Fragility of Assumptions: Response

Authors’ Response:

We appreciate the opportunity to provide a response to the recent thoughtful “Letter to the Editor” submission. Building on this important discussion, we advocate for the complementary use of both the standard Fragility Index (FI) for dichotomous data and the Continuous Fragility Index (CFI) for continuous outcomes, recognizing the distinct valuable insights each metric offers, thus providing more contextual data for the reader in determination of clinical decision-making.

The traditional FI, while useful, is inherently limited to binary outcomes and depends on assumptions about which group's data should be perturbed to assess stability. As highlighted in the recent letter, methods such as unit fragility represent important refinements but still operate within the dichotomous framework. This can be restrictive in trials where the primary outcomes are naturally continuous.

The CFI addresses this limitation by quantifying how much each individual value in a continuous outcome must be perturbed to shift the result from statistically significant to nonsignificant, or vice versa. The algorithm is described in detail in Caldwell et al's ¹ article. In practice, the method requires the entire data set of patients to be available; however, this is rarely available in published trials. Caldwell et al describe an approximation method to calculate the CFI, which relies only on descriptive statistics from the 2 groups. In this method, the sample size, mean, and SD from each patient group are used to generate a random, normally distributed data set of patient outcomes for each group. A tolerance parameter is also specified for the calculation, describing the maximal amount the simulated data's mean and standard deviation may differ from the provided mean and standard deviation. This new data set is used to calculate an approximation of the CFI of the original data set. This approach retains the intuitive appeal of the FI—measuring the robustness of statistical conclusions—while offering broader applicability and avoiding the loss of information that accompanies dichotomization. It also reflects clinical practice more accurately, where continuous variables such as pain scores, functional scales, and biomarker levels often drive decision-making.

Incorporating both FI and CFI into trial evaluation provides a more robust understanding of result stability and supports better-informed clinical interpretation. We encourage the continued development and application of both metrics to advance the reliability and relevance of evidence-based medicine.

Justin Chan, MD Michael Vrla, MDIrvine, California Claire Thompson, BA David Trofa, MDNew York, New York Xinning Li, MDBoston, Massachusetts Dean Wang, MDIrvine, California Robert L. Parisien, MDNew York, New York