Bayesian joint modeling of multivariate longitudinal and survival outcomes using Gaussian copulas.

There is an increasing interest in the use of joint models for the analysis of longitudinal and survival data. While random effects models have been extensively studied, these models can be hard to implement and the fixed effect regression parameters must be interpreted conditional on the random effects. Copulas provide a useful alternative framework for joint modeling. One advantage of using copulas is that practitioners can directly specify marginal models for the outcomes of interest. We develop a joint model using a Gaussian copula to characterize the association between multivariate longitudinal and survival outcomes. Rather than using an unstructured correlation matrix in the copula model to characterize dependence structure as is common, we propose a novel decomposition that allows practitioners to impose structure (e.g., auto-regressive) which provides efficiency gains in small to moderate sample sizes and reduces computational complexity. We develop a Markov chain Monte Carlo model fitting procedure for estimation. We illustrate the method's value using a simulation study and present a real data analysis of longitudinal quality of life and disease-free survival data from an International Breast Cancer Study Group trial.

Bayesian design of clinical trials using joint models for recurrent and terminating events.

Joint models for recurrent event and terminating event data are increasingly used for the analysis of clinical trials. However, few methods have been proposed for designing clinical trials using these models. In this article, we develop a Bayesian clinical trial design methodology focused on evaluating the effect of an investigational product (IP) on both recurrent event and terminating event processes considered as multiple primary endpoints, using a multifrailty joint model. Dependence between the recurrent and terminating event processes is accounted for using a shared frailty. Inferences for the multiple primary outcomes are based on posterior model probabilities corresponding to mutually exclusive hypotheses regarding the benefit of IP with respect to the recurrent and terminating event processes. We propose an approach for sample size determination to ensure the trial design has a high power and a well-controlled type I error rate, with both operating characteristics defined from a Bayesian perspective. We also consider a generalization of the proposed parametric model that uses a nonparametric mixture of Dirichlet processes to model the frailty distributions and compare its performance to the proposed approach. We demonstrate the methodology by designing a colorectal cancer clinical trial with a goal of demonstrating that the IP causes a favorable effect on at least one of the two outcomes but no harm on either.

A generalized phase 1-2-3 design integrating dose optimization with confirmatory treatment comparison.

A generalized phase 1-2-3 design, Gen 1-2-3, that includes all phases of clinical treatment evaluation is proposed. The design extends and modifies the design of Chapple and Thall (2019), denoted by CT. Both designs begin with a phase 1-2 trial including dose acceptability and optimality criteria, and both select an optimal dose for phase 3. The Gen 1-2-3 design has the following key differences. In stage 1, it uses phase 1-2 criteria to identify a set of candidate doses rather than 1 dose. In stage 2, which is intermediate between phase 1-2 and phase 3, it randomizes additional patients fairly among the candidate doses and an active control treatment arm and uses survival time data from both stage 1 and stage 2 patients to select an optimal dose. It then makes a Go/No Go decision of whether or not to conduct phase 3 based on the predictive probability that the selected optimal dose will provide a specified substantive improvement in survival time over the control. A simulation study shows that the Gen 1-2-3 design has desirable operating characteristics compared to the CT design and 2 conventional designs.

Improved mortality analysis in early-phase dose-ranging clinical trials for emergency medical diseases using Bayesian time-to-event models with active comparators.

Emergency medical diseases (EMDs) are the leading cause of death worldwide. A time-to-death analysis is needed to accurately identify the risks and describe the pattern of an EMD because the mortality rate can peak early and then decline. Dose-ranging Phase II clinical trials are essential for developing new therapies for EMDs. However, most dose-finding trials do not analyze mortality as a time-to-event endpoint. We propose three Bayesian dose-response time-to-event models for a secondary mortality analysis of a clinical trial: a two-group (active treatment vs control) model, a three-parameter sigmoid EMAX model, and a hierarchical EMAX model. The study also incorporates one specific active treatment as an active comparator in constructing three new models. We evaluated the performance of these six models and a very popular independent model using simulated data motivated by a randomized Phase II clinical trial focused on identifying the most effective hyperbaric oxygen dose to achieve favorable functional outcomes in patients with severe traumatic brain injury. The results show that the three-group, EMAX, and EMAX model with an active comparator produce the smallest averaged mean squared errors and smallest mean absolute biases. We provide a new approach for time-to-event analysis in early-phase dose-ranging clinical trials for EMDs. The EMAX model with an active comparator can provide valuable insights into the mortality analysis of new EMDs or other conditions that have changing risks over time. The restricted mean survival time, a function of the model's hazards, is recommended for displaying treatment effects for EMD research.

