Meta-Analysis of Clinical Dose–Response in a Large Drug Development Portfolio

Efficient Study Design and Analysis of Longitudinal Dose-Response Data Using Fractional Polynomials

Correctly characterising the dose-response relationship and taking the correct dose forward for further study is a critical part of the drug development process. We use optimal design theory to compare different designs and show that using longitudinal data from all available timepoints in a continuous-time dose-response model can substantially increase the efficiency of estimation of the dose-response compared to a single timepoint model. We give theoretical results to calculate the efficiency gains for a large class of these models. For example, a linearly growing Emax dose-response in a population with a between/within-patient variance ratio ranging from 0.1 to 1 measured at six visits can be estimated with between 1.43 and 2.22 times relative efficiency gain, or equivalently, with 30% to a 55% reduced sample size, compared to a single model of the final timepoint. Fractional polynomials are a flexible way to incorporate data from repeated measurements, increasing precision without imposing strong constraints. Longitudinal dose-response models using two fractional polynomial terms are robust to mis-specification of the true longitudinal process while maintaining, often large, efficiency gains. These models have applications for characterising the dose-response at interim or final analyses.

Statistical considerations in model-based dose finding for binary responses under model uncertainty

The statistical methodology for model-based dose finding under model uncertainty has attracted increasing attention in recent years. While the underlying principles are simple and easy to understand, developing and implementing an efficient approach for binary responses can be a formidable task in practice. Motivated by the statistical challenges encountered in a phase II dose finding study, we explore several key design and analysis issues related to the hybrid testing-modeling approaches for binary responses. The issues include candidate model selection and specifications, optimal design and efficient sample size allocations, and, notably, the methods for dose-response testing and estimation. Specifically, we consider a class of generalized linear models suited for the candidate set and establish D-optimal designs for these models. Additionally, we propose using permutation-based tests for dose-response testing to avoid asymptotic normality assumptions typically required for contrast-based tests. We perform trial simulations to enhance our understanding of these issues.

Toward the right treatment at the right time: Modeling the trajectory of cognitive decline to identify the earliest age of change in people with Alzheimer's disease

Introduction

Age is the greatest risk factor for Alzheimer's disease (AD). A limitation of randomized control trials in AD is a lack of specificity in the age ranges of participants who are enrolled in studies of disease-modifying therapies. We aimed to apply Emax (i.e., maximum effect) modeling as a novel approach to identity ideal treatment windows.

Methods

Emax curves were fitted to longitudinal cognitive data of 101 participants with AD and 1392 healthy controls. We included the Mini-Mental State Examination (MMSE) and tests of verbal fluency and executive functioning.

Results

In people with AD, the earliest decline in the MMSE could be detected in the 67-71 age band while verbal fluency declined from the 41-45 age band. In healthy controls, changes in cognition showed a later trajectory of decline.

Discussion

Emax modeling could be used to design more efficient trials which has implications for randomized control trials targeting the earlier stages of AD.

Calculation of Phase 2 dose-finding study sample size for reliable Phase 3 dose selection

Sample sizes of Phase 2 dose-finding studies, usually determined based on a power requirement to detect a significant dose-response relationship, will generally not provide adequate precision for Phase 3 target dose selection. We propose to calculate the sample size of a dose-finding study based on the probability of successfully identifying the target dose within an acceptable range (e.g., 80%-120% of the target) using the multiple comparison and modeling procedure (MCP-Mod). With the proposed approach, different design options for the Phase 2 dose-finding study can also be compared. Due to inherent uncertainty around an assumed true dose-response relationship, sensitivity analyses to assess the robustness of the sample size calculations to deviations from modeling assumptions are recommended. Planning for a hypothetical Phase 2 dose-finding study is used to illustrate the main points. Codes for the proposed approach is available at https://github.com/happysundae/posMCPMod.

Subgroup identification of targeted therapy effects on biomarker for time to event data

BACKGROUND

The initiation biomarker-driven trials have revolutionized oncology drug development by challenging the traditional phased approach and introducing basket studies. Notable successes in non-small cell lung cancer (NSCLC) with ALK, ALK/ROS1, and EGFR inhibitors have prompted the need to expand this approach to other cancer sites.

OBJECTIVES

This study explores the use of dose response modeling and time-to-event algorithms on the biomarker molecular targeted agent (MTA). By simulating subgroup identification in MTA-related time-to-event data, the study aims to develop statistical methodology supporting biomarker-driven trials in oncology.

METHODS

A total of n patients are selected assigned for different doses. A dataset is prepared to mimic the situation on Subgroup Identification of MTA for time to event data analysis. The response is measured through MTA. The MTA value is also measured through ROC. The Markov Chain Monte Carlo (MCMC) techniques are prepared to perform the proposed algorithm. The analysis is carried out with a simulation study. The subset selection is performed through the Threshold Limit Value (TLV) by the Bayesian approach.

