Discretized Bayesian Induction in Clinical Research: A Glass-Box Paradigm for Small Data, Adaptive Permanent Trials, and Meta-Analysis (Part 5/7)

Modern clinical research is constrained by Null Hypothesis Significance Testing (NHST) and fixed sample size dogmas that collapse rich clinical evidence into binary p-value verdicts (p < 0.05), suffer from the transposition fallacy, enforce unethical delays in delivering effective therapies, and induce severe publication bias. This paper establishes the application of the Discretized Bayesian Induction (BID) framework to clinical trial design, biostatistics, and health economics. By replacing continuous measure theory with exact discrete summations over virtual urns (Popu = 1,000), BID2 provides an audit-ready, glass-box decision-support engine. Baseline epidemiological registries are transformed into objective Maximum Entropy (Maxent) priors via the PEMPI algorithm, enforcing the Prevalence Axiom and reducing the ethical and financial burden of redundant control arms. We introduce the Permanent Clinical Trial paradigm: a continuous learning architecture where incoming patient outcomes update probability distribution vectors (dp) sequentially in real time. We specify ethical adaptive stopping rules: stopping early for efficacy when the lower bound of the 95% Closest-Tail credibility interval crosses the required therapeutic utility threshold, or stopping early for futility when the upper bound falls below profitability. Furthermore, BIDnC achieves causal d-separation on 2^m x n TCOB hypercubes to rebalance non-representative observational cohorts against national census demographics, while localized context tiling enables seamless meta-analyses. Finally, we formalize the EvalCout algorithm, coupling posterior probability vectors directly with monetary utility matrices to compute Expected Net Gain (EBBilan), Value at Risk (VaR), and exact Market Authorization Pivot Prices (AMM) in 1.59 milliseconds.