Propensity score weighted multi-source exchangeability models for incorporating external control data in randomized clinical trials.

Among clinical trialists, there has been a growing interest in using external data to improve decision-making and accelerate drug development in randomized clinical trials (RCTs). Here we propose a novel approach that combines the propensity score weighting (PW) and the multi-source exchangeability modelling (MEM) approaches to augment the control arm of a RCT in the rare disease setting. First, propensity score weighting is used to construct weighted external controls that have similar observed pre-treatment characteristics as the current trial population. Next, the MEM approach evaluates the similarity in outcome distributions between the weighted external controls and the concurrent control arm. The amount of external data we borrow is determined by the similarities in pretreatment characteristics and outcome distributions. The proposed approach can be applied to binary, continuous and count data. We evaluate the performance of the proposed PW-MEM method and several competing approaches based on simulation and re-sampling studies. Our results show that the PW-MEM approach improves the precision of treatment effect estimates while reducing the biases associated with borrowing data from external sources.

Fractional accumulative calibration-free odds (f-aCFO) design for delayed toxicity in phase I clinical trials.

The calibration-free odds (CFO) design has been demonstrated to be robust, model-free, and practically useful but faces challenges when dealing with late-onset toxicity. The emergence of the time-to-event (TITE) method and fractional method leads to the development of TITE-CFO and fractional CFO (fCFO) designs to accumulate delayed toxicity. Nevertheless, existing CFO-type designs have untapped potential because they primarily consider dose information from the current position and its two neighboring positions. To incorporate information from all doses, we propose the accumulative CFO (aCFO) design by utilizing data at all dose levels similar to a tug-of-war game where players distant from the center also contribute their strength. This approach enhances full information utilization while still preserving the model-free and calibration-free characteristics. Extensive simulation studies demonstrate performance improvement over the original CFO design, emphasizing the advantages of incorporating information from a broader range of dose levels. Furthermore, we propose to incorporate late-onset outcomes into the TITE-aCFO and f-aCFO designs, with f-aCFO displaying superior performance over existing methods in both fixed and random simulation scenarios. In conclusion, the aCFO and f-aCFO designs can be considered robust, efficient, and user-friendly approaches for conducting phase I trials without or with late-onsite toxicity.

Phase I/II Design for Selecting Subgroup-Specific Optimal Biological Doses for Prespecified Subgroups.

We propose a phase I/II trial design to support dose-finding when the optimal biological dose (OBD) may differ in two prespecified patient subgroups. The proposed design uses a utility function to quantify efficacy-toxicity trade-offs, and a Bayesian model with spike and slab prior distributions for the subgroup effect on toxicity and efficacy to guide dosing and to facilitate identifying either subgroup-specific OBDs or a common OBD depending on the resulting trial data. In a simulation study, we find the proposed design performs nearly as well as a design that ignores subgroups when the dose-toxicity and dose-efficacy relationships are the same in both subgroups, and nearly as well as a design with independent dose-finding within each subgroup when these relationships differ across subgroups. In other words, the proposed adaptive design performs similarly to the design that would be chosen if investigators possessed foreknowledge about whether the dose-toxicity and/or dose-efficacy relationship differs across two prespecified subgroups. Thus, the proposed design may be effective for OBD selection when uncertainty exists about whether the OBD differs in two prespecified subgroups.

On the distribution of the power function for the scale parameter of exponential families.

The expected value of the standard power function of a test, computed with respect to a design prior distribution, is often used to evaluate the probability of success of an experiment. However, looking only at the expected value might be reductive. Instead, the whole probability distribution of the power function induced by the design prior can be exploited. In this article we consider one-sided testing for the scale parameter of exponential families and we derive general unifying expressions for cumulative distribution and density functions of the random power. Sample size determination criteria based on alternative summaries of these functions are discussed. The study sheds light on the relevance of the choice of the design prior in order to construct a successful experiment.

