Bayesian Predictive Probability Research Articles

Abstract S5-02: Veliparib/carboplatin plus standard neoadjuvant therapy for high-risk breast cancer: First efficacy results from the I-SPY 2 TRIAL

Abstract Background: I-SPY 2 is a multicenter, phase 2 screening trial using adaptive randomization within biomarker subtypes to evaluate a series of novel agents/combinations when added to standard neoadjuvant therapy (paclitaxel q wk x 12, doxorubicin & cyclophosphamide q 2-3 wk x 4, T/AC) vs. T/AC (control arm) for women with high-risk stage II/III breast cancer. The primary endpoint is pathologic complete response (pCR) at surgery. Our goal is to identify/graduate regimens that have ≥85% Bayesian predictive probability of success (statistical significance) in a 300-patient biomarker-linked Phase 3 neoadjuvant trial. Experimental regimens can “graduate” in at least 1 of 10 possible signatures defined by hormone-receptor (HR) & HER2 status & MammaPrint (MP), with a maximum number of 120 total patients enrolled. We report final efficacy results of the oral PARP inhibitor veliparib (V, ABT-888) in combination with carboplatin (carbo), 1 of 7 experimental regimens evaluated in the trial to date. Methods: Women with tumors ≥2.5 cm by clinical exam and ≥2 cm by imaging are eligible for screening. Tumors that are MP low/HR+/HER2- are ineligible for randomization. MRI scans (baseline, 3 weeks after start of therapy, at completion of weekly T, and prior to surgery) were used in a longitudinal statistical model to improve the efficiency of adaptive randomization. V+carbo was assigned to HER2- tumors only, which limits its possible signatures to: all HER2-, HR+/HER2-, HR-/HER2-. For these 3 signatures we provide estimated pCR rates with associated 95% Bayesian probability intervals for V+carbo and concurrently randomized controls. Analysis is intent to treat with patients who switched to non-protocol therapy regarded as non-pCRs. For each signature we provide probabilities of superiority for V+carbo over control and Bayesian predictive probabilities of success in a neoadjuvant Phase 3 trial equally randomized between V+carbo and control. Results: When V+carbo met the 85% predictive probability criterion in HR-/HER2- and all HER2-, this regimen graduated and accrual to V+carbo was stopped. V+carbo was assigned to 72 patients, and there were 62 concurrently randomized controls (44 HER2- controls). The following table shows final results based on available pCR information. Two patients assigned to V+carbo withdrew consent during treatment and are not included in the table. SignatureEstimated pCR Rate (95% probability interval)Probability V+Carbo is Superior to ControlPredictive Probability of Success in Phase 3 V+CarboControl All HER2-35% (25-45%)20% (9-33%)97%71%HR+/HER2-14% (5-27%)15% (5-30%)44%16%HR-/HER2-52 (38-67%)24% (9-43%)99%92% Conclusion: Adaptive randomization successfully identified a biomarker signature for V+carbo on the basis of a modest number of patients. V+carbo has graduated with a triple-negative (TN) breast cancer signature, and is the subset recommended for this regimen's subsequent development. There is a suggestion that HR+/HER2- tumors benefit little from this regimen and inclusion of tumors in this subset would therefore dilute its effect in a subsequent trial. Analyses are currently underway to define additional biomarkers that may be predictive of response. The I-SPY 2 standing trial mechanism efficiently evaluates agents/combinations in biomarker-defined patient subsets, with future agents/combinations reported as available. Citation Information: Cancer Res 2013;73(24 Suppl): Abstract nr S5-02.

Age estimation by magnetic resonance imaging of the distal tibial epiphysis and the calcaneum

Age estimation of living individuals is of critical importance in forensic practice, especially because of the increased migration in developed countries. Recently, the contribution of magnetic resonance imaging (MRI) to age evaluation has been studied, as it seems to be an efficient technique to analyze growth plate maturation and epiphyseal fusion. We developed an MRI staging system for the distal tibial epiphysis and the calcaneal epiphysis and evaluated its reliability on 180 MRI scans of the ankle and foot in a sample of individuals aged from 8 to 25 years old. For both bones, the degree of union between the metaphysis and epiphysis was classified in three stages. Intra- and inter-observer variabilities were good, showing the validity and reproducibility of the method. Our results were consistent with data in the literature indicating that both epiphyses mature earlier in females than in males. Bayesian predictive probabilities were used to assess the validity of our method in estimating the age of an individual in relation to the 18-year threshold. MRI of the ankle and foot can be used in association with other methods to estimate age in living individuals.

