BAYESIAN PHASE I DOSE FINDING IN CANCER TRIALS

This dissertation explores phase I dose-finding designs in cancer trials from three perspectives: the alternative Bayesian dose-escalation rules, a design based on a time-to-dose-limiting toxicity (DLT) model, and a design based on a discrete-time multi-state (DTMS) model. We list alternative Bayesian dose-escalation rules and perform a simulation study for the intra-rule and inter-rule comparisons based on two statistical models to identify the most appropriate rule under certain scenarios. We provide evidence that all the Bayesian rules outperform the traditional ``3+3'' design in the allocation of patients and selection of the maximum tolerated dose. The design based on a time-to-DLT model uses patients' DLT information over multiple treatment cycles in estimating the probability of DLT at the end of treatment cycle 1. Dose-escalation decisions are made whenever a cycle-1 DLT occurs, or two months after the previous check point. Compared to the design based on a logistic regression model, the new design shows more safety benefits for trials in which more late-onset toxicities are expected. As a trade-off, the new design requires more patients on average. The design based on a discrete-time multi-state (DTMS) model has three important attributes: (1) Toxicities are categorized over a distribution of severity levels, (2) Early toxicity may inform dose escalation, and (3) No suspension is required between accrual cohorts. The proposed model accounts for the difference in the importance of the toxicity severity levels and for transitions between toxicity levels. We compare the operating characteristics of the proposed design with those from a similar design based on a fully-evaluated model that directly models the maximum observed toxicity level within the patients' entire assessment window. We describe settings in which, under comparable power, the proposed design shortens the trial. The proposed design offers more benefit compared to the alternative design as patient accrual becomes slower.

Comparison of Bispectral Index (BIS) and Patient State Index (PSI) as objective measures of sedation and analgesia in critically ill/injured patients

Critically ill and injured patients require pain relief and sedation to reduce the body's stress response and to facilitate painful diagnostic and therapeutic procedures. Presently, the level of sedation and analgesia is guided by the use of clinical scores which can be unreliable. There is therefore, a need for an objective measure of sedation and analgesia. The Bispectral Index (BIS) and Patient State Index (PSI) were recently introduced into clinical practice as objective measures of the depth of analgesia and sedation. ^ Aim. To compare the different measures of sedation and analgesia (BIS and PSI) to the standard and commonly used modified Ramsay Score (MRS) and determine if the monitors can be used interchangeably. ^ Methods. MRS, BIS and PSI values were obtained in 50 postoperative cardiac surgery patients requiring analgesia and sedation from June to December 2004. The MRS, BIS and PSI values were assessed hourly for up to 6-h by a single observer. ^ The relationship between BIS and PSI values were explored using scatter plots and correlation between MRS, BIS and PSI was determined using Spearman's correlation coefficient. Intra-class correlation (ICC) was used to determine the inter-rater reliability of MRS, BIS and PSI. Kappa statistics was used to further evaluate the agreement between BIS and PSI at light, moderate and deep levels of sedation. ^ Results. There was a positive correlation between BIS and PSI values (Rho = 0.731, p<0.001). Intra-class correlation between BIS and PSI was 0.58, MRS and BIS 0.43 and MRS and PSI 0.27. Using Kappa statistics, agreement between MRS and BIS was 0.35 (95% CI: 0.27–0.43) and for MRS and PSI was 0.21 (95% CI: 0.15–0.28). The kappa statistic for BIS and PSI was 0.45 (95% CI: 0.37–0.52). Receiver operating characteristics (ROC) curves constructed to detect undersedation indicated an area under the curve (AUC) of 0.91 (95% CI = 0.87 to 0.94) for the BIS and 0.84 (95% CI = 0.79 to 0.88) for the PSI. For detection of oversedation, AUC for the BIS was 0.89 (95% CI = 0.84 to 0.92) and 0.80 (95% CI = 0.75 to 0.85) for the PSI. ^ Conclusions. There is a statistically significant positive correlation between the BIS and PSI but poor correlation and poor test agreement between the MRS and BIS as well as MRS and PSI. Both the BIS and PSI demonstrated a high level of prediction for undersedation and oversedation; however, the BIS and PSI can not be considered interchangeable monitors of sedation. ^

