Conditional quantile regression models of melanoma tumor growth curves for assessing treatment effect in small sample studies.

ABSTRACT

Tumor growth curves provide a simple way to understand how tumors change over time. 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 use a 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 effect of a naturally derived biological peptide, P28, on tumor volumes in mice grafted with human melanoma cells. 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, Dacarbazine (DTIC), tended to inhibit growth for smaller quantiles, while the experimental treatment P28 produced slower rates of growth in the upper quantiles, especially in the 95th quantile.