A prospective randomized trial of perioperative seizure prophylaxis in patients with intraparenchymal brain tumors

Seizures are a potentially devastating complication of resection of brain tumors. Consequently, many neurosurgeons administer prophylactic antiepileptic drugs (AEDs) in the perioperative period. However, it is currently unclear whether perioperative AEDs should be routinely administered to patients with brain tumors who have never had a seizure. Therefore, the authors conducted a prospective, randomized trial examining the use of phenytoin for postoperative seizure prophylaxis in patients undergoing resection for supratentorial brain metastases or gliomas. Patients with brain tumors (metastases or gliomas) who did not have seizures and who were undergoing craniotomy for tumor resection were randomized to receive either phenytoin for 7 days after tumor resection (prophylaxis group) or no seizure prophylaxis (observation group). Phenytoin levels were monitored daily. Primary outcomes were seizures and adverse events. Using an estimated seizure incidence of 30% in the observation arm and 10% in the prophylaxis arm, a Type I error of 0.05 and a Type II error of 0.20, a target accrual of 142 patients (71 per arm) was planned. The trial was closed before completion of accrual because Bayesian predictive probability analyses performed by an independent data monitoring committee indicated a probability of 0.003 that at the end of the study prophylaxis would prove superior to observation and a probability of 0.997 that there would be insufficient evidence at the end of the trial to choose either arm as superior. At the time of trial closure, 123 patients (77 metastases and 46 gliomas) were randomized, with 62 receiving 7-day phenytoin (prophylaxis group) and 61 receiving no prophylaxis (observation group). The incidence of all seizures was 18% in the observation group and 24% in the prophylaxis group (p = 0.51). Importantly, the incidence of early seizures (< 30 days after surgery) was 8% in the observation group compared with 10% in the prophylaxis group (p = 1.0). Likewise, the incidence of clinically significant early seizures was 3% in the observation group and 2% in the prophylaxis group (p = 0.62). The prophylaxis group experienced significantly more adverse events (18% vs 0%, p < 0.01). Therapeutic phenytoin levels were maintained in 80% of patients. The incidence of seizures after surgery for brain tumors is low (8% [95% CI 3%-18%]) even without prophylactic AEDs, and the incidence of clinically significant seizures is even lower (3%). In contrast, routine phenytoin administration is associated with significant drug-related morbidity. Although the lower-than-anticipated incidence of seizures in the control group significantly limited the power of the study, the low baseline rate of perioperative seizures in patients with brain tumors raises concerns about the routine use of prophylactic phenytoin in this patient population.

Phase II Trial Design with Bayesian Adaptive Randomization and Predictive Probability

We propose a randomized phase II clinical trial design based on Bayesian adaptive randomization and predictive probability monitoring. Adaptive randomization assigns more patients to a more efficacious treatment arm by comparing the posterior probabilities of efficacy between different arms. We continuously monitor the trial by using the predictive probability. The trial is terminated early when it is shown that one treatment is overwhelmingly superior to others or that all the treatments are equivalent. We develop two methods to compute the predictive probability by considering the uncertainty of the sample size of the future data. We illustrate the proposed Bayesian adaptive randomization and predictive probability design by using a phase II lung cancer clinical trial, and we conduct extensive simulation studies to examine the operating characteristics of the design. By coupling adaptive randomization and predictive probability approaches, the trial can treat more patients with a more efficacious treatment and allow for early stopping whenever sufficient information is obtained to conclude treatment superiority or equivalence. The design proposed also controls both the type I and the type II errors and offers an alternative Bayesian approach to the frequentist group sequential design.

