Reducing uncertainty in causal effect measures via Information Geometry

Clinical trials use statistical measures of how effective their novel drugs are, in terms of improving health conditions and increasing the quality of life. The statistical properties of these measures determine how robust the trial decision-making processes can be. Furthermore these properties also determine whether causal effects are correctly identified - for example, prognostic biomarkers (i.e. biomarkers that influence the disease progression) may be falsely identified as predictive (i.e. biomarkers that influence the treatment effect) , or vice versa, depending on the effect scale chosen, and its uncertainty.

This project, working in collaboration with an industrial lab, will examine the statistical properties of various causal effect measures (e.g., risk difference, odds ratio, hazard ratio) and understand/reduce their inherent uncertainty with limited data samples. We will exploit principles of information geometry to understand phenomena, using Bregman divergences as the meeting point between the literature of causality and that of information geometry.

We will start with focus on the “collapsibility” of effect measures, which determine how effects can be aggregated across sub-groups of patients. An initial hypothesis to be examined is whether the presence of collapsibility in a measure can be related to the mathematics of Bregman divergences. Can we find alternative measures of aggregation to reduce variance, respecting the geometry of the chosen effect scale?

A secondary hypothesis will be around measures of uncertainty – are there measures of uncertainty that can be derived directly from the effect scale, using information geometric principles? Finally, how can we use the uncertainty measures, combined with a better understanding of the effect geometry, to come up with powerful methodologies for the identification of predictive biomarkers, while controlling false discovery rate.

The two primary deliverables will be (1) publications in machine learning and pharmaceutical statistics journals, (2) open-source software that can be used by pharma companies to analyse their trials.

The student will be co-supervised by a member of the Advanced Methodology and Data Science Group of Novartis (Switzerland), also with the possibility of internships.

References

https://pubmed.ncbi.nlm.nih.gov/33576019/ (collapsibility review) https://jmlr.org/papers/v18/17-514.html (stability of variable selection review) https://arxiv.org/abs/2301.03962 (info geometry review)

Additional information

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