Cancer Stem Cells: Some statistical issues  What you would like to do: Identify ways to design studies with increased statistical “power” in clinical trials of targeted therapies Develop statistically meaningful biologic response criteria  First things first: Current in vivo assays/measures have limitations How well is the biology understood?

Measuring Response  Relapse-free survival, Overall survival Pros: these are the “gold-standards” Problems: takes too long, too costly  Biomarkers (“correlative” outcomes) Pros: feasible in the short-term Cons:  can be costly  might have many to measure  might not know all the relevant markers  might not know how they all “fit together”  If Biomarkers are used as “surrogates” for response, then they need to be TRUE surrogates.  “Correlative” outcome is not good enough

“True” Surrogate Marker  Defining Characteristic: a marker must predict clinical outcome, in addition to predicting the effect of treatment on clinical outcome  Operational Definition establish an association between marker & clinical outcome establish an association between marker, treatment & clinical outcome, in which marker mediates relationship between clinical outcome and treatment

Surrogate Markers marker Clinical outcome treatment Clinical outcome 1) establish an association between marker & clinical outcome. 2) establish an association between marker, treatment & clinical outcome, in which marker completely mediates relationship between clinical outcome and treatment. marker

NOT Surrogate Markers marker treatment Clinical outcome treatment marker Clinical outcome

Alternative Approach: Bayesian Networks  Bayesian networks are complex diagrams that organize data They map out cause-and-effect relationships among key variables They encode them with numbers that represent the extent to which one variable is likely to affect another.  Use “network inference algorithms” to predict causal models of molecular networks from correlational data.  These systems can automatically generate optimal predictions or decisions even when key pieces of information are missing.  How to do this? HYPOTHESIZE BIOLOGICAL MODEL Collect data on hypothesized markers in the pathway/biologic model. Collect data serially, over a time course that fits with biologic model.

Example of Bayesian Network Yu, J., Smith, V., Wang, P., Hartemink, A., & Jarvis, E. (2002) “Using Bayesian Network“Using Bayesian Network Inference Algorithms to Recover Molecular Genetic Regulatory Networks.” Inference Algorithms to Recover Molecular Genetic Regulatory Networks.” International Conference on Systems Biology 2002 (ICSB02), December 2002.

Ongoing Optimization of Assays  Ideally, assays are “perfect” before clinical trial opens  In reality, many of our assays are still pretty rough  Can incorporate assay “sub-studies” within clinical trial  RELIABILITY How reproducible are the results?  Two samples taken from the same patient on the same day  One sample analyzed twice using the same method? Subjectivity? Inter-rater and Intra-rater agreement In what ways can ‘error’ come into the procedure? Provides understanding of measurement error in practice Benefit: Quantification of the ‘believability’ of the results Drawback: what will reviewers think?