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.

Risk-benefit trade-offs and precision utilities in phase I-II clinical trials.

BACKGROUND: Identifying optimal doses in early-phase clinical trials is critically important. Therapies administered at doses that are either unsafe or biologically ineffective are unlikely to be successful in subsequent clinical trials or to obtain regulatory approval. Identifying appropriate doses for new agents is a complex process that involves balancing the risks and benefits of outcomes such as biological efficacy, toxicity, and patient quality of life. PURPOSE: While conventional phase I trials rely solely on toxicity to determine doses, phase I-II trials explicitly account for both efficacy and toxicity, which enables them to identify doses that provide the most favorable risk-benefit trade-offs. It is also important to account for patient covariates, since one-size-fits-all treatment decisions are likely to be suboptimal within subgroups determined by prognostic variables or biomarkers. Notably, the selection of estimands can influence our conclusions based on the prognostic subgroup studied. For example, assuming monotonicity of the probability of response, higher treatment doses may yield more pronounced efficacy in favorable prognosis compared to poor prognosis subgroups when the estimand is mean or median survival. Conversely, when the estimand is the 3-month survival probability, higher treatment doses produce more pronounced efficacy in poor prognosis compared to favorable prognosis subgroups. METHODS AND CONCLUSIONS: Herein, we first describe why it is essential to consider clinical practice when designing a clinical trial and outline a stepwise process for doing this. We then review a precision phase I-II design based on utilities tailored to prognostic subgroups that characterize efficacy-toxicity risk-benefit trade-offs. The design chooses each patient's dose to optimize their expected utility and allows patients in different prognostic subgroups to have different optimal doses. We illustrate the design with a dose-finding trial of a new therapeutic agent for metastatic clear cell renal cell carcinoma.

Current issues in dose-finding designs: A response to the US Food and Drug Adminstration's Oncology Center of Excellence Project Optimus.

With the advent of targeted agents and immunological therapies, the medical research community has become increasingly aware that conventional methods for determining the best dose or schedule of a new agent are inadequate. It has been well established that conventional phase I designs cannot reliably identify safe and effective doses. This problem applies, generally, for cytotoxic agents, radiation therapy, targeted agents, and immunotherapies. To address this, the US Food and Drug Administration's Oncology Center of Excellence initiated Project Optimus, with the goal "to reform the dose optimization and dose selection paradigm in oncology drug development." As a response to Project Optimus, the articles in this special issue of Clinical Trials review recent advances in methods for choosing the dose or schedule of a new agent with an overall objective of informing clinical trialists of these innovative designs. This introductory article briefly reviews problems with conventional methods, the regulatory changes that encourage better dose optimization designs, and provides brief summaries of the articles that follow in this special issue.

Stereotactic body radiotherapy with or without selective dismutase mimetic in pancreatic adenocarcinoma: an adaptive, randomised, double-blind, placebo-controlled, phase 1b/2 trial.

