The document discusses challenges with small sample sizes including low statistical power, inability to detect associations, and computational issues with many variables. It notes that small sample sizes are common in rare disease research, rare exposure studies, and restricted sample clinical trials. The document proposes that topology, as an unsupervised learning and feature engineering method, can help address these challenges by providing robust input features for predictive models, even with small sample sizes. This allows for good predictive performance as well as recoverable insight into the problem while avoiding statistical power issues common in small samples.

1. Colleen M. Farrelly

2. Small Sample Size Examples
Rare
Diseases
(ex.
chordoma)
Rare
Exposures
(ex.
Fukushima
workers…)
Restricted
Sample
Trials (ex.
Phase I
trials)

3. •Find subgroups that exist in data
•Understand subgroup differences
Clustering
•Identify associations between predictors and
an outcome
Predictor
Identification
•Predict outcome/group assignment of new
observations based on a set of predictors
Forecasting/
Classifying

4. Violation of
typical model
assumptions
(inaccurate model
estimates)
Computational issues
with large
dimensionality (lots of
variables)
Low power to
detect significant
associations
• Bad
prediction
• Little insight
• Computability
issues
• Inaccurate
estimates

5. Topology provides a feature engineering and unsupervised
learning method robust to sample size, which provide
good input features for tree-based predictive models.

6. Data
Collection
Unsupervised
Learning
Feature
Engineering
Predictive
Modeling
Insight

7. Good Prediction/Classification Models
Recoverable Insight into Problem
Avoidance of Statistical Model Power Issues