A frailty model for quantifying the association between CompEx risk and variation in lung function in asthma
Ludvig Jakobsson (1,2,4), Mats Jirstrand (1), Philip Gerlee (2), Jason Cooper (3), Jacob Leander (4)
(1) Fraunhofer-Chalmers Research Centre for Industrial Mathematics, Gothenburg, Sweden, (2) Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, Gothenburg, Sweden, (3) R&I Biometrics & Statistical Innovation, Late R&I, BioPharmaceuticals R&D, AstraZeneca, Cambridge, UK, (4) Clinical Pharmacology and Quantitative Pharmacology, Clinical Pharmacology and Safety Sciences, R&D, AstraZeneca, Gothenburg, Sweden
Introduction: Seemingly random fluctuations in lung function have previously been shown to be associated with acute exacerbations in asthma (1, 2). One utilised measurement is peak expiratory flow (PEF), which has been used to develop the composite endpoint CompEx, allowing for shorter clinical trials in which exacerbations have previously been the primary endpoint (3). Understanding how measures of fluctuations in lung function are associated with CompEx risk may further increase the efficiency of clinical trials.
Objectives:
⦁ Study the association between variation in PEF and CompEx risk.
⦁ Evaluate the use of a frailty parameter to account for population heterogeneity in CompEx risk.
Methods: The analysis was conducted using data from a dose-finding Phase 2b randomized, placebo controlled, double-blind multicenter study of asthmatic patients symptomatic on low dose inhaled corticosteroids (4). This clinical trial featured a 3–4-week run-in period followed by a 12-week treatment period. Before the analysis, all informed consent forms were reviewed for data re-use in accordance with AstraZeneca data sharing rules.
Multiple measures of variation in PEF, including standard deviation and coefficient of variation, were calculated from the run-in period and a frailty model for recurrent events was developed to evaluate the association between CompEx risk and these measures of variation. Multiple probability distributions were considered for the frailty parameter and were evaluated using the likelihood and Akaike information criteria. During model development, baseline PEF and treatment were also used as covariates. Model parameters were estimated using the package frailtyEM in R (5).
Results: Standard deviation in PEF during the run-in period was found to have a significant (p<0.01) association with CompEx risk, with an estimated 2.4% increase in risk per unit increase in standard deviation. Given the distribution of standard deviations in the population, this estimate resulted in a 74% increased CompEx risk for a patient with standard deviation in the 90th percentile compared to the median, all other variables held constant. Additionally, using a gamma-distributed frailty parameter resulted in the largest likelihood and a statistically significant (p<0.001) likelihood increase compared to the no-frailty case. Further, significant associations were found for baseline PEF as well as for each treatment arm.
Conclusions: These findings suggest that standard deviation in PEF may be useful as a predictor of patient-level CompEx risk in clinical trials. This can increase the efficiency of future clinical trials by allowing for more control over patient selection before randomization is carried out. Furthermore, a strong heterogeneity in CompEx events was found which supports the use of a frailty model.
References:
(1) Leander J. et al. CPT Pharmacom & Syst Pharma 11, 212–224 (2022)
(2) Thamrin C. et al. Thorax 66, 1036–1042 (2011)
(3) Fuhlbrigge A. L. et al. The Lancet Respiratory Medicine 5, 577–590 (2017)
(4) Chupp G. L. et al. Am. Thorac. Soc. Int. Conf. Meet. Abstr. 203, A1202 (2021)
(5) Balan T. A. et al. https://CRAN.R-project.org/package=frailtyEM (2017)