Continuous safety screens for randomized controlled clinical trials with blinded treatment information

Standard methods for testing safety data are needed to ensure the safe conduct of clinical trials. In particular, objective rules for reliably identifying unsafe treatments need to be put into place to help protect patients from unnecessary harm. DMCs are uniquely qualified to evaluate accumulating unblinded data and make recommendations about the continuing safe conduct of a trial. However, it is the trial leadership who must make the tough ethical decision about stopping a trial, and they could benefit from objective statistical rules that help them judge the strength of evidence contained in the blinded data. We design early stopping rules for harm that act as continuous safety screens for randomized controlled clinical trials with blinded treatment information, which could be used by anyone, including trial investigators (and trial leadership). A Bayesian framework, with emphasis on the likelihood function, is used to allow for continuous monitoring without adjusting for multiple comparisons. Close collaboration between the statistician and the clinical investigators will be needed in order to design safety screens with good operating characteristics. Though the math underlying this procedure may be computationally intensive, implementation of the statistical rules will be easy and the continuous screening provided will give suitably early warning when real problems were to emerge. Trial investigators and trial leadership need these safety screens to help them to effectively monitor the ongoing safe conduct of clinical trials with blinded data.^

Performance evaluation in Bayesian adaptive randomization

Bayesian adaptive randomization (BAR) is an attractive approach to allocate more patients to the putatively superior arm based on the interim data while maintains good statistical properties attributed to randomization. Under this approach, patients are adaptively assigned to a treatment group based on the probability that the treatment is better. The basic randomization scheme can be modified by introducing a tuning parameter, replacing the posterior estimated response probability, setting a boundary to randomization probabilities. Under randomization settings comprised of the above modifications, operating characteristics, including type I error, power, sample size, imbalance of sample size, interim success rate, and overall success rate, were evaluated through simulation. All randomization settings have low and comparable type I errors. Increasing tuning parameter decreases power, but increases imbalance of sample size and interim success rate. Compared with settings using the posterior probability, settings using the estimated response rates have higher power and overall success rate, but less imbalance of sample size and lower interim success rate. Bounded settings have higher power but less imbalance of sample size than unbounded settings. All settings have better performance in the Bayesian design than in the frequentist design. This simulation study provided practical guidance on the choice of how to implement the adaptive design. ^

Apply response adaptive randomization to group sequential with early stopping

Group sequential methods and response adaptive randomization (RAR) procedures have been applied in clinical trials due to economical and ethical considerations. Group sequential methods are able to reduce the average sample size by inducing early stopping, but patients are equally allocated with half of chance to inferior arm. RAR procedures incline to allocate more patients to better arm; however it requires more sample size to obtain a certain power. This study intended to combine these two procedures. We applied the Bayesian decision theory approach to define our group sequential stopping rules and evaluated the operating characteristics under RAR setting. The results showed that Bayesian decision theory method was able to preserve the type I error rate as well as achieve a favorable power; further by comparing with the error spending function method, we concluded that Bayesian decision theory approach was more effective on reducing average sample size.^

An examination of the cross-cultural reliability and construct validity of a measure of loneliness

Loneliness is a pervasive, rather common experience in American culture, particularly notable among adolescents. However, the phenomenon is not well documented in the cross-cultural psychiatric literature. For psychiatric epidemiology to encompass a wide array of psychopathologic phenomena, it is important to develop useful measures to characterize and classify both non-clinical and clinical dysfunction in diverse subgroups and cultures.^ The goal of this research was to examine the cross-cultural reliability and construct validity of a scale designed to measure loneliness. The Roberts Loneliness Scale (RLS-8) was administered to 4,060 adolescents ages 10-19 years enrolled in high schools along either side of the Texas-Tamaulipas border region between the U.S. and Mexico. Data collected in 1988 from a study focusing on substance use and psychological distress among adolescents in these regions were used to examine the operating characteristics of the RLS-8. A sample stratified by nationality and language, age, gender, and grade was used for analysis.^ Results indicated that in general the RLS-8 has moderate reliability in the U.S. sample, but not in the Mexican sample. Validity analyses demonstrated that there was evidence for convergent validity of the RLS-8 in the U.S. sample, but none in the Mexican sample. Discriminant validity of the measures in neither sample could be established. Based on the factor structure of the RLS-8, two subscales were created and analyzed for construct validity. Evidence for convergent validity was established for both subscales in both national samples. However, the discriminant validity of the measure remains unsubstantiated in both national samples. Also, the dimensionality of the scale is unresolved.^ One primary goal for future cross-cultural research would be to develop and test better defined culture-specific models of loneliness within the two cultures. From such scientific endeavor, measures of loneliness can be developed or reconstructed to classify the phenomenon in the same manner across cultures. Since estimates of prevalence and incidence are contingent upon reliable and valid screening or diagnostic measures, this objective would serve as an important foundation for future psychiatric epidemiologic inquiry into loneliness. ^