Bayesian optimal stepped wedge design.

Recently, there has been a growing interest in designing cluster trials using stepped wedge design (SWD). An SWD is a type of cluster-crossover design in which clusters of individuals are randomized unidirectional from a control to an intervention at certain time points. The intraclass correlation coefficient (ICC) that measures the dependency of subject within a cluster plays an important role in design and analysis of stepped wedge trials. In this paper, we discuss a Bayesian approach to address the dependency of SWD on the ICC and robust Bayesian SWDs are proposed. Bayesian design is shown to be more robust against the misspecification of the parameter values compared to the locally optimal design. Designs are obtained for the various choices of priors assigned to the ICC. A detailed sensitivity analysis is performed to assess the robustness of proposed optimal designs. The power superiority of Bayesian design against the commonly used balanced design is demonstrated numerically using hypothetical as well as real scenarios.

Bayesian design of clinical trials using joint models for longitudinal and time-to-event data.

Joint models for longitudinal and time-to-event data are increasingly used for the analysis of clinical trial data. However, few methods have been proposed for designing clinical trials using these models. In this article, we develop a Bayesian clinical trial design methodology focused on evaluating the treatment's effect on the time-to-event endpoint using a flexible trajectory joint model. By incorporating the longitudinal outcome trajectory into the hazard model for the time-to-event endpoint, the joint modeling framework allows for non-proportional hazards (e.g., an increasing hazard ratio over time). Inference for the time-to-event endpoint is based on an average of a time-varying hazard ratio which can be decomposed according to the treatment's direct effect on the time-to-event endpoint and its indirect effect, mediated through the longitudinal outcome. We propose an approach for sample size determination for a trial such that the design has high power and a well-controlled type I error rate with both operating characteristics defined from a Bayesian perspective. We demonstrate the methodology by designing a breast cancer clinical trial with a primary time-to-event endpoint and where predictive longitudinal outcome measures are also collected periodically during follow-up.

Bayesian treatment screening and selection using subgroup-specific utilities of response and toxicity.

A Bayesian design is proposed for randomized phase II clinical trials that screen multiple experimental treatments compared to an active control based on ordinal categorical toxicity and response. The underlying model and design account for patient heterogeneity characterized by ordered prognostic subgroups. All decision criteria are subgroup specific, including interim rules for dropping unsafe or ineffective treatments, and criteria for selecting optimal treatments at the end of the trial. The design requires an elicited utility function of the two outcomes that varies with the subgroups. Final treatment selections are based on posterior mean utilities. The methodology is illustrated by a trial of targeted agents for metastatic renal cancer, which motivated the design methodology. In the context of this application, the design is evaluated by computer simulation, including comparison to three designs that conduct separate trials within subgroups, or conduct one trial while ignoring subgroups, or base treatment selection on estimated response rates while ignoring toxicity.

Selection of a statistical analysis method for the Glasgow Outcome Scale-Extended endpoint for estimating the probability of favorable outcome in future severe TBI clinical trials.

The Glasgow outcome scale-extended (GOS-E), an ordinal scale measure, is often selected as the endpoint for clinical trials of traumatic brain injury (TBI). Traditionally, GOS-E is analyzed as a fixed dichotomy with favorable outcome defined as GOS-E ≥ 5 and unfavorable outcome as GOS-E < 5. More recent studies have defined favorable vs unfavorable outcome utilizing a sliding dichotomy of the GOS-E that defines a favorable outcome as better than a subject's predicted prognosis at baseline. Both dichotomous approaches result in loss of statistical and clinical information. To improve on power, Yeatts et al proposed a sliding scoring of the GOS-E as the distance from the cutoff for favorable/unfavorable outcomes, and therefore used more information found in the original GOS-E to estimate the probability of favorable outcome. We used data from a published TBI trial to explore the ramifications to trial operating characteristics by analyzing the sliding scoring of the GOS-E as either dichotomous, continuous, or ordinal. We illustrated a connection between the ordinal data and time-to-event (TTE) data to allow use of Bayesian software that utilizes TTE-based modeling. The simulation results showed that the continuous method with continuity correction offers higher power and lower mean squared error for estimating the probability of favorable outcome compared to the dichotomous method, and similar power but higher precision compared to the ordinal method. Therefore, we recommended that future severe TBI clinical trials consider analyzing the sliding scoring of the GOS-E endpoint as continuous with continuity correction.