BACKGROUND: Stereotactic body radiotherapy (SBRT) has the potential to ablate localised pancreatic ductal adenocarcinoma. Selective dismutase mimetics sensitise tumours while reducing normal tissue toxicity. This trial was designed to establish the efficacy and toxicity afforded by the selective dismutase mimetic avasopasem manganese when combined with ablative SBRT for localised pancreatic ductal adenocarcinoma. METHODS: In this adaptive, randomised, double-blind, placebo-controlled, phase 1b/2 trial, patients aged 18 years or older with borderline resectable or locally advanced pancreatic cancer who had received at least 3 months of chemotherapy and had an Eastern Cooperative Oncology Group performance status of 0-2 were enrolled at six academic sites in the USA. Eligible patients were randomly assigned (1:1), with block randomisation (block sizes of 6-12) with a maximum of 24 patients per group, to receive daily avasopasem (90 mg) or placebo intravenously directly before (ie, within 180 min) SBRT (50, 55, or 60 Gy in five fractions, adaptively assigned in real time by Bayesian estimates of 90-day safety and efficacy). Patients and physicians were masked to treatment group allocation, but not to SBRT dose. The primary objective was to find the optimal dose of SBRT with avasopasem or placebo as determined by the late onset EffTox method. All analyses were done on an intention-to-treat basis. This study is registered with ClinicalTrials.gov, NCT03340974, and is complete. FINDINGS: Between Jan 25, 2018, and April 29, 2020, 47 patients were screened, of whom 42 were enrolled (median age was 71 years [IQR 63-75], 23 [55%] were male, 19 [45%] were female, 37 [88%] were White, three [7%] were Black, and one [2%] each were unknown or other races) and randomly assigned to avasopasem (n=24) or placebo (n=18); the placebo group was terminated early after failing to meet prespecified efficacy parameters. At data cutoff (June 28, 2021), the avasopasem group satisfied boundaries for both efficacy and toxicity. Late onset EffTox efficacy response was observed in 16 (89%) of 18 patients at 50 Gy and six (100%) of six patients at 55 Gy in the avasopasem group, and was observed in three (50%) of six patients at 50 Gy and nine (75%) of 12 patients at 55 Gy in the placebo group, and the Bayesian model recommended 50 Gy or 55 Gy in five fractions with avasopasem for further study. Serious adverse events of any cause were reported in three (17%) of 18 patients in the placebo group and six (25%) of 24 in the avasopasem group. In the placebo group, grade 3 adverse events within 90 days of SBRT were abdominal pain, acute cholangitis, pyrexia, increased blood lactic acid, and increased lipase (one [6%] each); no grade 4 events occurred. In the avasopasem group, grade 3-4 adverse events within 90 days of SBRT were acute kidney injury, increased blood alkaline phosphatase, haematoma, colitis, gastric obstruction, lung infection, abdominal abscess, post-surgical atrial fibrillation, and pneumonia leading to respiratory failure (one [4%] each).There were no treatment-related deaths but one late death in the avasopasem group due to sepsis in the setting of duodenal obstruction after off-study treatment was reported as potentially related to SBRT. INTERPRETATION: SBRT that uses 50 or 55 Gy in five fractions can be considered for patients with localised pancreatic ductal adenocarcinoma. The addition of avasopasem might further enhance disease outcomes. A larger phase 2 trial (GRECO-2, NCT04698915) is underway to validate these results. FUNDING: Galera Therapeutics.

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.

BASIC: A Bayesian adaptive synthetic-control design for phase II clinical trials.

BACKGROUND: Randomized controlled trials are considered the gold standard for evaluating experimental treatments but often require large sample sizes. Single-arm trials require smaller sample sizes but are subject to bias when using historical control data for comparative inferences. This article presents a Bayesian adaptive synthetic-control design that exploits historical control data to create a hybrid of a single-arm trial and a randomized controlled trial. METHODS: The Bayesian adaptive synthetic control design has two stages. In stage 1, a prespecified number of patients are enrolled in a single arm given the experimental treatment. Based on the stage 1 data, applying propensity score matching and Bayesian posterior prediction methods, the usefulness of the historical control data for identifying a pseudo sample of matched synthetic-control patients for making comparative inferences is evaluated. If a sufficient number of synthetic controls can be identified, the single-arm trial is continued. If not, the trial is switched to a randomized controlled trial. The performance of The Bayesian adaptive synthetic control design is evaluated by computer simulation. RESULTS: The Bayesian adaptive synthetic control design achieves power and unbiasedness similar to a randomized controlled trial but on average requires a much smaller sample size, provided that the historical control data patients are sufficiently comparable to the trial patients so that a good number of matched controls can be identified in the historical control data. Compared to a single-arm trial, The Bayesian adaptive synthetic control design yields much higher power and much smaller bias. CONCLUSION: The Bayesian adaptive synthetic-control design provides a useful tool for exploiting historical control data to improve the efficiency of single-arm phase II clinical trials, while addressing the problem of bias when comparing trial results to historical control data. The proposed design achieves power similar to a randomized controlled trial but may require a substantially smaller sample size.