Bayesian adaptive designs for drug combinations in early phase clinical trials

Treating patients with combined agents is a growing trend in cancer clinical trials. Evaluating the synergism of multiple drugs is often the primary motivation for such drug-combination studies. Focusing on the drug combination study in the early phase clinical trials, our research is composed of three parts: (1) We conduct a comprehensive comparison of four dose-finding designs in the two-dimensional toxicity probability space and propose using the Bayesian model averaging method to overcome the arbitrariness of the model specification and enhance the robustness of the design; (2) Motivated by a recent drug-combination trial at MD Anderson Cancer Center with a continuous-dose standard of care agent and a discrete-dose investigational agent, we propose a two-stage Bayesian adaptive dose-finding design based on an extended continual reassessment method; (3) By combining phase I and phase II clinical trials, we propose an extension of a single agent dose-finding design. We model the time-to-event toxicity and efficacy to direct dose finding in two-dimensional drug-combination studies. We conduct extensive simulation studies to examine the operating characteristics of the aforementioned designs and demonstrate the designs' good performances in various practical scenarios.^

Bayesian Adaptive Designs for Early Phase Clinical Trials

My dissertation focuses mainly on Bayesian adaptive designs for phase I and phase II clinical trials. It includes three specific topics: (1) proposing a novel two-dimensional dose-finding algorithm for biological agents, (2) developing Bayesian adaptive screening designs to provide more efficient and ethical clinical trials, and (3) incorporating missing late-onset responses to make an early stopping decision. Treating patients with novel biological agents is becoming a leading trend in oncology. Unlike cytotoxic agents, for which toxicity and efficacy monotonically increase with dose, biological agents may exhibit non-monotonic patterns in their dose-response relationships. Using a trial with two biological agents as an example, we propose a phase I/II trial design to identify the biologically optimal dose combination (BODC), which is defined as the dose combination of the two agents with the highest efficacy and tolerable toxicity. A change-point model is used to reflect the fact that the dose-toxicity surface of the combinational agents may plateau at higher dose levels, and a flexible logistic model is proposed to accommodate the possible non-monotonic pattern for the dose-efficacy relationship. During the trial, we continuously update the posterior estimates of toxicity and efficacy and assign patients to the most appropriate dose combination. We propose a novel dose-finding algorithm to encourage sufficient exploration of untried dose combinations in the two-dimensional space. Extensive simulation studies show that the proposed design has desirable operating characteristics in identifying the BODC under various patterns of dose-toxicity and dose-efficacy relationships. Trials of combination therapies for the treatment of cancer are playing an increasingly important role in the battle against this disease. To more efficiently handle the large number of combination therapies that must be tested, we propose a novel Bayesian phase II adaptive screening design to simultaneously select among possible treatment combinations involving multiple agents. Our design is based on formulating the selection procedure as a Bayesian hypothesis testing problem in which the superiority of each treatment combination is equated to a single hypothesis. During the trial conduct, we use the current values of the posterior probabilities of all hypotheses to adaptively allocate patients to treatment combinations. Simulation studies show that the proposed design substantially outperforms the conventional multi-arm balanced factorial trial design. The proposed design yields a significantly higher probability for selecting the best treatment while at the same time allocating substantially more patients to efficacious treatments. The proposed design is most appropriate for the trials combining multiple agents and screening out the efficacious combination to be further investigated. The proposed Bayesian adaptive phase II screening design substantially outperformed the conventional complete factorial design. Our design allocates more patients to better treatments while at the same time providing higher power to identify the best treatment at the end of the trial. Phase II trial studies usually are single-arm trials which are conducted to test the efficacy of experimental agents and decide whether agents are promising to be sent to phase III trials. Interim monitoring is employed to stop the trial early for futility to avoid assigning unacceptable number of patients to inferior treatments. We propose a Bayesian single-arm phase II design with continuous monitoring for estimating the response rate of the experimental drug. To address the issue of late-onset responses, we use a piece-wise exponential model to estimate the hazard function of time to response data and handle the missing responses using the multiple imputation approach. We evaluate the operating characteristics of the proposed method through extensive simulation studies. We show that the proposed method reduces the total length of the trial duration and yields desirable operating characteristics for different physician-specified lower bounds of response rate with different true response rates.

