Modeling Conditional Quantile Tumor Growth Curves By Combining Independent Small Sample Study Data
Gilbert Bassett, University of Illinois at Chicago, Department of Finance
Keywords: quantile regression, longitudinal data, combining information, small sample, bootstrap, cancer growth
Tumor growth curves provide a simple way to understand how tumors change over time and are a useful statistical tool in the development of successful cancer treatments. The traditional approach to fitting such curves to empirical data has been to estimate conditional mean regression functions which describe the average effect of covariates on growth. However, this method ignores the possibility that tumor growth dynamics are different for different quantiles of the possible distribution of growth patterns. Furthermore, typical individual preclinical cancer drug study designs have very small sample sizes and can have lower power to detect a statistically significant difference in tumor volume between treatment groups. In our work we begin to address these issues by combining several independent small sample studies of an experimental cancer treatment with differing study designs to construct quantile tumor growth curves. For modeling, we used Penalized Fixed Effects Quantile Regression with added study effects to control for study differences. We demonstrate this approach using data from a series of small sample studies that investigated the effects of an experimental treatment, P28, on Melanoma tumor volumes in mice. Relying on a stratified bootstrap for model inference and hypothesis testing, we find a statistically significant quantile treatment effect on tumor volume trajectories and baseline values. In particular, the experimental treatment and a corresponding conventional chemotherapy had different effects on tumor growth by quantile. The conventional treatment DTIC tended to inhibit growth for smaller quantiles, while an experimental treatment P28 produced slower rates of growth in the upper quantiles, especially in the 95th percentile. These results suggest that P28 may be effective in inhibiting growth in larger more aggressive tumors that are not responsive to conventional treatment.
Important Dates & Deadlines
- October 9 - 11, 2013