Bayesian design and analysis of two-arm cluster randomized trials using assurance.

We consider the design of a two-arm superiority cluster randomized controlled trial (RCT) with a continuous outcome. We detail Bayesian inference for the analysis of the trial using a linear mixed-effects model. The treatment is compared to control using the posterior distribution for the treatment effect. We develop the form of the assurance to choose the sample size based on this analysis, and its evaluation using a two loop Monte Carlo sampling scheme. We assess the proposed approach, considering the effect of different forms of prior distribution, and the number of Monte Carlo samples needed in both loops for accurate determination of the assurance and sample size. Based on this assessment, we provide general advice on each of these choices. We apply the approach to the choice of sample size for a cluster RCT into poststroke incontinence, and compare the resulting sample size to that from assurance based on a Wald test for the treatment effect. The Bayesian approach to design and analysis developed in this article can offer advantages in terms of an increase in the robustness of the chosen sample size to parameter mis-specification and reduced sample sizes if prior information indicates the treatment effect is likely to be larger than the minimal clinically important difference.

A randomized Bayesian optimal phase II design with binary endpoint.

In this paper, we propose a randomized Bayesian optimal phase II (RBOP2) design with a binary endpoint (e.g., response rate). A beta-binomial distribution is used to model the binary endpoint for a two-arm phase II trial. Posterior probabilities of the endpoint of interest are evaluated at each interim look and used in the decision to stop the trial due to futility. Compared with other Bayesian designs, the proposed RBOP2 design has the following merits: (i) strongly controls the type I error rate at a pre-defined level; (ii) optimizes the stopping boundaries, thus maximizing the power to detect treatment effects and minimizing the expected sample size for futile treatment; (iii) does not limit the number of interim looks, thus enabling frequent trial monitoring; and (iv) allows the stopping boundaries to be pre-defined in the protocol and is easy to implement. We conduct simulation studies to compare the proposed design with a group sequential design and other Bayesian randomized designs and evaluate its operating characteristics under different scenarios.

MIDAS-2: an enhanced Bayesian platform design for immunotherapy combinations with subgroup efficacy exploration.

Although immunotherapy combinations have revolutionised cancer treatment, the rapid screening of effective and optimal therapies from large numbers of candidate combinations, as well as exploring subgroup efficacy, remains challenging. This necessitates innovative, integrated, and efficient trial designs. In this study, we extend the MIDAS design to include subgroup exploration and propose an enhanced Bayesian information borrowing platform design called MIDAS-2. MIDAS-2 enables quick and continuous screening of promising combination strategies and exploration of their subgroup effects within a unified platform design framework. We use a regression model to characterize the efficacy pattern in subgroups. Information borrowing is applied through Bayesian hierarchical modelling to improve trial efficiency considering the limited sample size in subgroups. Time trend calibration is also employed to avoid potential baseline drifts. Simulation results demonstrate that MIDAS-2 yields high probabilities for identifying the effective drug combinations as well as promising subgroups, facilitating appropriate selection of the best treatments for each subgroup. The proposed design is robust against small time trend drifts, and the type I error is successfully controlled after calibration when a large drift is expected. Overall, MIDAS-2 provides an adaptive drug screening and subgroup exploring framework to accelerate immunotherapy development in an efficient, accurate, and integrated fashion.

Time-to-event calibration-free odds design: A robust efficient design for phase I trials with late-onset outcomes.

Compared with most of the existing phase I designs, the recently proposed calibration-free odds (CFO) design has been demonstrated to be robust, model-free, and easy to use in practice. However, the original CFO design cannot handle late-onset toxicities, which have been commonly encountered in phase I oncology dose-finding trials with targeted agents or immunotherapies. To account for late-onset outcomes, we extend the CFO design to its time-to-event (TITE) version, which inherits the calibration-free and model-free properties. One salient feature of CFO-type designs is to adopt game theory by competing three doses at a time, including the current dose and the two neighboring doses, while interval-based designs only use the data at the current dose and is thus less efficient. We conduct comprehensive numerical studies for the TITE-CFO design under both fixed and randomly generated scenarios. TITE-CFO shows robust and efficient performances compared with interval-based and model-based counterparts. As a conclusion, the TITE-CFO design provides robust, efficient, and easy-to-use alternatives for phase I trials when the toxicity outcome is late-onset.

