tooluniverse-statistical-modeling

Statistical Modeling for Biomedical Data Analysis

Comprehensive statistical modeling skill for fitting regression models, survival models, and mixed-effects models to biomedical data. Produces publication-quality statistical summaries with odds ratios, hazard ratios, confidence intervals, and p-values.

Features

✅ Linear Regression - OLS for continuous outcomes with diagnostic tests ✅ Logistic Regression - Binary, ordinal, and multinomial models with odds ratios ✅ Survival Analysis - Cox proportional hazards and Kaplan-Meier curves ✅ Mixed-Effects Models - LMM/GLMM for hierarchical/repeated measures data ✅ ANOVA - One-way/two-way ANOVA, per-feature ANOVA for omics data ✅ Model Diagnostics - Assumption checking, fit statistics, residual analysis ✅ Statistical Tests - t-tests, chi-square, Mann-Whitney, Kruskal-Wallis, etc.

Quick Start

Binary Logistic Regression

import statsmodels.formula.api as smf
import numpy as np

# Fit logistic regression
model = smf.logit('disease ~ exposure + age + sex', data=df).fit(disp=0)

# Extract odds ratios
odds_ratios = np.exp(model.params)
conf_int = np.exp(model.conf_int())

print(f"Odds Ratio for exposure: {odds_ratios['exposure']:.4f}")
print(f"95% CI: ({conf_int.loc['exposure', 0]:.4f}, {conf_int.loc['exposure', 1]:.4f})")
print(f"P-value: {model.pvalues['exposure']:.6f}")

Cox Proportional Hazards

from lifelines import CoxPHFitter

# Fit Cox model
cph = CoxPHFitter()
cph.fit(df[['time', 'event', 'treatment', 'age', 'stage']],
        duration_col='time', event_col='event')

# Get hazard ratio
hr = cph.hazard_ratios_['treatment']
print(f"Hazard Ratio: {hr:.4f}")
print(f"Concordance: {cph.concordance_index_:.4f}")

See QUICK_START.md for 8 complete examples.

Model Selection Decision Tree

START: What type of outcome variable?
│
├─ CONTINUOUS (height, blood pressure, score)
│  ├─ Independent observations → Linear Regression (OLS)
│  ├─ Repeated measures → Mixed-Effects Model (LMM)
│  └─ Count data → Poisson/Negative Binomial
│
├─ BINARY (yes/no, disease/healthy)
│  ├─ Independent observations → Logistic Regression
│  ├─ Repeated measures → Logistic Mixed-Effects (GLMM/GEE)
│  └─ Rare events → Firth logistic regression
│
├─ ORDINAL (mild/moderate/severe, stages I/II/III/IV)
│  └─ Ordinal Logistic Regression (Proportional Odds)
│
├─ MULTINOMIAL (>2 unordered categories)
│  └─ Multinomial Logistic Regression
│
└─ TIME-TO-EVENT (survival time + censoring)
   ├─ Regression → Cox Proportional Hazards
   └─ Survival curves → Kaplan-Meier