Impact of censoring on non-linear effect modeling of aggregate-level survival data
Renwei Zhang (1), Tingjie Guo (1), Li Qin (2), Rik de Greef (2), Matthew L. Zierhut (2), Laura B. Zwep (1), J. G. Coen van Hasselt (1)
(1) Systems Pharmacology and Pharmacy, Leiden Academic Centre for Drug Research, Leiden University, Leiden, The Netherlands; (2) Certara Inc., Princeton, New Jersey, USA.
Introduction: Model-based meta-analysis (MBMA) applies statistical models to aggregate-level trial data to compare the treatment effects across studies using data extracted from literature[1]. Within oncology, survival endpoints such as overall survival are the most commonly used study endpoints. For such studies, Kaplan-Meier (KM) curves are used to report survival probabilities over time. When digitized, such curves can be used to perform MBMA. Consideration of censoring in survival data, i.e. due to dropout, lost to follow-up, or end-of-study[2], is essential to prevent biased estimation of the hazard[3]. Although censoring information can sometimes be inferred from risk tables, it is often unavailable.
Objectives: The specific aims of this project are to: (1) evaluate the impact of ignoring censoring on bias in parameter estimates for aggregate-level survival data, (2) compare the performance of two potential data analytical strategies, and (3) assess which other factors may contribute to the magnitude of censoring-induced bias.
Methods:
Data: We used digitized survival curves from real clinical trials in non-small cell lung cancer as available in the CODEx database (Certara, Princeton, NJ) [4]. A subset of the curves for which censoring information was available was used, which included 34 drug treatments, 220 trials, and 281 arms involving 53105 patients. We simulated data to evaluate factors that may impact the magnitude of censoring-induced bias. Simulated survival curves were generated from an exponential distribution for a fixed hazard. Multiple sets of time-to-event data were sampled for different rates of censoring so that the hazard stayed similar over the different censoring rates. To assess the effect of hazard, we repeated the procedure for different values of hazard.
Analysis methodologies: We directly fit exponential curves to the aggregate-level survival probability over time data from the KM curve for each (simulated) trial, resulting in a study-level estimation of the hazard parameter (λ). To examine how omitting censoring information influences the bias in survival estimation, we used censoring information to reconstruct individual patient data (IPD) from the KM curves and then used survival analysis to account for the censoring in the hazard estimation[5]. An exponential distribution was used for the survival analysis, yielding a λ which can be used as a reference for a hazard estimate that does censoring into account.
The influence of censoring was further assessed for using an IPD reconstruction approach, but excluding all censoring information, which was also compared to the reference. The direct fit and the IPD without censoring methods were compared to evaluate which method would be preferred in case of lacking censoring information.
Evaluation metrics: To evaluate the performance of the methods as applied to both datasets, we calculated the standardized difference in between the parameter estimates (λ) of direct fitting and IPD reconstruction ignoring censoring against the references to evaluate the bias of parameter estimation.
Results:
Real clinical trial data: A bias was observed in the results of direct fitting on aggregate-level data compared to the reference and it increased with increasing censoring rate in the data. The median difference of λ was 11.2% and at censoring rate below 0.25, and for a higher censoring rate (0.5) the median bias was 14.3%. IPD reconstruction without censoring information performed well at low censoring rate but worse at higher rates. The median difference of λ was very low (1.64%) at censoring rate below 0.25 but increased with higher censoring rate (0.5) to 11.3%.
Simulation study: The median difference of λ for direct fitting against reference were 2.10% and 6.7% at censoring rates of 0.25 and 0.5, respectively. For IPD reconstruction without censoring the biases were 0.434% and 2.74% at censoring rates 0.25 and 0.5, respectively. A smaller number of patients and higher initial hazard (λ) during simulation resulted in a larger decrease of the survival curve, which caused a higher censoring effect on bias in parameter estimates.
Conclusions: Ignoring censoring in modeling of aggregate level survival data leads to biased estimation of the hazard, which is dependent on the censoring rate. IPD reconstruction showed improved performance as compared to a direct fitting strategy. These findings indicate that caution needs to be taken for MBMA of survival data.
References:
[1] Boucher M et al. CPT Pharmacometrics Syst Pharmacol. 2016;5(2):54-64.
[2] Jason T et al. Otolaryngol Head Neck Surg. 2010;143(3):331-336.
[3] Turkson A et al. Int J Math Math Sci. 2021;(2021), 9307475.
[4] https://codex.certara.com/
[5] Liu N et al. BMC Med Res Methodol. 2021;21(1):111.