Robert Palmér (1), Agnieszka Król (1,3), Virginie Rondeau (2), Ulf Eriksson (1), Alexandra Jauhiainen (3)
(1) Quantitative Clinical Pharmacology, Early Clinical Development, IMED Biotech Unit, AstraZeneca, Gothenburg, Sweden, (2) Biostatistics Team, INSERM CR1219, University of Bordeaux, Bordeaux, France, (3) Biometrics, Early Clinical Development, IMED Biotech Unit, AstraZeneca, Gothenburg, Sweden
Introduction: COPD clinical trials aimed at evaluating long-term treatment effects on exacerbations often suffer from a high rate of patient discontinuations. Discontinuations imply a loss of information and should ideally be considered in the statistical evaluation of study results, particularly if the discontinuations are related to disease severity or treatment and become unequally divided between treatment groups (differential discontinuations).
Objectives: In this work, we aimed to quantify the association between COPD exacerbation and discontinuation risks, and to evaluate the impact of this association on exacerbation treatment effect estimates, using a joint frailty model approach.
Methods: A joint frailty model[1] describing the hazards of recurrent episodes of exacerbations and early discontinuations was developed using the R-package frailtypack. The two risk processes were coupled using a gamma distributed shared random effect (frailty), where the effect of the frailty in the discontinuation hazard is scaled using an association parameter (α):
r_ex,ij(t|u_i) = Y_i(t) * u_i * r_0(t) * exp(x‘_ex,ij · β_ex)
λ_ed,i(t|u_i) = (u_i)^α * λ_0(t) * exp(x‘_ed,i · β_ed)
Here, r_ex,ij and λ_ed,i are the patient-specific hazards for recurrent exacerbations and early discontinuation, respectively. The variable u_i denotes the frailty for patient i, and the xs and βs are the covariates (e.g. treatments) and their related regression coefficients. r_0 and λ_0 denote the population baseline hazards and Y_i is the at-risk process for patient i.
The importance of modelling the association when estimating exacerbation treatment effects was first investigated using simulated data from the joint frailty model. The data included two treatment groups (control and active) and was simulated assuming (1) different discontinuation and exacerbation rates, (2) different frailty variances, and (3) different associations strengths (α) between the two risk processes. Treatment effect estimates of the joint frailty model were compared to those of conventional and simpler statistical models, such as the negative binomial and shared frailty model[1]. Since models like the negative binomial model estimates rate ratios rather than hazard ratios, constant baseline hazards were used in the simulations to allow for a fairer comparison.
The joint frailty model was then applied to data from five randomized controlled Phase III-IV trials in patients with moderate to severe COPD[2,3,4,5,6], and the same comparison to simpler models was made. Early discontinuations were defined as any discontinuation of investigational product before the predefined end of study, irrespective of reason.
Results: Simulations showed that simpler statistical models produce biased treatment effect estimates in the presence of differential discontinuations and a discontinuation-exacerbation association (α ≠ 0). In scenarios with a 2-fold higher discontinuation risk in the control group and a positive risk association (α = 0.5-1.5, frailty variance = 1.7), a true treatment effect of 40% exacerbation risk reduction (hazard/rate ratio = 0.6) was underestimated by 4-8 percentage points (hazard/rate ratio = 0.64-0.68) if ignoring the association in the statistical analysis. The joint frailty model produced less biased results (1-2 percentage points).
When analyzing the clinical trial data, significant (p<0.00001) and similar (α = 0.83-1.69) associations between exacerbations and discontinuations were found in all trials. The differences in treatment effect estimates between the joint frailty model and simpler models ranged from 1-11 percentage points. More than 5 percentage points differences between models were seen in the studies with the largest differences (>1.5-fold) in discontinuation rates between treatment groups. With the joint frailty model, we also saw up to 10% relative improvements in treatment effect standard errors in several of the trials.
Conclusions: We have found a significant association between early discontinuation and exacerbation risks in five Phase III-IV COPD clinical trials and show that this association may cause bias when estimating exacerbation treatment effects if discontinuations are unequally divided between treatment arms. The use of a joint frailty modelling approach can reduce bias and improve precision in treatment effect estimates in the presence of differential discontinuations.
References:
[1] Król et al., J Stat Softw 2017;81(3):1-52
[2] Rennard et al., Drugs 2009;69(5):549-565
[3] Sharafkhaneh et al., Respir Med 2012;106(2):257-268
[4] Tashkin et al., Drugs 2008;68(14):1975-2000
[5] Martinez et al., AJRCCM 2016;194(5):559-567
[6] Martinez et al., Lancet 2015;385(9971):857-866
Reference: PAGE 28 (2019) Abstr 9125 [www.page-meeting.org/?abstract=9125]
Poster: Drug/Disease Modelling - Other Topics