Prediction of accrual closure date in multi-center clinical trials with discrete-time Poisson process models

In a phase III multi‐center cancer clinical trial or a large public health study, sample size is predetermined to achieve desired power, and study participants are enrolled from tens or hundreds of participating institutions. As the accrual is closing to the target size, the coordinating data center needs to project the accrual closure date on the basis of the observed accrual pattern and notify the participating sites several weeks in advance. In the past, projections were simply based on some crude assessment, and conservative measures were incorporated in order to achieve the target accrual size. This approach often resulted in excessive accrual size and subsequently unnecessary financial burden on the study sponsors. Here we proposed a discrete‐time Poisson process‐based method to estimate the accrual rate at time of projection and subsequently the trial closure date. To ensure that target size would be reached with high confidence, we also proposed a conservative method for the closure date projection. The proposed method was illustrated through the analysis of the accrual data of the National Surgical Adjuvant Breast and Bowel Project trial B‐38. The results showed that application of the proposed method could help to save considerable amount of expenditure in patient management without compromising the accrual goal in multi‐center clinical trials. Copyright © 2012 John Wiley & Sons, Ltd.     

Predictive event modelling in multicenter clinical trials with waiting time to response

A new analytic statistical technique for predictive event modeling in ongoing multicenter clinical trials with waiting time to response is developed. It allows for the predictive mean and predictive bounds for the number of events to be constructed over time, accounting for the newly recruited patients and patients already at risk in the trial, and for different recruitment scenarios. For modeling patient recruitment, an advanced Poisson-gamma model is used, which accounts for the variation in recruitment over time, the variation in recruitment rates between different centers and the opening or closing of some centers in the future. A few models for event appearance allowing for 'recurrence', 'death' and 'lost-to-follow-up' events and using finite Markov chains in continuous time are considered. To predict the number of future events over time for an ongoing trial at some interim time, the parameters of the recruitment and event models are estimated using current data and then the predictive recruitment rates in each center are adjusted using individual data and Bayesian re-estimation. For a typical scenario (continue to recruit during some time interval, then stop recruitment and wait until a particular number of events happens), the closed-form expressions for the predictive mean and predictive bounds of the number of events at any future time point are derived under the assumptions of Markovian behavior of the event progression. The technique is efficiently applied to modeling different scenarios for some ongoing oncology trials. Case studies are considered.     

Assessing bias of multicenter trials with incomplete treatment allocation

Some multicenter randomized controlled trials (e.g. for rare diseases or with slow recruitment) involve many centers with few patients in each. Under within-center randomization, some centers might not assign each treatment to at least one patient; hence, such centers have no within-center treatment effect estimates and the center-stratified treatment effect estimate can be inefficient, perhaps to an extent with statistical and ethical implications. Recently, combining complete and incomplete centers with a priori weights has been suggested. However, a concern is whether using the incomplete centers increases bias. To study this concern, an approach with randomization models for a finite population was used to evaluate bias of the usual complete center estimator, the simple center-ignoring estimator, and the weighted estimator combining complete and incomplete centers. The situation with two treatments and many centers, each with either one or two patients, was evaluated. Various patient accrual mechanisms were considered, including one involving selection bias. The usual complete center estimator and the weighted estimator were unbiased under the overall null hypothesis, even with selection bias. An actual dermatology clinical trial motivates and illustrates these methods.     

TITE‐BOIN‐ET: Time‐to‐event Bayesian optimal interval design to accelerate dose‐finding based on both efficacy and toxicity outcomes

One of the primary purposes of an oncology dose‐finding trial is to identify an optimal dose (OD) that is both tolerable and has an indication of therapeutic benefit for subjects in subsequent clinical trials. In addition, it is quite important to accelerate early stage trials to shorten the entire period of drug development. However, it is often challenging to make adaptive decisions of dose escalation and de‐escalation in a timely manner because of the fast accrual rate, the difference of outcome evaluation periods for efficacy and toxicity and the late‐onset outcomes. To solve these issues, we propose the time‐to‐event Bayesian optimal interval design to accelerate dose‐finding based on cumulative and pending data of both efficacy and toxicity. The new design, named “TITE‐BOIN‐ET” design, is nonparametric and a model‐assisted design. Thus, it is robust, much simpler, and easier to implement in actual oncology dose‐finding trials compared with the model‐based approaches. These characteristics are quite useful from a practical point of view. A simulation study shows that the TITE‐BOIN‐ET design has advantages compared with the model‐based approaches in both the percentage of correct OD selection and the average number of patients allocated to the ODs across a variety of realistic settings. In addition, the TITE‐BOIN‐ET design significantly shortens the trial duration compared with the designs without sequential enrollment and therefore has the potential to accelerate early stage dose‐finding trials.     