Bayesian adaptive designs in early phase clinical trials

There are two practical challenges in the phase I clinical trial conduct: lack of transparency to physicians, and the late onset toxicity. In my dissertation, Bayesian approaches are used to address these two problems in clinical trial designs. The proposed simple optimal designs cast the dose finding problem as a decision making process for dose escalation and deescalation. The proposed designs minimize the incorrect decision error rate to find the maximum tolerated dose (MTD). For the late onset toxicity problem, a Bayesian adaptive dose-finding design for drug combination is proposed. The dose-toxicity relationship is modeled using the Finney model. The unobserved delayed toxicity outcomes are treated as missing data and Bayesian data augment is employed to handle the resulting missing data. Extensive simulation studies have been conducted to examine the operating characteristics of the proposed designs and demonstrated the designs' good performances in various practical scenarios.^

Adaptive clinical trial design for targeted therapy development

The development of targeted therapy involve many challenges. Our study will address some of the key issues involved in biomarker identification and clinical trial design. In our study, we propose two biomarker selection methods, and then apply them in two different clinical trial designs for targeted therapy development. In particular, we propose a Bayesian two-step lasso procedure for biomarker selection in the proportional hazards model in Chapter 2. In the first step of this strategy, we use the Bayesian group lasso to identify the important marker groups, wherein each group contains the main effect of a single marker and its interactions with treatments. In the second step, we zoom in to select each individual marker and the interactions between markers and treatments in order to identify prognostic or predictive markers using the Bayesian adaptive lasso. In Chapter 3, we propose a Bayesian two-stage adaptive design for targeted therapy development while implementing the variable selection method given in Chapter 2. In Chapter 4, we proposed an alternate frequentist adaptive randomization strategy for situations where a large number of biomarkers need to be incorporated in the study design. We also propose a new adaptive randomization rule, which takes into account the variations associated with the point estimates of survival times. In all of our designs, we seek to identify the key markers that are either prognostic or predictive with respect to treatment. We are going to use extensive simulation to evaluate the operating characteristics of our methods.^