RESULTS

The MTA is observed with range 12-16. It is expected that there is a marginal level shift of the MTA from pre to post-treatment. The Cox time-varying model can be adopted further as causal-effect relation to establishing the MTA on prolonging the survival duration. The proposed work in the statistical methodology to support the biomarker-driven trial for oncology research.

CONCLUSION

This study extends the application of biomarker-driven trials beyond NSCLC, opening possibilities for implementation in other cancer sites. By demonstrating the feasibility and efficacy of utilizing MTA as a biomarker, the research lays the foundation for refining and validating biomarker use in clinical trials. These advancements aim to enhance the precision and effectiveness of cancer treatments, ultimately benefiting patients.

The Acute Stroke Therapy by Inhibition of Neutrophils study - Key features and impact

The Acute Stroke Therapy by Inhibition of Neutrophils (ASTIN) study, initiated in November of the year 2000, is now widely recognized as having been a landmark study in the history of clinical trials. We look at why this is the case by considering its key features and impact. These key features are: the use of Bayesian design and analysis; the use of the normal dynamic linear model; the response adaptive nature of the study; the use of real-time dosing decisions; and the use of an integrated model to predict 90-day response on the Scandinavian Stroke Scale. Our overall conclusion is that the ASTIN study's main impact came from showing the clinical trial community the feasibility of the novel design and analysis used when most of these key features were rarely used in industry trials, let alone used together in one trial in a disease area with a tremendous unmet medical need.

Model selection characteristics when using MCP-Mod for dose-response gene expression data

We extend the scope of application for MCP-Mod (Multiple Comparison Procedure and Modeling) to in vitro gene expression data and assess its characteristics regarding model selection for concentration gene expression curves. Precisely, we apply MCP-Mod on single genes of a high-dimensional gene expression data set, where human embryonic stem cells were exposed to eight concentration levels of the compound valproic acid (VPA). As candidate models we consider the sigmoid E max $E_{\max }$ (four-parameter log-logistic), linear, quadratic, E max $E_{\max }$ , exponential, and beta model. Through simulations we investigate the impact of omitting one or more models from the candidate model set to uncover possibly superfluous models and to evaluate the precision and recall rates of selected models. Each model is selected according to Akaike information criterion (AIC) for a considerable number of genes. For less noisy cases the popular sigmoid E max $E_{\max }$ model is frequently selected. For more noisy data, often simpler models like the linear model are selected, but mostly without relevant performance advantage compared to the second best model. Also, the commonly used standard E max $E_{\max }$ model has an unexpected low performance.

Methods to assess evidence consistency in dose-response model based network meta-analysis

Network meta-analysis (NMA) simultaneously estimates multiple relative treatment effects based on evidence that forms a network of treatment comparisons. Heterogeneity in treatment definitions, such as dose, can lead to a violation of the consistency assumption that underpins NMA. Model-based NMA (MBNMA) methods have been proposed that allow functional dose-response relationships to be estimated within an NMA, which avoids lumping different doses together and thereby reduces the likelihood of inconsistency. Dose-response MBNMA relies on appropriate specification of the dose-response relationship as well as consistency of relative effects. In this article we describe methods to check for inconsistency in dose-response MBNMA models. Global and local (node-splitting) tests for inconsistency are described that account for studies with ≥3 arms that are typical in dose-finding trials. We show that consistency needs to be assessed with respect to the choice of dose-response function. We illustrate the methods using a network comparing biologics for moderate-to-severe psoriasis. By comparing results from an Emax and an exponential dose-response function we show that failure to correctly characterise the dose-response can introduce apparent inconsistency. The number of comparisons for which node-splitting is possible is also shown to be dependent on the complexity of the selected dose-response function. We highlight that the nature of dose-finding studies, which typically compare multiple doses of the same agent, provide limited scope to assess inconsistency, but these study designs help guard against inconsistency in the first place. We demonstrate the importance of assessing consistency to obtain robust relative effects to inform drug-development and policy decisions.