Generalized phase I-II designs to increase long term therapeutic success rate.

Designs for early phase dose finding clinical trials typically are either phase I based on toxicity, or phase I-II based on toxicity and efficacy. These designs rely on the implicit assumption that the dose of an experimental agent chosen using these short-term outcomes will maximize the agent's long-term therapeutic success rate. In many clinical settings, this assumption is not true. A dose selected in an early phase oncology trial may give suboptimal progression-free survival or overall survival time, often due to a high rate of relapse following response. To address this problem, a new family of Bayesian generalized phase I-II designs is proposed. First, a conventional phase I-II design based on short-term outcomes is used to identify a set of candidate doses, rather than selecting one dose. Additional patients then are randomized among the candidates, patients are followed for a predefined longer time period, and a final dose is selected to maximize the long-term therapeutic success rate, defined in terms of duration of response. Dose-specific sample sizes in the randomization are determined adaptively to obtain a desired level of selection reliability. The design was motivated by a phase I-II trial to find an optimal dose of natural killer cells as targeted immunotherapy for recurrent or treatment-resistant B-cell hematologic malignancies. A simulation study shows that, under a range of scenarios in the context of this trial, the proposed design has much better performance than two conventional phase I-II designs.

Bayesian Design of Clinical Trials Using Joint Cure Rate Models for Longitudinal and Time-to-Event Data.

For clinical trial design and analysis, there has been extensive work related to using joint models for longitudinal and time-to-event data without a cure fraction (i.e., when all patients are at risk for the event of interest), but comparatively little treatment has been given to design and analysis of clinical trials using joint models that incorporate a cure fraction. In this paper, we develop a Bayesian clinical trial design methodology focused on evaluating the treatment's effect on a time-to-event endpoint using a promotion time cure rate model, where the longitudinal process is incorporated into the hazard model for the promotion times. A piecewise linear hazard model for the period after assessment of the longitudinal measure ends is proposed as an alternative to extrapolating the longitudinal trajectory. This may be advantageous in scenarios where the period of time from the end of longitudinal measurements until the end of observation is substantial. Inference for the time-to-event endpoint is based on a novel estimand which combines the treatment's effect on the probability of cure and its effect on the promotion time distribution, mediated by the longitudinal outcome. We propose an approach for sample size determination such that the design has a high power and a well-controlled type I error rate with both operating characteristics defined from a Bayesian perspective. We demonstrate the methodology by designing a breast cancer clinical trial with a primary time-to-event endpoint where longitudinal outcomes are measured periodically during follow up.

Optimal sample size determination for single-arm trials in pediatric and rare populations with Bayesian borrowing.

In many therapeutic areas with unmet medical needs, such as pediatric oncology and rare diseases, one of the deterrent factors for clinical trial interpretability is the limited sample size with less-than-ideal operating characteristics. Single arm is usually the only viable design due to feasibility and ethical concerns. For the trial results to be more interpretable and conclusive, the evaluation of operating characteristics, such as type I error rate and power, and the appropriate utilization of prior information for study design, shall be prespecified and fully investigated during the trial planning phase. So far, very few existing literature addressed optimal sample size determination issues for the planning of pediatric and rare population trials, with majority of research focusing on analysis perspective with focus on Bayesian borrowing. In practice, when a single-arm trial is designed for rare population, it is not uncommon that the only information available is from an earlier trial and/or a few clinical publications based on observational studies, often constituting mixed or uncertain conclusions. In light of this, an optimal Bayesian sample size determination method for single-arm trial with binary or continuous endpoint is proposed, where conflicting prior beliefs can be readily incorporated. Prior effective sample size can be calculated to assess the robustness as well as the prior information borrowed. Moreover, due to the lack of closed-form posterior distributions in general, an alternative approach for calculating Bayesian power is described. Simulation studies are provided to demonstrate the utility of the proposed methods. In addition, a case study in pediatric patients with leukemia is included to illustrate the proposed method with the existing approaches.

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.