Scalable spatio‐temporal Bayesian analysis of high‐dimensional electroencephalography data

We present a scalable Bayesian modelling approach for identifying brain regions that respond to a certain stimulus and use them to classify subjects. More specifically, we deal with multi‐subject electroencephalography (EEG) data with a binary response distinguishing between alcoholic and control groups. The covariates are matrix‐variate with measurements taken from each subject at different locations across multiple time points. EEG data have a complex structure with both spatial and temporal attributes. We use a divide‐and‐conquer strategy and build separate local models, that is, one model at each time point. We employ Bayesian variable selection approaches using a structured continuous spike‐and‐slab prior to identify the locations that respond to a certain stimulus. We incorporate the spatio‐temporal structure through a Kronecker product of the spatial and temporal correlation matrices. We develop a highly scalable estimation algorithm, using likelihood approximation, to deal with large number of parameters in the model. Variable selection is done via clustering of the locations based on their duration of activation. We use scoring rules to evaluate the prediction performance. Simulation studies demonstrate the efficiency of our scalable algorithm in terms of estimation and fast computation. We present results using our scalable approach on a case study of multi‐subject EEG data.     

Predicting analysis time in events‐driven clinical trials using accumulating time‐to‐event surrogate information

For clinical trials with time‐to‐event endpoints, predicting the accrual of the events of interest with precision is critical in determining the timing of interim and final analyses. For example, overall survival (OS) is often chosen as the primary efficacy endpoint in oncology studies, with planned interim and final analyses at a pre‐specified number of deaths. Often, correlated surrogate information, such as time‐to‐progression (TTP) and progression‐free survival, are also collected as secondary efficacy endpoints. It would be appealing to borrow strength from the surrogate information to improve the precision of the analysis time prediction. Currently available methods in the literature for predicting analysis timings do not consider utilizing the surrogate information. In this article, using OS and TTP as an example, a general parametric model for OS and TTP is proposed, with the assumption that disease progression could change the course of the overall survival. Progression‐free survival, related both to OS and TTP, will be handled separately, as it can be derived from OS and TTP. The authors seek to develop a prediction procedure using a Bayesian method and provide detailed implementation strategies under certain assumptions. Simulations are performed to evaluate the performance of the proposed method. An application to a real study is also provided. Copyright © 2015 John Wiley & Sons, Ltd.     

Dose finding with continuous outcome in phase I oncology trials

The goal of a phase I clinical trial in oncology is to find a dose with acceptable dose‐limiting toxicity rate. Often, when a cytostatic drug is investigated or when the maximum tolerated dose is defined using a toxicity score, the main endpoint in a phase I trial is continuous. We propose a new method to use in a dose‐finding trial with continuous endpoints. The new method selects the right dose on par with other methods and provides more flexibility in assigning patients to doses in the course of the trial when the rate of accrual is fast relative to the follow‐up time. Copyright © 2014 John Wiley & Sons, Ltd.     

Response‐adaptive designs for binary responses: How to offer patient benefit while being robust to time trends?

Response‐adaptive randomisation (RAR) can considerably improve the chances of a successful treatment outcome for patients in a clinical trial by skewing the allocation probability towards better performing treatments as data accumulates. There is considerable interest in using RAR designs in drug development for rare diseases, where traditional designs are not either feasible or ethically questionable. In this paper, we discuss and address a major criticism levelled at RAR: namely, type I error inflation due to an unknown time trend over the course of the trial. The most common cause of this phenomenon is changes in the characteristics of recruited patients—referred to as patient drift. This is a realistic concern for clinical trials in rare diseases due to their lengthly accrual rate. We compute the type I error inflation as a function of the time trend magnitude to determine in which contexts the problem is most exacerbated. We then assess the ability of different correction methods to preserve type I error in these contexts and their performance in terms of other operating characteristics, including patient benefit and power. We make recommendations as to which correction methods are most suitable in the rare disease context for several RAR rules, differentiating between the 2‐armed and the multi‐armed case. We further propose a RAR design for multi‐armed clinical trials, which is computationally efficient and robust to several time trends considered.     