A Bayesian piecewise exponential phase II design for monitoring a time-to-event endpoint.

A robust Bayesian design is presented for a single-arm phase II trial with an early stopping rule to monitor a time to event endpoint. The assumed model is a piecewise exponential distribution with non-informative gamma priors on the hazard parameters in subintervals of a fixed follow up interval. As an additional comparator, we also define and evaluate a version of the design based on an assumed Weibull distribution. Except for the assumed models, the piecewise exponential and Weibull model based designs are identical to an established design that assumes an exponential event time distribution with an inverse gamma prior on the mean event time. The three designs are compared by simulation under several log-logistic and Weibull distributions having different shape parameters, and for different monitoring schedules. The simulations show that, compared to the exponential inverse gamma model based design, the piecewise exponential design has substantially better performance, with much higher probabilities of correctly stopping the trial early, and shorter and less variable trial duration, when the assumed median event time is unacceptably low. Compared to the Weibull model based design, the piecewise exponential design does a much better job of maintaining small incorrect stopping probabilities in cases where the true median survival time is desirably large.

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 group sequential enrichment designs based on adaptive regression of response and survival time on baseline biomarkers.

Precision medicine relies on the idea that, for a particular targeted agent, only a subpopulation of patients is sensitive to it and thus may benefit from it therapeutically. In practice, it is often assumed based on preclinical data that a treatment-sensitive subpopulation is known, and moreover that the agent is substantively efficacious in that subpopulation. Due to important differences between preclinical settings and human biology, however, data from patients treated with a new targeted agent often show that one or both of these assumptions are false. This paper provides a Bayesian randomized group sequential enrichment design that compares an experimental treatment to a control based on survival time and uses early response as an ancillary outcome to assist with adaptive variable selection and enrichment. Initially, the design enrolls patients under broad eligibility criteria. At each interim decision, submodels for regression of response and survival time on a baseline covariate vector and treatment are fit; variable selection is used to identify a covariate subvector that characterizes treatment-sensitive patients and determines a personalized benefit index, and comparative superiority and futility decisions are made. Enrollment of each cohort is restricted to the most recent adaptively identified treatment-sensitive patients. Group sequential decision cutoffs are calibrated to control overall type I error and account for the adaptive enrollment restriction. The design provides a basis for precision medicine by identifying a treatment-sensitive subpopulation, if it exists, and determining whether the experimental treatment is superior to the control in that subpopulation. A simulation study shows that the proposed design reliably identifies a sensitive subpopulation, yields much higher generalized power compared to several existing enrichment designs and a conventional all-comers group sequential design, and is robust.

Conditional survival among patients with oropharyngeal cancer treated with radiation therapy and alive without recurrence 5 years after diagnosis.

BACKGROUND: Risk of recurrence among patients with oropharyngeal cancer (OPC) who survive 5 years is low. The goal of this study was to assess long-term survival of patients with OPC alive without recurrence 5 years after diagnosis. METHODS: This study included newly diagnosed patients with OPC, who had been treated with radiation and were alive without recurrence 5 years after diagnosis. Overall survival (OS) probabilities beyond 5 years were estimated using the Kaplan-Meier method. Factors associated with OS were determined using Bayesian piecewise exponential survival regression. Standardized mortality ratios for all-cause death were estimated controlling for study year, age, and sex in the US general population. RESULTS: Among 1699 patients, the additional 2-year, 5-year, and 10-year OS probabilities were 94%, 83%, and 63%, respectively, and were lower than those in the general population. Patients who were older, were current or former smokers, had other than tonsil or base of tongue tumors, or had T4 tumors had a higher risk of death. Patients who had base of tongue tumors and had received intensity-modulated radiation therapy (IMRT) or lower-radiation doses had a lower risk of death. Standardized mortality ratios were higher among current and heavy smokers and lower among recipients of IMRT and lower radiation doses. CONCLUSIONS: In this large cohort, long-term survival among patients with OPC was good but lower than predicted for the general population. Patients treated with IMRT and those with less tobacco exposure had better outcomes.

