Bayesian HPD-based sample size determination using semi-parametric prior elicitation

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.