Interim analysis of clinical trials: Simulation studies of fractional Brownian motion

Interim clinical trial monitoring procedures were motivated by ethical and economic considerations. Classical Brownian motion (Bm) techniques for statistical monitoring of clinical trials were widely used. Conditional power argument and α-spending function based boundary crossing probabilities are popular statistical hypothesis testing procedures under the assumption of Brownian motion. However, it is not rare that the assumptions of Brownian motion are only partially met for trial data. Therefore, I used a more generalized form of stochastic process, called fractional Brownian motion (fBm), to model the test statistics. Fractional Brownian motion does not hold Markov property and future observations depend not only on the present observations but also on the past ones. In this dissertation, we simulated a wide range of fBm data, e.g., H = 0.5 (that is, classical Bm) vs. 0.5< H <1, with treatment effects vs. without treatment effects. Then the performance of conditional power and boundary-crossing based interim analyses were compared by assuming that the data follow Bm or fBm. Our simulation study suggested that the conditional power or boundaries under fBm assumptions are generally higher than those under Bm assumptions when H > 0.5 and also matches better with the empirical results. ^

A simulation study using the hybrid statistic and the meta-analysis t-test for data with matched and unmatched subjects in the interim analysis of clinical trials

An interim analysis is usually applied in later phase II or phase III trials to find convincing evidence of a significant treatment difference that may lead to trial termination at an earlier point than planned at the beginning. This can result in the saving of patient resources and shortening of drug development and approval time. In addition, ethics and economics are also the reasons to stop a trial earlier. In clinical trials of eyes, ears, knees, arms, kidneys, lungs, and other clustered treatments, data may include distribution-free random variables with matched and unmatched subjects in one study. It is important to properly include both subjects in the interim and the final analyses so that the maximum efficiency of statistical and clinical inferences can be obtained at different stages of the trials. So far, no publication has applied a statistical method for distribution-free data with matched and unmatched subjects in the interim analysis of clinical trials. In this simulation study, the hybrid statistic was used to estimate the empirical powers and the empirical type I errors among the simulated datasets with different sample sizes, different effect sizes, different correlation coefficients for matched pairs, and different data distributions, respectively, in the interim and final analysis with 4 different group sequential methods. Empirical powers and empirical type I errors were also compared to those estimated by using the meta-analysis t-test among the same simulated datasets. Results from this simulation study show that, compared to the meta-analysis t-test commonly used for data with normally distributed observations, the hybrid statistic has a greater power for data observed from normally, log-normally, and multinomially distributed random variables with matched and unmatched subjects and with outliers. Powers rose with the increase in sample size, effect size, and correlation coefficient for the matched pairs. In addition, lower type I errors were observed estimated by using the hybrid statistic, which indicates that this test is also conservative for data with outliers in the interim analysis of clinical trials.^

A RANDOMIZED TRIAL OF BILEVEL POSITIVE AIRWAY PRESSURE DEVICE AND HIGH FLOW OXYGEN FOR PERSISTENT DYSPNEA IN

Background: Dyspnea is a common and distressing symptom among patients with advanced cancer. The role of bilevel positive airway pressure (BIPAP) and Vapotherm in the relief of dyspnea have not been well defined. We aimed to determine and to compare the efficacy of BIPAP and VapoTherm for cancer related dyspnea. Methods: In this randomized, open-label, crossover study, we randomly assigned advanced cancer patients with persistent dyspnea >=3/10 to either Vapotherm for 2 hours followed by BiPAP for 2 hours, or BiPAP followed by Vaptherm. A variable washout period was instituted between interventions. The primary end point was change in numeric rating scale before and after each intervention. We planned to enroll 50 patients in total. Results: Among the 803 patients screened over the last 8 months, 62 (26%) were eligible, and 16 (2%) were enrolled so far. Five patients completed the entire study successfully, 4 discontinued the study prematurely due to prolonged relief of dyspnea, and 7 dropped out for various reasons, including inability to tolerate BiPAP (N=3), anxiety (N=2), fatigue (N=1) and pain requiring opioids (N=1). The median baseline numeric rating score for dyspnea was 7/10 (interquartile range (IQR) 5-8), and the median baseline Borg score was 4/10 (3-7). Interim analysis revealed that BiPAP was associated with a median change in numeric rating score of -3 (N=10, IQR -6.3 to -1, p=0.007) and modified Borg score of -1 (N=10, IQR -3 to 0.3, p=0.058), while Vapotherm was associated with a median change in numeric rating score of -2 (N=9, IQR -3 to -1, p=0.011) and modified Borg score of -2.5 (N=8, IQR -5.5 to -0.1, p=0.051). Among the 5 individuals who completed the entire study, 2 preferred Vapotherm, 2 favored BiPAP, and 1 liked both. The respiratory rate decreased and the oxygen saturation improved with both interventions. No significant toxicities were observed. Conclusions: We were successfully able to enroll patients onto this clinic trial. Our preliminary results suggest that BiPAP and Vapotherm are highly efficacious in providing relief for patients with persistent refractory dyspnea. A direct comparison of the two interventions will be done upon study completion. Further research is necessary to confirm our findings.

