Discussion on "Bayesian meta-analysis of penetrance for cancer risk" by Thanthirige Lakshika M. Ruberu, Danielle Braun, Giovanni Parmigiani, and Swati Biswas.

We congratulate the authors for the new meta-analysis model that accounts for different outcomes. We discuss the modeling choice and the Bayesian setting, specifically, we point out the connection between the Bayesian hierarchical model and a mixed-effect model formulation to subsequently discuss possible future method extensions.

Bayesian dose regimen assessment in early phase oncology incorporating pharmacokinetics and pharmacodynamics.

Phase I dose-finding trials in oncology seek to find the maximum tolerated dose of a drug under a specific schedule. Evaluating drug schedules aims at improving treatment safety while maintaining efficacy. However, while we can reasonably assume that toxicity increases with the dose for cytotoxic drugs, the relationship between toxicity and multiple schedules remains elusive. We proposed a Bayesian dose regimen assessment method (DRtox) using pharmacokinetics/pharmacodynamics (PK/PD) to estimate the maximum tolerated dose regimen (MTD-regimen) at the end of the dose-escalation stage of a trial. We modeled the binary toxicity via a PD endpoint and estimated the dose regimen toxicity relationship through the integration of a dose regimen PD model and a PD toxicity model. For the first model, we considered nonlinear mixed-effects models, and for the second one, we proposed the following two Bayesian approaches: a logistic model and a hierarchical model. In an extensive simulation study, the DRtox outperformed traditional designs in terms of proportion of correctly selecting the MTD-regimen. Moreover, the inclusion of PK/PD information helped provide more precise estimates for the entire dose regimen toxicity curve; therefore the DRtox may recommend alternative untested regimens for expansion cohorts. The DRtox was developed to be applied at the end of the dose-escalation stage of an ongoing trial for patients with relapsed or refractory acute myeloid leukemia (NCT03594955) once all toxicity and PK/PD data are collected.

A straightforward meta-analysis approach for oncology phase I dose-finding studies.

Phase I early-phase clinical studies aim at investigating the safety and the underlying dose-toxicity relationship of a drug or combination. While little may still be known about the compound's properties, it is crucial to consider quantitative information available from any studies that may have been conducted previously on the same drug. A meta-analytic approach has the advantages of being able to properly account for between-study heterogeneity, and it may be readily extended to prediction or shrinkage applications. Here we propose a simple and robust two-stage approach for the estimation of maximum tolerated dose(s) utilizing penalized logistic regression and Bayesian random-effects meta-analysis methodology. Implementation is facilitated using standard R packages. The properties of the proposed methods are investigated in Monte Carlo simulations. The investigations are motivated and illustrated by two examples from oncology.

Bayesian modeling of a bivariate toxicity outcome for early phase oncology trials evaluating dose regimens.

Most phase I trials in oncology aim to find the maximum tolerated dose (MTD) based on the occurrence of dose limiting toxicities (DLT). Evaluating the schedule of administration in addition to the dose may improve drug tolerance. Moreover, for some molecules, a bivariate toxicity endpoint may be more appropriate than a single endpoint. However, standard dose-finding designs do not account for multiple dose regimens and bivariate toxicity endpoint within the same design. In this context, following a phase I motivating trial, we proposed modeling the first type of DLT, cytokine release syndrome, with the entire dose regimen using pharmacokinetics and pharmacodynamics (PK/PD), whereas the other DLT (DLTo ) was modeled with the cumulative dose. We developed three approaches to model the joint distribution of DLT, defining it as a bivariate binary outcome from the two toxicity types, under various assumptions about the correlation between toxicities: an independent model, a copula model and a conditional model. Our Bayesian approaches were developed to be applied at the end of the dose-allocation stage of the trial, once all data, including PK/PD measurements, were available. The approaches were evaluated through an extensive simulation study that showed that they can improve the performance of selecting the true MTD-regimen compared to the recommendation of the dose-allocation method implemented. Our joint approaches can also predict the DLT probabilities of new dose regimens that were not tested in the study and could be investigated in further stages of the trial.

Dose-finding designs for cumulative toxicities using multiple constraints.

