Principles of Conditionality and Layering of Error Rates with Application to Platform Trials

Abstract

There has been a misconception that only one type of error rate control is necessary in clinical trials, leading to debates over whether to prioritize Familywise Error Rate (FWER) or False Discovery Rate (FDR). This misconception has led to misleading statements about FWER control and proposals to shift towards FDR control, which could be manipulated by the industry. In reality, since the early 2000s, biopharmaceutical statistics have implicitly applied two layers of Type I error rate control. This aligns with Tukey's 1953 invention of Error Rate per Family (ERpF) for controlling error across studies, while FWER applies within each study. Our paper clarifies this layering, using Platform trials to demonstrate the verifiable conditions needed across studies for the FDA to fulfill its regulatory mission. We show that controlling FWER within a study at $5\%$ inherently controls ERpF across studies at 5-per-100, regardless of study correlations. This supports current regulatory practices that protect public health while fostering innovation. We also address concerns about ERpF stability in Platform trials, where shared controls introduce dependencies. By applying the Conditionality Principle and utilizing an innovative Shiny app, we explore how correlations impact ERpF variability, providing deeper insights for informed decision-making. Our findings, supported by principles like Layering of Error Rate Controls and the Conditionality Principle, are particularly relevant as Platform trials gain popularity for their efficiency in testing multiple treatments simultaneously.