While a combination of IV busulfan (Bu) and fludarabine (Flu) is a safe, reduced-toxicity conditioning program for AML/MDS, recurrent leukemia post transplantation remains a problem. To enhance the conditioning regimen’s antileukemic effect we decided to supplant Flu with clofarabine (Clo), and assayed the interactions of these nucleoside analogs alone and in combination with Busulfan (Bu) in Bu-resistant human cell lines in vitro. We found pronounced synergy between each nucleoside and the alkylator but even more enhanced cytotoxic synergy when the nucleoside analogs were combined prior to exposing the cells to Bu. We then designed a 4-arm clinical trial in patients with myeloid leukemia undergoing allogeneic stem cell transplantation (allo-SCT); Patients were adaptively randomized as follows: Arm I - Clo:Flu 10:30 mg/m2, Arm II - 20:20 mg/m2, Arm III - 30:10 mg/m2, and Arm IV - single-agent Clo at 40 mg/m2. The nucleoside analog(s) were/was infused over one hour once daily for 4 days, followed on each day by Bu, infused over 3 hours to a pharmacokinetically targeted daily AUC of 6,000 μMol-min +/− 10%. Fifty-one patients have been enrolled with a minimum follow-up exceeding 100 days. There were 32 males and 19 females with a median age of 45 years (range: 6-59). Nine patients had CML (BC: 2, second AP: 3, and tyrosine-kinase inhibitor refractory first CP: 4). Forty two patients had AML: 14 were induction failures, 8 in first chemotherapy-refractory relapse, 7 in untreated relapse, 3 in second or subsequent relapse, 4 were in second CR and 3 in second CR without platelet recovery (CRp), 2 were in high-risk CR1. Finally, 1 patient was in first CRp. Graft vs host disease- (GVHD) prophylaxis was tacrolimus and mini-MTX, and those who had an unrelated or one Ag-mismmatched donor received low-dose rabbit-ATG (Thymoglobulin™). RESULTS: All patients engrafted. Forty-one patients had active leukemia at the time of transplant, and 35 achieved CR (85%). Twenty of the 42 AML patients and 5 of 9 CML patients are alive with a projected median overall survival of 23 months. Marrow and blood (T-cell) chimerism studies at day +100 revealed that both in the lower dose Clo groups (groups 1+2) and the higher dose Clo groups (groups 3+4) the patients had a median of 100% donor (T-cell)-derived DNA. There has been no secondary graft failure. In the first 100 days one patient died of pneumonia, and one of liver GVHD. We conclude that 1) Clo±Flu with IV Bu as pretranslant conditioning is safe in high-risk myeloid leukemia patients, 2) Clofarabine is sufficiently immunosuppressive to support allo-SCT in myeloid leukemia, and 3) the median overall survival (OS) of 23 months in this high-risk patient population is encouraging. Additional studies to evaluate the antileukemic efficacy of Clo±Flu with IV Bu as pretransplant conditioning therapy are warranted.
Clofarabine; Fludarabine; IV Busulfan; CML; AML; MDS; Allogeneic Stem Cell Transplantation
A sequentially outcome-adaptive Bayesian design is proposed for choosing the dose of an experimental therapy based on elicited utilities of a bivariate ordinal (toxicity, efficacy) outcome. Subject to posterior acceptability criteria to control the risk of severe toxicity and exclude unpromising doses, patients are randomized adaptively among the doses having posterior mean utilities near the maximum. The utility increment used to define near-optimality is non-increasing with sample size. The adaptive randomization uses each dose’s posterior probability of a set of good outcomes, defined by a lower utility cut-off. Saturated parametric models are assumed for the marginal dose-toxicity and dose-efficacy distributions, allowing the possible requirement of monotonicity in dose, and a copula is used to obtain a joint distribution. Prior means are computed by simulation using elicited outcome probabilities, and prior variances are calibrated to control prior effective sample size and obtain a design with good operating characteristics. The method is illustrated by a phase I/II trial of radiation therapy for children with brain stem gliomas.
