Table 7.

Summary of the BOIN Design and its Extensions.

Design	Description of Design	Advantages	Disadvantages	Software	References
BOIN	The BOIN design uses the observed DLT rate at each dose for determining the MTD of a new drug. This phase I design can be implemented in a simple manner, similar to that of the 3 + 3 design but has better operating characteristics, and has comparable or better operating characteristics than many model-based designs such as CRM, and model-assisted designs such as mTPI-2.	Although built upon Bayesian probability models, the BOIN design is operationally simple, since once λe and λd are pre-determined for the given target DLT rate, the dosing decision for each new cohort of patients is based mainly on comparing the observed DLT rate at the current dose with λe and λd. The design selects the MTD more accurately and doses a larger percentage of patients at the MTD than the 3 + 3 design does, and it has a lower probability of overdosing patients than some other designs [10].	This design considers only toxicity in its dosing decisions without using efficacy data, which is an important limitation for immuno-oncology drugs where efficacy does not always increase with higher doses. It also does not consider late-onset toxicities or efficacy responses. BOIN mainly uses the data from the current dose level for dosing decisions and not data collected across all doses. However, it is a sequential design where the consecutive dosing decisions indirectly use the information from the adjacent doses, and this results in good statistical operating characteristics.	1) www.trialdesign.org 2) R package: BOIN 3) Desktop application: https://biostatistics.mdanderson.org/SoftwareDownload/SingleSoftware/Index/99	[5,10,11]
MT-BOIN	The MT-BOIN design(s) is an extension of the BOIN design that considers different toxicity types and grades.	MT-BOIN is simple to implement and has comparable operating characteristics to those of model-based designs such as MC-CRM. MT-BOIN is also more robust than model-based designs since it does not rely on a parametric dose-response assumption. In addition to non-nested and nested toxicities, MT-BOIN can handle drug combinations.	MT-BOIN does not consider late-onset toxicities or efficacy responses.	The boundaries of MT-BOIN are exactly the same as those in the standard BOIN design for non-nested outcomes. Thus, the BOIN software can be used to implement MT-BOIN.	[15]
gBOIN	The gBOIN design is a more general version of the BOIN design that can handle continuous, quasi-binary, and binary toxicity endpoints.	The gBOIN design has good statistical operating characteristics compared to existing designs that handle toxicity grades such as the quasi-CRM design [16]. It is simple to implement, since its dosing decisions involve comparing the sample mean of the endpoint with the two pre-specified boundaries of dose escalation and de-escalation, and do not involve any model fitting. It does not require a lead-in phase and its decision rules can be applied throughout the trial, unlike some model-based designs that need to collect preliminary data through a pre-phase before the model can be reliably estimated. Although gBOIN mainly uses data from the current dose level for dosing decisions, its performance is usually as good as or better than the model-based designs that borrow information across doses.	The required elicitation of weights (to determine a toxicity score) and a target involves a time-consuming collaboration between clinicians and biostatisticians. gBOIN does not consider late-onset toxicities or efficacy responses.	gBOIN can be implemented using the UnifiedDoseFinding R package available at https://cran.r-project.org/web/packages/UnifiedDoseFinding/index.html.	[16]
TITE-BOIN	In the TITE-BOIN design, new patients can be enrolled even when the DLT data are pending for some of the patients in the previous cohort. When there are no pending DLT data, it reduces to the BOIN design.	TITE-BOIN is easy to implement and is well-performing. It takes into account late-onset DLTs and rapid accrual, allowing dosing decisions even with pending DLT data from some patients in the current cohort. TITE-BOIN generally shortens the trial duration substantially compared to waiting for the occurrence of pending toxicity events. It is more flexible in choosing the target DLT rate and more accurate in MTD selection than the rolling 6 design. It has similar accuracy in MTD selection as TITE-CRM, but it has better overdose control and is easier to implement.	TITE-BOIN uses DLT data only at the current dose for dosing decisions, in contrast to TITE-CRM, which considers data from all dose levels. However, simulations show that the effect of using only the current dose data leads to negligible efficiency loss [25, 38]. TITE-BOIN assumes that the time to DLT is distributed uniformly over the DLT assessment window, similar to what TITE-CRM does. This design is robust to this uniformity assumption, but if reliable prior information is available on the distribution of the time to DLT, then an informative prior can be used to improve design efficiency [22]. TITE-BOIN does not consider efficacy endpoints for its dosing decisions.	www.trialdesign.org	[22,25]
