Theory of clinical therapeutic progress: reconciling equipoise with fat-tailed (skewed) outcomes

Randomized controlled trials (RCTs) embody a paradox: they require equipoise-genuine uncertainty about treatment effects-to ethically protect participants, yet this very requirement can slow therapeutic innovation by discouraging trials of promising new treatments. We sought to determine which statistical distribution best reflects the balance between protecting trial participants and advancing therapeutic discoveries.

We performed a systematic review to analyze 716 cancer RCTs (1955-2018; published by 2022), encompassing 984 experimental vs standard treatments and ∼350,000 patients. Treatment effects were expressed as odds ratios (ORs >1 favoring new therapy). We compared multiple statistical models to identify the distribution that best describes observed effects while preserving equipoise.

Treatment effects were not normally distributed but followed a piecewise log-normal-generalized Pareto distribution (log-normal-GPD). This model captured the heavy right tail of large treatment effects (∼3% breakthroughs) better than competing distributions. Entropy, a measure of uncertainty, reached 96%-a modest 4% reduction from the theoretical maximum under normal theory, yet sufficient to maintain near-maximum unpredictability in patient-level randomization. Importantly, the heavier tail of the log-normal-GPD model increased the probability of identifying breakthrough therapies by ∼3% without undermining the ethical principle of 50:50 allocation. Standard assumptions of normality, frequently used in meta-analysis, overstated precision and failed to capture extreme outcomes, whereas the log-normal-GPD more accurately reflected trial data.

We show that linking ethics (equipoise) with the science of uncertainty (entropy) identifies the optimal statistical distribution driving therapeutic discoveries (log-normal-GPD). Our model preserves ethical unpredictability for patients while modestly enhancing the likelihood of breakthroughs, thereby reconciling patient protection with societal need for innovation. Our findings highlight the limitations of assuming normality in RCTs and meta-analyses and call for reevaluating statistical assumptions in trial design, Bayesian prior specification, and guideline development. Recognizing the skewed distribution of treatment effects can accelerate therapeutic progress while maintaining the ethical foundation of clinical research. Fat tails enable breakthroughs; thin tails truncate and hide them.

Medical progress relies on research that ultimately must rest, in part, on experimentation in randomized controlled trials (RCTs) involving human subjects. Researchers are ethically required to protect trial patients from being knowingly exposed to inferior treatments. This is achieved by requiring that investigators are truly uncertain whether new treatments are better than others. On the other hand, funders and investigators spend years developing new treatments. As a result, they often have informative hunches about which treatments would be better. Under which circumstances do the societal interests in developing new treatments align with the protection of patients volunteering in trials? We analyzed a large number of cancer trials published from 1955 to 2022 and found that a special statistical approach (log-normal-GPD distribution) best supports both developing better treatments while upholding patient protection in RCTs. Adopting these principles in future research could enhance the conduct of clinical trials, leading to advances in therapeutics and improved methods for developing treatment guidelines, ultimately benefiting both society at large and individual patients. When ethics align with science, the discovery of new treatments advances.