This article addresses the concern regarding late-onset dose-limiting toxicities (DLT), moderate toxicities below the threshold of a DLT and cumulative toxicities that may lead to a DLT, which are mostly disregarded or handled in an ad hoc manner when determining the maximum tolerated dose (MTD) in dose-finding cancer clinical trials. An extension of the Time-to-Event Continual Reassessment Method (TITE-CRM) which allows for the specification of toxicity constraints on both DLT and moderate toxicities, and can account for partial information is proposed. The method is illustrated in the context of an Erlotinib dose-finding trial with low DLT rates, but a significant number of moderate toxicities leading to treatment discontinuation in later cycles. Based on simulations, our method performs well at selecting the dose level that satisfies both the DLT and moderate-toxicity constraints. Moreover, it has similar probability of correct selection compared to the TITE-CRM when the true MTD based on DLT only and the true MTD based on grade 2 or higher toxicities alone coincide, but reduces the probability of recommending a dose above the MTD.

Effect of Hydrocortisone on 21-Day Mortality or Respiratory Support Among Critically Ill Patients With COVID-19: A Randomized Clinical Trial.

Importance: Coronavirus disease 2019 (COVID-19) is associated with severe lung damage. Corticosteroids are a possible therapeutic option. Objective: To determine the effect of hydrocortisone on treatment failure on day 21 in critically ill patients with severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection and acute respiratory failure. Design, Setting, and Participants: Multicenter randomized double-blind sequential trial conducted in France, with interim analyses planned every 50 patients. Patients admitted to the intensive care unit (ICU) for COVID-19-related acute respiratory failure were enrolled from March 7 to June 1, 2020, with last follow-up on June 29, 2020. The study intended to enroll 290 patients but was stopped early following the recommendation of the data and safety monitoring board. Interventions: Patients were randomized to receive low-dose hydrocortisone (n = 76) or placebo (n = 73). Main Outcomes and Measures: The primary outcome, treatment failure on day 21, was defined as death or persistent dependency on mechanical ventilation or high-flow oxygen therapy. Prespecified secondary outcomes included the need for tracheal intubation (among patients not intubated at baseline); cumulative incidences (until day 21) of prone position sessions, extracorporeal membrane oxygenation, and inhaled nitric oxide; Pao2:Fio2 ratio measured daily from day 1 to day 7, then on days 14 and 21; and the proportion of patients with secondary infections during their ICU stay. Results: The study was stopped after 149 patients (mean age, 62.2 years; 30.2% women; 81.2% mechanically ventilated) were enrolled. One hundred forty-eight patients (99.3%) completed the study, and there were 69 treatment failure events, including 11 deaths in the hydrocortisone group and 20 deaths in the placebo group. The primary outcome, treatment failure on day 21, occurred in 32 of 76 patients (42.1%) in the hydrocortisone group compared with 37 of 73 (50.7%) in the placebo group (difference of proportions, -8.6% [95.48% CI, -24.9% to 7.7%]; P = .29). Of the 4 prespecified secondary outcomes, none showed a significant difference. No serious adverse events were related to the study treatment. Conclusions and Relevance: In this study of critically ill patients with COVID-19 and acute respiratory failure, low-dose hydrocortisone, compared with placebo, did not significantly reduce treatment failure (defined as death or persistent respiratory support) at day 21. However, the study was stopped early and likely was underpowered to find a statistically and clinically important difference in the primary outcome. Trial Registration: ClinicalTrials.gov Identifier: NCT02517489.

Recommendations for the design of therapeutic trials for neonatal seizures.

Although seizures have a higher incidence in neonates than any other age group and are associated with significant mortality and neurodevelopmental disability, treatment is largely guided by physician preference and tradition, due to a lack of data from well-designed clinical trials. There is increasing interest in conducting trials of novel drugs to treat neonatal seizures, but the unique characteristics of this disorder and patient population require special consideration with regard to trial design. The Critical Path Institute formed a global working group of experts and key stakeholders from academia, the pharmaceutical industry, regulatory agencies, neonatal nurse associations, and patient advocacy groups to develop consensus recommendations for design of clinical trials to treat neonatal seizures. The broad expertise and perspectives of this group were invaluable in developing recommendations addressing: (1) use of neonate-specific adaptive trial designs, (2) inclusion/exclusion criteria, (3) stratification and randomization, (4) statistical analysis, (5) safety monitoring, and (6) definitions of important outcomes. The guidelines are based on available literature and expert consensus, pharmacokinetic analyses, ethical considerations, and parental concerns. These recommendations will ultimately facilitate development of a Master Protocol and design of efficient and successful drug trials to improve the treatment and outcome for this highly vulnerable population.

