may be a limitation for certain types of drugs, particularly in immuno-oncology where efficacy doesn't always increase with dose.

## BOIN Design for Determining Multiple MDTs for Combination Therapies

The BOIN Waterfall design is an extension of the combination BOIN approach that aims to find an MTD contour - a set of multiple MTDs rather than a single MTD. This is particularly useful in drug combination trials where identifying multiple safe and effective dose combinations can provide more flexibility in treatment options. The Waterfall design operates by conducting a series of one-dimensional dose-finding tasks, called sub-trials, across the two-dimensional dose matrix. These sub-trials are conducted sequentially from the top to the bottom of the matrix. This approach allows the design to explore the entire dose space efficiently.

At each step, the design estimates the DLT rate for each dose combination using data from all completed sub-trials. This is done using two-dimensional isotonic regression, ensuring that the estimated DLT rates are monotonically non-decreasing when one drug's dose is fixed. For each row of the dose matrix, the MTD is selected as the dose combination with the smoothed DLT rate closest to the target rate. If all combinations in a row are overly toxic, no MTD is selected for that row. This process results in the identification of an MTD contour across the dose matrix.

The BOIN Waterfall design shares many advantages with the single MTD combination design, including ease of implementation and good performance characteristics. However, it requires a larger sample size than trials aiming to find a single MTD, which may be a consideration in some clinical settings. Both the single MTD and MTD contour BOIN combination designs are limited to considering only toxicity outcomes and do not account for efficacy or late-onset toxicities, which may be important factors in some drug combination trials, particularly in immuno-oncology.

## Conclusion

The BOIN design and its recent extensions have emerged as valuable model-assisted dose-finding methods in early phase clinical trials. The ability of the BOIN design to adaptively modify doses based on real-time data significantly enhances the accuracy of identifying the MTD or OBD. This method not only ensures greater patient safety by minimising exposure to suboptimal dosing but also improves the efficiency of trials by potentially reducing their duration and cost. Additionally, BOIN designs are operationally simple despite their Bayesian foundations and have demonstrated good statistical performance compared to other dose-finding designs. The FDA's fit-for-purpose designation for the standard BOIN design underscores its significance as a drug development tool.

Furthermore, the comprehensive framework of extended BOIN designs allows for the investigation of several dose-finding aspects, including toxicity, efficacy, binary or continuous outcomes, delayed toxicity and efficacy, and combination therapies. This versatility provides researchers with a consistent approach to explore complex scenarios within a unified system. Many variants, including BOIN, TITE-BOIN, and BOIN Comb, have been successfully implemented in real clinical trials, and the recent BOIN12 design is also currently being implemented.

Despite the promising recent advancements in the BOIN design framework, there are still some limitations that need addressing. Due to the small sample sizes typical in early-phase trials, they cannot account for patient heterogeneity that may affect efficacy and toxicity at the individual level. This can sometimes be dealt with by pre-defining patient subpopulations, and applying separate BOIN designs to each group. This does not work when subpopulations are unknown and need to be identified during the trial however. Future research will likely focus on addressing these limitations and expanding the applicability of BOIN designs to more complex scenarios in precision medicine.

### Bring Study Design Efficiencies to your Phase 1 Oncology Trial

Quanticate’s Statistical Consultancy Team are dedicated to ensuring high quality clinical study designs and have a wealth of experience in advanced statistical methodologies across a range of therapeutic areas, including complex oncology trials. If you would like more information on how we can assist your clinical trial submit an RFI.

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