(B-014) Bayesian Analysis of Linear Tumor Growth Rate: Case Study in VHL Disease

Background: Tumor growth rates can inform therapeutic decisions for patients with von Hippel-Lindau (VHL) disease. To estimate growth rates, linear mixed modeling (LMM) can be used to address individual variability and population trends. However, LLM estimates can be biased towards the overall average (called shrinkage) when data are sparse. For VHL patients, faster-growing tumors may be under-represented in growth rate modeling due to censoring from surgery.

Objectives: To model the linear growth rate (LGR) for renal tumors using VHL natural history study (NHS) data while incorporating prior knowledge from the published literature into a Bayesian LMM to minimize the potential impact of shrinkage.

Methods: The model with random intercept and slope had the best fit, with smallest LOOIC of 12,322 and 12,312 using the informative and non-informative priors, respectively. The estimated mean LGR (mm/yr) was comparable using these priors, at 1.6 (standard error (SE) = 0.2) and 1.7 (SE = 0.2). Sensitivity analysis showed that increasing the weight of the informative prior improved model fit, with the smallest LOOIC observed at SD=0.1. Further SD reductions led to a decline in model performance, as indicated by increasing LOOIC values. The LGR estimates (mm/year) showed notable changes with decreasing SD, increasing from 1.7 at SD=4 and SD=1, to 5.2 at SD=0.1.

Results: The model with random intercept and slope had the best fit, with smallest LOOIC of 12,322 and 12,312 using the informative and non-informative priors, respectively. The estimated mean LGR (mm/yr) was comparable using these priors, at 1.6 (standard error (SE) = 0.2) and 1.7 (SE = 0.2). Sensitivity analysis showed that increasing the weight of the informative prior improved model fit, with the smallest LOOIC observed at SD=0.1. Further SD reductions led to a decline in model performance, as indicated by increasing LOOIC values. The LGR estimates (mm/year) showed notable changes with decreasing SD, increasing from 1.7 at SD=4 and SD=1, to 5.2 at SD=0.1.

Conclusions: Proper estimation of tumor growth rates among VHL patients must account for variability between patients and within individual tumors. Hierarchical models, while effective, are prone to shrinkage in limited data settings. These findings highlight the importance of informative prior selection in Bayesian modeling to mitigate shrinkage. Results should be interpreted cautiously, and the impact of influential data points requires further examination.