Phase 1/2 Dose-Finding Designs

Definition

Dose-finding designs are early-phase trial designs used to identify a recommended dose for later-phase evaluation. In cytotoxic oncology the historical target is the Maximum Tolerated Dose (MTD) — the highest dose with a dose-limiting toxicity (DLT) rate at or below a pre-specified target (commonly 25–33%). In modern molecularly targeted and immuno-oncology settings the target has shifted toward the Optimal Biological Dose (OBD) — the dose that jointly optimizes toxicity, pharmacodynamic activity, pharmacokinetic exposure, and efficacy.

FDA 2019 (Final guidance, Adaptive Designs §V.F): "the continual reassessment method (CRM) is an approach to adaptively escalate the doses evaluated in early-phase trials based on observed toxicities in order to reliably and efficiently" identify a dose for further study.

FDA 2019 (Final): "the speed of escalation should be considered in choosing a specific adaptation rule in an adaptive dose-escalation trial." Adaptation rules that allow for successive cohorts to receive quickly escalating doses could lead to subjects receiving unsafe exposures, particularly when DLTs are delayed.

Regulatory Position

Design	Regulatory status	Typical use
3+3	Acceptable but discouraged by FDA Project Optimus	First-in-human cytotoxics; ultra-rare populations
CRM / BOIN / mTPI-2 / EWOC	FDA-preferred model-based/model-assisted approaches	Contemporary Phase 1 oncology
Seamless 1/2 (dose-finding → dose-optimization → expansion)	Supported under adaptive guidance	Targeted therapy, IO, ADC

FDA 2019 (Final) explicitly endorses CRM-class adaptive dose-escalation as a well-understood method when operating characteristics are prespecified and simulation-based type I error and safety metrics are submitted to the Agency.

Project Optimus (FDA OCE, 2023): Sponsors are expected to characterize dose–response for efficacy and toxicity and select an OBD rather than rely solely on MTD. Randomized dose-ranging (e.g., two active doses vs. comparator) in Phase 2 is now frequently required before registration. (Draft Project Optimus guidance on dose optimization for oncology drugs is DRAFT, 2023.)

ICH E20 (2025, DRAFT Step 2b): Reinforces that adaptive dose-escalation designs should be accompanied by simulation reports covering safety (probability of assigning unsafe doses), accuracy (PCS – probability of correct selection), and average sample size per dose.

When to Use

3+3: Acceptable when no prior toxicity information exists and the study is ultra-small (n≤15). Still dominant in academic investigator-initiated trials. Poorly suited to delayed-toxicity agents (IO, ADCs) or when OBD < MTD.
CRM / BOIN / mTPI-2: Standard choice for first-in-human cytotoxics, small molecules, and targeted therapies where DLT rate is meaningful and assessable within one cycle.
EWOC: Preferred when regulators or IRBs emphasize controlled overdose probability (e.g., pediatric oncology, narrow therapeutic index agents).
BOIN-comb / waterfall: Two-drug combination dose-finding — e.g., PARP + ATR inhibitor, IO + targeted kinase, chemo + antibody-drug conjugate.
Seamless Phase 1/2: Modern IO and targeted therapy programs (e.g., KRAS G12C, BTK, BCMA CAR-T) combining escalation → backfill → randomized dose optimization.

Design Considerations

3+3 Design

Mechanics:

Enroll cohort of 3 at dose level k.
If 0/3 DLT → escalate to k+1.
If 1/3 DLT → enroll 3 more at k. If ≤1/6 DLT → escalate; if ≥2/6 → declare MTD at k-1.
If ≥2/3 DLT → declare MTD at k-1.

Operating characteristics:

Implicit DLT target ≈ 20–25%, not selectable.
Probability of correct MTD selection (PCS) typically 30–40% for 5–6 dose levels.
Allocates only ~35% of patients to the true MTD.
No formal escalation rule for delayed toxicity.

Limitations: Cannot incorporate prior information, does not converge to any target DLT rate, ignores toxicities beyond Cycle 1, and performs poorly when true MTD is at the highest or lowest level.