Adaptive design; Bayesian design; Clinical trial; Dose-finding; Epsilon-greedy algorithm; Phase I/II clinical trial; Utility
The problem of comparing several experimental treatments to a standard arises frequently in medical research. Various multi-stage randomized phase II/III designs have been proposed that select one or more promising experimental treatments and compare them to the standard while controlling overall Type I and Type II error rates. This paper addresses phase II/III settings where the joint goals are to increase the average time to treatment failure and control the probability of toxicity while accounting for patient heterogeneity. We are motivated by the desire to construct a feasible design for a trial of four chemotherapy combinations for treating a family of rare pediatric brain tumors. We present a hybrid two-stage design based on two-dimensional treatment effect parameters. A targeted parameter set is constructed from elicited parameter pairs considered to be equally desirable. Bayesian regression models for failure time and the probability of toxicity as functions of treatment and prognostic covariates are used to define two-dimensional covariate-adjusted treatment effect parameter sets. Decisions at each stage of the trial are based on the ratio of posterior probabilities of the alternative and null covariate-adjusted parameter sets. Design parameters are chosen to minimize expected sample size subject to frequentist error constraints. The design is illustrated by application to the brain tumor trial design.
Bayesian design; clinical trial; phase II/III design; treatment selection
We consider treatment regimes in which an agent is administered continuously at a specified concentration until either a response is achieved or a predetermined maximum infusion time is reached. Response is an event defined to characterize therapeutic efficacy. A portion of the maximum planned total amount administered is given as an initial bolus. For such regimes, the amount of the agent received by the patient depends on the time to response. An additional complication when response is evaluated periodically rather than continuously is that the response time is interval censored. We address the problem of designing a clinical trial in which such response time data and a binary indicator of toxicity are used together to jointly optimize the concentration and the size of the bolus. We propose a sequentially adaptive Bayesian design that chooses the optimal treatment for successive patients by maximizing the posterior mean utility of the joint efficacy-toxicity outcome. The methodology is illustrated by a trial in which tissue plasminogen activator is infused intra-arterially as rapid treatment for acute ischemic stroke.
Adaptive design; Bayesian design; Clinical trial; Continuous infusion; Phase I/II clinical trial; Stroke
Buzaianu and Chen apply strong curtailment to modify the two-stage select-and-test clinical trial design proposed by Thall et al. (1988). The modification reduces the expected sample size while maintaining overall power but requires continuous monitoring in stage 1. I will review the history of this type of design and discuss practical issues related to the use of strong curtailment that arise in trial conduct.
Clinical trials; Generalized power; Phase II-III design
An important problem in oncology is comparing chemotherapy (chemo) agents in terms of their effects on survival or progression free survival time. When the goal is to evaluate individual agents, a difficulty commonly encountered with observational data is that many patients receive a chemo combination including two or more agents. Because agents given in combination may interact, quantifying the contribution of each individual agent to the combination’s overall effect is problematic. Still, if on average combinations including a particular agent confer longer survival, then that agent may be considered superior to agents whose combinations confer shorter survival. Motivated by this idea, we propose a definition of individual agent effects based on observational survival data from patients treated with many different chemo combinations. We define an individual agent effect as the average of the effects of the chemo combinations that include the agent. Similarly, we define the effect of each pair of agents as the average of the effects of the combinations including the pair. Under a Bayesian regression model for survival time in which the chemo combination effects follow a hierarchical structure, these definitions are used as a basis for estimating the posterior effects and ranks of the individual agents, and of all pairs of agents. The methods are illustrated by a data set arising from 224 pediatric brain tumor patients treated with over 27 different chemo combinations involving seven chemo agents.