Water quality thresholds for coastal contaminant impacts on corals: A systematic review and meta-analysis

Reduced water quality degrades coral reefs, resulting in compromised ecosystem function and services to coastal communities. Increasing management capacity on reefs requires prioritization of the development of data-based water-quality thresholds and tipping points. To meet this urgent need of marine resource managers, we conducted a systematic review and meta-analysis that quantified the effects on scleractinian corals of chemical pollutants from land-based and atmospheric sources. We compiled a global dataset addressing the effects of these pollutants on coral growth, mortality, reproduction, physiology, and behavior. The resulting quantitative review of 55 articles includes information about industrial sources, modes of action, experimentally tested concentrations, and previously identified tolerance thresholds of corals to 13 metals, 18 pesticides, 5 polycyclic aromatic hydrocarbons (PAHs), a polychlorinated biphenyl (PCB), and a pharmaceutical. For data-rich contaminants, we make more robust threshold estimates by adapting models for Bayesian hierarchical meta-analysis that were originally developed for biopharmaceutical application. These models use information from multiple studies to characterize the dose-response relationships (i.e., E_max curves) between a pollutant's concentration and various measures of coral health. Metals used in antifouling paints, especially copper, have received a great deal of attention to-date, thus enabling us to estimate the cumulative impact of copper across coral's early life-history. The effects of other land-based pollutants on corals are comparatively understudied, which precludes more quantitative analysis. We discuss opportunities to improve future research so that it can be better integrated into quantitative assessments of the effects of more pollutant types on sublethal coral stress-responses. We also recommend that managers use this information to establish more conservative water quality thresholds that account for the synergistic effects of multiple pollutants on coral reefs. Ultimately, active remediation of local stressors will improve the resistance, resilience, and recovery of individual reefs and reef ecosystems facing the global threat of climate change.

The design of a Bayesian adaptive clinical trial of tranexamic acid in severely injured children

BACKGROUND

Trauma is the leading cause of death and disability in children in the USA. Tranexamic acid (TXA) reduces the blood transfusion requirements in adults and children during surgery. Several studies have evaluated TXA in adults with hemorrhagic trauma, but no randomized controlled trials have occurred in children with trauma. We propose a Bayesian adaptive clinical trial to investigate TXA in children with brain and/or torso hemorrhagic trauma.

METHODS/DESIGN

We designed a double-blind, Bayesian adaptive clinical trial that will enroll up to 2000 patients. We extend the traditional Emax dose-response model to incorporate a hierarchical structure so multiple doses of TXA can be evaluated in different injury populations (isolated head injury, isolated torso injury, or both head and torso injury). Up to 3 doses of TXA (15 mg/kg, 30 mg/kg, and 45 mg/kg bolus doses) will be compared to placebo. Equal allocation between placebo, 15 mg/kg, and 30 mg/kg will be used for an initial period within each injury group. Depending on the dose-response curve, the 45 mg/kg arm may open in an injury group if there is a trend towards increasing efficacy based on the observed relationship using the data from the lower doses. Response-adaptive randomization allows each injury group to differ in allocation proportions of TXA so an optimal dose can be identified for each injury group. Frequent interim stopping periods are included to evaluate efficacy and futility. The statistical design is evaluated through extensive simulations to determine the operating characteristics in several plausible scenarios. This trial achieves adequate power in each injury group.

DISCUSSION

This trial design evaluating TXA in pediatric hemorrhagic trauma allows for three separate injury populations to be analyzed and compared within a single study framework. Individual conclusions regarding optimal dosing of TXA can be made within each injury group. Identifying the optimal dose of TXA, if any, for various injury types in childhood may reduce death and disability.

Bayesian EMAX model with a mixture of normal distributions for dose-response in clinical trials

When a dose-response relationship is monotonic, the EMAX model has been shown to provide a good empirical fit for designing and analyzing dose-response data across a wide range of pharmaceutical studies. However, the EMAX model has never been applied to a finite mixture distribution. Motivated by a proposal investigating DHA dose effect on preterm birth (PTB, <37 weeks gestation) rate, we developed a Bayesian EMAX mixture model incorporating the three normal components finite mixture model into the EMAX framework. The proposed Bayesian EMAX mixture model analyzes gestational age as a continuous variable, which allows for statistically efficient estimates of PTB rate using various cut point with the same parsimonious model. For example, we can estimate the rate of early PTB (ePTB, <34 weeks gestation), PTB (<37 weeks gestation), and late-term birth (>41 weeks gestation) using the same model. We compared our proposed EMAX mixture model with an EMAX logistic model and an independent doses logistic model for a dichotomized endpoint using extensive simulations. Across the scenarios under consideration, the EMAX mixture model achieved higher power than the EMAX logistic model and the independent doses logistic model in detecting the effect of DHA supplementation on the PTB rate. The EMAX mixture model also resulted in smaller mean squared errors (MSE) in PTB rate estimates.