Continual Reassessment Method (CRM)

Target: Prespecified DLT rate θ (typically 0.25 or 0.30).
Dose–toxicity model: Typically one-parameter power (empiric) model: p(d_k) = s_k^exp(a), where s_k is the skeleton (prior DLT probability at dose k) and a ~ N(0, σ²) is the single estimable parameter.
Skeleton: Prior DLT rates at each dose level, elicited from clinicians or prior studies, e.g., skeleton = (0.05, 0.12, 0.25, 0.40, 0.55) with target 0.25 → dose 3 is prior MTD.
Prior: Normal or gamma on a; σ² = 1.34 is a standard weakly informative default (O'Quigley & Shen 1996).
Dose assignment: After each patient/cohort, update posterior on a, compute posterior mean p̂(d_k), and assign next cohort to dose k* that minimizes |p̂(d_k) − θ|.
Safety constraints: No-skip-escalation rule; coherence constraint (never escalate after a DLT, never de-escalate after a non-DLT).
R package: dfcrm (Cheung) — functions crm(), getprior(), titesim() for time-to-event CRM.

BOIN (Bayesian Optimal Interval)

Approach: Model-assisted — uses a fixed decision table, not a longitudinal Bayesian model.
Decision boundaries: For target DLT rate φ = 0.30, default interval is [λ_e, λ_d] = [0.236, 0.359] (derived to minimize probability of incorrect dose assignment under local hypotheses φ_1 = 0.6·φ, φ_2 = 1.4·φ).

BOIN decision table (target φ = 0.30):

Observed DLT rate at current dose	Action
≤ 0.236	Escalate
0.236 – 0.359	Stay
≥ 0.359	De-escalate
Pr(p > φ \| data) > 0.95 and n ≥ 3	Eliminate dose and all above

MTD selection: Isotonic regression on observed DLT rates at trial end; select dose closest to φ.
Operating characteristics: PCS 55–65% for 5-level designs; allocates 50–60% of patients at or adjacent to MTD; published equivalence to CRM with substantially simpler implementation.
R package: BOIN — functions get.boundary(), select.mtd(), get.oc() for simulation.

mTPI-2 (Modified Toxicity Probability Interval 2)

Partitions unit interval into equivalence interval (EI) around target ± ε₁, ε₂ (typically ±0.05) and sub-intervals.
Decision based on unit probability mass (UPM) of the posterior beta(α+x, β+n−x) falling in each sub-interval.
Fixes overdose problem of original mTPI by reducing granularity of the overdose region.
R package: UnifiedDoseFinding.

EWOC (Escalation With Overdose Control)

Bayesian two-parameter logistic model on probability of toxicity.
Key feature: constrains Pr(next dose > MTD) ≤ α (overdose control parameter, typically starting at 0.25 and relaxed to 0.5 as trial matures).
Produces more conservative early escalation than CRM.
R package: ewoc.

Combination Dose-Finding

BOIN-comb (Lin & Yin 2017): Extends BOIN to 2-D dose matrices. After each cohort, determines admissible escalation moves (E, N, S, W) and selects among them by minimizing distance to target in the isotonic neighborhood.
Waterfall (Huang et al. 2007 / Zhang & Yuan 2016): Decomposes the 2-D search into a sequence of 1-D subtrials along rows/columns; efficient for finding an MTD contour rather than a single MTD.
R packages: BOIN (functions get.boundary.comb(), select.mtd.comb()); pocrm for partial-order CRM.

RP2D Selection: MTD vs OBD

MTD paradigm (cytotoxic era): Highest dose with DLT rate ≤ target. Assumes monotone dose–efficacy.

OBD paradigm (targeted therapy / IO, Project Optimus):

Jointly evaluate toxicity, PK (target exposure), PD (target engagement), and efficacy (response rate, pharmacodynamic biomarker).
Typical designs: BOIN12 and BOIN-ET (efficacy–toxicity joint), EffTox (Thall & Cook), TITE-BOIN12.
Utility-based selection: Specify utility matrix over (toxicity, efficacy) outcomes; choose dose maximizing posterior expected utility.
R packages: BOIN (contains boin12()), trialr (EffTox), escalation (unified interface for CRM/BOIN/3+3/TPI).

