Dose selection is a key component of drug development, yet inadequate dose-response characterization remains a major challenge, contributing to late-stage attrition and post-marketing regulatory commitments. Effective dose-response characterization for both efficacy and safety supports benefit-risk assessments of therapeutic interventions and relies on two main elements: Trial design and trial analysis. In trial design, selecting an appropriate dose range, determining the number of dose levels, and ensuring proper dose spacing are essential to capture both the steep and plateau regions of a dose-response curve. Adaptive trial designs provide additional flexibility to address uncertainties during trial planning and execution, increasing the chances of identifying optimal doses and improving trial efficiency. In trial analysis, modeling approaches support dose-response characterization by utilizing data across dose levels to fit a continuous curve rather than analyzing each dose level separately. Model-based methods, such as Emax modeling or MCP-Mod (which combines multiple comparison procedures and modeling), incorporate assumptions about the dose-response relationship to improve the precision of dose-response and target dose estimation. Additional precision can often be achieved by modeling dose-exposure-response relationships, recognizing that exposure (e.g. drug concentration in the plasma) often mediates the relationship between dose and clinical response. Dose-exposure response models may also enable the prediction of dose-response relationships of alternative regimens (e.g. when applying a different frequency of administration than the tested ones). This article reviews key considerations for the design and analysis of dose-response trials, focusing on strategies to improve decision-making and regulatory alignment.
SacksLVShamsuddinHHYasinskayaYI, et al. Scientific and regulatory reasons for delay and denial of FDA approval of initial applications for new drugs, 2000–2012. JAMA2014; 311(4): 378–384.
5.
CrossJLeeHWestelinckA, et al. Postmarketing drug dosage changes of 499 FDA-approved new molecular entities, 1980–1999. Pharmacoepidemiol Drug Saf2002; 11(6): 439–446.
6.
MinnemaLAGiezenTJGardarsdottirH, et al. Post-marketing dosing changes in the label of biologicals. Br J Clin Pharmacol2019; 85(4): 715–721.
International Council for Harmonisation of Technical Requirements for Pharmaceuticals for Human Use (ICH). E4: dose-response information to support drug registration, https://database.ich.org/sites/default/files/E4_Guideline.pdf (1994, accessed 8 February 2025)
9.
US Food and Drug Administration (FDA). Exposure—Response Relationships—Study Design, Data Analysis, and Regulatory Applications, 2003, https://www.fda.gov/media/71277/download (accessed 8 February 2025).
JiPNikolovNSeymourS, et al. A novel pharmacokinetic bridging strategy to support a change in the route of administration for biologics. J Pharm Sci2019; 108(7): 2490–2499.
PeletierLAGabrielssonJ.Dynamics of target-mediated drug disposition: characteristic profiles and parameter identification. J Pharmacokinet Pharmacodyn2012; 39(5): 429–451.
14.
DuaPHawkinsEvan der GraafPH.A tutorial on target-mediated drug disposition (TMDD) models. CPT Pharmacometrics Syst Pharmacol2015; 4(6): 324–337.
15.
de VisserSJvan der PostJPietersMS, et al. Biomarkers for the effects of antipsychotic drugs in healthy volunteers. Br J Clin Pharmacol2001; 51(2): 119–132.
YuanGTingN.First dose ranging clinical trial design—More doses? Or a wider range. In: YoungWRChenD-G (eds) Clinical Trial Biostatistics and Biopharmaceutical Applications. New York: Chapman and Hall/CRC Press, 2014, pp. 91–110.
18.
DetteHBretzFPepelyshevA, et al. Optimal designs for dose-finding studies. J Am Stat Assoc2008; 103(483): 1225–1237.
19.
RobertsonDSLeeKMLópez-KolkovskaBC, et al. Response-adaptive randomization in clinical trials: from myths to practical considerations. Stat Sci2023; 38(2): 185–208.
20.
BornkampBZhouJXiD, et al. Futility analyses for the MCP-Mod methodology based on longitudinal models. arXiv preprint. arXiv:2406.19965, https://arxiv.org/pdf/2406.19965 (2024, accessed 8 February 2025)
21.
LiuQHuGYeB, et al. Sample size re-estimation in Phase 2 dose-finding: conditional power versus Bayesian predictive power. Pharm Stat2023; 22(2): 349–364.
22.
PapachristofiOBornkampBWrightM, et al. Interim decision making in seamless trial designs: an application in an adaptive dose-finding study in a rare kidney disease. Pharm Stat2024; 23(1): 20–30.
23.
HolfordN.Pharmacodynamic principles and the time course of immediate drug effect. Transl Clin Pharmacol2017; 25(4): 157–162.
24.
ThomasN.Meta-analysis of clinical dose–response in a large drug development portfolio. J Biopharm Stat2014; 24(5): 923–944.
SharmaAJuskoWJ.Characterization of four basic models of indirect pharmacodynamic responses. J Pharmacokinet Biopharm1996; 24(6): 611–635.
27.
