Abstract: Incorporating different sources of clinical and molecular data, e.g. different
omics data types, results in more accurate and more interpretable models for predict-
ing disease progress and allows treatment decisions that are tailored to the individual
patient. The main challenge is how the multi-omics data should be integrated in sta-
tistical models. This project will focus on the application of cooperative learning to
include multiple sources of data.
Key Words: Cooperative learning, pliable lasso, interaction models, multi-omics, per-
sonalized medicine.
Supervisors: Theophilus Quachie Asenso, Manuela Zucknick
Project description
A recent approach to modeling with multiple data sources is known as cooperative
learning (Ding, Li, Narasimhan, & Tibshirani, 2021). The approach of cooperative
learning is summarized for two data sources as follows: Consider a data set of N
responses, with y as and N −vector of outcomes having individual entries as yi, X as
an N × px matrix of predictor variables from one source and Z as an N × pz as matrix
of predictor variables from another source. Cooperative learning aims at minimizing
\(E\Big[\frac{1}{2} (y − f_X(X) − f_Z(Z))2 + \frac{\rho}{2} (f_X (X) − f_Z (Z))^2 \Big],\)
where ρ ≥ 0 is a hyper-parameter, the first term is the prediction error and the second
term is what is called an “agreement” penalty which ensures that there is agreement
between predictions from the two different sources. The method has successfully been
applied to lasso-type models and we aim to extend it to the pliable lasso model.
The aim of this MSc project will be an extension of the pliable lasso model
(Tibshirani & Friedman, 2020) to allow the model to consider multiple data sources.
One approach could be to transform the matrix of the input data so that we can
directly use the pliable lasso R package. Another alternative will be to use the alter-
nating direction method of multipliers (ADMM) algorithm to tackle the problem in
blocks. The project work will involve the following aspects:
(1) explore options how to implement cooperative learning in the context of pliable
lasso, with focus on how to deal with the interaction terms;
(2) establish the model and implement a software solution in R;
(3) explore model performance using simulation studies and compare with the stan-
dard pliable lasso without cooperative learning;
(4) apply the model to a real data set from pharmacogenomics, where multi-omics
characterisations of cancer cell lines can be used to predict whether the cell lines
will respond to certain anti-cancer drugs.
References
- Ding, D. Y., Li, S., Narasimhan, B., & Tibshirani, R. (2021). Cooperative learning for multiview analysis. arXiv. Retrieved from https://arxiv.org/abs/2112.12337 doi:
- Tibshirani, R., & Friedman, J. (2020). A pliable lasso. Journal of Computational and Graphical Statistics, 29 (1), 215-225, DOI: 10.1080/10618600.2019.1648271. Retrieved from https://doi.org/10.1080/10618600.2019.1648271 doi: