Academic literature on the topic 'Bayesian Sample size, Prior Elicitation, Clinical trial'

Sample size estimation is a fundamental element of a clinical trial, and a binomial experiment is the most common situation faced in clinical trial design. A Bayesian method to determine sample size is an alternative solution to a frequentist design, especially for studies conducted on small sample sizes. The Bayesian approach uses the available knowledge, which is translated into a prior distribution, instead of a point estimate, to perform the final inference. This procedure takes the uncertainty in data prediction entirely into account. When objective data, historical information, and literature data are not available, it may be indispensable to use expert opinion to derive the prior distribution by performing an elicitation process. Expert elicitation is the process of translating expert opinion into a prior probability distribution. We investigated the estimation of a binomial sample size providing a generalized version of the average length, coverage criteria, and worst outcome criterion. The original method was proposed by Joseph and is defined in a parametric framework based on a Beta-Binomial model. We propose a more flexible approach for binary data sample size estimation in this theoretical setting by considering parametric approaches (Beta priors) and semiparametric priors based on B-splines.

Background Evidence is lacking for safe and effective treatments for juvenile localised scleroderma (JLS). Methotrexate (MTX) is commonly used first line and mycophenolate mofetil (MMF) second line, despite a limited evidence base. A head to head trial of these two medications would provide data on relative efficacy and tolerability. However, a frequentist approach is difficult to deliver in JLS, because of the numbers needed to sufficiently power a trial. A Bayesian approach could be considered. Methods An international consensus meeting was convened including an elicitation exercise where opinion was sought on the relative efficacy and tolerability of MTX compared to MMF to produce prior distributions for a future Bayesian trial. Secondary aims were to achieve consensus agreement on critical aspects of a future trial. Results An international group of 12 clinical experts participated. Opinion suggested superior efficacy and tolerability of MMF compared to MTX; where most likely value of efficacy of MMF was 0.70 (95% confidence interval (CI) 0.34-0.90) and of MTX was 0.68 (95% CI 0.41-0.8). The most likely value of tolerability of MMF was 0.77 (95% CI 0.3-0.94) and of MTX was 0.62 (95% CI 0.32-0.84). The wider CI for MMF highlights that experts were less sure about relative efficacy and tolerability of MMF compared to MTX. Despite using a Bayesian approach, power calculations still produced a total sample size of 240 participants, reflecting the uncertainty amongst experts about the performance of MMF. Conclusions Key factors have been defined regarding the design of a future Bayesian approach clinical trial including elicitation of prior opinion of the efficacy and tolerability of MTX and MMF in JLS. Combining further efficacy data on MTX and MMF with prior opinion could potentially reduce the pre-trial uncertainty so that, when combined with smaller trial sample sizes a compelling evidence base is available.

Medical research has evolved conventions for choosing sample size in randomized clinical trials that rest on the theory of hypothesis testing. Bayesian statisticians have argued that trials should be designed to maximize subjective expected utility in settings of clinical interest. This perspective is compelling given a credible prior distribution on treatment response, but there is rarely consensus on what the subjective prior beliefs should be. We use Wald’s frequentist statistical decision theory to study design of trials under ambiguity. We show that ε-optimal rules exist when trials have large enough sample size. An ε-optimal rule has expected welfare within ε of the welfare of the best treatment in every state of nature. Equivalently, it has maximum regret no larger than ε. We consider trials that draw predetermined numbers of subjects at random within groups stratified by covariates and treatments. We report exact results for the special case of two treatments and binary outcomes. We give simple sufficient conditions on sample sizes that ensure existence of ε-optimal treatment rules when there are multiple treatments and outcomes are bounded. These conditions are obtained by application of Hoeffding large deviations inequalities to evaluate the performance of empirical success rules.

6576 Background: The aim of phase II trials is to determine if a new treatment is promising for further testing in confirmatory clinical trials. Most phase II clinical trials are designed as single-arm trials using a binary outcome with or without interim monitoring for early stopping. In this context, we propose a Bayesian adaptive design denoted as PSSD, predictive sample size selection design (Statistics in Medicine 2012;31:4243-4254). Methods: The design allows for sample size selection followed by any planned interim analyses for early stopping of a trial, together with sample size determination before starting the trial. In the PSSD, we determined the sample size using the predictive probability criterion with two kinds of prior distributions, that is, an ‘analysis prior’ used to compute posterior probabilities and a ‘design prior’ used to obtain prior predictive distributions. In the sample size determination, we provide two sample sizes, that is, N and Nmax, using two types of design priors. At each interim analysis, we calculate the predictive probability of achieving a successful result at the end of the trial using analysis prior in order to stop the trial in case of low or high efficacy, and we select an optimal sample size, that is, either N or Nmax as needed, on the basis of the predictive probabilities. Results: We investigated the operating characteristics through simulation studies, and the PSSD retrospectively applies to a lung cancer clinical trial. As the number of interim looks increases, the probability of type I errors slightly decreases, and that of type II errors increases. The type I error probabilities of the probabilities of the proposed PSSD are almost similar to those of the non-adaptive design. The type II error probabilities in the PSSD are between those of the two fixed sample size (N or Nmax) designs. Conclusions: From a practical standpoint, the proposed design could be useful in phase II single-arm clinical trials with a binary endpoint. In the near future, this approach will be implemented in actual clinical trials to assess its usefulness and to extend it to more complicated clinical trials.

When designing studies involving a continuous endpoint, the hypothesized difference in means ([Formula: see text]) and the assumed variability of the endpoint ([Formula: see text]) play an important role in sample size and power calculations. Traditional methods of sample size re-estimation often update one or both of these parameters using statistics observed from an internal pilot study. However, the uncertainty in these estimates is rarely addressed. We propose a hybrid classical and Bayesian method to formally integrate prior beliefs about the study parameters and the results observed from an internal pilot study into the sample size re-estimation of a two-stage study design. The proposed method is based on a measure of power called conditional expected power (CEP), which averages the traditional power curve using the prior distributions of θ and [Formula: see text] as the averaging weight, conditional on the presence of a positive treatment effect. The proposed sample size re-estimation procedure finds the second stage per-group sample size necessary to achieve the desired level of conditional expected interim power, an updated CEP calculation that conditions on the observed first-stage results. The CEP re-estimation method retains the assumption that the parameters are not known with certainty at an interim point in the trial. Notional scenarios are evaluated to compare the behavior of the proposed method of sample size re-estimation to three traditional methods.

Background: The efficacy–toxicity trade-off based design is a practical Bayesian phase I–II dose-finding methodology. Because the design’s performance is very sensitive to prior hyperparameters and the shape of the target trade-off contour, specifying these two design elements properly is essential. Purpose: The goals are to provide a method that uses elicited mean outcome probabilities to derive a prior that is neither overly informative nor overly disperse, and practical guidelines for specifying the target trade-off contour. Methods: A general algorithm is presented that determines prior hyperparameters using least squares penalized by effective sample size. Guidelines for specifying the trade-off contour are provided. These methods are illustrated by a clinical trial in advanced prostate cancer. A new version of the efficacy–toxicity program is provided for implementation. Results: Together, the algorithm and guidelines provide substantive improvements in the design’s operating characteristics. Limitations: The method requires a substantial number of elicited values and design parameters, and computer simulations are required to obtain an acceptable design. Conclusion: The two key improvements greatly enhance the efficacy–toxicity design’s practical usefulness and are straightforward to implement using the updated computer program. The algorithm for determining prior hyperparameters to ensure a specified level of informativeness is general, and may be applied to models other than that underlying the efficacy–toxicity method.

During drug evaluation trials, information from clinical trials previously conducted on another population, indications or schedules may be available. In these cases, it might be desirable to share information by efficiently using the available resources. In this work, we developed an adaptive power prior with a commensurability parameter for using historical or external information. It allows, at each stage, full borrowing when the data are not in conflict, no borrowing when the data are in conflict or “tuned” borrowing when the data are in between. We propose to apply our adaptive power prior method to bridging studies between Caucasians and Asians, and we focus on the sequential adaptive allocation design, although other design settings can be used. We weight the prior information in two steps: the effective sample size approach is used to set the maximum desirable amount of information to be shared from historical data at each step of the trial; then, in a sort of Empirical Bayes approach, a commensurability parameter is chosen using a measure of distribution distance. This approach avoids elicitation and computational issues regarding the usual Empirical Bayes approach. We propose several versions of our method, and we conducted an extensive simulation study evaluating the robustness and sensitivity to prior choices.

SummaryBackground: Response-adaptive randomisation designs have been proposed to im -prove the efficiency of phase III randomised clinical trials and improve the outcomes of the clinical trial population. In the setting of failure time outcomes, Zhang and Rosen -berger (2007) developed a response-adaptive randomisation approach that targets an optimal allocation, based on a fixed sample size. Objectives: The aim of this research is to propose a response-adaptive randomisation procedure for survival trials with an interim monitoring plan, based on the following optimal criterion: for fixed variance of the esti -mated log hazard ratio, what allocation minimizes the expected hazard of failure? We demonstrate the utility of the design by re -designing a clinical trial on multiple myeloma. Methods: To handle continuous monitoring of data, we propose a Bayesian response-adap -tive randomisation procedure, where the log hazard ratio is the effect measure of interest. Combining the prior with the normal likelihood, the mean posterior estimate of the log hazard ratio allows derivation of the optimal target allocation. We perform a simu lationstudy to assess and compare the perform -ance of this proposed Bayesian hybrid adaptive design to those of fixed, sequential or adaptive – either frequentist or fully Bayesian – designs. Non informative normal priors of the log hazard ratio were used, as well as mixture of enthusiastic and skeptical priors. Stopping rules based on the posterior dis -tribution of the log hazard ratio were com -puted. The method is then illus trated by redesigning a phase III randomised clinical trial of chemotherapy in patients with multiple myeloma, with mixture of normal priors elicited from experts. Results: As expected, there was a reduction in the proportion of observed deaths in the adaptive vs. non-adaptive designs; this reduction was maximized using a Bayes mix -ture prior, with no clear-cut improvement by using a fully Bayesian procedure. The use of stopping rules allows a slight decrease in the observed proportion of deaths under the alternate hypothesis compared with the adaptive designs with no stopping rules. Conclusions: Such Bayesian hybrid adaptive survival trials may be promising alternatives to traditional designs, reducing the duration of survival trials, as well as optimizing the ethical concerns for patients enrolled in the trial.

The aim of this narrative review is to introduce the reader to Bayesian methods that, in our opinion, appear to be the most important in the context of rare diseases. A disease is defined as rare depending on the prevalence of the affected patients in the considered population, for example, about 1 in 1500 people in U.S.; about 1 in 2500 people in Japan; and fewer than 1 in 2000 people in Europe. There are between 6000 and 8000 rare diseases and the main issue in drug development is linked to the challenge of achieving robust evidence from clinical trials in small populations. A better use of all available information can help the development process and Bayesian statistics can provide a solid framework at the design stage, during the conduct of the trial, and at the analysis stage. The focus of this manuscript is to provide a review of Bayesian methods for sample size computation or reassessment during phase II or phase III trial, for response adaptive randomization and of for meta-analysis in rare disease. Challenges regarding prior distribution choice, computational burden and dissemination are also discussed.

Abstract Background Clinical development of new therapies in transfusion-dependent beta-thalassemia has several challenges. Patient enrollment in rare diseases requires multi-center multi-country studies, and the lack of reliable surrogate endpoint for dose selection requires powering for clinical endpoints usually used in Phase 3 trials. An acceptable endpoint from a regulatory perspective which is based on responders analysis, such as proportion of patients experiencing ≥50% reduction in Red Blood Cell (RBC) transfusion burden and a reduction of ≥2 units, requires 12 weeks screening period to establish baseline transfusion burden for reliable comparison. Importantly, higher randomization ratio of treatment:placebo can improve patients' motivation to enroll into a trial, but it is less statistically efficient and requires higher sample size. We designed a Phase-2b, double-blind, randomized, placebo controlled, multi-center study with Vamifeport (NCT04938635) to assess the efficacy and safety of multiple doses of a new therapy in adults with transfusion-dependent beta-thalassemia. The proposed design follows the Bayesian framework with borrowing from published historical control data. The historical control data is used to construct an informative prior for the control arm to reduce the burden of patients randomized to a control arm and improve the trial's efficiency in performing dose selection. Study Design and Methods Adults (18 to 65 y.o.) with documented diagnosis of β-thalassemia or hemoglobin E / β-thalassemia will be randomized to three doses of the investigational drug or placebo plus best supportive care. RBC transfusion dependence is defined as at least 6 RBC Units in the 24 weeks prior to randomization and no transfusion-free period for ≥35 days during that period. The primary endpoint is the proportion of patients experiencing ≥33% reduction of RBC units from baseline and a reduction of ≥2 units assessed from week 13 to week 24. The key secondary endpoints include proportion of patients experiencing ≥33% reduction from week 37 to week 48; proportion of patients experiencing ≥50% reduction over any consecutive 12-week interval from week 1 to week 48 and the mean change from baseline in RBC transfusions (units) from week 13 to week 24. The primary and key-secondary analysis will be conducted in a hierarchical fashion to account for multiplicity. We proposed a Bayesian design with the use of noninformative, or weakly informative, priors for the active dose arms while using a robustified informative prior for the control arm. Historical control data will be "borrowed" in an informative prior for the control arm rate from the Phase 3 trial - BELIEVE. The robustification is required in order to control the level of borrowing depending on the level of prior-data conflict. Prior-data conflict can arise from multiple sources like population heterogeneity between the historical and current study. Therefore, the selection of historical data (BELIEVE trial) addresses similarity in inclusion / exclusion criteria, standard of care etc. The robustification of the informative prior does not take into account prior-data conflict in terms of population or study characteristics but directly focuses on the informative prior of the parameter of interest and the corresponding likelihood of the current data. For example, in the BELIEVE study, out of 112 patients randomized to the control arm, 5 patients (4.5%) had a ≥33% reduction in transfusion burden over 24 weeks. A prior-data conflict may arise if the Phase-2b trial of interest here, suggests that the proportion is substantially different that 4.5% and this can inflate the frequentist Type-I or Type-II error rates examined via simulations. We evaluated Type-I error rates of the proposed design with 5000 Monte-Carlo runs for each scenario of the response rates. Using informative prior with no prior-data conflict the type-I error with no robustification is ≈ 2.4%. As the prior-data conflict increases, without robustification, the type-I error cannot be controlled. However, with a robustification weight of 0.5 the type-I errors can be controlled in line with regulatory requirements. Discussion A proposed Bayesian design with robustified informative prior for the control arm helps reduce patients' burden of randomization to control arm and reduce overall sample size for a rare disease trial when recruitment and trial duration are challenging. Disclosures Muehlemann: Vifor Pharma AG: Consultancy. Mukherjee: Vifor Pharma AG: Consultancy. Taher: Bristol Myers Squibb: Consultancy, Research Funding; Vifor Pharma: Consultancy, Research Funding; Agios Pharmaceuticals: Consultancy; Ionis Pharmaceuticals: Consultancy, Research Funding; Novartis: Consultancy, Research Funding. Gudmundsdottir: Vifor Pharma AG: Current Employment. Morin: Vifor Pharma AG: Current Employment. Richard: Vifor Pharma AG: Current Employment.

In several clinical trial settings, it is challenging to recruit the overall sample provided at the design stage. Several factors (i.e., high costs, regulatory barriers, narrow eligibility criteria and cultural attitudes towards research) can impact on the recruitment process. The poor accrual problem is evident in the clinical research involving adults but also in the pediatric research, but also in pediatric research, where 37% of clinical trials terminate early due to inadequate accrual. From a methodological-statistical standpoint, reduced sample size and the rarity of some diseases under consideration reduce a study’s statistical power, compromising the ability to accurately answer the primary research question due to a reduction in the likelihood to detect a treatment effect. This statistical point of view favors the use of a Bayesian approach to the analysis of clinical trial data. In recent years, Bayesian methods have increasingly been used in the design, monitoring, and analysis of clinical trials due to their flexibility. In clinical trials candidate for early termination for poor accrual reasons, a Bayesian approach can incorporate the available knowledge provided by literature (objective prior) or by elicitation of Experts’ opinions (subjective prior) on the treatment effect under investigation in order to reduce uncertainty in treatment effect estimation. The first article (Chapter 1) shows the potentiality of the Bayesian method for use in pediatric research, demonstrating the possibility to include, in the final inference, prior information and trial data, especially when the small sample size is available to estimate the treatment effect. Moreover, this study aims to underline the importance of a sensitivity analysis conducted on prior definitions in order to investigate the stability of inferential conclusions concerning the different prior choices. In a research setting where objective data to derive prior distribution are not available, an informative inference complemented with an expert elicitation procedure can be used to translate into prior probability distribution (elicitation) the available expert knowledge about treatment effect. The elicitation process in the Bayesian inference can quantify the presence of uncertainty in treatment effect belief. Additionally, this information can be used to plan a study design, e.g., the sample size calculations] and interim analysis. Elicitation may be conducted in a parametric setting, assuming that experts’ opinion may be represented by a good note family of probability distributions identified by hyper-parameters, or in a not parametric and semiparametric hybrid setting. It is widely assessed that the primary limit of a parametric approach is to constrain expert belief into a pre-specified family distribution. The second article (Chapter 2) aims to investigate the state-of-art of the Bayesian prior elicitation methods in clinical trial research performing an in-depth analysis of the discrepancy between the approaches available in the statistical literature and the elicitation procedures currently applied within the clinical trial research. A Bayesian approach to clinical trial data may be defined before the start of the study, by the protocol, defining a sample size taking into account of expert opinion providing the possibility to use also nonparametric approaches. A more flexible sample size method may be suitable, for example, to design a study conducted on small sample sizes as a Phase II clinical trial, which is generally one sample, single stage in which accrued patients, are treated, and are then observed for a possible response. Generally, Bayesian methods, available in the literature to obtain a sample size estimation for binary data, are based on parametric Beta-binomial solutions, considering an inference performed in term of posterior Highest Posterior Density interval (HPD). The aim of the third article (Chapter 3) is to extend the main criteria adopted for the Bayesian Sample size estimation, Average Coverage Criterion (ACC), Average Length Criterion (ALC) and Worse Outcome Criterion (WOC), proposing a sample size estimation method which includes also prior defined in a semiparametric approach to the prior elicitation of the expert’s opinion. In the research article also a practical application of the method to a Phase II clinical trial study design has been reported. The semiparametric solution adopted is a very flexible considering a prior distribution obtained as a balanced optimization of a weighed sum two components; one is a linear combination of B-Spline adapted among expert’s quantiles, another one is an uninformative prior distribution.

In classical group sequential designs, a clinical trial is considered as a success if the experimental treatment is statistically significantly better than placebo. The criteria for stopping or continuing the trial are chosen to control the false-positive rate (type I error). Bayesian group sequential design has an advantage of allowing inclusion of prior information in the analysis. The decision criteria can be based on the posterior or predictive distribution of the treatment effect to stop for success or futility, or to continue for each interim analysis and the final analysis. This chapter introduces Bayesian group sequential designs with examples in a confirmatory setting, including how to calibrate the tuning parameters to set up decision criteria for the interim and final analyses, how to derive the sample size, and how to evaluate the operating characteristics via simulations.