Bayesian variable selection based on clinical relevance weights in small sample studies-Application to colon cancer.

Using clinical data to model the medical decisions behind sequential treatment actions raises methodological challenges. Physicians often have access to many covariates that may be used when making sequential treatment decisions for individual patients. Statistical variable selection methods may help finding which of these variables are used for this decision in everyday practice. When the sample size is not large, Bayesian variable selection methods can address this setting and allow for expert information to be incorporated into prior distributions. Motivated by clinical practice data involving repeated dose adaptation for Irinotecan in colorectal metastatic cancer, we propose a modification of the stochastic search variable selection (SSVS) method, which we call weight-based SSVS (WBS). We use clinical relevance weights elicited from physician experts to construct prior distributions, with the goal to identify the most influential toxicities and other covariates used for dose adjustment. We evaluate and compare the WBS model performance to the Lasso and SSVS through an extensive simulation study. The simulations show that WBS has better performance and lower rates of false positives and false negatives than the other methods but depends strongly on the covariate weights.

A Bayesian non-inferiority approach using experts' margin elicitation - application to the monitoring of safety events.

BACKGROUND: When conducing Phase-III trial, regulatory agencies and investigators might want to get reliable information about rare but serious safety outcomes during the trial. Bayesian non-inferiority approaches have been developed, but commonly utilize historical placebo-controlled data to define the margin, depend on a single final analysis, and no recommendation is provided to define the prespecified decision threshold. In this study, we propose a non-inferiority Bayesian approach for sequential monitoring of rare dichotomous safety events incorporating experts' opinions on margins. METHODS: A Bayesian decision criterion was constructed to monitor four safety events during a non-inferiority trial conducted on pregnant women at risk for premature delivery. Based on experts' elicitation, margins were built using mixtures of beta distributions that preserve experts' variability. Non-informative and informative prior distributions and several decision thresholds were evaluated through an extensive sensitivity analysis. The parameters were selected in order to maintain two rates of misclassifications under prespecified rates, that is, trials that wrongly concluded an unacceptable excess in the experimental arm, or otherwise. RESULTS: The opinions of 44 experts were elicited about each event non-inferiority margins and its relative severity. In the illustrative trial, the maximal misclassification rates were adapted to events' severity. Using those maximal rates, several priors gave good results and one of them was retained for all events. Each event was associated with a specific decision threshold choice, allowing for the consideration of some differences in their prevalence, margins and severity. Our decision rule has been applied to a simulated dataset. CONCLUSIONS: In settings where evidence is lacking and where some rare but serious safety events have to be monitored during non-inferiority trials, we propose a methodology that avoids an arbitrary margin choice and helps in the decision making at each interim analysis. This decision rule is parametrized to consider the rarity and the relative severity of the events and requires a strong collaboration between physicians and the trial statisticians for the benefit of all. This Bayesian approach could be applied as a complement to the frequentist analysis, so both Data Safety Monitoring Boards and investigators can benefit from such an approach.

Bayesian sample size determination for phase IIA clinical trials using historical data and semi-parametric prior's elicitation.

The Simon's two-stage design is the most commonly applied among multi-stage designs in phase IIA clinical trials. It combines the sample sizes at the two stages in order to minimize either the expected or the maximum sample size. When the uncertainty about pre-trial beliefs on the expected or desired response rate is high, a Bayesian alternative should be considered since it allows to deal with the entire distribution of the parameter of interest in a more natural way. In this setting, a crucial issue is how to construct a distribution from the available summaries to use as a clinical prior in a Bayesian design. In this work, we explore the Bayesian counterparts of the Simon's two-stage design based on the predictive version of the single threshold design. This design requires specifying two prior distributions: the analysis prior, which is used to compute the posterior probabilities, and the design prior, which is employed to obtain the prior predictive distribution. While the usual approach is to build beta priors for carrying out a conjugate analysis, we derived both the analysis and the design distributions through linear combinations of B-splines. The motivating example is the planning of the phase IIA two-stage trial on anti-HER2 DNA vaccine in breast cancer, where initial beliefs formed from elicited experts' opinions and historical data showed a high level of uncertainty. In a sample size determination problem, the impact of different priors is evaluated.