Precision Bayesian phase I-II dose-finding based on utilities tailored to prognostic subgroups.

A Bayesian phase I-II design is presented that optimizes the dose of a new agent within predefined prognostic subgroups. The design is motivated by a trial to evaluate targeted agents for treating metastatic clear cell renal carcinoma, where a prognostic risk score defined by clinical variables and biomarkers is well established. Two clinical outcomes are used for dose-finding, time-to-toxicity during a prespecified follow-up period, and efficacy characterized by ordinal disease status evaluated at the end of follow-up. A joint probability model is constructed for these outcomes as functions of dose and subgroup. The model performs adaptive clustering of adjacent subgroups having similar dose-outcome distributions to facilitate borrowing information across subgroups. To quantify toxicity-efficacy risk-benefit trade-offs that may differ between subgroups, the objective function is based on outcome utilities elicited separately for each subgroup. In the context of the renal cancer trial, a design is constructed and a simulation study is presented to evaluate the design's reliability, safety, and robustness, and to compare it to designs that either ignore subgroups or run a separate trial within each subgroup.

An adaptive trial design to optimize dose-schedule regimes with delayed outcomes.

This paper proposes a two-stage phase I-II clinical trial design to optimize dose-schedule regimes of an experimental agent within ordered disease subgroups in terms of the toxicity-efficacy trade-off. The design is motivated by settings where prior biological information indicates it is certain that efficacy will improve with ordinal subgroup level. We formulate a flexible Bayesian hierarchical model to account for associations among subgroups and regimes, and to characterize ordered subgroup effects. Sequentially adaptive decision-making is complicated by the problem, arising from the motivating application, that efficacy is scored on day 90 and toxicity is evaluated within 30 days from the start of therapy, while the patient accrual rate is fast relative to these outcome evaluation intervals. To deal with this in a practical manner, we take a likelihood-based approach that treats unobserved toxicity and efficacy outcomes as missing values, and use elicited utilities that quantify the efficacy-toxicity trade-off as a decision criterion. Adaptive randomization is used to assign patients to regimes while accounting for subgroups, with randomization probabilities depending on the posterior predictive distributions of utilities. A simulation study is presented to evaluate the design's performance under a variety of scenarios, and to assess its sensitivity to the amount of missing data, the prior, and model misspecification.

Comparing Bayesian early stopping boundaries for phase II clinical trials.

When designing phase II clinical trials, it is important to construct interim monitoring rules that achieve a balance between reliable early stopping for futility or safety and maintaining a high true positive probability (TPP), which is the probability of not stopping if the new treatment is truly safe and effective. We define and compare several methods for specifying early stopping boundaries as functions of interim sample size, rather than as fixed cut-offs, using Bayesian posterior probabilities as decision criteria. We consider boundaries with constant, linear, or exponential shapes. For design optimization criteria, we use the TPP and mean number of patients enrolled in the trial. Simulations to evaluate and compare the designs' operating characteristics under a range of scenarios show that, while there is no uniformly optimal boundary, an appropriately calibrated exponential shape maintains high TPP while limiting the number of patients assigned to a treatment with an inferior response rate or an excessive toxicity rate.

A hybrid phase I-II/III clinical trial design allowing dose re-optimization in phase III.

Conventionally, evaluation of a new drug, A, is done in three phases. Phase I is based on toxicity to determine a "maximum tolerable dose" (MTD) of A, phase II is conducted to decide whether A at the MTD is promising in terms of response probability, and if so a large randomized phase III trial is conducted to compare A to a control treatment, C, usually based on survival time or progression free survival time. It is widely recognized that this paradigm has many flaws. A recent approach combines the first two phases by conducting a phase I-II trial, which chooses an optimal dose based on both efficacy and toxicity, and evaluation of A at the selected optimal phase I-II dose then is done in a phase III trial. This paper proposes a new design paradigm, motivated by the possibility that the optimal phase I-II dose may not maximize mean survival time with A. We propose a hybridized design, which we call phase I-II/III, that combines phase I-II and phase III by allowing the chosen optimal phase I-II dose of A to be re-optimized based on survival time data from phase I-II patients and the first portion of phase III. The phase I-II/III design uses adaptive randomization in phase I-II, and relies on a mixture model for the survival time distribution as a function of efficacy, toxicity, and dose. A simulation study is presented to evaluate the phase I-II/III design and compare it to the usual approach that does not re-optimize the dose of A in phase III.