A SEMIPARAMETRIC HIERARCHICAL METHOD FOR A REGRESSION MODEL WITH AN INTERVAL-CENSORED COVARIATE

A Bayesian framework is proposed for analysing regression models in which one of the covariates is interval‐censored. Such a situation was encountered in an AIDS clinical trial in which the goal was to examine the association between delays in initiating a new treatment after Indinavir failure and the subsequent viral load level of patients at the time of enrolment into the new treatment. The new method uses a mixture of Dirichlet processes allowing all the components in the model to be specified parametrically, except for the distribution of the interval‐censored covariate, which is treated non‐parametrically. The paper explains the proposed method for the linear regression model in detail. The performance of the method is assessed by simulations and illustrated using the AIDS clinical trial.     

A simulation study of methods for selecting subgroup‐specific doses in phase 1 trials

Patient heterogeneity may complicate dose‐finding in phase 1 clinical trials if the dose‐toxicity curves differ between subgroups. Conducting separate trials within subgroups may lead to infeasibly small sample sizes in subgroups having low prevalence. Alternatively,it is not obvious how to conduct a single trial while accounting for heterogeneity. To address this problem,we consider a generalization of the continual reassessment method on the basis of a hierarchical Bayesian dose‐toxicity model that borrows strength between subgroups under the assumption that the subgroups are exchangeable. We evaluate a design using this model that includes subgroup‐specific dose selection and safety rules. A simulation study is presented that includes comparison of this method to 3 alternative approaches,on the basis of nonhierarchical models,that make different types of assumptions about within‐subgroup dose‐toxicity curves. The simulations show that the hierarchical model‐based method is recommended in settings where the dose‐toxicity curves are exchangeable between subgroups. We present practical guidelines for application and provide computer programs for trial simulation and conduct.     

A mixture model using likelihood‐based and Bayesian approaches for identifying responders and non‐responders in longitudinal clinical trials

A longitudinal mixture model for classifying patients into responders and non‐responders is established using both likelihood‐based and Bayesian approaches. The model takes into consideration responders in the control group. Therefore, it is especially useful in situations where the placebo response is strong, or in equivalence trials where the drug in development is compared with a standard treatment. Under our model, a treatment shows evidence of being effective if it increases the proportion of responders or increases the response rate among responders in the treated group compared with the control group. Therefore, the model has flexibility to accommodate different situations. The proposed method is illustrated using simulation and a depression clinical trial dataset for the likelihood‐based approach, and the same depression clinical trial dataset for the Bayesian approach. The likelihood‐based and Bayesian approaches generated consistent results for the depression trial data. In both the placebo group and the treated group, patients are classified into two components with distinct response rate. The proportion of responders is shown to be significantly higher in the treated group compared with the control group, suggesting the treatment paroxetine is effective. Copyright © 2014 John Wiley & Sons, Ltd.     

Meta Analysis of Functional Neuroimaging Data via Bayesian Spatial Point Processes

As the discipline of functional neuroimaging grows there is an increasing interest in meta analysis of brain imaging studies. A typical neuroimaging meta analysis collects peak activation coordinates (foci) from several studies and identifies areas of consistent activation. Most imaging meta analysis methods only produce null hypothesis inferences and do not provide an interpretable fitted model. To overcome these limitations, we propose a Bayesian spatial hierarchical model using a marked independent cluster process. We model the foci as offspring of a latent study center process, and the study centers are in turn offspring of a latent population center process. The posterior intensity function of the population center process provides inference on the location of population centers, as well as the inter-study variability of foci about the population centers. We illustrate our model with a meta analysis consisting of 437 studies from 164 publications, show how two subpopulations of studies can be compared and assess our model via sensitivity analyses and simulation studies. Supplemental materials are available online.     

Planning the duration of a survival group sequential trial with a fixed follow-up time for all subjects

To explore the operation characteristics of survival group sequential trials with a fixed follow-up period, the accrual time and total trial duration to ensure power and type I error rate requirements are explained and investigated for hazard ratios ranging from 1.3 to 3.0, with slow or high accrual rate, and in the presence or absence of censoring. Impacts of hazard rate, accrual rate, and competitive censoring on accrual time and subsequently on total trial duration are carefully illustrated. Real time for interim analyses, needed number of events, and recruited number of subjects at time of interim analyses are also tabulated.     

Model averaging for treatment effect estimation in subgroups

In many clinical trials, biological, pharmacological, or clinical information is used to define candidate subgroups of patients that might have a differential treatment effect. Once the trial results are available, interest will focus on subgroups with an increased treatment effect. Estimating a treatment effect for these groups, together with an adequate uncertainty statement is challenging, owing to the resulting “random high” / selection bias. In this paper, we will investigate Bayesian model averaging to address this problem. The general motivation for the use of model averaging is to realize that subgroup selection can be viewed as model selection, so that methods to deal with model selection uncertainty, such as model averaging, can be used also in this setting. Simulations are used to evaluate the performance of the proposed approach. We illustrate it on an example early‐phase clinical trial.     

