Precision Dose-Finding in Oncology

• Precision dose-finding (PDF) is a framework for selecting safe and effective doses by integrating PK data, biomarkers, and individualized patient factors.
• It shifts the traditional focus from a single maximum tolerated dose to identifying optimal biological doses using model-based, Bayesian, or randomized designs.
• PDF methodologies enhance trial efficiency by adapting dosing to patient heterogeneity through multidimensional evidence from efficacy and toxicity outcomes.

Precision dose-finding (PDF) is a class of methodological approaches for selecting doses that are safe, efficacious, and, when relevant, individualized to patient characteristics, pharmacokinetics (PK), biomarkers, or other sources of heterogeneity. In contemporary oncology development, PDF is closely associated with the shift from identifying a single maximum tolerated dose (MTD) toward identifying an optimal biological dose (OBD) that offers the best benefit-risk balance, a shift emphasized by Project Optimus and reflected in a growing literature on model-based, model-assisted, randomized, Bayesian, and personalized dose-optimization designs (Yuan et al., 2023, Guo et al., 2022, Wang et al., 6 May 2025).

1. Definitions and conceptual scope

Traditional oncology dose finding was centered on the MTD and often relied on the assumption that toxicity increases with dose and that higher doses are preferable if tolerable. Several papers explicitly argue that this paradigm is often inadequate for targeted therapies and immunotherapies, where efficacy may plateau, toxicity may be cumulative or late-onset, and patient heterogeneity may materially alter the dose-toxicity or dose-efficacy relationship (Yuan et al., 2023, Liao et al., 2023, Barnett et al., 2022). In that setting, PDF denotes a broader objective: identifying a dose, or a patient-specific dose rule, that balances safety and efficacy and may depend on PK, pharmacodynamic (PD) information, biomarkers, or covariates (Maity et al., 2024, Willard et al., 2024, Zhu et al., 2020).

The terminology used in the literature is not uniform. Some papers define the target as the OBD, especially in Project Optimus–aligned designs (Wang et al., 6 May 2025, Guo et al., 2022, Yang et al., 2024). Others retain the MTD but seek to estimate it more precisely, including in heterogeneous populations or with individual PK profiles (Lee et al., 5 Sep 2025, Silva et al., 2023). Still others formulate PDF as learning an optimal individualized dose rule over a continuous safe dose range, with the goal of maximizing an expected outcome under standard causal assumptions (Zhu et al., 2020). This suggests that PDF is best understood as an umbrella concept spanning both population-level dose optimization and individualized dose assignment.

A recurring theme is that PDF requires multidimensional evidence. Reviews of dose-optimization trials emphasize simultaneous consideration of toxicity outcomes, efficacy outcomes, PK/PD data, biomarkers, and sometimes patient-reported outcomes or quality of life (Yuan et al., 2023). In phase I/II settings, the OBD is commonly defined as a dose that is both safe and efficacious and that maximizes some optimality criterion based on safety and efficacy (Barnett et al., 2022). In personalized combination-therapy trials, the OBD may be stratum- or patient-specific and defined as a safe dose combination that maximizes therapeutic benefit for a specific covariate pattern (Willard et al., 2024).

2. Statistical foundations and objective functions

A central statistical distinction in PDF is whether the primary target is toxicity control, explicit benefit-risk tradeoff, or direct value maximization. In dose-optimization reviews, a simple benefit-risk tradeoff (BRT) is written as

$\text{BRT} = \pi_E - w\pi_T$

and a more general utility-based form is

$\text{BRT} = \sum_{k=1}^K \pi_k u_k,$

where $\pi_E$ and $\pi_T$ are efficacy and toxicity probabilities, and $u_k$ are utilities for joint outcomes (Yuan et al., 2023). Related utility formulations appear in designs for late-onset efficacy and toxicity, where dose selection is based on maximizing

$U(\pi_E, \pi_T) = \pi_E - \omega_1 \pi_T - \omega_2 \pi_T \cdot \mathds{I}(\pi_T > \phi_T)$

over admissible doses (Barnett et al., 2022).

Another line of work focuses on individualized dose rules. In kernel assisted learning for personalized dose finding, an individualized dose rule is a map $\pi: X \mapsto \mathcal{A}$, the value function is

$V(\pi) = E[ Y^* \{ \pi(X) \} ],$

and the optimal rule is

$\pi^{opt} = \arg\max_{\pi} V(\pi).$

Under consistency, no unmeasured confounders, and positivity, this value is identified as

$V(\pi) = E_X [ E\{Y|A = \pi(X), X\} ].$

The paper then restricts attention to rules of the form $\text{BRT} = \sum_{k=1}^K \pi_k u_k,$0 and estimates $\text{BRT} = \sum_{k=1}^K \pi_k u_k,$1 by maximizing a kernel-smoothed empirical value function (Zhu et al., 2020). This formulation places PDF in direct continuity with individualized treatment rule estimation and continuous decision-making.

