Complex Statistical Models: Elderly Falls Analysis

Overview

This project analyzes predictors of fall frequency in 100 elderly patients using the full family of count regression models, from basic Poisson to Hurdle-Negative Binomial. The response variable is overdispersed and zero-inflated, making model selection both necessary and non-trivial. Every decision from EDA to final interpretation is documented in a numbered project log, emphasizing rigor and transparency.

Models & Selection

All eight models were fit with predictors exercise (binary), gender (binary), balance, and strength.

Overdispersion test (LRT) rejected Poisson in favor of NB (p < 0.05). AIC/BIC favored Hurdle-Poisson and NB respectively. Backward elimination dropped gender (LRT p = 0.499). All three retained predictors (exercise, balance, strength) were significant at p < 0.01 and remained significant under Bonferroni and BH correction.

Final Model & Interpretation

Model: Negative Binomial, falls ~ exercise + balance + strength, θ = 4.751.

• Exercise RR = 0.153: patients who exercise regularly have 84.7% fewer expected falls at equivalent balance and strength
• Balance RR = 1.014: 1.4% increase in expected falls per unit increase in balance score
• Strength RR = 1.020: 2.0% increase in expected falls per unit increase in strength score

Analysis Log

Every step from data loading to final interpretation is documented in a numbered log (47 entries). The log records what was done, why, and the explicit justification for each methodological choice, including test selection, variable retention, and acknowledged limitations.

• [4] Poisson fit by ML: visual mismatch with empirical PMF/CDF indicates poor fit
• [21] Formal χ² GOF omitted: unreliable with ungrouped continuous predictors; LRTs used throughout
• [28] Three interactions tested; none significant at α = 0.10; none retained
• [35] Limitations documented: zero count discrepancy and 6 influential observations retained without full sensitivity analysis