Identifying treatment effect heterogeneity in dose-finding trials using Bayesian hierarchical models

An important task in drug development is to identify patients, which respond better or worse to an experimental treatment. Identifying predictive covariates, which influence the treatment effect and can be used to define subgroups of patients, is a key aspect of this task. Analyses of treatment effect heterogeneity are however known to be challenging, since the number of possible covariates or subgroups is often large, while samples sizes in earlier phases of drug development are often small. In addition, distinguishing predictive covariates from prognostic covariates, which influence the response independent of the given treatment, can often be difficult. While many approaches for these types of problems have been proposed, most of them focus on the two-arm clinical trial setting, where patients are given either the treatment or a control. In this article we consider parallel groups dose-finding trials, in which patients are administered different doses of the same treatment. To investigate treatment effect heterogeneity in this setting we propose a Bayesian hierarchical dose-response model with covariate effects on dose-response parameters. We make use of shrinkage priors to prevent overfitting, which can easily occur, when the number of considered covariates is large and sample sizes are small. We compare several such priors in simulations and also investigate dependent modeling of prognostic and predictive effects to better distinguish these two types of effects. We illustrate the use of our proposed approach using a Phase II dose-finding trial and show how it can be used to identify predictive covariates and subgroups of patients with increased treatment effects.

Utility-Based Dose Selection for Phase II Dose-Finding Studies

BACKGROUND AND OBJECTIVES

Dose selection is a key feature of clinical development. Poor dose selection has been recognized as a major driver of development failure in late phase. It usually involves both efficacy and safety criteria. The objective of this paper is to develop and implement a novel fully Bayesian statistical framework to optimize the dose selection process by maximizing the expected utility in phase III.

METHODS

The success probability is characterized by means of a utility function with two components, one for efficacy and one for safety. Each component refers to a dose-response model. Moreover, a sequential design (with futility and efficacy rules at the interim analysis) is compared to a fixed design in order to allow one to hasten the decision to perform the late phase study. Operating characteristics of this approach are extensively assessed by simulations under a wide range of dose-response scenarios.

RESULTS AND CONCLUSIONS

Simulation results illustrate the difficulty of simultaneously estimating two complex dose-response models with enough accuracy to properly rank doses using an utility function combining the two. The probability of making the good decision increases with the sample size. For some scenarios, the sequential design has good properties: with a quite large probability of study termination at interim analysis, it enables to reduce the sample size while maintaining the properties of the fixed design.

Joining the Dots: Linking Disconnected Networks of Evidence Using Dose-Response Model-Based Network Meta-Analysis

BACKGROUND

Network meta-analysis (NMA) synthesizes direct and indirect evidence on multiple treatments to estimate their relative effectiveness. However, comparisons between disconnected treatments are not possible without making strong assumptions. When studies including multiple doses of the same drug are available, model-based NMA (MBNMA) presents a novel solution to this problem by modeling a parametric dose-response relationship within an NMA framework. In this article, we illustrate several scenarios in which dose-response MBNMA can connect and strengthen evidence networks.

METHODS

We created illustrative data sets by removing studies or treatments from an NMA of triptans for migraine relief. We fitted MBNMA models with different dose-response relationships. For connected networks, we compared MBNMA estimates with NMA estimates. For disconnected networks, we compared MBNMA estimates with NMA estimates from an "augmented" network connected by adding studies or treatments back into the data set.

RESULTS

In connected networks, relative effect estimates from MBNMA were more precise than those from NMA models (ratio of posterior SDs NMA v. MBNMA: median = 1.13; range = 1.04-1.68). In disconnected networks, MBNMA provided estimates for all treatments where NMA could not and were consistent with NMA estimates from augmented networks for 15 of 18 data sets. In the remaining 3 of 18 data sets, a more complex dose-response relationship was required than could be fitted with the available evidence.

CONCLUSIONS

Where information on multiple doses is available, MBNMA can connect disconnected networks and increase precision while making less strong assumptions than alternative approaches. MBNMA relies on correct specification of the dose-response relationship, which requires sufficient data at different doses to allow reliable estimation. We recommend that systematic reviews for NMA search for and include evidence (including phase II trials) on multiple doses of agents where available.

Endothelial-protective effects of a G-protein-biased sphingosine-1 phosphate receptor-1 agonist, SAR247799, in type-2 diabetes rats and a randomized placebo-controlled patient trial

Aims

SAR247799 is a G‐protein‐biased sphingosine‐1 phosphate receptor‐1 (S1P₁) agonist designed to activate endothelial S1P₁ and provide endothelial‐protective properties, while limiting S1P₁ desensitization and consequent lymphocyte‐count reduction associated with higher doses. The aim was to show whether S1P₁ activation can promote endothelial effects in patients and, if so, select SAR247799 doses for further clinical investigation.