TITE-gBOIN	The TITE-gBOIN is a non-parametric, model-assisted design that is an extension of the gBOIN design that accounts for toxicity grades based on both cumulative and pending numeric toxicity scores.	TITE-gBOIN is a robust design that is simple to implement. Simulations in various realistic scenarios show that TITE-gBOIN is comparable in performance to gBOIN and it has a higher probability of selecting the MTD correctly and allocating more patients to the MTD than other available approaches [26]. It reduces trial duration compared to designs that do not allow sequential dose allocation.	The design performance may depend on the appropriate specification of the quasi-Bernoulli endpoint such as the normalized ETS [26]. A time-consuming collaboration between clinicians and biostatisticians is required to accurately derive the quasi-Bernoulli endpoint utilizing the weight for each toxicity grade and the drug-specific toxicity profiles [26]. TITE-gBOIN does not consider efficacy responses.	Software to implement the TITE-gBOIN design is available at https://github.com/qingxiaa/titegboin.	[26]
BOIN-ET	BOIN-ET design, a phase I/II design, is an extension of the BOIN design that utilizes both binary efficacy and toxicity outcomes in determining the OBD	In general, the BOIN-ET design selects the OBD more accurately and puts a higher average number of patients at the OBD than the model-based TC and SHH designs [27]. It is simpler and easier to implement, is safer, and provides much better overdosing control than these designs [27].	When the efficacy rate is sufficient at lower doses, BOIN-ET tends to allocate more patients to doses higher than the OBD. BOIN-ET may not be suitable for solid tumors, where the RECIST criteria are used for the efficacy assessment; it may cause delays in implementing the dosing decisions because the RECIST efficacy evaluation usually occurs later than the toxicity evaluation. Hence, the design may be most applicable to trials where the response assessment period and the DLT assessment period are on similar time scales.	Takeda et al. provide SAS code upon request to implement the BOIN-ET design. The following reference provides example dosing decision tables for cohort sizes of 3 and 6 to implement the BOIN-ET design [27].	[27]
BOIN12	BOIN12 is a flexible phase I/II design that can be used to determine the OBD. Each cohort of patients is allocated to the dose that optimizes the toxicity-efficacy trade-off. While U-BOIN has 2 stages with only toxicity data being used in the first stage and both toxicity and efficacy data being used in the second stage, BOIN12 has only one stage and uses both categorical toxicity and efficacy data in this single stage.	BOIN12 is based on a utility trade-off function and is more general, while BOIN-ET is based on marginal toxicity and marginal efficacy rates and does not incorporate toxicity-efficacy trade-off in dose finding. The BOIN12 design is simple to implement, and it selects the OBD more accurately and doses more patients at the OBD compared to existing dose-finding designs such as the TC method, TEPI and 3 + 3 CE designs. The dosing decision table for the BOIN12 design can be used easily to make dosing decisions and allocate patients to a dose without any complex calculations [21].	In some immunotherapy trials, late onset toxicities and responses may be observed. This will preclude using the BOIN12 design, since it assumes that the toxicity and efficacy outcomes are available by the time of the dose assignment of the next cohort.	www.trialdesign.org	[21]
U-BOIN	U-BOIN is a utility-based, seamless Bayesian phase I/II design used to determine the OBD. The weights used in the utility function for different combinations of efficacy and toxicity (e.g. no response and no DLT, response and no DLT, no response and DLT and response and DLT) are chosen based on discussions with clinicians.	The U-BOIN design is simple to implement and is well-performing. It can be implemented in a trial using pre-determined decision tables and does not require complex model fitting and estimation [35]. Compared to a model-based design such as the TC method, U-BOIN identifies the OBD more accurately and is more robust [34]. Due to the incorporation of the first stage, U-BOIN also estimates the MTD accurately.	U-BOIN models efficacy and toxicity at each dose independently while model-based designs such as the TC method model efficacy and toxicity across all doses. Thus, there may be a potential efficiency loss for U-BOIN, although this loss is believed to be minimal or negligible [34]. U-BOIN is comparable to BOIN12 in accuracy of OBD selection, but it requires a relatively large sample size to guarantee a desirable performance due to the use of two stages. The sample size required by U-BOIN is usually greater than the sample size used in MTD-finding trials. In stage 2, U-BOIN assumes that both the toxicity and efficacy outcomes are available by the time of the dose assignment of the next cohort.	www.trialdesign.org	[34,35]
