🤖 AI Summary
Traditional efficacy metrics struggle to capture the upper-tail persistence characteristics of high responders in biosimilar assessments. This work proposes a novel quantile-based efficacy persistence function, defined as the ratio of the tail mean to the quantile function, thereby introducing the concept of expected shortfall from risk theory into clinical persistence analysis for the first time. We demonstrate its equivalence to a scaled upper-tail first-order L-moment and develop a corresponding nonparametric estimator along with a two-sample equivalence test calibrated via bootstrap inference. Simulation studies and real-data analyses show that the proposed method effectively detects upper-tail differences undetectable by median- or mean-based approaches, substantially enhancing both sensitivity and specificity in biosimilar efficacy evaluation.
📝 Abstract
In clinical studies, persistence, which measures the duration of time a patient continues to take a prescribed medication without discontinuation, is increasingly recognized as a critical indicator of adherence to medication. Adherence encompasses not only whether a patient takes their medication as prescribed but also the consistency and duration with which they do so. Among the various metrics used to evaluate adherence, persistence stands out as a particularly robust measure because it provides a temporal dimension, reflecting the sustained commitment of patients to their therapeutic regimens. This focus on persistence offers unique insights into adherence-related quality and performance, shedding light on the challenges and opportunities to optimize long-term medication use. The comparison of upper-tail clinical performance, which measures the extent to which very large responses persist among top responders, is often more decisive in therapy evaluation than conventional summaries. In this paper, we introduce the quantile-based effectiveness persistence function defined as the ratio between the tail mean and the quantile function. The notion parallels expected shortfall in risk theory and is tailored to detect clinically meaningful deviations in the upper tail. We establish key properties and show that the function is equivalent to the first L-moment of the scaled tail, yielding robust inference tools. We derive a simple nonparametric estimator of the function and develop a bootstrap-calibrated two-sample (upper-tail) equivalence test. Simulation studies and real-data analysis illustrate that the proposed measures captures clinically relevant tail persistence that complements median and mean-based summaries.