Abstract:

Background and Objectives: The two-period, two-sequence (2x2) crossover design is a cornerstone of clinical research, valued for its statistical efficiency. However, its validity rests on the assumption of precise, deterministic measurements, a condition often unmet in practical clinical settings where inherent indeterminacy can lead to misleading conclusions. This study aims to introduce and apply a rigorous neutrosophic statistical framework to a 2x2 crossover trial, providing a more conservative and realistic assessment of treatment effects by formally incorporating measurement uncertainty.

Methods: We re-analysed data from a published pediatric asthma trial comparing formoterol and salbutamol, as reported by Lim and In (2021). A proportional measurement indeterminacy of δ=5%  was introduced to transform each Peak Expiratory Flow (PEF) observation into a neutrosophic interval. We first replicated the classical Analysis of Variance (ANOVA) to establish a baseline. Subsequently, we applied neutrosophic interval arithmetic to derive interval-valued estimates for treatment, period, and carryover effects, along with their corresponding test statistics (F -value) and P -values. A sensitivity analysis was also performed to evaluate the impact of varying levels of indeterminacy.

Results: The classical analysis yielded a statistically significant treatment effect (τ=46.61  L/min) with an F -statistic of 18.70 and a P -value of 0.0012, strongly favouring formoterol. In stark contrast, the neutrosophic analysis produced a treatment effect interval of τN∈[14.79,78.43]  L/min and a corresponding P -value interval of pN∈[0.0000,0.2006] . The neutrosophic 95% confidence interval expanded substantially to [-9.0,102.3]  L/min.

Conclusions: The study demonstrates that a classical conclusion of "highly significant" can be fragile. The introduction of a modest 5% measurement uncertainty renders the statistical significance of the treatment effect "indeterminate," as its neutrosophic P -value interval straddles the α=0.05  threshold. This framework highlights the critical importance of data quality and provides a method for researchers to transparently report the robustness of their findings against realistic measurement imprecision.

Keywords:

Crossover Design, Indeterminacy, Neutrosophic Statistics, Uncertainty Quantification, Clinical Inference, ANOVA.

Aim/Objectives

Methods