A third family of methods treats dose finding as structured inference on dose-response surfaces. In generalized MCP-Mod, the response is represented by $\text{BRT} = \sum_{k=1}^K \pi_k u_k,$2, candidate dose-response shapes are prespecified, and optimal contrasts are used for multiple comparisons under model uncertainty (Pinheiro et al., 2013). In MAP-curvature, the mean response is $\text{BRT} = \sum_{k=1}^K \pi_k u_k,$3, smoothness is enforced by penalizing total curvature relative to a default model, and proof-of-concept is based on

$\text{BRT} = \sum_{k=1}^K \pi_k u_k,$4

The same framework estimates the minimum effective dose (MED) from the interpolated dose-response curve (Han et al., 28 Sep 2025). These approaches are less directly patient-specific than PK- or covariate-driven methods, but they address a different precision problem: robust inference when the dose-response shape is uncertain.

3. Personalization through PK, covariates, and heterogeneity

A defining strand of PDF research formalizes patient heterogeneity rather than treating trial participants as exchangeable. One oncology paper argues that conventional cohort-wise dose escalation is “inherently unsafe” because it assumes exchangeability despite “widely appreciated inter-individual heterogeneity in pharmacokinetics and pharmacodynamics (PKPD),” and advocates precision dose-finding grounded in patient-centered dose titration and Bayesian updating (Norris, 2020). This controversy over exchangeability versus individualized adaptation remains one of the sharpest conceptual divides in the area.

Formal incorporation of PK is one response to that problem. In a Bayesian joint model for dose escalation, PK exposure $\text{BRT} = \sum_{k=1}^K \pi_k u_k,$5 is linked to dose through

$\text{BRT} = \sum_{k=1}^K \pi_k u_k,$6

and dose-limiting toxicity (DLT) is modeled by logistic regression on log-exposure,

$\text{BRT} = \sum_{k=1}^K \pi_k u_k,$7

This BLRM-PK framework jointly explores the dose-PK and PK-DLT relationships and uses Escalation With Overdose Control (EWOC) for dose recommendation (Maity et al., 2024).

A later phase I design makes the personalization more explicit. In that Precision Dose-Finding design, a one-compartment first-order IV PK model is assumed,

$\text{BRT} = \sum_{k=1}^K \pi_k u_k,$8

and the individual DLT probability is

$\text{BRT} = \sum_{k=1}^K \pi_k u_k,$9

The trial uses an initial training stage with cohort-based escalation and a subsequent precision stage in which each new patient is assigned the dose whose predicted toxicity probability is closest to the target $\pi_E$0 (Lee et al., 5 Sep 2025). This is one of the clearest examples of PDF as N-of-1–style dose assignment within a trial.

Covariate-driven heterogeneity can also be handled when the relevant subgroups are unknown. In P-CRM for broadened eligibility settings, the general dose-toxicity model is

$\pi_E$1

with a sparsity assumption $\pi_E$2. The design begins with standard CRM, then sequentially screens covariates for marginal association with toxicity and recommends subgroup-specific MTDs if covariates are selected; otherwise it defaults to a single MTD (Silva et al., 2023). This suggests a compromise between fully individualized PK-based dosing and standard homogeneous models.

For combination therapies, personalization has also been expressed through Gaussian-process (GP) surrogates over dose-covariate space. In Bayesian optimization for patient-specific OBD combinations, efficacy $\pi_E$3 and toxicity $\pi_E$4 are modeled as independent GPs, and dose assignment is driven by a constrained expected improvement acquisition function that balances efficacy improvement against the probability of satisfying a stratum-specific toxicity threshold (Willard et al., 2024).

4. Major design families in current PDF research

Several broad design families recur across the literature. Fully sequential efficacy-integrated designs update dose assignment in real time using both safety and efficacy or utility information. Reviews cite model-based designs such as EffTox and delayed-outcome extensions, as well as model-assisted designs such as BOIN12, uTPI, and STEIN (Yuan et al., 2023). For late-onset bivariate outcomes, the Joint TITE-CRM uses parallel logistic models for efficacy and toxicity, time-dependent weights based on the proportion of follow-up completed, and a Gumbel copula for dependence between efficacy and toxicity outcomes (Barnett et al., 2022).