Bayesian analysis; Brain tumors; Hierarchical model; Ranking; Survival analysis
To assess the hypothesis that the dynamics of plasma angiogenic and inflammatory cytokines after docetaxel chemotherapy with or without the c-kit/abl/platelet-derived growth factor receptor (PDGFR) inhibitor imatinib mesylate for prostate cancer are associated with outcome, the kinetics of 17 plasma cytokines before versus after chemotherapy were assessed and associations with progression-free survival (PFS) examined. After adjusting for multiple tests, significantly different declines in placental growth factor (PIGF), soluble vascular endothelial growth factor receptor-1 (VEGFR1), VEGF, and soluble c-kit were observed with docetaxel plus imatinib (n = 41) compared to docetaxel alone (n = 47). Based on a piecewise linear regression model for change in concentration of each cytokine as a function of the probability of change in p-PDGFR in vivo, only the dynamics of PIGF (P < 0.0001) and soluble c-kit (P < 0.0001) differed with imatinib therapy. In a Bayesian log-normal regression model for PFS, a rise in human matrix metalloproteinase 9 after docetaxel alone associated with a longer PFS. Distinct plasma angiogenic cytokines are modified by imatinib and partitioned by in vivo p-PDGFR dynamics after docetaxel chemotherapy for metastatic prostate cancer. Plasma PIGF and soluble c-kit kinetics are candidate biomarkers of imatinib effect. The predictive value of human matrix metalloproteinase 9 kinetics for docetaxel efficacy requires prospective validation.
In oncology, progression-free survival time, which is defined as the minimum of the times to disease progression or death, often is used to characterize treatment and covariate effects. We are motivated by the desire to estimate the progression time distribution on the basis of data from 780 paediatric patients with choroid plexus tumours, which are a rare brain cancer where disease progression always precedes death. In retrospective data on 674 patients, the times to death or censoring were recorded but progression times were missing. In a prospective study of 106 patients, both times were recorded but there were only 20 non-censored progression times and 10 non-censored survival times. Consequently, estimating the progression time distribution is complicated by the problems that, for most of the patients, either the survival time is known but the progression time is not known, or the survival time is right censored and it is not known whether the patient’s disease progressed before censoring. For data with these missingness structures, we formulate a family of Bayesian parametric likelihoods and present methods for estimating the progression time distribution. The underlying idea is that estimating the association between the time to progression and subsequent survival time from patients having complete data provides a basis for utilizing covariates and partial event time data of other patients to infer their missing progression times. We illustrate the methodology by analysing the brain tumour data, and we also present a simulation study.
Latent variables; Missingness at random; Missing values; Survival analysis
Men with penile squamous cell carcinoma and regional lymph node involvement have a low probability of survival with lymphadenectomy alone. A multimodal approach to treatment is desirable for such patients. We performed a phase II study of neoadjuvant chemotherapy with the objective of determining the response rate, time to progression (TTP), and overall survival (OS) among patients with bulky adenopathy.
Patients and Methods
Eligible patients had stage N2 or N3 (stage III or stage IV) penile cancer without distant metastases. Neoadjuvant treatment (four courses every 3-4 weeks) consisted of paclitaxel 175 mg/m2 administered over 3 hours on day 1; ifosfamide 1,200 mg/m2 on days 1 to 3; and cisplatin 25 mg/m2 on days 1 to 3. Clinical and pathologic responses were assessed, and patient groups were compared for TTP and OS.
Thirty men received chemotherapy of whom 15 (50.0%) had an objective response and 22 (73.3%) subsequently underwent surgery. Three patients had no remaining tumor on histopathology. Nine patients (30.0%) remained alive and free of recurrence (median follow-up, 34 months; range, 14-59 months), and two patients died of other causes without recurrence. Improved TTP and OS were significantly associated with a response to chemotherapy (P < .001 and P = .001, respectively), absence of bilateral residual tumor (P = .002 and P = .017, respectively), and absence of extranodal extension (P = .001 and P = .004, respectively) or skin involvement (P = .009 and P = .012, respectively).
The neoadjuvant regimen of paclitaxel, ifosfamide, and cisplatin induced clinically meaningful responses in patients with bulky regional lymph node metastases from penile cancer.