SanghaviKRibbingJRogersJA, et al. Covariate modeling in pharmacometrics: general points for consideration. CPT Pharmacometrics Syst Pharmacol2024; 13(5): 710–728.
28.
PisalDSLiYGoldingA, et al. Model-informed drug development-based approval of intravenous secukinumab for the treatment of adult patients with active psoriatic arthritis, active ankylosing spondylitis, and active non-radiographic axial spondyloarthritis. Clin Pharmacol Ther2025; 117(2): 475–484.
29.
LeuJHShiffNJClarkM, et al. Intravenous golimumab in patients with polyarticular juvenile idiopathic arthritis and juvenile psoriatic arthritis and subcutaneous ustekinumab in patients with juvenile psoriatic arthritis: extrapolation of data from studies in adults and adjacent pediatric populations. Paediatr Drugs2022; 24(6): 699–714.
30.
ChatfieldC.Model uncertainty, data mining and statistical inference (with discussion). J R Stat Soc Ser A1995; 158: 419–466.
31.
DraperD.Assessment and propagation of model uncertainty. J R Stat Soc Ser B1995; 57: 45–97.
32.
BretzFPinheiroJCBransonM.Combining multiple comparisons and modeling techniques in dose response studies. Biometrics2005; 61(3): 738–748.
33.
XunXBretzF.The MCP-Mod methodology: practical considerations and the DoseFinding R Package. In: O’quigleyJIasonosABornkampB (eds) Handbook of Methods for Designing, Monitoring, and Analyzing Dose-finding Trials, Handbooks of Modern Statistical Methods. Boca Raton, FL: CRC Press, 2017.
34.
VerrierDSivapregassamSSolenteAC.Dose-finding studies, MCP-Mod, model selection, and model averaging: two applications in the real world. Clin Trials2014; 11(4): 476–484.
35.
SchorningKBornkampBBretzF, et al. Model selection versus model averaging in dose finding studies. Stat Med2016; 35(22): 4021–4040.
36.
PinheiroJBornkampBGlimmE, et al. Model-based dose finding under model uncertainty using general parametric models. Stat Med2014; 33(10): 1646–1661.
37.
BuatoisSUeckertSFreyN, et al. cLRT-Mod: an efficient methodology for pharmacometric model-based analysis of longitudinal Phase II dose-finding studies under model uncertainty. Stat Med2021; 40(10): 2435–2451.
38.
YamaguchiYSugitaniT.Sample size allocation in multiregional dose-finding study using MCP-Mod. Stat Biopharm Res2021; 13(4): 395–404.
39.
PinLSverdlovOBretzF, et al. Randomization-based inference for MCP-Mod. arXiv preprint, arXiv:2410. 11716, https://arxiv.org/abs/2410.11716. (2024, accessed 8 February 2025)
40.
ZhangHRizkDVPerkovicV, et al. Results of a randomized double-blind placebo-controlled Phase 2 study propose iptacopan as an alternative complement pathway inhibitor for IgA nephropathy. Kidney Int2024; 105(1): 189–199.
41.
BurdenADBissonnetteRTeruiT, et al. Spesolimab efficacy and safety in patients with moderate-to-severe palmoplantar pustulosis: a multicentre, double-blind, randomised, placebo-controlled, phase IIb, dose-finding study. Dermatol Ther (Heidelb)2023; 13(10): 2279–2297.
42.
SharmaMMolinaCAToyodaK, et al. Safety and efficacy of factorXIa inhibition with milvexian for secondary stroke prevention (AXIOMATIC-SSP): a phase 2, international, randomised, double-blind, placebo-controlled, dose-finding trial. Lancet Neurol2024; 23(1): 46–59.
US Food and Drug Administration (FDA). Model-informed drug development: tools and strategies. https://www.fda.gov/media/99313/download. (2016, accessed 8 February 2025).
46.
TurnerDC.Pembrolizumab exposure–response assessments challenged by association of cancer cachexia and catabolic clearance. Clin Cancer Res2018; 24(23): 5841–5849.
MusuambaFTManolisEHolfordN, et al. Advanced methods for dose and regimen finding during drug development: summary of the EMA/EFPIA workshop on dose finding (London 4-5 December 2014). CPT Pharmacometrics Syst Pharmacol2017; 6(7): 418–429.
51.
RitzCJensenSMGerhardD, et al. Dose-Response Analysis Using R. Boca Raton, FL: CRC Press, 2017.
52.
DudaJCKappenbergFRahnenführerJ.Model selection characteristics when using MCP-Mod for dose–response gene expression data. Biom J2022; 64(5): 883–897.
53.
BiethBBornkampBToutainC, et al. Multiple comparison procedure and modeling: a versatile tool for evaluating dose–response relationships in veterinary pharmacology–a case study with furosemide. J Vet Pharmacol Ther2016; 39(6): 539–546.
54.
BentleyKSKirklandDMurphyM, et al. Evaluation of thresholds for benomyl- and carbendazim-induced aneuploidy in cultured human lymphocytes using fluorescence in situ hybridization. Mutat Res2000; 464(1): 41–51.
