Aggregation-Sensitive Mortality Associations and Firth Penalized Logistic Regression After Hip Fracture Surgery: A Retrospective Cohort Study

Background/Objectives: Hip fracture mortality analyses may be influenced by aggregation-related changes in association estimates and sparse data bias, particularly for early mortality outcomes. Methods: This retrospective study included 297 patients who underwent hip fracture surgery between 2020 and 2025. One-year mortality was the primary outcome, and 30-day mortality was the secondary outcome. Pooled, stratum-specific, and Mantel–Haenszel odds ratios were compared to explore aggregation-sensitive changes in association estimates. Conventional maximum likelihood logistic regression and Firth penalized logistic regression were fitted using the same predictor set. The model performance was evaluated using the area under the curve (AUC), the Brier score, calibration measures, and bootstrap internal validation with 1000 resamples. Results: Mortality occurred in 36 of 294 evaluable patients within 30 days and 95 of 252 evaluable patients within one year. No complete reversal of the association was observed. Exploratory comparisons suggested age-related attenuation for male sex, modest masking for low hemoglobin levels across sex strata, and mild amplification for dementia and elevated NLR. In the 1-year models, age, male sex, ASA IV status, dementia or cognitive impairment, and lower preoperative hemoglobin levels were independently associated with mortality. The conventional and Firth models demonstrated nearly identical discrimination for 1-year mortality, with apparent AUC values of 0.807 and 0.806, respectively. In bootstrap validation, the conventional model yielded converged estimates in 902 of 1000 resample sets, whereas the Firth model remained estimable in all 1000 resamples. For 30-day mortality, conventional logistic regression was affected by quasi-complete separation, whereas Firth regression produced finite estimates; however, these early mortality findings were considered exploratory because only 36 deaths occurred and some estimates remained highly imprecise. Conclusions: Several mortality associations differed in magnitude between pooled and stratification-adjusted estimates without a complete reversal of association. Firth penalization improved estimability and resampling stability under sparse-event conditions, although it did not materially enhance the discrimination of 1-year mortality. The 30-day mortality findings should be interpreted as exploratory because of the limited number of early deaths and resulting imprecision of some estimates.