BAYESIAN STATISTICAL METHODS IN GENE-ENVIRONMENT AND GENE-GENE INTERACTION STUDIES

Complex diseases such as cancer result from multiple genetic changes and environmental exposures. Due to the rapid development of genotyping and sequencing technologies, we are now able to more accurately assess causal effects of many genetic and environmental factors. Genome-wide association studies have been able to localize many causal genetic variants predisposing to certain diseases. However, these studies only explain a small portion of variations in the heritability of diseases. More advanced statistical models are urgently needed to identify and characterize some additional genetic and environmental factors and their interactions, which will enable us to better understand the causes of complex diseases. In the past decade, thanks to the increasing computational capabilities and novel statistical developments, Bayesian methods have been widely applied in the genetics/genomics researches and demonstrating superiority over some regular approaches in certain research areas. Gene-environment and gene-gene interaction studies are among the areas where Bayesian methods may fully exert its functionalities and advantages. This dissertation focuses on developing new Bayesian statistical methods for data analysis with complex gene-environment and gene-gene interactions, as well as extending some existing methods for gene-environment interactions to other related areas. It includes three sections: (1) Deriving the Bayesian variable selection framework for the hierarchical gene-environment and gene-gene interactions; (2) Developing the Bayesian Natural and Orthogonal Interaction (NOIA) models for gene-environment interactions; and (3) extending the applications of two Bayesian statistical methods which were developed for gene-environment interaction studies, to other related types of studies such as adaptive borrowing historical data. We propose a Bayesian hierarchical mixture model framework that allows us to investigate the genetic and environmental effects, gene by gene interactions (epistasis) and gene by environment interactions in the same model. It is well known that, in many practical situations, there exists a natural hierarchical structure between the main effects and interactions in the linear model. Here we propose a model that incorporates this hierarchical structure into the Bayesian mixture model, such that the irrelevant interaction effects can be removed more efficiently, resulting in more robust, parsimonious and powerful models. We evaluate both of the 'strong hierarchical' and 'weak hierarchical' models, which specify that both or one of the main effects between interacting factors must be present for the interactions to be included in the model. The extensive simulation results show that the proposed strong and weak hierarchical mixture models control the proportion of false positive discoveries and yield a powerful approach to identify the predisposing main effects and interactions in the studies with complex gene-environment and gene-gene interactions. We also compare these two models with the 'independent' model that does not impose this hierarchical constraint and observe their superior performances in most of the considered situations. The proposed models are implemented in the real data analysis of gene and environment interactions in the cases of lung cancer and cutaneous melanoma case-control studies. The Bayesian statistical models enjoy the properties of being allowed to incorporate useful prior information in the modeling process. Moreover, the Bayesian mixture model outperforms the multivariate logistic model in terms of the performances on the parameter estimation and variable selection in most cases. Our proposed models hold the hierarchical constraints, that further improve the Bayesian mixture model by reducing the proportion of false positive findings among the identified interactions and successfully identifying the reported associations. This is practically appealing for the study of investigating the causal factors from a moderate number of candidate genetic and environmental factors along with a relatively large number of interactions. The natural and orthogonal interaction (NOIA) models of genetic effects have previously been developed to provide an analysis framework, by which the estimates of effects for a quantitative trait are statistically orthogonal regardless of the existence of Hardy-Weinberg Equilibrium (HWE) within loci. Ma et al. (2012) recently developed a NOIA model for the gene-environment interaction studies and have shown the advantages of using the model for detecting the true main effects and interactions, compared with the usual functional model. In this project, we propose a novel Bayesian statistical model that combines the Bayesian hierarchical mixture model with the NOIA statistical model and the usual functional model. The proposed Bayesian NOIA model demonstrates more power at detecting the non-null effects with higher marginal posterior probabilities. Also, we review two Bayesian statistical models (Bayesian empirical shrinkage-type estimator and Bayesian model averaging), which were developed for the gene-environment interaction studies. Inspired by these Bayesian models, we develop two novel statistical methods that are able to handle the related problems such as borrowing data from historical studies. The proposed methods are analogous to the methods for the gene-environment interactions on behalf of the success on balancing the statistical efficiency and bias in a unified model. By extensive simulation studies, we compare the operating characteristics of the proposed models with the existing models including the hierarchical meta-analysis model. The results show that the proposed approaches adaptively borrow the historical data in a data-driven way. These novel models may have a broad range of statistical applications in both of genetic/genomic and clinical studies.

Modified 3+3 design for phase I clinical trials

Phase I clinical trial is mainly designed to determine the maximum tolerated dose (MTD) of a new drug. Optimization of phase I trial design is crucial to minimize the number of enrolled patients exposed to unsafe dose levels and to provide reliable information to the later phases of clinical trials. Although it has been criticized about its inefficient MTD estimation, nowadays the traditional 3+3 method remains dominant in practice due to its simplicity and conservative estimation. There are many new designs that have been proven to generate more credible MTD estimation, such as the Continual Reassessment Method (CRM). Despite its accepted better performance, the CRM design is still not widely used in real trials. There are several factors that contribute to the difficulties of CRM adaption in practice. First, CRM is not widely accepted by the regulatory agencies such as FDA in terms of safety. It is considered to be less conservative and tend to expose more patients above the MTD level than the traditional design. Second, CRM is relatively complex and not intuitive for the clinicians to fully understand. Third, the CRM method take much more time and need statistical experts and computer programs throughout the trial. The current situation is that the clinicians still tend to follow the trial process that they are comfortable with. This situation is not likely to change in the near future. Based on this situation, we have the motivation to improve the accuracy of MTD selection while follow the procedure of the traditional design to maintain simplicity. We found that in 3+3 method, the dose transition and the MTD determination are relatively independent. Thus we proposed to separate the two stages. The dose transition rule remained the same as 3+3 method. After getting the toxicity information from the dose transition stage, we combined the isotonic transformation to ensure the monotonic increasing order before selecting the optimal MTD. To compare the operating characteristics of the proposed isotonic method and the other designs, we carried out 10,000 simulation trials under different dose setting scenarios to compare the design characteristics of the isotonic modified method with standard 3+3 method, CRM, biased coin design (BC) and k-in-a-row design (KIAW). The isotonic modified method improved MTD estimation of the standard 3+3 in 39 out of 40 scenarios. The improvement is much greater when the target is 0.3 other than 0.25. The modified design is also competitive when comparing with other selected methods. A CRM method performed better in general but was not as stable as the isotonic method throughout the different dose settings. The results demonstrated that our proposed isotonic modified method is not only easily conducted using the same procedure as 3+3 but also outperforms the conventional 3+3 design. It can also be applied to determine MTD for any given TTL. These features make the isotonic modified method of practical value in phase I clinical trials.^