gBOIN-ET	The gBOIN-ET design is a phase I/II model-assisted, non-parametric design that is an extension of the BOIN-ET design and that accounts for ordinal graded efficacy and toxicity.	gBOIN-ET is simple and easy to implement in oncology trials than model-based approaches. Simulations investigating the operating characteristics of gBOIN-ET show that it has a higher performance than BOIN12, gBOIN, BOIN-ET in terms of the correct OBD selection, the average number of patients allocated to the OBDs, not selecting overdoses as the OBDs and not assigning patients to overdoses.	The design performance may depend on the appropriate specification of the quasi-Bernoulli endpoints. A time-consuming collaboration between clinicians and biostatisticians is required to accurately derive the quasi-Bernoulli endpoints utilizing the weight for each toxicity grade and efficacy grade. gBOIN-ET may select lower doses as OBDs if the low quasi-Bernoulli efficacy probability is mis-specified as the target quasi-Bernoulli efficacy probability. gBOIN-ET does not consider the accrual rate, the outcome evaluation period and the late-onset outcomes [36].	SAS code is available to implement the gBOIN-ET design.	[36]
TITE-BOIN-ET	This model-assisted design is an extension of the BOIN-ET design that considers both pending efficacy and toxicity data in the dosing decisions.	The design is robust, much simpler, and easier to implement than model-based approaches. TITE-BOIN-ET selects the OBD more accurately and puts a higher average number of patients at the OBD than model-based approaches such as the design by Thall and Cook and that by Jin et al. [37]. The trial duration is significantly shortened when using TITE-BOIN-ET compared to using designs without sequential enrollment [37].	When the efficacy response rate is sufficient at lower doses, the TITE-BOIN-ET design tends to allocate more patients to doses higher than the OBD. If patient accrual is faster than the outcome evaluation, then the available information may still not be sufficient even if the pending data are considered. In such a case, suspension rules as in Refs. [22,25] may need to be considered to delay the dosing decisions until adequate information is available [37].	Takeda et al. provide SAS code upon request to implement the TITE-BOIN-ET design. The following reference provides an example dosing decision table for cohort size 3 to implement the TITE-BOIN-ET design [37].	[37]
TITE-BOIN12	TITE-BOIN12 design is a utility-based phase I/II design that deals with late-onset toxicities and responses and allows the study to proceed with dosing the next cohort of patients even in the presence of pending outcomes for toxicity or response for some patients. It reduces to the BOIN12 design when there are no pending outcomes for toxicity or response.	TITE-BOIN12 is a well-performing design that allows continuous accrual while still ensuring patient safety and accuracy of OBD identification. In most cases, it has better over-dose control and higher accuracy of OBD identification, than model-based designs such as the TC method [39]. TITE-BOIN12 accommodates different shapes of dose-efficacy curves compared to the TC method. It shortens the trial duration and incorporates risk-benefit trade-off with input on the utility values from clinicians [39].	TITE-BOIN12 assumes that the time to DLT and efficacy are distributed uniformly over the assessment window, while calculating the STFT, which is similar to what is assumed in the TITE-BOIN and TITE-CRM designs [39]. This design is robust to this assumption, similar to what is demonstrated for TITE-CRM [40] and for TITE-BOIN [22]. However, if reliable prior information is available on the distribution of the time to DLT or efficacy, an informative prior can be used for either or both to improve design efficiency. No decision table can be generated for TITE-BOIN12 prior to the trial conduct.	www.trialdesign.org	[39]
Combination BOIN	The combination BOIN design(s) is used to design phase I trials that investigate a combination of two drugs with multiple dose levels for each drug. These designs can be used to determine the MTD or the MTD contour for a combination of drugs.	As drug combination trials are becoming increasingly common, these designs are increasing in importance and use. The combination BOIN designs are easy to understand and implement and have comparable performance characteristics to model-based designs such as the partial ordering CRM and copula-type regression method [29].	The combination BOIN designs consider only toxicity and not efficacy in dosing decisions, which is important for immuno-oncology drugs where efficacy does not always increase with an increase in dose. They do not consider late-onset toxicities or responses.	www.trialdesign.org R package: BOIN	[14,29,41,42]