SPIRIT: A seamless phase I/II randomized design for immunotherapy trials

Immunotherapy—treatments that enlist the immune system to battle tumors—has received widespread attention in cancer research. Due to its unique features and mechanisms for treating cancer, immunotherapy requires novel clinical trial designs. We propose a Bayesian seamless phase I/II randomized design for immunotherapy trials (SPIRIT) to find the optimal biological dose (OBD) defined in terms of the restricted mean survival time. We jointly model progression‐free survival and the immune response. Progression‐free survival is used as the primary endpoint to determine the OBD, and the immune response is used as an ancillary endpoint to quickly screen out futile doses. Toxicity is monitored throughout the trial. The design consists of two seamlessly connected stages. The first stage identifies a set of safe doses. The second stage adaptively randomizes patients to the safe doses identified and uses their progression‐free survival and immune response to find the OBD. The simulation study shows that the SPIRIT has desirable operating characteristics and outperforms the conventional design.     

Sequential analysis methodology for a Poisson GLMM with applications to multicenter randomized clinical trials

Sequential analyses in clinical trials have ethical and economic advantages over fixed sample size methods. The sequential probability ratio test (SPRT) is a hypothesis testing procedure which evaluates data as it is collected. The original SPRT was developed by Wald for one-parameter families of distributions and later extended by Bartlett to handle the case of nuisance parameters. However, Bartlett's SPRT requires independent and identically distributed observations. In this paper we show that Bartlett's SPRT can be applied to generalized linear model (GLM) contexts. Then we propose an SPRT analysis methodology for a Poisson generalized linear mixed model (GLMM) that is suitable for our application to the design of a multicenter randomized clinical trial that compares two preventive treatments for surgical site infections. We validate the methodology with a simulation study that includes a comparison to Neyman–Pearson and Bayesian fixed sample size test designs and the Wald SPRT.     

Application of Bayesian hierarchical models for phase I/II clinical trials in oncology

Treatment during cancer clinical trials sometimes involves the combination of multiple drugs. In addition, in recent years there has been a trend toward phase I/II trials in which a phase I and a phase II trial are combined into a single trial to accelerate drug development. Methods for the seamless combination of phases I and II parts are currently under investigation. In the phase II part, adaptive randomization on the basis of patient efficacy outcomes allocates more patients to the dose combinations considered to have higher efficacy. Patient toxicity outcomes are used for determining admissibility to each dose combination and are not used for selection of the dose combination itself. In cases where the objective is not to find the optimum dose combination solely for efficacy but regarding both toxicity and efficacy, the need exists to allocate patients to dose combinations with consideration of the balance of existing trade‐offs between toxicity and efficacy. We propose a Bayesian hierarchical model and an adaptive randomization with consideration for the relationship with toxicity and efficacy. Using the toxicity and efficacy outcomes of patients, the Bayesian hierarchical model is used to estimate the toxicity probability and efficacy probability in each of the dose combinations. Here, we use Bayesian moving‐reference adaptive randomization on the basis of desirability computed from the obtained estimator. Computer simulations suggest that the proposed method will likely recommend a higher percentage of target dose combinations than a previously proposed method.     

Phase I trial design for drug combinations with Bayesian model averaging

Various statistical models have been proposed for two‐dimensional dose finding in drug‐combination trials. However, it is often a dilemma to decide which model to use when conducting a particular drug‐combination trial. We make a comprehensive comparison of four dose‐finding methods, and for fairness, we apply the same dose‐finding algorithm under the four model structures. Through extensive simulation studies, we compare the operating characteristics of these methods in various practical scenarios. The results show that different models may lead to different design properties and that no single model performs uniformly better in all scenarios. As a result, we propose using Bayesian model averaging to overcome the arbitrariness of the model specification and enhance the robustness of the design. We assign a discrete probability mass to each model as the prior model probability and then estimate the toxicity probabilities of combined doses in the Bayesian model averaging framework. During the trial, we adaptively allocated each new cohort of patients to the most appropriate dose combination by comparing the posterior estimates of the toxicity probabilities with the prespecified toxicity target. The simulation results demonstrate that the Bayesian model averaging approach is robust under various scenarios. Copyright © 2015 John Wiley & Sons, Ltd.