Blesson Chacko, Jonathan J Moss, Rupert Austin and Joachim Grevel
BAST Inc Limited, Loughborough, LE11 5XR, United Kingdom
Objectives: To show that patients may not always benefit from an effective treatment through competing risks analysis of simulated data. To qualify the parametric models with simulation-based informative graphical displays.
Methods: 200 studies were repeatedly simulated while varying sample size (100 to 1000) and magnitude (γ=0,0.2,…,2) of binary covariate influence (exposure above and below median) on event of interest (response). Exposure influence on a competing event (dropout due to adverse events) was fixed in order to increase the dropout hazard by a factor of 2.7 for exposure above the median. The end of the observation period varied randomly between two months and two years. Response and dropout times were simulated using a Weibull hazard function with a 7-fold higher baseline hazard rate for response than for dropout.
The exposure effect on response rate in all simulated studies was investigated by the cause-specific hazard (CSH) approach using the standard Cox proportional hazard (Cox-PH) method. The exposure effect on the response risk in all simulated studies was investigated by the sub-distribution hazard (SDH) approach which evaluates the influence of exposure on the cumulative incidence function (CIF). Exposure effects on the SDH were analysed with the semi-parametric Fine-Gray method [1] and by directly modelling the CIF with a modified three-parameter logistic hazard function and a generalised odds-rate link function under the constraint that the asymptotes of CIFs for the competing events must add up to one [2]. A patient population is said to have benefitted if a significant exposure effect could be found on response risk in the presence of competing events.
Results: A significant (p<0.05) exposure effect on response rate was found in 53 of 200 simulated studies with 100 patients and γ=0.4 using the Cox-PH methodology (median hazard ratio, HR, of 1.9 and 90 percentiles ranging from 1.7 to 2.6). However, a significant exposure effect on response risk was found in only 16 of 200 studies with 100 patients and γ=0.4 using the Fine-Gray approach, despite only an average of 18% (+/- 4%) of patients dropping out. This indicates that a significant exposure effect on response rate does not always correspond to a beneficial effect for the patient population.
This finding was confirmed when the sample size of otherwise identical studies was increased to 1000, in which case a significant exposure effect on response rate was found in all studies (HR [90%] = 1.49 [1.3-1.7]). Whereas only 78 of 200 studies showed a significant exposure effect on response risk. Thus, lack of statistical power was not obscuring the possible benefit of a patient population.
Discussion: The simple binary exposure covariate can be replaced by a continuous covariate and the simulations yield a similar conclusion. Our definition of patient benefit is simplistic by claiming that absence of dropout alone paves the way to therapeutic benefit. A novel method to address goodness-of-fit with the model-derived and data-driven CIFs facilitates visual model qualification.
Conclusions: Treatment effectiveness and patient benefit can be evaluated at the same time by dealing with dropout as a competing risk and not as a case of right-censoring. It became clear, that under a range of conditions, treatment effects identified by their HR failed to translate into patient benefit.
References:
[1] Fine, J. P., & Gray, R. J. (1999). A proportional hazards model for the subdistribution of a competing risk. Journal of the American statistical association, 94(446), 496-509.
[2] Shi, H., Cheng, Y., & Jeong, J. H. (2013). Constrained parametric model for simultaneous inference of two cumulative incidence functions. Biometrical Journal, 55(1), 82-96.
Reference: PAGE 28 (2019) Abstr 9096 [www.page-meeting.org/?abstract=9096]
Poster: Methodology - New Modelling Approaches