*Limitations*

We are aware of several limitations of our study: (i) The design was retrospective, based on administrative data, and we could not assess complications due to AKI such as fluid overload, electrolyte abnormalities, and coagulopathy. It has been reported that complications related to AKI such as fluid overload could be associated with a risk of death [39]. However, our results sugges<sup>t</sup> that conditions diagnosed well before the detection of AKI could be associated with IHM; (ii) we did not provide reasons for admission, specific cause of death, intensive care level, including aggressive therapy and/or device use, neither did we identify AKI on the basis of international Kidney Disease Improving Global Outcomes (KDIGO) guidelines [40]; (iii) we could not evaluate the impact of clinical or biochemical parameters due to the fact that they were not available. There are evident disadvantages in studies based on administrative databases, such as a lack of specific clinical information, the e ffects of administrative use (i.e., reimbursement), possible misclassification of outcomes, and di fficulties in controlling confounding factors [41]. Moreover, as previously stated, race and clinical settings (i.e., surgical and intensive care settings) were not considered; (iv) patients could be wrongly coded, and subjects that are nowadays coded with AKI may have su ffered a less severe renal insult than previously. This could be because awareness of AKI has improved; (v) we did not di fferentiate patients on the basis of the cause of AKI and the treatment setting, we only considered dialysis treatment. On the other hand, only advanced stages of AKI undergo renal replacement therapy. Furthermore, we could not distinguish if AKI happened before or during admission. In 2006, Waikar et al. [42] calculated the performance of ICD-9-CM for acute renal failure and found that the sensitivity was 35.4%, specificity 97.7%, positive predictive value 47.9%, and negative predictive value 96.1% [42]. The validity of AKI codes in administrative databases was analyzed in 2011 in Canada: sensitivity was poor, the median value was 29% (in the range 1%–81%), and median of the positive predictive value was 67% (in the range 15%–96%) [43]. In 2013, Tomlinson et al. [44] calculated a positive predictive value for patients with AKI of 95%. In 2014, Grams et al. [45] validated administrative codes for AKI against the KDIGO AKI definition. They calculated a sensitivity of 17.2% if the comparison was the evaluation of serum creatinine criteria, and 11.7% if the comparison was serum creatinine and urine output-based criteria, whilst specificity was >98% in both cases. Sensitivity was significantly higher when they considered a more recent time period and individuals aged ≥65 years. AKI diagnosed by administrative data was related to more severe disease and higher in-hospital mortality [45]. All these data seem to reinforce our results.

Our study also has some strengths: (i) The high number of records derived from a national administrative database, recording all real diagnoses of AKI; (ii) the long period considered; (iii) the choice of IHM as hard outcome indicator.

## **5. Conclusions**

Nowadays, multi-morbidity is receiving greater attention [15], and our findings confirm that comorbidity stratification is crucial to understanding the reasons for IHM of hospitalized elderly patients with AKI. The results of this study emphasize that in elderly subjects, IHM is associated with a degree of renal impairment (especially if the damage needs dialysis treatment), sepsis development, and an increasing burden of comorbidity. Increasing comorbidity score, ascribed to cardiovascular and liver disease, cachexia and cancer, diagnosis of sepsis and advanced renal damage requiring dialysis treatment should be taken into account when evaluating the risk of IHM in hospitalized elderly subjects with AKI.

**Author Contributions:** Conceptualization, F.F., M.G., A.S., and R.M.; methodology, C.S., A.D.G.; software, A.D.G.; validation, C.S., R.C., E.D.S., and B.B.; formal analysis, C.S., A.D.G., E.D.S., R.C., and B.B.; investigation, F.F., E.D.S., R.C., and B.B.; resources, M.G., A.S., and R.M.; data curation, F.F. and M.G.; writing—original draft preparation, F.F. and C.S.; writing—review and editing, R.M.; supervision, A.S. and M.G.; project administration, M.G.; funding acquisition, R.M.

**Funding:** This study is supported by a scientific gran<sup>t</sup> by the University of Ferrara (Fondo Ateneo Ricerca, FAR 2018, prof. Roberto Manfredini).

**Acknowledgments:** We would thank Franco Guerzoni and Nicola Napoli, Center for Health Statistics, Azienda Ospedaliero-Universitaria "S.Anna", Ferrara, Italy, for precious and valuable collaboration.

**Conflicts of Interest:** The authors declare no conflict of interest.