Methods

Type‐2 diabetes patients, enriched for endothelial dysfunction (flow‐mediated dilation, FMD <7%; n = 54), were randomized, in 2 sequential cohorts, to 28‐day once‐daily treatment with SAR247799 (1 or 5 mg in ascending cohorts), placebo or 50 mg sildenafil (positive control) in a 5:2:2 ratio per cohort. Endothelial function was assessed by brachial artery FMD. Renal function, biomarkers and lymphocytes were measured following 5‐week SAR247799 treatment (3 doses) to Zucker diabetic fatty rats and the data used to select the doses for human testing.

Results

The maximum FMD change from baseline vs placebo for all treatments was reached on day 35; mean differences vs placebo were 0.60% (95% confidence interval [CI] −0.34 to 1.53%; P = .203) for 1 mg SAR247799, 1.07% (95% CI 0.13 to 2.01%; P = .026) for 5 mg SAR247799 and 0.88% (95% CI −0.15 to 1.91%; P = .093) for 50 mg sildenafil. Both doses of SAR247799 were well tolerated, did not affect blood pressure, and were associated with minimal‐to‐no lymphocyte reduction and small‐to‐moderate heart rate decrease.

Conclusion

These data provide the first human evidence suggesting endothelial‐protective properties of S1P₁ activation, with SAR247799 being as effective as the clinical benchmark, sildenafil. Further clinical testing of SAR247799, at sub‐lymphocyte‐reducing doses (≤5 mg), is warranted in vascular diseases associated with endothelial dysfunction.

Exposure-response modelling approaches for determining optimal dosing rules in children

Within paediatric populations, there may be distinct age groups characterised by different exposure-response relationships. Several regulatory guidance documents have suggested general age groupings. However, it is not clear whether these categorisations will be suitable for all new medicines and in all disease areas. We consider two model-based approaches to quantify how exposure-response model parameters vary over a continuum of ages: Bayesian penalised B-splines and model-based recursive partitioning. We propose an approach for deriving an optimal dosing rule given an estimate of how exposure-response model parameters vary with age. Methods are initially developed for a linear exposure-response model. We perform a simulation study to systematically evaluate how well the various approaches estimate linear exposure-response model parameters and the accuracy of recommended dosing rules. Simulation scenarios are motivated by an application to epilepsy drug development. Results suggest that both bootstrapped model-based recursive partitioning and Bayesian penalised B-splines can estimate underlying changes in linear exposure-response model parameters as well as (and in many scenarios, better than) a comparator linear model adjusting for a categorical age covariate with levels following International Conference on Harmonisation E11 groupings. Furthermore, the Bayesian penalised B-splines approach consistently estimates the intercept and slope more accurately than the bootstrapped model-based recursive partitioning. Finally, approaches are extended to estimate Emax exposure-response models and are illustrated with an example motivated by an in vitro study of cyclosporine.

Comparison of hierarchical EMAX and NDLM models in dose-response for early phase clinical trials

Background

Phase II clinical trials primarily aim to find the optimal dose and investigate the relationship between dose and efficacy relative to standard of care (control). Therefore, before moving forward to a phase III confirmatory trial, the most effective dose is needed to be identified.

Methods

The primary endpoint of a phase II trial is typically a binary endpoint of success or failure. The EMAX model, ubiquitous in pharmacology research, was fit for many compounds and described the data well, except for a single compound, which had nonmonotone dose–response (Thomas et al., Stat Biopharmaceutical Res. 6:302-317 2014). To mitigate the risk of nonmonotone dose response one of the alternative options is a Bayesian hierarchical EMAX model (Gajewski et al., Stat Med. 38:3123-3138 2019). The hierarchical EMAX adapts to its environment.

Results

When the dose-response curve is monotonic it enjoys the efficiency of EMAX. When the dose-response curve is non-monotonic the additional random effect hyperprior makes the hierarchical EMAX model more adjustable and flexible. However, the normal dynamic linear model (NDLM) is a useful model to explore dose-response relationships in that the efficacy at the current dose depends on the efficacy of the previous dose(s). Previous research has compared the EMAX to the hierarchical EMAX (Gajewski et al., Stat Med. 38:3123-3138 2019) and the EMAX to the NDLM (Liu et al., BMC Med Res Method 17:149 2017), however, the hierarchical EMAX has not been directly compared to the NDLM.

Conclusions

The focus of this paper is to compare these models and discuss the relative merit for each of their uses for an ongoing early phase dose selection study.