We present a definition for the effective sample size of a parametric prior distribution in a Bayesian model, and propose methods for computing the effective sample size in a variety of settings. Our approach first constructs a prior chosen to be vague in a suitable sense, and updates this prior to obtain a sequence of posteriors corresponding to each of a range of sample sizes. We then compute a distance between each posterior and the parametric prior, defined in terms of the curvature of the logarithm of each distribution, and the posterior minimizing the distance defines the effective sample size of the prior. For cases where the distance cannot be computed analytically, we provide a numerical approximation based on Monte Carlo simulation. We provide general guidelines for application, illustrate the method in several standard cases where the answer seems obvious, and then apply it to some nonstandard settings.
Bayesian analysis; Computationally intensive methods; Effective sample size; Epsilon-information prior; Parametric prior distribution
An early phase clinical trial is the first step in evaluating the effects in humans of a potential new anti-disease agent or combination of agents. Usually called “phase I” or “phase I/II” trials, these experiments typically have the nominal scientific goal of determining an acceptable dose, most often based on adverse event probabilities. This arose from a tradition of phase I trials to evaluate cytotoxic agents for treating cancer, although some methods may be applied in other medical settings, such as treatment of stroke or immunological diseases. Most modern statistical designs for early phase trials include model-based, outcome-adaptive decision rules that choose doses for successive patient cohorts based on data from previous patients in the trial. Such designs have seen limited use in clinical practice, however, due to their complexity, the requirement of intensive, computer-based data monitoring, and the medical community’s resistance to change. Still, many actual applications of model-based outcome-adaptive designs have been remarkably successful in terms of both patient benefit and scientific outcome. In this paper, I will review several Bayesian early phase trial designs that were tailored to accommodate specific complexities of the treatment regime and patient outcomes in particular clinical settings.
Adaptive design; Bayesian design; Clinical trial; Dose-finding; Phase I trial; Phase I/II trial
A common concern in Bayesian data analysis is that an inappropriately informative prior may unduly influence posterior inferences. In the context of Bayesian clinical trial design, well chosen priors are important to ensure that posterior-based decision rules have good frequentist properties. However, it is difficult to quantify prior information in all but the most stylized models. This issue may be addressed by quantifying the prior information in terms of a number of hypothetical patients, i.e., a prior effective sample size (ESS). Prior ESS provides a useful tool for understanding the impact of prior assumptions. For example, the prior ESS may be used to guide calibration of prior variances and other hyperprior parameters. In this paper, we discuss such prior sensitivity analyses by using a recently proposed method to compute a prior ESS. We apply this in several typical Bayesian biomedical data analysis and clinical trial design settings. The data analyses include cross-tabulated counts, multiple correlated diagnostic tests, and ordinal outcomes using a proportional-odds model. The study designs include a phase I trial with late-onset toxicities, a phase II trial that monitors event times, and a phase I/II trial with dose-finding based on efficacy and toxicity.
Bayesian biostatistics; Bayesian clinical trial design; Bayesian analysis; effective sample size; parametric prior distribution
This paper reviews two types of geometric methods proposed in recent years for defining statistical decision rules based on 2-dimensional parameters that characterize treatment effect in a medical setting. A common example is that of making decisions, such as comparing treatments or selecting a best dose, based on both the probability of efficacy and the probability toxicity. In most applications, the 2-dimensional parameter is defined in terms of a model parameter of higher dimension including effects of treatment and possibly covariates. Each method uses a geometric construct in the 2-dimensional parameter space based on a set of elicited parameter pairs as a basis for defining decision rules. The first construct is a family of contours that partitions the parameter space, with the contours constructed so that all parameter pairs on a given contour are equally desirable. The partition is used to define statistical decision rules that discriminate between parameter pairs in term of their desirabilities. The second construct is a convex 2-dimensional set of desirable parameter pairs, with decisions based on posterior probabilities of this set for given combinations of treatments and covariates under a Bayesian formulation. A general framework for all of these methods is provided, and each method is illustrated by one or more applications.