FDA Project Optimus expectations:

At least two active doses randomized in Phase 2 dose-optimization.
Prespecified dose-response analysis for both toxicity and efficacy.
Characterization of PK/PD across the explored range.

Seamless Phase 1/2 Transitions

Phase 1 escalation (CRM/BOIN) → backfill cohorts at safe doses to accrue PK/PD/efficacy → randomized Phase 2 dose optimization (e.g., two doses 1:1 or 1:1:1 with control) → registrational expansion.
Master protocol with pre-specified decision rules for each transition.
Type I error control: When the Phase 2 arms are not used for inference on primary registrational endpoints, no α adjustment needed; otherwise conditional error functions or combination tests (e.g., Bauer–Köhne) should be prespecified.
ICH E20 (DRAFT) emphasizes prospective simulation of end-to-end operating characteristics.

FDA Expectations for Model-Based Designs

Per FDA 2019 (Final) and Project Optimus (DRAFT):

Prespecify dose–toxicity model, skeleton/decision table, target DLT rate, and stopping rules in the protocol.
Submit simulation report with at least 1,000 replicates across plausible scenarios covering: (a) true MTD at each dose level, (b) no safe dose, (c) all doses safe, (d) delayed toxicity if relevant.
Report: PCS, percent allocated to MTD, percent allocated above MTD, average N, stopping probability.
Specify cohort size, starting dose justification (typically 1/10 STD10 or 1/6 HNSTD), and rules for intra-patient escalation.
For combinations, specify whether the goal is single MTD or MTD contour.

Formulas

CRM posterior (empiric model): L(a | data) ∝ ∏ s_k^{exp(a)·x_k} · (1−s_k^{exp(a)})^{n_k−x_k} · π(a). Dose for next cohort = argmin_k |E[s_k^{exp(a)} | data] − θ|.
BOIN boundaries: λ_e = log((1−φ_1)/(1−φ)) / log(φ(1−φ_1)/(φ_1(1−φ))); λ_d analogous. [Liu & Yuan 2015].
Sample size heuristic (CRM): N ≈ 6·(number of dose levels) — conventional minimum; for BOIN, N = 30–36 for 5 levels with cohort size 3 is typical.

Concrete Oncology Example

Phase 1 first-in-human ADC in advanced solid tumors, 5 dose levels (0.5, 1.0, 1.8, 2.6, 3.5 mg/kg q3w), target DLT rate = 0.30:

3+3: Expected N ≈ 18–24; PCS ≈ 35%; ~25% of patients at MTD.
BOIN with cohort 3, N=36: PCS ≈ 62%; ~55% of patients at or adjacent to MTD; boundaries (0.236, 0.359); elimination threshold Pr(p>0.30)>0.95.
CRM, skeleton (0.05, 0.12, 0.25, 0.40, 0.55), σ²=1.34, N=36: PCS ≈ 60%; similar allocation profile; slightly better when true MTD is at the extremes.

Intercurrent Events

Dose-finding is typically pre-estimand, but ICH E9(R1) principles still apply to the MTD/OBD estimand:

Dose modification / dose reduction before Cycle-1 DLT window completion
- Strategy: Composite — patient counted as DLT if modification was toxicity-driven.
- Consequence: Inflates observed DLT rate; conservative for MTD.
- SAP template: "Subjects who discontinue or reduce dose within the DLT observation window due to toxicity will be counted as DLT. Subjects who discontinue for reasons unrelated to toxicity and have received <75% of planned dose will be replaced."
Disease progression during DLT window
- Strategy: While-on-treatment or treatment policy; subject typically replaced.
- Consequence: Reduces effective N at that dose level; protocol should prespecify replacement rule.
- SAP template: "Subjects who progress and are removed from study before completing the DLT window without experiencing a DLT will be considered non-evaluable and replaced."
Delayed toxicity beyond Cycle-1 window (IO, ADC)
- Strategy: Hypothetical / extended DLT window with TITE weighting.
- Consequence: Standard CRM/BOIN under-estimates true toxicity rate; use TITE-CRM or TITE-BOIN with fractional weighting.
- SAP template: "Late-onset toxicities will be captured using a TITE-BOIN model with a DLT window of 42 days; the weight for a subject observed for t days is min(t/42, 1) if no DLT has occurred."

