Carlos Traynor (1,2), Tarjinder Sahota (2), Neil Evans (1), Helen Tomkinson (2), and Michael Chappell (1).
(1) School of Engineering, University of Warwick, Coventry, UK. (2) Quantitative Clinical Pharmacology, AstraZeneca, UK.
Objectives: Evaluate the predictive performance of variable selection methods for high-dimensional feature space in tumour growth and resistance models with applications to patient-derived tumour xenograft clinical trials (PCT).
Methods: Let the tumour volume y(t) to be approximately proportional to the total cell population. Assume that initially, the tumour grows with rate k. To describe the observed initial drug-induced tumour regression followed by an eventual re-growth, consider that the treatment modifies k to a lower value k – λ. Then, as time goes on the net growth changes from negative (k – λ) back to positive (k) with rate α, representing the rise of resistance. Recently, [1] discussed a similar empirical model showing it to be practical and identifiable even for non-informative priors. Here, we extend the approach in [1] in two ways. We demonstrate an implementation of a hierarchical model to infer the impact of multiple treatments in pre-clinical studies involving various tumour samples. We examine the case when microarray data contribute to the sample effects of the tumour growth rate k. The strategy followed in conducting variable selection is split into two stages. First, a full reference model with a linear genomic predictor on k defined by μ=βX is fitted, where X is the transformed data matrix of copy number measurements and β the effect on the tumour growth rate associated with each feature. Second, project the reference model to a sub-model while preserving enough of the explanatory power of the full model. The benefits are illustrated in a real-world example of PCT [2], including 2,000 copy number (CN) measurements in 1200 mice, treated with 50 different treatments. The CN dataset is log-normalised and merged with the longitudinal tumour growth dataset in R (V5.1) [3]. Parameter estimation is conducted in Stan (V21.0) [4]. Predictive performance and the projective prediction algorithm [5] are used in a forward search of a minimal subset of predictive biomarkers.
Results: The variation in the tumour volume leads to a skewed error distribution. Hence, the log-Normal distribution is an appropriate choice in order to approximate y(t). Besides, all measurements that fall below the limit of quantification are integrated out using the cumulative log-Normal distribution. The rate parameters k, and λ are also skewed, and it can be shown that a log-Normal prior has the right constraints. Weakly informative priors are used to prevent excursions during Monte Carlo sampling, for example, λ is placed a log-Normal(0,3) prior with an upper 89% credible interval (CI) corresponding to a halving time of 2 days. The results show that the intensity of efficacy for an average treatment is 0.017 day-1 (95% HPDI 0.013 – 0.021) and the rise of resistance to treatment is estimated to be 2e-3 day-1 (95% HPDI 1e-3 – 4e-3) increasing the growth rate exponentially. The predictive performance increases when supplanting the average tumour growth rate with candidate biomarkers. In the test dataset, the first biomarker attains 70% of the explanatory power, the five best reach over 85% and fifteen are needed to reach over 90%. The analysis suggests five relevant biomarkers associated with the tumour growth rate with a further fifteen warranting further investigation.
Conclusions: The projective prediction algorithm presented herein for tumour growth PCT models can find applications elsewhere in variable selection problems in pharmacometrics. Our novel approach avoids selection bias related to multiple hypothesis testing in exploratory research. It improves interpretability over the reference model and can estimate the credible intervals for unknown parameters, which is not straightforward with traditional approaches such as LASSO. The projective prediction approach alone, however, describes associations and is not sufficient to find a causal relationship. Our recommendation is to also adjust for confounders and account for inter-individual variation in the mixed-effect modelling framework.
References:
[1] Nagase, M., Aksenov, S., Yan, H., Dunyak, J., & Al‐Huniti, N. (2020). Modeling Tumor Growth and Treatment Resistance Dynamics Characterizes Different Response to Gefitinib or Chemotherapy in Non‐Small Cell Lung Cancer. CPT: Pharmacometrics & Systems Pharmacology.
[2] Gao, H., Korn, J. M., Ferretti, S., Monahan, J. E., Wang, Y., Singh, M., … & Balbin, O. A. (2015). High-throughput screening using patient-derived tumor xenografts to predict clinical trial drug response. Nature medicine, 21(11), 1318.
[3] R Core Team (2017). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/.
[4] Carpenter, et al. Stan: A Probabilistic Programming Language. Journal of Statistical Software, 76, 2017. http://mc-stan.org
[5] Piironen, J., Paasiniemi, M., & Vehtari, A. (2018). Projective inference in high-dimensional problems: prediction and feature selection. arXiv preprint arXiv:1810.02406.
Reference: PAGE () Abstr 9459 [www.page-meeting.org/?abstract=9459]
Poster: Methodology – AI/Machine Learning