Two-stage and multi-stage designs are a second major family. In the “three steps towards dose optimization” framework, step 1 uses a hybrid dose-escalation design to identify the MTD or maximum administered dose, step 2 selects recommended doses for expansion (RDEs) using safety, PK, PD, and biomarker information, and step 3 uses a randomized fractional factorial design with multiple RDEs explored across tumor cohorts (Liao et al., 2023). DROID likewise uses two seamlessly connected stages: stage I adaptively establishes a therapeutic dose range (TDR) and recommended phase 2 dose set (RP2S), while stage II randomizes patients to RP2S doses to assess dose-response and identify the optimal dose (Guo et al., 2022). MATS applies a related idea across multiple indications: stage 1 evaluates the higher dose for preliminary activity, and stage 2 randomizes promising indications between a higher and lower dose under a Bayesian hierarchical model (Jiang et al., 2023).

Randomized dose-selection designs aligned with Project Optimus have become especially prominent. ROSE is a randomized optimal selection design for choosing between two doses by comparing observed response rates $\pi_E$5 and $\pi_E$6 against a decision boundary $\pi_E$7, with explicit probability-of-correct-selection constraints under both a plateau hypothesis $\pi_E$8 and a superiority hypothesis $\pi_E$9 (Wang et al., 6 May 2025). In the same regulatory context, BE-BOIN combines backfilling, time-to-event handling for late-onset toxicity, and utility-based OBD determination, thereby extending interval-based methods to settings requiring richer multi-dose evidence (Chen et al., 14 Sep 2025).

A somewhat different family treats dose finding as active learning on a dose-response function. In the level-set estimation design, the unknown DLT probability $\pi_T$0 is modeled through $\pi_T$1 with $\pi_T$2 given a GP prior, and MTD estimation is recast as determining the boundary of the level set $\pi_T$3. The next dose is chosen by maximizing an acquisition function

$\pi_T$4

where $\pi_T$5 and $\pi_T$6 penalizes likely overdoses (Seno et al., 12 Apr 2025).

5. Dose-response modeling, borrowing, and model uncertainty

A major technical challenge in PDF is how to represent dose-response relationships without imposing untenable parametric assumptions. Generalized MCP-Mod addresses this by prespecifying candidate shapes and separating testing from modeling. For candidate model $\pi_T$7, the optimal contrast is

$\pi_T$8

followed by generalized least-squares fitting of the selected dose-response model (Pinheiro et al., 2013). This framework was developed precisely because binary, count, time-to-event, crossover, and longitudinal settings are common and do not fit the simplest normal-endpoint assumptions.

MAP-curvature and SEMAP-curvature take a different route. The dose-response curve is regularized by penalizing total curvature relative to a default model $\pi_T$9, with SEMAP-curvature using the sigmoid Emax model

$u_k$0

as the default. Historical borrowing is incorporated through a Bayesian hierarchical model with current and historical responses

$u_k$1

where $u_k$2 and $u_k$3 model prognostic and predictive heterogeneity (Han et al., 28 Sep 2025). The paper explicitly positions this as a model-free alternative to MCP-Mod when misspecification is a concern.

Borrowing can also occur across studies rather than across models. In a Bayesian random-effects meta-analysis of phase I dose-finding studies, the toxicity counts satisfy

$u_k$4

with random effects $u_k$5 and OU covariance

$u_k$6

The fixed effects $u_k$7 are given latent Gamma-process priors to enforce monotonicity (Ursino et al., 2019). This line of work suggests that precision can mean improved MTD estimation through principled synthesis of heterogeneous phase I studies, not only through within-trial individualization.

A related issue is prior calibration in curve-free Bayesian designs. In c-CFBD, after each cohort the updated Beta priors at all dose levels are recalibrated so that the effective sample size (ESS) is identical across doses: $u_k$8 Only the prior specification step is modified; the utility and stopping rules remain unchanged (Xu et al., 20 Mar 2025). Here, “precision” refers to stabilizing uncertainty across the dose grid so that allocation concentrates more accurately around the MTD.

6. Endpoints, operational constraints, and regulatory context

The move toward PDF has been tightly linked to operational and regulatory changes. Project Optimus is repeatedly cited as shifting dose selection away from the MTD toward the OBD and as encouraging randomized comparisons among multiple doses rather than a single dose-escalation path (Yuan et al., 2023, Wang et al., 6 May 2025, Guo et al., 2022). This regulatory context has favored designs that make explicit tradeoffs between accuracy and feasibility, such as ROSE, which targets prespecified probabilities of correct selection while keeping per-arm sample sizes in the 15 to 40 range for 60% to 70% correct selection in simulations (Wang et al., 6 May 2025).