Bayes Prediction of Future Observables from Exponentiated Populations with Fixed and Random Sample Size

Bayesian predictive probability density function is obtained when the underlying pop-ulation distribution is exponentiated and subjective prior is used. The corresponding predictive survival function is then obtained and used in constructing 100(1 – ?)% predictive interval, using one- and two- sample schemes when the size of the future sample is fixed and random. In the random case, the size of the future sample is assumed to follow the truncated Poisson distribution with parameter λ. Special attention is paid to the exponentiated Burr type XII population, from which the data are drawn. Two illustrative examples are given, one of which uses simulated data and the other uses data that represent the breaking strength of 64 single carbon fibers of length 10, found in Lawless [40].

Abstract S6-3: Four vs 6 Cycles of Doxorubicin and Cyclophosphamide (AC) or Paclitaxel (T) as Adjuvant Therapy for Breast Cancer in Women with 0-3 Positive Axillary Nodes: CALGB 40101 — A 2x2 Factorial Phase III Trial: First Results Comparing 4 vs 6 Cycles of Therapy

Abstract Background: Four cycles of chemotherapy are frequently used as standard adjuvant chemotherapy for patients with low-risk primary breast cancer, though other regimens such as CAF, CMF, and TAC frequently are given for 6 cycles. Using a phase 3 factorial design we attempted to define whether 6 cycles of one chemotherapy regimen are superior to 4 cycles in patients with low-risk primary breast cancer. We also sought to determine if T would be equally efficacious as compared to AC, with reduced toxicity. Methods: The study enrolled women with operable breast cancer and 0-3 positive nodes. Study stratifiers were ER/PgR, HER2, and menopausal status. When the study was activated in May 2002, AC (60 and 600 mg/m2) was administered every 3 wks for 4 or 6 cycles, and T (80mg/m2) weekly for 12 or 18 wks. In 2003 (after 570 enrolled patients) treatment schedule was changed to every 2 wks for both AC and T (175 mg/m2), each given for 4 or 6 cycles. In 2008 accrual to the 6-cycle regimens was permanently closed due to slow accrual, with 3173 patients enrolled. The primary endpoint for this comparison was the superiority of 6 vs 4 cycles in relapse-free survival (RFS). The study was powered to have 567 RFS events. Data comparing AC with T are not yet available. Results: This report describes the impact of treatment duration and includes the 3173 patients randomized to 6- versus 4-cycles of chemotherapy, 93% of whom had node-negative disease. At a median follow-up of 4.6 years (2.5 - 8 yrs), the number of RFS events is 288 (with 138 on 4 cycles vs 150 on 6 cycles). The 4-yr RFS was 91.6% and 91.8% for 6 and 4 cycles, respectively. The Hazard Ratio of 6 to 4 cycles was 1.10 (95% CI = 0.87-1.39, p=0.42). Four-year OS was 95.3% and 96.4% for 6 and 4 cycles, respectively, with a HR of 6 to 4 cycles of 1.31 (95% CI = 0.95-1.82, p=0.097). Based on the present data the Bayesian predictive probability of concluding superiority of 6 cycles [a primary goal of the study] with 567 RFS events is only 0.001. There was no interaction between the number of cycles and type of chemotherapy, ER/PgR status, or HER2 status. In particular, the effect of number of cycles on RFS and OS was similar for both AC and T. Conclusions: For women with primary breast cancer and 0-3 positive nodes, we found no evidence that extending chemotherapy from 4 to 6 cycles improves clinical outcome. Citation Information: Cancer Res 2010;70(24 Suppl):Abstract nr S6-3.

Killeen's probability of replication and predictive probabilities: How to compute, use, and interpret them.