Value of information methods to design a clinical trial in a small population to optimise a health economic utility function.

BACKGROUND: Most confirmatory randomised controlled clinical trials (RCTs) are designed with specified power, usually 80% or 90%, for a hypothesis test conducted at a given significance level, usually 2.5% for a one-sided test. Approval of the experimental treatment by regulatory agencies is then based on the result of such a significance test with other information to balance the risk of adverse events against the benefit of the treatment to future patients. In the setting of a rare disease, recruiting sufficient patients to achieve conventional error rates for clinically reasonable effect sizes may be infeasible, suggesting that the decision-making process should reflect the size of the target population. METHODS: We considered the use of a decision-theoretic value of information (VOI) method to obtain the optimal sample size and significance level for confirmatory RCTs in a range of settings. We assume the decision maker represents society. For simplicity we assume the primary endpoint to be normally distributed with unknown mean following some normal prior distribution representing information on the anticipated effectiveness of the therapy available before the trial. The method is illustrated by an application in an RCT in haemophilia A. We explicitly specify the utility in terms of improvement in primary outcome and compare this with the costs of treating patients, both financial and in terms of potential harm, during the trial and in the future. RESULTS: The optimal sample size for the clinical trial decreases as the size of the population decreases. For non-zero cost of treating future patients, either monetary or in terms of potential harmful effects, stronger evidence is required for approval as the population size increases, though this is not the case if the costs of treating future patients are ignored. CONCLUSIONS: Decision-theoretic VOI methods offer a flexible approach with both type I error rate and power (or equivalently trial sample size) depending on the size of the future population for whom the treatment under investigation is intended. This might be particularly suitable for small populations when there is considerable information about the patient population.

Approaches to sample size calculation for clinical trials in rare diseases.

We discuss 3 alternative approaches to sample size calculation: traditional sample size calculation based on power to show a statistically significant effect, sample size calculation based on assurance, and sample size based on a decision-theoretic approach. These approaches are compared head-to-head for clinical trial situations in rare diseases. Specifically, we consider 3 case studies of rare diseases (Lyell disease, adult-onset Still disease, and cystic fibrosis) with the aim to plan the sample size for an upcoming clinical trial. We outline in detail the reasonable choice of parameters for these approaches for each of the 3 case studies and calculate sample sizes. We stress that the influence of the input parameters needs to be investigated in all approaches and recommend investigating different sample size approaches before deciding finally on the trial size. Highly influencing for the sample size are choice of treatment effect parameter in all approaches and the parameter for the additional cost of the new treatment in the decision-theoretic approach. These should therefore be discussed extensively.

Dose-finding methods for Phase I clinical trials using pharmacokinetics in small populations.

The aim of phase I clinical trials is to obtain reliable information on safety, tolerability, pharmacokinetics (PK), and mechanism of action of drugs with the objective of determining the maximum tolerated dose (MTD). In most phase I studies, dose-finding and PK analysis are done separately and no attempt is made to combine them during dose allocation. In cases such as rare diseases, paediatrics, and studies in a biomarker-defined subgroup of a defined population, the available population size will limit the number of possible clinical trials that can be conducted. Combining dose-finding and PK analyses to allow better estimation of the dose-toxicity curve should then be considered. In this work, we propose, study, and compare methods to incorporate PK measures in the dose allocation process during a phase I clinical trial. These methods do this in different ways, including using PK observations as a covariate, as the dependent variable or in a hierarchical model. We conducted a large simulation study that showed that adding PK measurements as a covariate only does not improve the efficiency of dose-finding trials either in terms of the number of observed dose limiting toxicities or the probability of correct dose selection. However, incorporating PK measures does allow better estimation of the dose-toxicity curve while maintaining the performance in terms of MTD selection compared to dose-finding designs that do not incorporate PK information. In conclusion, using PK information in the dose allocation process enriches the knowledge of the dose-toxicity relationship, facilitating better dose recommendation for subsequent trials.

