Diagnostic Entropy as an Administrative Measure of Cross-System Diagnostic Dispersion in Noncommunicable Disease Inpatients: A Methodological Validation Study

BACKGROUND: Existing comorbidity indices such as the Charlson Comorbidity Index (CCI) summarise comorbidity burden but do not capture how a patient's diagnoses are distributed across clinical speciality domains, a dimension hypothesised to relate to cross-system care coordination demands. This gap limits their utility for nursing workforce planning in settings with high multimorbidity prevalence. AIM: This study aimed to provide preliminary evidence for the construct validity of diagnostic entropy as an administrative measure of cross-system diagnostic dispersion, by testing its incremental predictive value for prolonged hospitalisation, beyond diagnosis count and the CCI. METHODS: A retrospective methodological validation study used inpatient discharge records from a tertiary hospital in southwest China, 2023-2025 (n = 31,470). Diagnostic entropy was calculated using the Shannon entropy formula applied to ICD-10 chapter distributions across each patient's valid diagnoses. Four nested binary logistic regression models were fitted with LOS > 10 days as the primary outcome. Four sensitivity analyses examined robustness to extreme LOS values, coding inclusion rules, insurance-type stratification and repeat admissions from the same patient. RESULTS: Diagnostic entropy had a mean of 1.746 (SD: 0.569); 72.3% of patients were in the high-entropy group (H ≥ 1.5). Entropy showed low-to-moderate correlation with the CCI (Spearman r = 0.304, p < 0.001) and moderate correlation with diagnosis count (r = 0.544, p < 0.001), suggesting that entropy captures a related but nonequivalent aspect of comorbidity-related complexity. After controlling for demographic characteristics, diagnosis count and CCI, entropy remained independently associated with prolonged hospitalisation (OR = 1.112, 95% CI: 1.072-1.153, p < 0.001), with an incremental Nagelkerke R² = 0.0014. This association was evident primarily among patients with seven or more diagnoses and was not statistically significant among patients with fewer diagnoses. High-entropy patients had longer stays, higher costs and higher rates of prolonged hospitalisation compared to low-entropy patients. Sensitivity analyses produced consistent results (OR range: 1.103-1.126). CONCLUSIONS: These findings contribute discriminant evidence toward the construct validity of diagnostic entropy as an administrative measure of cross-system diagnostic dispersion. Whether this dispersion translates into greater nursing coordination burden remains a hypothesis requiring prospective validation. IMPLICATIONS FOR NURSING MANAGEMENT: Diagnostic entropy, calculated from routinely collected discharge diagnoses, may offer nurse managers a low-cost, scalable indicator of cross-system diagnostic dispersion among NCD inpatients. Wards with a higher proportion of high-entropy patients could potentially require greater coordination across speciality teams, though this application awaits prospective, multicentre validation linking entropy to nursing-sensitive outcomes.