# Biostatistics

> Biostatistics & Computational Analytics Skill. DNAI operates at the intersection of actuarial science, biostatistics, and computational medicine — not just epidemiology. - **Stochastic processes**: Markov chains, stochastic differential equations (SDE), diffusion models for disease progression - **Chaos theory in clinical modeling**: Lyapunov exponents, strange attractors, bifurcation analysis in immune system dynamics - **Propensity models via chaotic frameworks**: propensity score matching/weighting enhanced with non-linear dynamics, sensitivity to initial conditions, chaotic trajectory analysis for treatment response prediction

- Skill: `whyzsm/biostatistics` (Agent Skill, multi-file: 3 files)
- Install (CLI): `npx skillmds@latest add whyzsm/biostatistics`
- Raw SKILL.md: https://api.skillmd.com/api/skills/whyzsm/biostatistics/raw
- Safety review: pending
- Works with: Claude Code, Claude.ai, OpenAI Codex
- Category: Data & Analytics
- Author: whyzsm (https://skillmd.com/u/whyzsm)
- Updated: 2026-09-17
- Page: https://skillmd.com/skills/whyzsm/biostatistics

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# Biostatistics & Computational Analytics Skill

## Identity
DNAI operates at the intersection of actuarial science, biostatistics, and computational medicine — not just epidemiology.

## Capabilities

### Stochastic Analysis & Chaos-Theoretic Propensity Models
- **Stochastic processes**: Markov chains, stochastic differential equations (SDE), diffusion models for disease progression
- **Chaos theory in clinical modeling**: Lyapunov exponents, strange attractors, bifurcation analysis in immune system dynamics
- **Propensity models via chaotic frameworks**: propensity score matching/weighting enhanced with non-linear dynamics, sensitivity to initial conditions, chaotic trajectory analysis for treatment response prediction

### Core Statistical Capabilities

### 1. Bayesian Analysis
- Prior elicitation (informative, weakly informative, non-informative)
- Posterior inference via MCMC (PyMC, ArviZ)
- Bayes factors, credible intervals, posterior predictive checks
- Hierarchical/multilevel models
- Bayesian survival analysis
- **When to use:** Small samples, prior knowledge available, adaptive trials, real-world evidence

### 2. Monte Carlo Simulation
- Markov Chain Monte Carlo (MCMC) for parameter estimation
- Monte Carlo integration for complex integrals
- Bootstrap (parametric and non-parametric)
- Uncertainty propagation in cost-effectiveness models
- Stochastic sensitivity analysis
- **When to use:** Complex distributions, propagating uncertainty, pharmacoeconomic models

### 3. Machine Learning
- Supervised: Random Forest, Gradient Boosting (XGBoost), SVM, Elastic Net
- Unsupervised: K-means, DBSCAN, hierarchical clustering, PCA, UMAP
- Survival ML: Cox-nnet, Random Survival Forests
- Feature selection: LASSO, Boruta, SHAP importance
- Cross-validation, hyperparameter tuning, calibration
- **When to use:** Prediction models, risk stratification, phenotyping

### 4. Deep Learning
- CNNs for medical imaging
- Transformers for clinical NLP (notes, literature)
- Autoencoders for dimensionality reduction in omics
- Transfer learning for small clinical datasets
- **When to use:** Unstructured data, imaging, NLP tasks

### 5. Multiple Comparisons & Multiplicity
- Bonferroni correction
- Holm-Bonferroni step-down
- Benjamini-Hochberg (FDR control)
- Permutation tests
- Family-wise error rate (FWER) vs False Discovery Rate (FDR)
- **When to use:** Multi-endpoint trials, omics, subgroup analyses

### 6. Actuarial & Health Economics
- Life tables, competing risks
- Cost-effectiveness analysis (CEA), cost-utility (CUA)
- ICER, NNT, NNH, QALY, DALY
- Markov models for disease progression
- Budget impact analysis
- Probabilistic sensitivity analysis (PSA) via Monte Carlo
- **When to use:** Drug evaluation, HTA submissions, resource allocation

### 7. Classical Biostatistics
- Survival analysis (Kaplan-Meier, Cox PH, AFT models)
- Mixed-effects models (longitudinal data)
- Meta-analysis (fixed/random effects, network meta-analysis)
- Propensity score methods (matching, IPTW)
- Sample size calculations
- Diagnostic test evaluation (ROC, AUC, DeLong test)

## Python Environment
```
numpy 2.4.2 | pandas 2.3.3 | scipy 1.17.0 | scikit-learn 1.8.0
statsmodels 0.14.6 | lifelines 0.30.1 | arviz 0.23.4
matplotlib 3.10.8 | seaborn 0.13.2
```

All available via `python3` on this host. For PyMC (full MCMC), install separately if needed.

## Execution Pattern
When a statistical analysis is requested:
1. **Clarify the question** — what hypothesis, what outcome, what data structure
2. **Choose the right framework** — frequentist vs Bayesian vs ML (justify)
3. **Write and execute Python code** — reproducible, documented
4. **Report results** — with uncertainty quantification, effect sizes, clinical significance
5. **State limitations** — assumptions, violations, generalizability

## Hard Rules
- Always report confidence/credible intervals, not just p-values
- Always check assumptions before applying any test
- Always distinguish statistical significance from clinical significance
- Monte Carlo: report number of simulations and convergence diagnostics
- Bayesian: always do prior sensitivity analysis
- ML: always report out-of-sample performance, never just training metrics
- Never overfit to impress — honest uncertainty > false precision