P. R. Killeen's (2005a) probability of replication (prep) of an experimental result is the fiducial Bayesian predictive probability of finding a same-sign effect in a replication of an experiment. prep is now routinely reported in Psychological Science and has also begun to appear in other journals. However, there is little concrete, practical guidance for use of prep, and the procedure has not received the scrutiny that it deserves. Furthermore, only a solution that assumes a known variance has been implemented. A practical problem with prep is identified: In many articles, prep appears to be incorrectly computed, due to the confusion between 1-tailed and 2-tailed p values. Experimental findings reveal the risk of misinterpreting prep as the predictive probability of finding a same-sign and significant effect in a replication (p srep). Conceptual and practical guidelines are given to avoid these pitfalls. They include an extension to the case of unknown variance. Moreover, other uses of fiducial Bayesian predictive probabilities for analyzing, designing ("how many subjects?"), and monitoring ("when to stop?") experiments are presented. Concluding remarks emphasize the role of predictive procedures in statistical methodology.

A predictive probability design for phase II cancer clinical trials

Two- or three-stage designs are commonly used in phase II cancer clinical trials. These designs possess good frequentist properties and allow early termination of the trial when the interim data indicate that the experimental regimen is inefficacious. The rigid study design, however, can be difficult to follow exactly because the response has to be evaluated at prespecified fixed number of patients. Our goal is to develop an efficient and flexible design that possesses desirable statistical properties. A flexible design based on Bayesian predictive probability and the minimax criterion is constructed. A three-dimensional search algorithm is implemented to determine the design parameters. The new design controls type I and type II error rates, and allows continuous monitoring of the trial outcome. Consequently, under the null hypothesis when the experimental treatment is not efficacious, the design is more efficient in stopping the trial earlier, which results in a smaller expected sample size. Exact computation and simulation studies demonstrate that the predictive probability design possesses good operating characteristics. The predictive probability design is more computationally intensive than two- or three-stage designs. Similar to all designs with early stopping due to futility, the resulting estimate of treatment efficacy may be biased. The predictive probability design is efficient and remains robust in controlling type I and type II error rates when the trial conduct deviates from the original design. It is more adaptable than traditional multi-stage designs in evaluating the study outcome, hence, it is easier to implement. S-PLUS/R programs are provided to assist the study design.

Identification and assessment of ongoing trials in health technology assessment reviews

To assess the importance of ongoing trials in health technology assessment reviews (HTARs) for the National Institute for Clinical Excellence and to provide practical recommendations for identifying ongoing trials and assessing their possible impact. Electronic databases. Ongoing trials (or trials in progress) were defined as any trials that have started but where the results are not yet available or only interim results are available for HTARs. This methodological review included: (1) an assessment of ongoing trials in HTARs completed by the end of August 2002, (2) a survey and assessment of trial registers and other sources of ongoing trials and (3) a summary and assessment of available methods for assessing the possible impacts of ongoing trials. The identification of ongoing trials is a common phenomenon in reviews of health technology assessment. Twenty-three of the 32 HTARs identified one or more ongoing trials and in eight of these the information on identified ongoing trials was not considered in the evidence synthesis and research recommendations. All but one HTAR that considered the potential impact of ongoing trials adopted a narrative approach. Trial registers and grey literature are important sources of information on ongoing trials. All 32 HTARs explicitly or implicitly searched for unpublished studies, and/or ongoing trials and/or grey literature and trial registers. The assessment of six commonly used trial registers suggested that most registers provided sufficient information for reviewers to decide the relevance of identified ongoing trials. However, it is sometimes extremely difficult to know whether ongoing trials identified from different sources (registers) are the same trials or belong to the same multicentre trials. The ISRCTN (the International Standard Randomised Controlled Trial Number) is the most reliable system but it has not been widely adopted. The qualitative assessment of ongoing trials compared major features of completed and ongoing trials, providing information about the possible impact of ongoing trials in terms of relevance, validity, reliability and generalisability. Quantitative methods to assess the impact of ongoing trials include cumulative meta-analysis related methods, fail-safe N, Bayesian data monitoring, and Bayesian interim predictions. The most useful method may be the Bayesian predictive probability, which estimates predictive probabilities for any possible values of treatment effect. A case study indicated that the appropriate use of quantitative methods would strengthen findings from narrative assessment of possible impact of ongoing trials. Identification of ongoing trials is common in HTARs. Searching for ongoing trials in effectiveness reviews should be more thorough and explicit. Conversely, primary researchers, in particular those working with in multicentre trials, should label ongoing trials more clearly, preferably by ISRCTN. Qualitative assessment of identified ongoing trials is crucial and informative. Available quantitative methods could be used to strengthen findings from narrative assessment, although further research and more empirical examples are required. Information from ongoing trials may contribute to syntheses of results, conclusions and recommendations for future research. Future research is suggested into the identification and assessment of ongoing trials in other systematic reviews of effectiveness of health care interventions; existing and new methods for incorporating information on ongoing trials; comparing estimated impacts with the actual results of ongoing trials; and to incorporate findings from the assessment of ongoing trials into decision models.