Determination of the optimal sample size for a clinical trial accounting for the population size.

The problem of choosing a sample size for a clinical trial is a very common one. In some settings, such as rare diseases or other small populations, the large sample sizes usually associated with the standard frequentist approach may be infeasible, suggesting that the sample size chosen should reflect the size of the population under consideration. Incorporation of the population size is possible in a decision-theoretic approach either explicitly by assuming that the population size is fixed and known, or implicitly through geometric discounting of the gain from future patients reflecting the expected population size. This paper develops such approaches. Building on previous work, an asymptotic expression is derived for the sample size for single and two-arm clinical trials in the general case of a clinical trial with a primary endpoint with a distribution of one parameter exponential family form that optimizes a utility function that quantifies the cost and gain per patient as a continuous function of this parameter. It is shown that as the size of the population, N, or expected size, N∗ in the case of geometric discounting, becomes large, the optimal trial size is O(N1/2) or O(N∗1/2). The sample size obtained from the asymptotic expression is also compared with the exact optimal sample size in examples with responses with Bernoulli and Poisson distributions, showing that the asymptotic approximations can also be reasonable in relatively small sample sizes.

Designing a Pediatric Study for an Antimalarial Drug by Using Information from Adults.

The objectives of this study were to design a pharmacokinetic (PK) study by using information about adults and evaluate the robustness of the recommended design through a case study of mefloquine. PK data about adults and children were available from two different randomized studies of the treatment of malaria with the same artesunate-mefloquine combination regimen. A recommended design for pediatric studies of mefloquine was optimized on the basis of an extrapolated model built from adult data through the following approach. (i) An adult PK model was built, and parameters were estimated by using the stochastic approximation expectation-maximization algorithm. (ii) Pediatric PK parameters were then obtained by adding allometry and maturation to the adult model. (iii) A D-optimal design for children was obtained with PFIM by assuming the extrapolated design. Finally, the robustness of the recommended design was evaluated in terms of the relative bias and relative standard errors (RSE) of the parameters in a simulation study with four different models and was compared to the empirical design used for the pediatric study. Combining PK modeling, extrapolation, and design optimization led to a design for children with five sampling times. PK parameters were well estimated by this design with few RSE. Although the extrapolated model did not predict the observed mefloquine concentrations in children very accurately, it allowed precise and unbiased estimates across various model assumptions, contrary to the empirical design. Using information from adult studies combined with allometry and maturation can help provide robust designs for pediatric studies.

An extension of Bayesian predictive sample size selection designs for monitoring efficacy and safety.

Most exploratory clinical trials in cancer are designed as single-arm trials using a binary efficacy outcome with or without interim monitoring. In this context, we have proposed a Bayesian adaptive design denoted as predictive sample size selection design (PSSD), which considered a binary efficacy outcome associated with early futility stopping (Statistics in Medicine 2012; 31: 4243-4254). As a matter of course, it would be more ethical and informative to evaluate safety as well as efficacy during the course of a trial. However, in most of the trials, only major adverse events are taken into account for early termination of the trial, and safety itself is used as a secondary endpoint. In this paper, we propose an extension of the PSSD to monitor efficacy, take into consideration the sample size adaptation during the trial and add continuous monitoring of safety to the trial design. This method is developed in the Bayesian framework, in which a decision to stop for reasons of safety can be made based on the posterior probability or predictive probability, not necessarily at the time of pre-specified monitoring for efficacy. We investigate the operating characteristics of the proposed method through simulation studies and show that the posterior probability-based method with less informative prior to monitor safety has more reasonable performance.

A Bayesian dose-finding design for drug combination clinical trials based on the logistic model.

In early phase dose-finding cancer studies, the objective is to determine the maximum tolerated dose, defined as the highest dose with an acceptable dose-limiting toxicity rate. Finding this dose for drug-combination trials is complicated because of drug-drug interactions, and many trial designs have been proposed to address this issue. These designs rely on complicated statistical models that typically are not familiar to clinicians, and are rarely used in practice. The aim of this paper is to propose a Bayesian dose-finding design for drug combination trials based on standard logistic regression. Under the proposed design, we continuously update the posterior estimates of the model parameters to make the decisions of dose assignment and early stopping. Simulation studies show that the proposed design is competitive and outperforms some existing designs. We also extend our design to handle delayed toxicities.