Sequential updating via dynamic hierarchical models: A Bayesian approach to longitudinal data analysis

Most statistical analysis, theory and practice, is concerned with static models; models with a proposed set of parameters whose values are fixed across observational units. Static models implicitly assume that the quantified relationships remain the same across the design space of the data. While this is reasonable under many circumstances this can be a dangerous assumption when dealing with sequentially ordered data. The mere passage of time always brings fresh considerations and the interrelationships among parameters, or subsets of parameters, may need to be continually revised. ^ When data are gathered sequentially dynamic interim monitoring may be useful as new subject-specific parameters are introduced with each new observational unit. Sequential imputation via dynamic hierarchical models is an efficient strategy for handling missing data and analyzing longitudinal studies. Dynamic conditional independence models offers a flexible framework that exploits the Bayesian updating scheme for capturing the evolution of both the population and individual effects over time. While static models often describe aggregate information well they often do not reflect conflicts in the information at the individual level. Dynamic models prove advantageous over static models in capturing both individual and aggregate trends. Computations for such models can be carried out via the Gibbs sampler. An application using a small sample repeated measures normally distributed growth curve data is presented. ^

Bayesian doubly optimal group sequential designs for randomized clinical trials

When conducting a randomized comparative clinical trial, ethical, scientific or economic considerations often motivate the use of interim decision rules after successive groups of patients have been treated. These decisions may pertain to the comparative efficacy or safety of the treatments under study, cost considerations, the desire to accelerate the drug evaluation process, or the likelihood of therapeutic benefit for future patients. At the time of each interim decision, an important question is whether patient enrollment should continue or be terminated; either due to a high probability that one treatment is superior to the other, or a low probability that the experimental treatment will ultimately prove to be superior. The use of frequentist group sequential decision rules has become routine in the conduct of phase III clinical trials. In this dissertation, we will present a new Bayesian decision-theoretic approach to the problem of designing a randomized group sequential clinical trial, focusing on two-arm trials with time-to-failure outcomes. Forward simulation is used to obtain optimal decision boundaries for each of a set of possible models. At each interim analysis, we use Bayesian model selection to adaptively choose the model having the largest posterior probability of being correct, and we then make the interim decision based on the boundaries that are optimal under the chosen model. We provide a simulation study to compare this method, which we call Bayesian Doubly Optimal Group Sequential (BDOGS), to corresponding frequentist designs using either O'Brien-Fleming (OF) or Pocock boundaries, as obtained from EaSt 2000. Our simulation results show that, over a wide variety of different cases, BDOGS either performs at least as well as both OF and Pocock, or on average provides a much smaller trial. ^

Bayesian dual threshold design with Dirichlet distribution: An alternative way to frequentist multi-stage phase II designs in oncology

Many phase II clinical studies in oncology use two-stage frequentist design such as Simon's optimal design. However, they have a common logistical problem regarding the patient accrual at the interim. Strictly speaking, patient accrual at the end of the first stage may have to be suspended until all patients have events, success or failure. For example, when the study endpoint is six-month progression free survival, patient accrual has to be stopped until all outcomes from stage I is observed. However, study investigators may have concern when accrual is suspended after the first stage due to the loss of accrual momentum during this hiatus. We propose a two-stage phase II design that resolves the patient accrual problem due to an interim analysis, and it can be used as an alternative way to frequentist two-stage phase II studies in oncology. ^

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. ^

The role of chronic irritation and inflammation in tumor promotion in CD-1 mice by petroleum middle distillates

An initiation-promotion bioassay in CD-1 mice was used to examine the role of chronic irritation and inflammation in tumor promotion by petroleum middle distillates. A representative hydrodesulfurized middle distillate (API 81-07) was selected as the test article. Test groups (54 mice per group) were initiated once with 50 ug of 7,12-dimethylbenzanthracene (DMBA). Promotion with API 81-07 consisted of twice weekly treatments for 25 weeks with either 25 ul, 50 ul, 50 ul + daily treatment with 15 ug dexamethasone, 50 ul + post-application washings, and 100 ul. Three mice from each group were sacrificed at 21 day intervals (24 total per group). The skin from interim sacrificed (IS) mice was examined histopathologically for tumor, acanthosis, hyperkeratosis, pseudo-epitheliomatous hyperplasia, epidermal crusting, and subacute inflammation. In-life observations included examination of all mice for erythema and edema for 8 weeks following the first promotion treatment. Tumor incident at study termination was as follows: 25 ul (45%), 50 ul (43%), 50 ul + dexamethasone (0%), 50 ul + washing (70%), and 100 ul (81%). An overall correlation of $>$0.90 between tumor incidence and group means for acanthosis and hyperkeratosis was observed in IS mice at all intervals. Correlations of $<$0.75 were observed for other group mean histopathological parameters and tumor incidence. The overall correlation of group mean erythema and edema with tumor incident was $>$0.90. The results of this study support the hypothesis that induction of a lasting, albeit mild, hyperplasia is an essential, but not sufficient requirement, for tumor promotion. Furthermore, subacute inflammation does not appear to be a significant factor in tumor promotion by petroleum middle distillates. However, inflammation may be a factor in tumor progression. ^

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.