The harmonic mean χ 2 ‐test to substantiate scientific findings

Beyond the two-trials rule

The two-trials rule for drug approval requires "at least two adequate and well-controlled studies, each convincing on its own, to establish effectiveness." This is usually implemented by requiring two significant pivotal trials and is the standard regulatory requirement to provide evidence for a new drug's efficacy. However, there is need to develop suitable alternatives to this rule for a number of reasons, including the possible availability of data from more than two trials. I consider the case of up to three studies and stress the importance to control the partial Type-I error rate, where only some studies have a true null effect, while maintaining the overall Type-I error rate of the two-trials rule, where all studies have a null effect. Some less-knownP $$ P $$ -value combination methods are useful to achieve this: Pearson's method, Edgington's method and the recently proposed harmonic meanχ 2 $$ {\chi}^2 $$ -test. I study their properties and discuss how they can be extended to a sequential assessment of success while still ensuring overall Type-I error control. I compare the different methods in terms of partial Type-I error rate, project power and the expected number of studies required. Edgington's method is eventually recommended as it is easy to implement and communicate, has only moderate partial Type-I error rate inflation but substantially increased project power.

Combining evidence from clinical trials in conditional or accelerated approval

Conditional (European Medicines Agency) or accelerated (U.S. Food and Drug Administration) approval of drugs allows earlier access to promising new treatments that address unmet medical needs. Certain post-marketing requirements must typically be met in order to obtain full approval, such as conducting a new post-market clinical trial. We study the applicability of the recently developed harmonic mean χ 2 $$ {\chi}^2 $$ -test to this conditional or accelerated approval framework. The proposed approach can be used both to support the design of the post-market trial and the analysis of the combined evidence provided by both trials. Other methods considered are the two-trials rule, Fisher's criterion and Stouffer's method. In contrast to some of the traditional methods, the harmonic mean χ 2 $$ {\chi}^2 $$ -test always requires a post-market clinical trial. If the p $$ p $$ -value from the pre-market clinical trial is ≪ 0.025 $$ \ll 0.025 $$ , a smaller sample size for the post-market clinical trial is needed than with the two-trials rule. For illustration, we apply the harmonic mean χ 2 $$ {\chi}^2 $$ -test to a drug which received conditional (and later full) market licensing by the EMA. A simulation study is conducted to study the operating characteristics of the harmonic mean χ 2 $$ {\chi}^2 $$ -test and two-trials rule in more detail. We finally investigate the applicability of these two methods to compute the power at interim of an ongoing post-market trial. These results are expected to aid in the design and assessment of the required post-market studies in terms of the level of evidence required for full approval.

Should the two-trial paradigm still be the gold standard in drug assessment?

Two significant pivotal trials are usually required for a new drug approval by a regulatory agency. This standard requirement is known as the two-trial paradigm. However, several authors have questioned why we need exactly two pivotal trials, what statistical error the regulators are trying to protect against, and potential alternative approaches. Therefore, it is important to investigate these questions to better understand the regulatory decision-making in the assessment of drugs' effectiveness. It is common that two identically designed trials are run solely to adhere to the two-trial rule. Previous work showed that combining the data from the two trials into a single trial (one-trial paradigm) would increase the power while ensuring the same level of type I error protection as the two-trial paradigm. However, this is true only under a specific scenario and there is little investigation on the type I error protection over the whole null region. In this article, we compare the two paradigms by considering scenarios in which the two trials are conducted in identical or different populations as well as with equal or unequal size. With identical populations, the results show that a single trial provides better type I error protection and higher power. Conversely, with different populations, although the one-trial rule is more powerful in some cases, it does not always protect against the type I error. Hence, there is the need for appropriate flexibility around the two-trial paradigm and the appropriate approach should be chosen based on the questions we are interested in.

HSL1 and BAM1/2 impact epidermal cell development by sensing distinct signaling peptides

The membrane receptor kinases HAESA and HSL2 recognize a family of IDA/IDL signaling peptides to control cell separation processes in different plant organs. The homologous HSL1 has been reported to regulate epidermal cell patterning by interacting with a different class of signaling peptides from the CLE family. Here we demonstrate that HSL1 binds IDA/IDL peptides with high, and CLE peptides with lower affinity, respectively. Ligand sensing capability and receptor activation of HSL1 require a SERK co-receptor kinase. Crystal structures with IDA/IDLs or with CLE9 reveal that HSL1-SERK1 complex recognizes the entire IDA/IDL signaling peptide, while only parts of CLE9 are bound to the receptor. In contrast, the receptor kinase BAM1 interacts with the entire CLE9 peptide with high affinity and specificity. Furthermore, the receptor tandem BAM1/BAM2 regulates epidermal cell division homeostasis. Consequently, HSL1-IDLs and BAM1/BAM2-CLEs independently regulate cell patterning in the leaf epidermal tissue.