"Prediction of best-corrected visual acuity for wet age-related macular degeneration patients in HAWK and HARRIER studies via a Bayesian hierarchical linear model"
Se Yoon Lee, Biostatistics Intern, Ophthalmology Department, Novartis International AG
Project Supervisor: Liansheng Zhu, Ph.D.
(The slides is made to show the only results. Software has been made in R.)
Wet age-related macular degeneration (wetAMD) is a chronic, progressive disease and a leading cause of vision loss. Intravitreally administered anti-vascular endothelial growth factor A (VEGF-A) therapy for wetAMD treatment has greatly improved patient outcomes in enhancing best-corrected visual acuity (BCVA). However, the need for frequent clinic and injection visits coupled with the anticipated increased prevalence of patients with AMD portend a scenario that is not sustainable.
The HAWK and HARRIER studies are two similarly designed phase 3, multicenter, randomized, double-masked trials with a 2-year study (96 weeks). The objective of HAWK and HARRIER is to compare two anti-VEGFs, aflibercept (2mg) and brolucizumab (3mg/6mg), to treat wetAMD. Interventions for the treatments are given by (a) aflibercept: after loading with 3 monthly injections, patients are treated with every 8 weeks (q8w); and (b) brolucizumab: after loading with 3 monthly injections, patients are treated with every 12 weeks (q12w). Particularly, for brolucizumab-treated patients if disease activity (DA) were found after the loading phase, then patients are interval adjusted and treated with q8w, and maintained with the q8w until the end of the study.
The primary object of the project is to propose a novel statistical model to predict BCVA trajectory over the maintenance phase at the individual patient level. Additionally, we want the predicted BCVA trajectory to be adjusted by ocular coherence tomography (OCT) parameters such as central sub-field thickness (CSFT). The second end point is to identify possible risk factors explaining deterioration of the BCVA (i) during the 2-year treatments and (ii) with the initial injection effect.
Characteristics of the WetAMD patients' data can be summarized as follows: (i) unbalanced longitudinal data (i.e., patients can have different numbers of visits.); (ii) tall data (around 1,800 patients with the maximum number of visit is 25); (iii) known five subgroups that represent five treatment arms; (iv) highly extreme heterogeneity in BCVA/CSFT trajectories at individual patient level; and (v) clear pattern in BCVA/CSFT trajectories at the subgroup level.
One of the bottlenecks in developing a possible statistical model is the presence of extremely high heterogeneity commonly manifested in almost all BCVA/CSFT trajectories at "individual patient level". The other challenge is how to reasonably utilize the CSFT as a time-varying covariate in a possible model in adjusting the predicted BCVA trajectory to improve the predictive accuracy.
We proposed a Bayesian hierarchical linear model (BHLM) which aggregates patients' information from five treatment subgroups in HAWK and HARRIER (in total around 1,800 patients), while extracting as many patients' information (for e.g., clinical information, OCT parameters, etc) as possible from the HAWK and HARRIER studies. The proposed BHLM is a a Bayesian version of two-stage linear mixed effect model with the Lindley-Smith form. Briefly speaking, the first stage of the model is associated with the curve fitting for BCVA trajectory adjusted by the CSFT, whereas on the second stage the sparse horseshoe prior performs feature selection to identify possible risk factors for the wetAMD.
The proposed model has been trained by the actual data from HAWK and HARRIER (with number of patients 1,800), and the results demonstrated that that the model possesses nice operating characteristics: an estimate for the residual error is 4.11 letters. Several risk factors found from the model are coincided with some findings in published medical papers. For instance, the model discovered that the area of choroidal neo-vascularization (CNV) lesion is one of the most significant risk factors for the wetAMD which can deteriorate visual improvement during the treatments and from the initial injection effect.
The model produced reasonable prediction results. To see this, we divided the full datasets in HAWK and HARRIER with the ratio 7:3 for training:testing datasets. The root mean squared error (RMSE) for the predicted BCVA trajectories was 6.65 letters. Several other results suggest that the model retains a promising utility in predicting the visual acuity for the wetAMD patient.
References
Dugel, Pravin U., et al. "HAWK and HARRIER: phase 3, multicenter, randomized, double-masked trials of brolucizumab for neovascular age-related macular degeneration." Ophthalmology 127.1 (2020): 72-84.
Lindley, Dennis V., and Adrian FM Smith. "Bayes estimates for the linear model." Journal of the Royal Statistical Society: Series B (Methodological) 34.1 (1972): 1-18.
Carvalho, Carlos M., Nicholas G. Polson, and James G. Scott. "The horseshoe estimator for sparse signals." Biometrika 97.2 (2010): 465-480.
Lee, Se Yoon, Bowen Lei, and Bani K. Mallick. "Estimation of COVID-19 spread curves integrating global data and borrowing information." PLOS ONE (2020).