Bayesian hierarchical EMAX model for dose-response in early phase efficacy clinical trials

A primary goal of a phase II dose-ranging trial is to identify a correct dose before moving forward to a phase III confirmatory trial. A correct dose is one that is actually better than control. A popular model in phase II is an independent model that puts no structure on the dose-response relationship. Unfortunately, the independent model does not efficiently use information from related doses. One very successful alternate model improves power using a pre-specified dose-response structure. Past research indicates that EMAX models are broadly successful and therefore attractive for designing dose-response trials. However, there may be instances of slight risk of nonmonotone trends that need to be addressed when planning a clinical trial design. We propose to add hierarchical parameters to the EMAX model. The added layer allows information about the treatment effect in one dose to be "borrowed" when estimating the treatment effect in another dose. This is referred to as the hierarchical EMAX model. Our paper compares three different models (independent, EMAX, and hierarchical EMAX) and two different design strategies. The first design considered is Bayesian with a fixed trial design, and it has a fixed schedule for randomization. The second design is Bayesian but adaptive, and it uses response adaptive randomization. In this article, a randomized trial of patients with severe traumatic brain injury is provided as a motivating example.

Fosdagrocorat (PF-04171327) versus prednisone or placebo in rheumatoid arthritis: a randomised, double-blind, multicentre, phase IIb study

Objectives

Glucocorticoids have anti-inflammatory, transrepression-mediated effects, although adverse events (AEs; transactivation-mediated effects) limit long-term use in patients with rheumatoid arthritis (RA). We evaluated the efficacy and safety of fosdagrocorat (PF-04171327), a dissociated agonist of the glucocorticoid receptor, versus prednisone or placebo.

Methods

In this 12-week, phase II, randomised controlled trial, 323 patients with moderate to severe RA were randomised 1:1:1:1:1:1:1 to fosdagrocorat (1 mg, 5 mg, 10 mg or 15 mg), prednisone (5 mg or 10 mg) or placebo, once daily. The primary endpoints (week 8) were American College of Rheumatology 20% improvement criteria (ACR20) responses, and percentage changes from baseline in biomarkers of bone formation (procollagen type 1 N-terminal peptide [P1NP]) and resorption (urinary N-telopeptide to urinary creatinine ratio [uNTx:uCr]). Safety was assessed.

Results

ACR20 responses with fosdagrocorat 10 mg and 15 mg were superior to placebo, and fosdagrocorat 15 mg was non-inferior to prednisone 10 mg (week 8 model-predicted ACR20 responses: 47%, 61%, 69% and 73% vs 51%, 71% and 37% with fosdagrocorat 1 mg, 5 mg, 10 mg and 15 mg vs prednisone 5 mg, 10 mg and placebo, respectively). Percentage changes from baseline in P1NP with fosdagrocorat 1 mg, 5 mg and 10 mg met non-inferiority criteria to prednisone 5 mg. Corresponding changes in uNTx:uCr varied considerably. All fosdagrocorat doses reduced glycosylated haemoglobin levels. AEs were similar between groups; 63 (19.5%) patients reported treatment-related AEs; 9 (2.8%) patients reported serious AEs. No patients had adrenal insufficiency, treatment-related significant infections or laboratory abnormalities. No deaths were reported.

Conclusion

In patients with RA, fosdagrocorat 10 mg and 15 mg demonstrated efficacy similar to prednisone 10 mg and safety similar to prednisone 5 mg.

Trial registration number

NCT01393639

Design considerations and analysis planning of a phase 2a proof of concept study in rheumatoid arthritis in the presence of possible non-monotonicity

Background

It is important to quantify the dose response for a drug in phase 2a clinical trials so the optimal doses can then be selected for subsequent late phase trials. In a phase 2a clinical trial of new lead drug being developed for the treatment of rheumatoid arthritis (RA), a U-shaped dose response curve was observed. In the light of this result further research was undertaken to design an efficient phase 2a proof of concept (PoC) trial for a follow-on compound using the lessons learnt from the lead compound.

Methods

The planned analysis for the Phase 2a trial for GSK123456 was a Bayesian Emax model which assumes the dose-response relationship follows a monotonic sigmoid “S” shaped curve. This model was found to be suboptimal to model the U-shaped dose response observed in the data from this trial and alternatives approaches were needed to be considered for the next compound for which a Normal dynamic linear model (NDLM) is proposed. This paper compares the statistical properties of the Bayesian Emax model and NDLM model and both models are evaluated using simulation in the context of adaptive Phase 2a PoC design under a variety of assumed dose response curves: linear, Emax model, U-shaped model, and flat response.

Results

It is shown that the NDLM method is flexible and can handle a wide variety of dose-responses, including monotonic and non-monotonic relationships. In comparison to the NDLM model the Emax model excelled with higher probability of selecting ED90 and smaller average sample size, when the true dose response followed Emax like curve. In addition, the type I error, probability of incorrectly concluding a drug may work when it does not, is inflated with the Bayesian NDLM model in all scenarios which would represent a development risk to pharmaceutical company.