External validation study of a clinical prediction rule for ambulation outcomes after traumatic spinal cord injury

The main objective of this study was to determine the external validity of a clinical prediction rule developed by the European Multicenter Study on Human Spinal Cord Injury (EM-SCI) to predict the ambulation outcomes 12 months after traumatic spinal cord injury. Data from the North American Clinical Trials Network (NACTN) data registry with approximately 500 SCI cases were used for this validity study. The predictive accuracy of the EM-SCI prognostic model was evaluated using calibration and discrimination based on 231 NACTN cases. The area under the receiver-operating-characteristics curve (ROC) curve was 0.927 (95% CI 0.894 – 0.959) for the EM-SCI model when applied to NACTN population. This is lower than the AUC of 0.956 (95% CI 0.936 – 0.976) reported for the EM-SCI population, but suggests that the EM-SCI clinical prediction rule distinguished well between those patients in the NACTN population who were able to achieve independent ambulation and those who did not achieve independent ambulation. The calibration curve suggests that higher the prediction score is, the better the probability of walking with the best prediction for AIS D patients. In conclusion, the EM-SCI clinical prediction rule was determined to be generalizable to the adult NACTN SCI population.^

Optimal, minimax, and Bayesian two-stage designs in two-dose phase II clinical trials

Background: For most cytotoxic and biologic anti-cancer agents, the response rate of the drug is commonly assumed to be non-decreasing with an increasing dose. However, an increasing dose does not always result in an appreciable increase in the response rate. This may especially be true at high doses for a biologic agent. Therefore, in a phase II trial the investigators may be interested in testing the anti-tumor activity of a drug at more than one (often two) doses, instead of only at the maximum tolerated dose (MTD). This way, when the lower dose appears equally effective, this dose can be recommended for further confirmatory testing in a phase III trial under potential long-term toxicity and cost considerations. A common approach to designing such a phase II trial has been to use an independent (e.g., Simon's two-stage) design at each dose ignoring the prior knowledge about the ordering of the response probabilities at the different doses. However, failure to account for this ordering constraint in estimating the response probabilities may result in an inefficient design. In this dissertation, we developed extensions of Simon's optimal and minimax two-stage designs, including both frequentist and Bayesian methods, for two doses that assume ordered response rates between doses. ^ Methods: Optimal and minimax two-stage designs are proposed for phase II clinical trials in settings where the true response rates at two dose levels are ordered. We borrow strength between doses using isotonic regression and control the joint and/or marginal error probabilities. Bayesian two-stage designs are also proposed under a stochastic ordering constraint. ^ Results: Compared to Simon's designs, when controlling the power and type I error at the same levels, the proposed frequentist and Bayesian designs reduce the maximum and expected sample sizes. Most of the proposed designs also increase the probability of early termination when the true response rates are poor. ^ Conclusion: Proposed frequentist and Bayesian designs are superior to Simon's designs in terms of operating characteristics (expected sample size and probability of early termination, when the response rates are poor) Thus, the proposed designs lead to more cost-efficient and ethical trials, and may consequently improve and expedite the drug discovery process. The proposed designs may be extended to designs of multiple group trials and drug combination trials.^