Laura B. Zwep (1,2), Kevin L.W. Duisters (1), J. G. Coen van Hasselt (2)
(1) Mathematical Institute, Leiden University, the Netherlands, (2) Leiden Academic Centre for Drug Research, Leiden University, the Netherlands
Objectives:
High-dimensional molecular profiling technologies (‘omics’) including genomics and transcriptomics are rapidly emerging as promising approach to personalize drug treatments. The development and implementation of statistical methodologies to identify predictors for treatment response using high-dimensional omics data in the context of pharmacometric models is therefore becoming increasingly important.
LASSO variable selection has been implemented for non-linear mixed effect PK-PD models [1] and for high-dimensional linear mixed effect models [2]. However, one important aspect not yet included in these models is the consideration of hierarchical interaction terms [3], which can be used to identify predictor interactions within or across omics datasets, or drug treatment-omics interactions.
In the current study we first develop a tumor growth inhibition model for a large dataset of patient-derived tumor growth data. We subsequently implement a linear mixed model extension of the hierarchical group LASSO to facilitate identification of high-dimensional predictors including interactions from a multi-omics dataset derived from tumor biopsies.
Methods:
Data: We demonstrate our methodological contribution using a large dataset of tumor growth curves derived from patient-derived xenograft (PDX) experiments. A total of 3276 tumor growth profiles was generated from 174 unique patient-derived tumors for which 54 anti-cancer drug treatments were evaluated as monotherapy or in combination [4]. For each tumor biopsy, high-dimensional transcriptomics (RNA) and copy number variations (CN) data was generated at baseline.
Tumor growth inhibition model: A nonlinear mixed effect tumor growth model was implemented in NONMEM using ordinary differential equations [5]. The model included parameters for tumor growth rate (KG), and the treatment-specific parameters for drug effect (KD) and a time-dependent resistance development term (KR).
Hierarchical group LASSO implementation: The hierarchical group LASSO technique [3] was used to assess the relation of the drug-specific outcome metrics (KD or KR) with respect to omics-predictors (RNA and/or CN), the treatments, and their two-way interactions; resulting in the simultaneous analysis of over one million effects. The penalty parameter for the LASSO was obtained using 5-fold cross-validation. To reflect compound symmetry-dependence between PDX data derived from the same tumor, we have extended the method of high-dimensional regularized interactions with a random intercept term [2], combining both techniques through iterative Expectation-Maximization.
Results:
Tumor growth inhibition model: The predictions of the tumor growth model were visually inspected. Curves with less than 5 observations and biased fits were removed by putting a threshold on the absolute error and the covariance between the individual predictions (IPRED) and the measured tumor volume. The KD and KR of 2899 PDX tumor growth curves showed a good fit and were included in the second part of the analysis.
Hierarchical group LASSO implementation: Our extended algorithm could successfully estimate a linear random intercept in the hierarchical group LASSO. We identified multiple interactions between drugs and CN variations affecting KD. For the treatments with LGH447, encorafenib and dacarbazine we identified interactions with specific CN variations. Positive interaction effects, such as the interaction between encorafenib and the gene HSF2BP show that tumors with a higher CN in HSF2BP have a better treatment response . A positive intra-tumor correlation of 0.2 was estimated, confirming that some tumors are more receptive to drug treatments than others.
Conclusions:
We implemented and applied the modelling of predictor interactions with the LASSO for extracting drug-response biomarkers and demonstrate the relevance of this method to identify interactions in high-dimensional omics datasets. The positive intratumor correlation shows the benefit of the proposed random effect extension. Our two-step approach allows many types of outcomes derived in the first step to be coupled to high-dimensional LASSO analysis in the second step. The linear mixed model extension allows modeling of dependent data such as encountered in repeated measurements. To this end, our approach is generalizable to a wide variety of applications in pharmacometrics where identification of predictors from high-dimensional datasets is required.
References:
[1] Ribbing J, Nyberg J, Caster O, Jonsson EN (2007). J Pharmacokinet Pharmacodyn 34(4):485–517.
[2] Schelldorfer J, Bühlmann P, De Geer S Van. Scand J Stat. 2011;38(2):197-214.
[3] Lim M, Hastie T. J Comput Graph Stat. 2015;24(3):627-654.
[4] Gao H, Korn JM, Ferretti S, et al. Nat Med. 2015;21(11):1318-1325.
[5] Claret L, Girard P, Hoff PM, et al. J Clin Oncol. 2009;27(25).
Reference: PAGE 28 (2019) Abstr 9183 [www.page-meeting.org/?abstract=9183]
Poster: Methodology - New Modelling Approaches