Phase II Trial of High-Dose Gemcitabine/Busulfan/Melphalan with Autologous Stem Cell Transplantation for Primary Refractory or Poor-Risk Relapsed Hodgkin Lymphoma.

We conducted a prospective phase 2 trial of gemcitabine, busulfan and melphalan (Gem/Bu/Mel) with autologous stem cell transplantation (ASCT) in patients with primary refractory or poor-risk relapsed Hodgkin lymphoma (HL) (ie, extranodal relapse or within 1 year of frontline therapy). The trial was powered to detect an improvement in 2-year progression-free survival (PFS) from a historical 50% using a BEAM regimen (carmustine/etoposide/cytarabine/melphalan) to 65%. We compared the study population with all other concurrent patients who were eligible for the trial but instead received the BEAM regimen at our center. No patient received post-ASCT maintenance therapy. The Gem/Bu/Mel trial enrolled 80 patients with a median age of 31 years, 41% with primary refractory HL and 59% with relapsed HL (36% extranodal relapses), and 30% with positron emission tomography (PET)-positive lesions at ASCT. The concurrent BEAM (n = 45) and Gem/Bu/Mel cohorts were well balanced except for higher rates of bulky relapse and PET-positive tumors in the Gem/Bu/Mel cohort. There were no transplantation-related deaths in either cohort. At a median follow-up of 34.5 months (range, 26 to 72 months), Gem/Bu/Mel was associated with better 2-year PFS (65% versus 51%; P = .008) and overall survival (89% versus 73%; P = .0003). In conclusion, our data show that Gem/Bu/Mel is safe, in this nonrandomized comparison yielding improved outcomes compared with a concurrently treated and prognostically matched cohort of patients with primary refractory or poor-risk relapsed HL receiving BEAM.

A utility-based design for randomized comparative trials with ordinal outcomes and prognostic subgroups.

A design is proposed for randomized comparative trials with ordinal outcomes and prognostic subgroups. The design accounts for patient heterogeneity by allowing possibly different comparative conclusions within subgroups. The comparative testing criterion is based on utilities for the levels of the ordinal outcome and a Bayesian probability model. Designs based on two alternative models that include treatment-subgroup interactions are considered, the proportional odds model and a non-proportional odds model with a hierarchical prior that shrinks toward the proportional odds model. A third design that assumes homogeneity and ignores possible treatment-subgroup interactions also is considered. The three approaches are applied to construct group sequential designs for a trial of nutritional prehabilitation versus standard of care for esophageal cancer patients undergoing chemoradiation and surgery, including both untreated patients and salvage patients whose disease has recurred following previous therapy. A simulation study is presented that compares the three designs, including evaluation of within-subgroup type I and II error probabilities under a variety of scenarios including different combinations of treatment-subgroup interactions.

Subgroup-specific dose finding in phase I clinical trials based on time to toxicity allowing adaptive subgroup combination.

A Bayesian design is presented that does precision dose finding based on time to toxicity in a phase I clinical trial with two or more patient subgroups. The design, called Sub-TITE, makes sequentially adaptive subgroup-specific decisions while possibly combining subgroups that have similar estimated dose-toxicity curves. Decisions are based on posterior quantities computed under a logistic regression model for the probability of toxicity within a fixed follow-up period, as a function of dose and subgroup. Similarly to the time-to-event continual reassessment method (TITE-CRM, Cheung and Chappell), the Sub-TITE design downweights each patient's likelihood contribution using a function of follow-up time. Spike-and-slab priors are assumed for subgroup parameters, with latent subgroup combination variables included in the logistic model to allow different subgroups to be combined for dose finding if they are homogeneous. This framework can be used in trials where clinicians have identified patient subgroups but are not certain whether they will have different dose-toxicity curves. A simulation study shows that, when the dose-toxicity curves differ between all subgroups, Sub-TITE has superior performance compared with applying the TITE-CRM while ignoring subgroups and has slightly better performance than applying the TITE-CRM separately within subgroups or using the two-group maximum likelihood approach of Salter et al that borrows strength among the two groups. When two or more subgroups are truly homogeneous but differ from other subgroups, the Sub-TITE design is substantially superior to either ignoring subgroups, running separate trials within all subgroups, or the maximum likelihood approach of Salter et al. Practical guidelines and computer software are provided to facilitate application.