The bias, which is the difference between the estimated effect from the Emax and NDLM models and the simulated value, is comparable if the true dose response follows a placebo like curve, an Emax like curve, or log linear shape curve under fixed dose allocation, no adaptive allocation, half adaptive and adaptive scenarios. The bias though is significantly increased for the Emax model if the true dose response follows a U-shaped curve.

Conclusions

In most cases the Bayesian Emax model works effectively and efficiently, with low bias and good probability of success in case of monotonic dose response. However, if there is a belief that the dose response could be non-monotonic then the NDLM is the superior model to assess the dose response.

Electronic supplementary material

The online version of this article (10.1186/s12874-017-0416-3) contains supplementary material, which is available to authorized users.

Advanced Methods for Dose and Regimen Finding During Drug Development: Summary of the EMA/EFPIA Workshop on Dose Finding (London 4-5 December 2014)

Inadequate dose selection for confirmatory trials is currently still one of the most challenging issues in drug development, as illustrated by high rates of late‐stage attritions in clinical development and postmarketing commitments required by regulatory institutions. In an effort to shift the current paradigm in dose and regimen selection and highlight the availability and usefulness of well‐established and regulatory‐acceptable methods, the European Medicines Agency (EMA) in collaboration with the European Federation of Pharmaceutical Industries Association (EFPIA) hosted a multistakeholder workshop on dose finding (London 4–5 December 2014). Some methodologies that could constitute a toolkit for drug developers and regulators were presented. These methods are described in the present report: they include five advanced methods for data analysis (empirical regression models, pharmacometrics models, quantitative systems pharmacology models, MCP‐Mod, and model averaging) and three methods for study design optimization (Fisher information matrix (FIM)‐based methods, clinical trial simulations, and adaptive studies). Pairwise comparisons were also discussed during the workshop; however, mostly for historical reasons. This paper discusses the added value and limitations of these methods as well as challenges for their implementation. Some applications in different therapeutic areas are also summarized, in line with the discussions at the workshop. There was agreement at the workshop on the fact that selection of dose for phase III is an estimation problem and should not be addressed via hypothesis testing. Dose selection for phase III trials should be informed by well‐designed dose‐finding studies; however, the specific choice of method(s) will depend on several aspects and it is not possible to recommend a generalized decision tree. There are many valuable methods available, the methods are not mutually exclusive, and they should be used in conjunction to ensure a scientifically rigorous understanding of the dosing rationale.

Phase II dose-response trials: A simulation study to compare analysis method performance under design considerations

Phase II trials are intended to provide information about the dose-response relationship and to support the choice of doses for a pivotal phase III trial. Recently, new analysis methods have been proposed to address these objectives, and guidance is needed to select the most appropriate analysis method in specific situations. We set up a simulation study to evaluate multiple performance measures of one traditional and three more recent dose-finding approaches under four design options and illustrate the investigated analysis methods with an example from clinical practice. Our results reveal no general recommendation for a particular analysis method across all design options and performance measures. However, we also demonstrate that the new analysis methods are worth the effort compared to the traditional ANOVA-based approach.

Asymmetric inner wedge group sequential tests with applications to verifying whether effective drug concentrations are similar in adults and children

Extrapolating from information available on one patient group to support conclusions about another is common in clinical research. For example, the findings of clinical trials, often conducted in highly selective patient cohorts, are routinely extrapolated to wider populations by policy makers. Meanwhile, the results of adult trials may be used to support conclusions about the effects of a medicine in children. For example, if the effective concentration of a drug can be assumed to be similar in adults and children, an appropriate paediatric dosing rule may be found by 'bridging', that is, by matching the adult effective concentration. However, this strategy may result in children receiving an ineffective or hazardous dose if, in fact, effective concentrations differ between adults and children. When there is uncertainty about the equality of effective concentrations, some pharmacokinetic-pharmacodynamic data may be needed in children to verify that differences are small. In this paper, we derive optimal group sequential tests that can be used to verify this assumption efficiently. Asymmetric inner wedge tests are constructed that permit early stopping to accept or reject an assumption of similar effective drug concentrations in adults and children. Asymmetry arises because the consequences of under- and over-dosing may differ. We show how confidence intervals can be obtained on termination of these tests and illustrate the small sample operating characteristics of designs using simulation. Copyright © 2016 John Wiley & Sons, Ltd.