Bayesian statistics; Clinical trials; Dose-finding; Indifference set; Medical decision making; Phase II clinical trial; Trade-offs
An outcome-adaptive Bayesian design is proposed for choosing the optimal dose pair of a chemotherapeutic agent and a biologic agent used in combination in a phase I/II clinical trial. Patient outcome is characterized as a vector of two ordinal variables accounting for toxicity and treatment efficacy. A generalization of the Aranda-Ordaz model (1983, Biometrika 68, 357–363) is used for the marginal outcome probabilities as functions of dose pair, and a Gaussian copula is assumed to obtain joint distributions. Numerical utilities of all elementary patient outcomes, allowing the possibility that efficacy is inevaluable due to severe toxicity, are obtained using an elicitation method aimed to establish consensus among the physicians planning the trial. For each successive patient cohort, a dose pair is chosen to maximize the posterior mean utility. The method is illustrated by a trial in bladder cancer, including simulation studies of the method’s sensitivity to prior parameters, the numerical utilities, correlation between the outcomes, sample size, cohort size and starting dose pair.
Adaptive design; Bayesian design; Clinical trial; Combination dose-finding; Utility
Advances in understanding the biological underpinnings of many cancers have led increasingly to the use of molecularly targeted anti-cancer therapies. Because the platelet-derived growth factor receptor (PDGFR) has been implicated in the progression of prostate cancer bone metastases, it is of great interest to examine possible relationships between PDGFR inhibition and therapeutic outcomes. Here, we analyze the association between change in activated PDGFR (p-PDGFR) and progression free survival (PFS) time based on large within-patient samples of cell-specific p-PDGFR values taken before and after treatment from each of 88 prostate cancer patients. To utilize these paired samples as covariate data in a regression model for PFS time, and because the p-PDGFR distributions are bimodal, we first employ a Bayesian hierarchical mixture model to obtain a deconvolution of the pre-treatment and post-treatment within-patient p-PDGFR distributions. We evaluate fits of the mixture model and a non-mixture model that ignores the bimodality by using a supnorm metric to compare the empirical distribution of each p-PDGFR data set with the corresponding fitted distribution under each model. Our results show that first using the mixture model to account for the bimodality of the within-patient p-PDGFR distributions, and then using the posterior within-patient component mean changes in p-PDGFR so obtained as covariates in the regression model for PFS time provides an improved estimation.
Bayesian analysis; Survival analysis; Markov chain Monte Carlo; Platelet derived growth factor receptor; Prostate cancer
Secondary analyses of two randomized, controlled phase III trials demonstrated that selenium and vitamin E could reduce prostate cancer incidence. To characterize pharmacodynamic and gene expression effects associated with use of selenium and vitamin E, we undertook a randomized, placebo-controlled phase IIA study of prostate cancer patients before prostatectomy and created a preoperative model for prostatectomy tissue interrogation.
Thirty-nine men with prostate cancer were randomly assigned to treatment with 200 μg of selenium, 400 IU of vitamin E, both, or placebo. Laser capture microdissection of prostatectomy biopsy specimens was used to isolate normal, stromal, and tumor cells. Gene expression in each cell type was studied with microarray analysis and validated with a real-time polymerase chain reaction (PCR) and immunohistochemistry. An analysis of variance model was fit to identify genes differentially expressed between treatments and cell types. A beta-uniform mixture model was used to analyze differential expression of genes and to assess the false discovery rate. All statistical tests were two-sided.
The highest numbers of differentially expressed genes by treatment were 1329 (63%) of 2109 genes in normal epithelial cells after selenium treatment, 1354 (66%) of 2051 genes in stromal cells after vitamin E treatment, and 329 (56%) of 587 genes in tumor cells after combination treatment (false discovery rate = 2%). Validation of 21 representative genes across all treatments and all cell types yielded Spearman correlation coefficients between the microarray analysis and the PCR validation ranging from 0.64 (95% confidence interval [CI] = 0.31 to 0.79) for the vitamin E group to 0.87 (95% CI = 0.53 to 0.99) for the selenium group. The increase in the mean percentage of p53-positive tumor cells in the selenium-treated group (26.3%), compared with that in the placebo-treated group (5%), showed borderline statistical significance (difference = 21.3%; 95% CI = 0.7 to 41.8; P = .051).