Endpoint complexity is another defining feature. Reviews emphasize that toxicity may be binary, ordinal, or continuous, and that efficacy may be delayed, requiring surrogate or intermediate endpoints (Yuan et al., 2023). DEMO addresses this directly by incorporating a continuous early biological mediator $u_k$9, modeling

$U(\pi_E, \pi_T) = \pi_E - \omega_1 \pi_T - \omega_2 \pi_T \cdot \mathds{I}(\pi_T > \phi_T)$0

in stage 1 with a step-function model for biological activity, then using an Emax model for $U(\pi_E, \pi_T) = \pi_E - \omega_1 \pi_T - \omega_2 \pi_T \cdot \mathds{I}(\pi_T > \phi_T)$1, logistic regressions for toxicity and response conditional on $U(\pi_E, \pi_T) = \pi_E - \omega_1 \pi_T - \omega_2 \pi_T \cdot \mathds{I}(\pi_T > \phi_T)$2, and a Weibull model for survival. The final dose is chosen to maximize restricted mean survival time (RMST) among doses that are biologically active, safe, and clinically effective (Yang et al., 2024).

Late-onset and cumulative toxicity complicate real-time decision-making. Joint TITE-CRM addresses delayed efficacy and toxicity by weighting partial follow-up, while BE-BOIN uses time-to-event imputation for pending DLT outcomes and permits backfilling to safe, active lower doses during escalation (Barnett et al., 2022, Chen et al., 14 Sep 2025). These methods are responses to a practical misconception: that precise dose optimization can be layered onto conventional escalation without redesigning accrual, follow-up, and decision rules. The literature instead treats timeliness of endpoint ascertainment as a first-order design constraint.

Software and implementation have also become part of the field’s infrastructure. The generalized MCP-Mod framework is implemented in the DoseFinding R package (Pinheiro et al., 2013). Reviews point to trialdesign.org modules for BOIN12, TITE-BOIN12, MERIT, and DROID, and to dedicated EffTox software (Yuan et al., 2023). MATS and hybrid dose-escalation designs are accompanied by Shiny applications (Jiang et al., 2023, Liao et al., 2023). A plausible implication is that the recent expansion of PDF methods is inseparable from simulation-based calibration and deployable software, because most of the proposed designs are adaptive, multi-criterion, and operationally nontrivial.

7. Debates, limitations, and future directions

The literature contains several active debates. The first concerns whether MTD-centered designs remain defensible. Critics argue that conventional escalation is incompatible with reasonable expectations of safety when PKPD heterogeneity is large, and that treating patients as exchangeable is “indefensible” (Norris, 2020). More moderate accounts do not reject escalation entirely, but replace single-dose thinking with staged optimization in which MTD or maximum administered dose is merely an upper boundary before RDE or OBD evaluation (Liao et al., 2023).

The second debate concerns model specification. MCP-Mod is widely used and regulator-endorsed, but recent work emphasizes its sensitivity to misspecification and proposes model-free alternatives such as MAP-curvature and SEMAP-curvature (Han et al., 28 Sep 2025). Similar tensions appear between fully model-based methods, which can borrow information efficiently but may be computationally heavier or assumption-sensitive, and model-assisted methods, which are often simpler and more transparent but may be less flexible (Barnett et al., 2022, Chen et al., 14 Sep 2025).

A third issue is how far personalization can realistically go in early-phase trials. PK-driven individualization and GP-based personalized combination optimization offer formal mechanisms for patient-specific dosing (Lee et al., 5 Sep 2025, Willard et al., 2024). At the same time, several papers note practical prerequisites: timely PK profiling, reliable predictive modeling, small-sample feasibility, and careful prior specification (Lee et al., 5 Sep 2025, Zhu et al., 2020, Han et al., 28 Sep 2025). This suggests that “precision” may range from modest subgroup-specific recommendations to genuinely individualized dose assignment, depending on the data structure and operational capacity.

Future directions named in the literature include broader use of historical borrowing, extension to multiple historical datasets, adaptive and longitudinal designs, and richer integration of biological mediators, PK/PD, and patient heterogeneity (Han et al., 28 Sep 2025, Yang et al., 2024, Maity et al., 2024). Across these strands, the core trajectory is consistent: PDF is evolving from a toxicity-threshold exercise into a general framework for adaptive decision-making under heterogeneity, model uncertainty, delayed outcomes, and multidimensional evidence.