Bayesian Predictive Probability Functions for Count Data that are Subject to Misclassification

AbstractWe develop three Bayesian predictive probability functions based on data in the form of a double sample. One Bayesian predictive probability function is for predicting the true unobservable count of interest in a future sample for a Poisson model with data subject to misclassification and two Bayesian predictive probability functions for predicting the number of misclassified counts in a current observable fallible count for an event of interest. We formulate a Gibbs sampler to calculate prediction intervals for these three unobservable random variables and apply our new predictive models to calculate prediction intervals for a real‐data example. (© 2004 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Significantly higher pathological complete remission (PCR) rate following neoadjuvant therapy with trastuzumab (H), paclitaxel (P), and anthracycline-containing chemotherapy (CT): Initial results of a randomized trial in operable breast cancer (BC) with HER/2 positive disease

520 Background: In patients (pts) with metastatic BC, trastuzumab [Herceptin (H)] in combination with CT results in higher response rates, longer control of disease, and superior survival. The objective of this study was to determine whether the addition of H to CT in the neoadjuvant setting could increase PCR rate in pts with HER/2 positive disease. Methods: 42 pts with HER/2-positive disease (IHC 3+ or FISH +) with operable BC were randomized to 4 cycles of P followed by 4 cycles of FEC, or the same CT with simultaneous weekly H at 2 mg/kg for 24 weeks.The primary objective was to demonstrate a 20% improvement in PCR (assumed 21% to 41%) with addition of H to CT. At the end of CT±H, pts had definitive surgery. The planned sample size was 164 pts. Results: Prognostic factors were similar in the two groups. After 34 pts had completed therapy, the trial's Data Monitoring Committee stopped the trial for superiority of CT + H. PCR rates were 25% and 67%, respectively, for CT alone (n=16) and CT + H (n=18) (P=0.02). Additional results are included in the table. Fever during neutropenia occurred in 9 and 11 pts, respectively, in CT alone and CT + H. Of those, 3 pts in each subgroup were hospitalized. Decrease in cardiac ejection fraction (>10%) was observed in 6 and 4 pts, respectively, in CT and CT + H. No pts had clinical CHF or other clinically relevant cardiac toxicity. Troponin-T levels remained normal in all pts. The trial was stopped by an independent DMC based on a Bayesian predictive probability of 0.95 that the trial would conclude a significant benefit for CT+H if completed to originally planned 164 pts. Conclusions: Despite the small sample size, these data indicate that adding H to CT as utilized in this trial significantly increased PCR without clinical CHF. Author Disclosure Employment or Leadership Consultant or Advisory Stock Ownership Honoraria Research Funding Expert Testimony Other Remuneration Genentech Genentech Genentech

Bayesian hazard analysis of heavy precipitation in eastern Spain

AbstractThe hazard due to heavy daily rainfall in the Valencia region (eastern Iberian Peninsula) is analysed by using 30‐year records at 72 rain gauge stations. The proposed method is a Bayesian version of the commonly used point over threshold or exceedance methods. For each site, the occurrence of events in time are assumed to be Poisson distributed and the excesses over a selected high threshold are assumed to follow some generalized Pareto distribution. A large uncertainty about the type of distribution for the excesses is observed for each station and the preferred distribution changes from station to station. The large uncertainty in estimated occurrence probabilities or return periods suggests the use of Bayesian predictive occurrence probabilities as the main parameters describing the hazard. Two stations are selected for a detailed analysis. The whole database has been used to obtain predictive exceedance probability spatial distributions for thresholds of 150, 300 and 500 mm of daily precipitation. These maps confirm the most hazardous sites are placed at the northeast of the main mountain range of the region, where it is speculated that deep convection develops when humid northeasterly flows cross the coastal range. Copyright © 2001 Royal Meteorological Society