Regulatory Precedent

Fewer than 3 explicit dose-finding precedent examples appear in the provided FDA 2019 and ICH E20 chunks; both documents reference CRM as an example but do not tabulate specific program precedents. The FDA 2019 guidance cites:

Reference	Topic	Source
Le Tourneau, Lee, Siu 2009 (JNCI 101:708–720)	Dose Escalation Methods in Phase 1 Cancer Clinical Trials	FDA 2019 bibliography
CRM (O'Quigley, Pepe, Fisher 1990)	Canonical model-based design	FDA 2019 §V.F
FDA 2019 §V.F.1	Adaptive dose-ranging with CRM	Final guidance

Contemporary registrational programs applying dose optimization under Project Optimus (e.g., sotorasib KRYSTAL/CodeBreaK, adagrasib KRYSTAL-1, selpercatinib LIBRETTO) are not enumerated in the provided chunks and are omitted to avoid fabrication.

Limitations and Pitfalls

3+3 is discouraged but persistent: Poor operating characteristics, cannot target a specific DLT rate, ignores prior information, and does not handle delayed toxicity. Still appears in academic protocols.
MTD ≠ OBD: For targeted therapies and IO, MTD may exceed the dose required for maximal efficacy, producing unnecessary toxicity and long-term tolerability problems. Project Optimus now routinely requires randomized dose optimization in Phase 2.
Skeleton misspecification (CRM): Overly steep or shallow skeletons degrade performance. Sensitivity analysis across 3–5 skeletons is standard.
Delayed toxicity: Standard CRM/BOIN assume toxicity is fully observed in the DLT window. IO and ADCs commonly produce late-onset immune-related AEs; use TITE variants.
Combination dose-finding ambiguity: 2-D MTD may not be unique (contour of equivalent dose combinations); protocol must prespecify selection rule.
Simulation reporting gaps: Regulators increasingly reject submissions without end-to-end simulation over clinically plausible scenarios including null (no safe dose) scenarios.
Indication bias: Expansion cohorts at RP2D often overestimate response because patients are selected; randomized dose-optimization avoids this.
Small n precludes subgroup dose-finding: Separate escalation by organ function or prior therapy usually infeasible; pooled analysis with covariate-adjusted CRM is an option.

SAP Language Template

"Dose escalation will follow the Bayesian Optimal Interval (BOIN) design targeting a DLT rate of 0.30 with decision boundaries (λ_e, λ_d) = (0.236, 0.359) and dose elimination when Pr(p_k > 0.30 | data) > 0.95 with n_k ≥ 3 (Liu & Yuan 2015). Cohorts of 3 subjects will be enrolled sequentially across 5 dose levels with a maximum sample size of 36. The MTD will be selected using isotonic regression as the dose with estimated DLT rate closest to 0.30 among admissible doses. Operating characteristics (PCS, allocation, over-dose probability) were evaluated via 2,000-replicate simulation under 6 scenarios (BOIN R package v2.7). Late-onset toxicities beyond the 28-day Cycle-1 DLT window will be captured in a sensitivity analysis using TITE-BOIN with 42-day window. Following MTD determination, a randomized Phase 2 dose-optimization cohort will compare MTD to MTD·0.75 (1:1, n=40/arm) per FDA Project Optimus expectations; the recommended Phase 2 dose (OBD) will be selected on the basis of response rate, PK exposure, and grade ≥3 adverse event rate by week 12."

Backlinks

Source: FDA Adaptive Designs for Clinical Trials of Drugs and Biologics (2019, Final §V.F); ICH E20 Adaptive Clinical Trials (2025, Step 2b DRAFT); Liu & Yuan 2015 (BOIN); O'Quigley, Pepe & Fisher 1990 (CRM); Le Tourneau et al. 2009; FDA Project Optimus draft guidance (2023, DRAFT). Status: Mixed — FDA 2019 Final; ICH E20 and Project Optimus DRAFT. Compiled from retrieved FDA chunks + dose_finding_boin_crm_summary literature notes.