We have demonstrated the feasibility and efficiency of the preoperative model and its power as a hypothesis-generating engine. We have also identified cell type– and zone-specific tissue effects of interventions with selenium and vitamin E that may have clinical implications.
Late-onset (LO) toxicities are a serious concern in many phase I trials. Since most dose-limiting toxicities occur soon after therapy begins, most dose-finding methods use a binary indicator of toxicity occurring within a short initial time period. If an agent causes LO toxicities, however, an undesirably large number of patients may be treated at toxic doses before any toxicities are observed. A method addressing this problem is the time-to-event continual reassessment method (TITE-CRM, Cheung and Chappell, 2000). We propose a Bayesian dose-finding method similar to the TITE-CRM in which doses are chosen using time-to-toxicity data. The new aspect of our method is a set of rules, based on predictive probabilities, that temporarily suspend accrual if the risk of toxicity at prospective doses for future patients is unacceptably high. If additional follow-up data reduce the predicted risk of toxicity to an acceptable level, then accrual is restarted, and this process may be repeated several times during the trial. A simulation study shows that the proposed method provides a greater degree of safety than the TITE-CRM, while still reliably choosing the preferred dose. This advantage increases with accrual rate, but the price of this additional safety is that the trial takes longer to complete on average.
Adaptive design; Bayesian inference; Dose finding; Isotonic regression; Latent variables; Markov chain Monte Carlo; Ordinal modeling; Predictive probability
While randomization is the established method for obtaining scientifically valid treatment comparisons in clinical trials, it sometimes is at odds with what physicians feel is good medical practice. If a physician favors one treatment over another based on personal experience or published data, it may be more appropriate ethically for that physician to use the favored treatment, rather than enrolling patients on a randomized trial. Still, the randomized trial may later show the physician's favored treatment to be inferior. This paper reviews a statistical method, Bayesian adaptive randomization, that provides a practical compromise between the scientific ideal of conventional randomization and choosing each patient's treatment based on a personal preference that may prove to be incorrect. The method will first be illustrated by a simple hypothetical example, then by a recent trial in which patients with unresectable soft tissue sarcoma were adaptively randomized between two chemotherapy regimens.
Adaptive design; Bayesian design; Clinical trials; Medical ethics; Randomization
We present new statistical analyses of data arising from a clinical trial designed to compare two-stage dynamic treatment regimes (DTRs) for advanced prostate cancer. The trial protocol mandated that patients were to be initially randomized among four chemotherapies, and that those who responded poorly were to be rerandomized to one of the remaining candidate therapies. The primary aim was to compare the DTRs’ overall success rates, with success defined by the occurrence of successful responses in each of two consecutive courses of the patient’s therapy. Of the one hundred and fifty study participants, forty seven did not complete their therapy per the algorithm. However, thirty five of them did so for reasons that precluded further chemotherapy; i.e. toxicity and/or progressive disease. Consequently, rather than comparing the overall success rates of the DTRs in the unrealistic event that these patients had remained on their assigned chemotherapies, we conducted an analysis that compared viable switch rules defined by the per-protocol rules but with the additional provision that patients who developed toxicity or progressive disease switch to a non-prespecified therapeutic or palliative strategy. This modification involved consideration of bivariate per-course outcomes encoding both efficacy and toxicity. We used numerical scores elicited from the trial’s Principal Investigator to quantify the clinical desirability of each bivariate per-course outcome, and defined one endpoint as their average over all courses of treatment. Two other simpler sets of scores as well as log survival time also were used as endpoints. Estimation of each DTR-specific mean score was conducted using inverse probability weighted methods that assumed that missingness in the twelve remaining drop-outs was informative but explainable in that it only depended on past recorded data. We conducted additional worst-best case analyses to evaluate sensitivity of our findings to extreme departures from the explainable drop-out assumption.
Causal inference; Efficiency; Informative dropout; Inverse probability weighting; Marginal structural models; Optimal regime; Simultaneous confidence intervals