Bayesian prediction with approximate frequentist validity

We characterize priors which asymptotically match the posterior coverage probability of a Bayesian prediction region with the corresponding frequentist coverage probability. This is done considering both posterior quantiles and highest predictive density regions with reference to a future observation. The resulting priors are shown to be invariant under reparameterization. The role of Jeffreys’ prior in this regard is also investigated. It is further shown that, for any given prior, it may be possible to choose an interval whose Bayesian predictive and frequentist coverage probabilities are asymptotically matched.

USE OF PREDICTIVE PROBABILITIES IN PHASE II AND PHASE III CLINICAL TRIALS

Predictive probability is particularly useful in aiding a decision-making process related to drug development. This is especially true for decisions occurring as the result of interim analyses of clinical trials. Examples of clinical trial applications of Bayesian predictive probability and the use of the beta-binomial distribution are described.

An Assessment of Cumulative Classification

We present a method for building systematics when new knowledge is continuously accumulated. The resulting classification is self-correcting and improves itself by sorting new items as they are added to the material and studied. The formulation is based on Bayesian predictive probability distributions. A new item that has not yet been classified is assigned to the class that has maximal posterior probability or is made to form a group of its own. Such a cumulative classification depends on the order in which the items are classified. The introduction of an already classified training set considerably improves the repeatability of the method. As a case study we applied the method to a large data set for the Enterobacteriaceae. The resulting classifications corresponded well to the general structure of the prevailing taxonomy of Enterobacteriaceae.

Bayesian Predictive Identification and Cumulative Classification of Bacteria

In this paper we give a mathematically precise formulation of an old idea in bacterial taxonomy, namely cumulative classification, where the taxonomy is continuously updated and possibly augmented as new strains are identified. Our formulation is based on Bayesian predictive probability distributions. The criterion for founding a new taxon is given a firm theoretical foundation based on prediction and it is given a clear-cut interpretation. We formulate an algorithm for cumulative classification and apply it to a large database of bacteria belonging to the familyEnterobacteriaceae. The resulting taxonomy makes microbiological sense.

Bayesian predictive approach for inference about proportions.

This paper investigates the Bayesian procedures for comparing proportions. These procedures are especially suitable for accepting (or rejecting) the equivalence of two population proportions. Furthermore the Bayesian predictive probabilities provide a natural and flexible tool in monitoring trials, especially for choosing a sample size and for conducting interim analyses. These methods are illustrated with two examples where antithrombotic treatments are administrated to prevent further occurrences of thromboses.

Predictive comparisons in ordinal models

Bayesian predictive probability function approximations are derived and compared for ordinal logistic regression models. Classification and variable selection problems are also discussed. The methods are illustrated on a large data set of head injury patients.

Predictive Judgments in Situations of Statistical Analysis

Probabilistic judgments made by researchers in psychology were investigated in statistical prediction situations. From these situations, it is possible to test the "representativeness hypothesis" (Tversky & Kahneman, 1971) and the "significance hypothesis" (Oakes, 1986). The predictive judgments concerned both an elementary descriptive statistic and a significance test statistic. In the first case, the predictive judgments were generally coherent and fit comparatively well to Bayesian standard predictive probabilities. In the second case, they were generally incoherent and fit poorly to Bayesian standard predictive probabilities. As for the two hypotheses tested, our findings are compatible with the significance hypothesis, but go against the representativeness hypothesis.

Predictive distributions in life tests under competing causes of failure

SUMMARY In life testing suppose that the units under test can fail due to one of several competing risks. The estimation of parameters in such compound models has been well investigated; see, for example, Chiang (1968, Chapter 11), Boardman & Kendell (1970) and Gail (1975). In this paper Bayesian predictive distributions and probabilities are derived for such situations, and the predictions obtained are compared with some of the classical analogues.