Bayesian framework for multi-source data integration-Application to human extrapolation from preclinical studies.

In preclinical investigations, for example, in in vitro, in vivo, and in silico studies, the pharmacokinetic, pharmacodynamic, and toxicological characteristics of a drug are evaluated before advancing to first-in-man trial. Usually, each study is analyzed independently and the human dose range does not leverage the knowledge gained from all studies. Taking into account all preclinical data through inferential procedures can be particularly interesting in obtaining a more precise and reliable starting dose and dose range. Our objective is to propose a Bayesian framework for multi-source data integration, customizable, and tailored to the specific research question. We focused on preclinical results extrapolated to humans, which allowed us to predict the quantities of interest (e.g. maximum tolerated dose, etc.) in humans. We build an approach, divided into four steps, based on a sequential parameter estimation for each study, extrapolation to human, commensurability checking between posterior distributions and final information merging to increase the precision of estimation. The new framework is evaluated via an extensive simulation study, based on a real-life example in oncology. Our approach allows us to better use all the information compared to a standard framework, reducing uncertainty in the predictions and potentially leading to a more efficient dose selection.

Application of the continual reassessment method to dose-finding studies in regional anesthesia: an estimate of the ED95 dose for 0.5% bupivacaine for ultrasound-guided supraclavicular block.

BACKGROUND: Previously reported estimates of the ED95 doses for local anesthetics used in brachial plexus blocks vary. The authors used the continual reassessment method, already established in oncology trials, to determine the ED95 dose for 0.5% bupivacaine for the ultrasound-guided supraclavicular block. METHODS: A double-blind, prospective trial was scheduled for 40 patients of American Society of Anesthesiologists class I-III presenting for upper limb surgery and supraclavicular block. The study dose to be administered was arbitrarily divided into six dose levels (12, 15, 18, 21, 24, and 27 ml) with a priori probabilities of success of 0.5, 0.75, 0.90, 0.95, 0.98, and 0.99 respectively. A continual reassessment method statistical program created a dose-response curve, which would shift direction depending on the success or failure of the block. Our starting dose was 21 ml and the next allocated dose was reestimated by the program to be the dose level with the updated posterior response probability closest to 0.95. RESULTS: After recruitment of eight patients, our initial dose levels and associated probabilities were deemed too low to determine the ED95. Updated a prioris were calculated from the statistical program, and the study recommenced with a new starting dose of 30 ml. On completion, the ED95 dose was estimated to be 27 ml (95% CI, 24-28 ml). CONCLUSIONS: The continual reassessment method trial design provided a credible estimate for the ED95 dose for 0.5% bupivacaine for our technique of supraclavicular block and may be of value as a statistically robust method for dose-finding studies in anesthesiology.

Dose-finding designs using a novel quasi-continuous endpoint for multiple toxicities.

The aim of a phase I oncology trial is to identify a dose with an acceptable safety profile. Most phase I designs use the dose-limiting toxicity, a binary endpoint, to assess the unacceptable level of toxicity. The dose-limiting toxicity might be incomplete for investigating molecularly targeted therapies as much useful toxicity information is discarded. In this work, we propose a quasi-continuous toxicity score, the total toxicity profile (TTP), to measure quantitatively and comprehensively the overall severity of multiple toxicities. We define the TTP as the Euclidean norm of the weights of toxicities experienced by a patient, where the weights reflect the relative clinical importance of each grade and toxicity type. We propose a dose-finding design, the quasi-likelihood continual reassessment method (CRM), incorporating the TTP score into the CRM, with a logistic model for the dose-toxicity relationship in a frequentist framework. Using simulations, we compared our design with three existing designs for quasi-continuous toxicity score (the Bayesian quasi-CRM with an empiric model and two nonparametric designs), all using the TTP score, under eight different scenarios. All designs using the TTP score to identify the recommended dose had good performance characteristics for most scenarios, with good overdosing control. For a sample size of 36, the percentage of correct selection for the quasi-likelihood CRM ranged from 80% to 90%, with similar results for the quasi-CRM design. These designs with TTP score present an appealing alternative to the conventional dose-finding designs, especially in the context of molecularly targeted agents.