A decision-theoretic phase I-II design for ordinal outcomes in two cycles.

This paper is motivated by a phase I-II clinical trial of a targeted agent for advanced solid tumors. We study a stylized version of this trial with the goal to determine optimal actions in each of two cycles of therapy. A design is presented that generalizes the decision-theoretic two-cycle design of Lee and others (2015. Bayesian dose-finding in two treatment cycles based on the joint utility of efficacy and toxicity. Journal of the American Statistical Association, to appear) to accommodate ordinal outcomes. Backward induction is used to jointly optimize the actions taken for each patient in each of the two cycles, with the second action accounting for the patient's cycle 1 dose and outcomes. A simulation study shows that simpler designs obtained by dichotomizing the ordinal outcomes either perform very similarly to the proposed design, or have much worse performance in some scenarios. We also compare the proposed design with the simpler approaches of optimizing the doses in each cycle separately, or ignoring the distinction between cycles 1 and 2.

A simulation study of outcome adaptive randomization in multi-arm clinical trials.

Randomizing patients among treatments with equal probabilities in clinical trials is the established method to obtain unbiased comparisons. In recent years, motivated by ethical considerations, many authors have proposed outcome adaptive randomization, wherein the randomization probabilities are unbalanced, based on interim data, to favor treatment arms having more favorable outcomes. While there has been substantial controversy regarding the merits and flaws of adaptive versus equal randomization, there has not yet been a systematic simulation study in the multi-arm setting. A simulation study was conducted to evaluate four different Bayesian adaptive randomization methods and compare them to equal randomization in five-arm clinical trials. All adaptive randomization methods included an initial burn-in with equal randomization and some combination of other modifications to avoid extreme randomization probabilities. Trials either with or without a control arm were evaluated, using designs that may terminate arms early for futility and select one or more experimental treatments at the end. The designs were evaluated under a range of scenarios and sample sizes. For trials with a control arm and maximum same size 250 or 500, several commonly used adaptive randomization methods have very low probabilities of correctly selecting a truly superior treatment. Of those studied, the only adaptive randomization method with desirable properties has a burn-in with equal randomization and thereafter randomization probabilities restricted to the interval 0.10-0.90. Compared to equal randomization, this method has a favorable sample size imbalance but lower probability of correctly selecting a superior treatment. In multi-arm trials, compared to equal randomization, several commonly used adaptive randomization methods give much lower probabilities of selecting superior treatments. Aside from randomization method, conducting a multi-arm trial without a control arm may lead to very low probabilities of selecting any superior treatments if differences between the treatment success probabilities are small.

Bayesian variable selection for a semi-competing risks model with three hazard functions.

A variable selection procedure is developed for a semi-competing risks regression model with three hazard functions that uses spike-and-slab priors and stochastic search variable selection algorithms for posterior inference. A rule is devised for choosing the threshold on the marginal posterior probability of variable inclusion based on the Deviance Information Criterion (DIC) that is examined in a simulation study. The method is applied to data from esophageal cancer patients from the MD Anderson Cancer Center, Houston, TX, where the most important covariates are selected in each of the hazards of effusion, death before effusion, and death after effusion. The DIC procedure that is proposed leads to similar selected models regardless of the choices of some of the hyperparameters. The application results show that patients with intensity-modulated radiation therapy have significantly reduced risks of pericardial effusion, pleural effusion, and death before either effusion type.