Clinical dose-response for a broad set of biological products: A model-based meta-analysis

Characterizing clinical dose-response is a critical step in drug development. Uncertainty in the dose-response model when planning a dose-ranging study can often undermine efficiency in both the design and analysis of the trial. Results of a previous meta-analysis on a portfolio of small molecule compounds from a large pharmaceutical company demonstrated a consistent dose-response relationship that was well described by the maximal effect model. Biologics are different from small molecules due to their large molecular sizes and their potential to induce immunogenicity. A model-based meta-analysis was conducted on the clinical efficacy of 71 distinct biologics evaluated in 91 placebo-controlled dose-response studies published between 1995 and 2014. The maximal effect model, arising from receptor occupancy theory, described the clinical dose-response data for the majority of the biologics (81.7%, n = 58). Five biologics (7%) with data showing non-monotonic trend assuming the maximal effect model were identified and discussed. A Bayesian model-based hierarchical approach using different joint specifications of prior densities for the maximal effect model parameters was used to meta-analyze the whole set of biologics excluding these five biologics ( n = 66). Posterior predictive distributions of the maximal effect model parameters were reported and they could be used to aid the design of future dose-ranging studies. Compared to the meta-analysis of small molecules, the combination of fewer doses, narrower dosing ranges, and small sample sizes further limited the information available to estimate clinical dose-response among biologics.

Dose-response meta-analysis of differences in means

Background

Meta-analytical methods are frequently used to combine dose-response findings expressed in terms of relative risks. However, no methodology has been established when results are summarized in terms of differences in means of quantitative outcomes.

Methods

We proposed a two-stage approach. A flexible dose-response model is estimated within each study (first stage) taking into account the covariance of the data points (mean differences, standardized mean differences). Parameters describing the study-specific curves are then combined using a multivariate random-effects model (second stage) to address heterogeneity across studies.

Results

The method is fairly general and can accommodate a variety of parametric functions. Compared to traditional non-linear models (e.g. E_max, logistic), spline models do not assume any pre-specified dose-response curve. Spline models allow inclusion of studies with a small number of dose levels, and almost any shape, even non monotonic ones, can be estimated using only two parameters. We illustrated the method using dose-response data arising from five clinical trials on an antipsychotic drug, aripiprazole, and improvement in symptoms in shizoaffective patients. Using the Positive and Negative Syndrome Scale (PANSS), pooled results indicated a non-linear association with the maximum change in mean PANSS score equal to 10.40 (95 % confidence interval 7.48, 13.30) observed for 19.32 mg/day of aripiprazole. No substantial change in PANSS score was observed above this value. An estimated dose of 10.43 mg/day was found to produce 80 % of the maximum predicted response.

Conclusion

The described approach should be adopted to combine correlated differences in means of quantitative outcomes arising from multiple studies. Sensitivity analysis can be a useful tool to assess the robustness of the overall dose-response curve to different modelling strategies. A user-friendly R package has been developed to facilitate applications by practitioners.

Analyzing clinical trial outcomes based on incomplete daily diary reports

A case study is presented assessing the impact of missing data on the analysis of daily diary data from a study evaluating the effect of a drug for the treatment of insomnia. The primary analysis averaged daily diary values for each patient into a weekly variable. Following the commonly used approach, missing daily values within a week were ignored provided there was a minimum number of diary reports (i.e., at least 4). A longitudinal model was then fit with treatment, time, and patient-specific effects. A treatment effect at a pre-specified landmark time was obtained from the model. Weekly values following dropout were regarded as missing, but intermittent daily missing values were obscured. Graphical summaries and tables are presented to characterize the complex missing data patterns. We use multiple imputation for daily diary data to create completed data sets so that exactly 7 daily diary values contribute to each weekly patient average. Standard analysis methods are then applied for landmark analysis of the completed data sets, and the resulting estimates are combined using the standard multiple imputation approach. The observed data are subject to digit heaping and patterned responses (e.g., identical values for several consecutive days), which makes accurate modeling of the response data difficult. Sensitivity analyses under different modeling assumptions for the data were performed, along with pattern mixture models assessing the sensitivity to the missing at random assumption. The emphasis is on graphical displays and computational methods that can be implemented with general-purpose software. Copyright © 2016 John Wiley & Sons, Ltd.

Model selection versus model averaging in dose finding studies

A key objective of Phase II dose finding studies in clinical drug development is to adequately characterize the dose response relationship of a new drug. An important decision is then on the choice of a suitable dose response function to support dose selection for the subsequent Phase III studies. In this paper, we compare different approaches for model selection and model averaging using mathematical properties as well as simulations. We review and illustrate asymptotic properties of model selection criteria and investigate their behavior when changing the sample size but keeping the effect size constant. In a simulation study, we investigate how the various approaches perform in realistically chosen settings. Finally, the different methods are illustrated with a recently conducted Phase II dose finding study in patients with chronic obstructive pulmonary disease. Copyright © 2016 John Wiley & Sons, Ltd.