Comorbidity and thirty-day hospital readmission odds in chronic obstructive pulmonary disease: a comparison of the Charlson and Elixhauser comorbidity indices

Background Readmissions following exacerbations of chronic obstructive pulmonary disease (COPD) are prevalent and costly. Multimorbidity is common in COPD and understanding how comorbidity influences readmission risk will enable health systems to manage these complex patients. Objectives We compared two commonly used comorbidity indices published by Charlson and Elixhauser regarding their ability to estimate readmission odds in COPD and determine which one provided a superior model. Methods We analyzed discharge records for COPD from the Nationwide Readmissions Database spanning 2010 to 2016. Inclusion and readmission criteria from the Hospital Readmissions Reduction Program were utilized. Elixhauser and Charlson Comorbidity Index scores were calculated from published methodology. A mixed-effects logistic regression model with random intercepts for hospital clusters was fit for each comorbidity index, including year, patient-level, and hospital-level covariates to estimate odds of thirty-day readmissions. Sensitivity analyses included testing age inclusion thresholds and model stability across time. Results In analysis of 1.6 million COPD discharges, readmission odds increased by 9% for each half standard deviation increase of Charlson Index scores and 13% per half standard deviation increase of Elixhauser Index scores. Model fit was slightly better for the Elixhauser Index using information criteria. Model parameters were stable in our sensitivity analyses. Conclusions Both comorbidity indices provide meaningful information in prediction readmission odds in COPD with slightly better model fit in the Elixhauser model. Incorporation of comorbidity information into risk prediction models and hospital discharge planning may be informative to mitigate readmissions.


Background
The burden of chronic obstructive pulmonary disease (COPD) continues to rise [1,2], and in the United States, COPD remains the 4th leading cause of death as of 2017 [3]. Exacerbations are common, and economic burdens from related hospitalizations are substantial [4,5]. In October 2014, the Centers for Medicare and Medicaid Services (CMS) Hospital Readmissions Reduction Program (HRRP) began assessing financial penalties for excessive 30-day hospital readmissions of Medicare patients following COPD hospitalizations [6]. Efforts to understand and reduce readmission risk highly important to health systems. COPD patients have high burdens of various comorbid conditions [7][8][9], with multiple comorbidities associated with symptom burden, mortality, and hospital utilization [10][11][12][13]. COPD patients often meet the threshold of the "multimorbid" patient [14].
The performance of risk adjustment measures in the HRRP remain debated [15], in particular whether risk adjustments adequately control for factors outside the control of a treating hospital. Accurate quantification of comorbidity is crucial for programs that leverage financial penalties to reduce readmissions. Two comorbidity indices are frequently used for research and could potentially adjust for between hospital differences in burden of chronic illness, having previously been shown to be valid for predicting key outcomes of interest [16]. The Charlson Comorbidity Index (CCI) predicts mortality in hospitalized patients [17][18][19]. Higher CCI scores correlate with mortality, risk of readmission, and lower likelihood of receiving appropriate COPD treatments [20]. The Elixhauser Comorbidity Index (ECI) is an inventory of comorbidities [21], later updated to predict mortality [22,23] and readmission [24]. Both the Charlson and Elixhauser indices have been associated with readmission outcomes in surgical conditions [25][26][27], psychiatric conditions [28], and hospitalizations due to other medical conditions and procedures [29][30][31].
Previous studies show variance between these two indices' ability to discriminate important outcomes in the COPD population [32]. Understanding the milieu of comorbidity among COPD patients could improve methodology to adjust for readmission risk and enable providers and delivery networks to estimate risk and plan readmission reduction efforts. In order to do this most effectively, an optimal system for quantifying comorbidity and its relationship to readmissions must be identified. Doing so would enable resources within health systems to be directed at those at highest risk of readmission, and also inform policy makers on further improvement in risk stratification methodology within the Hospital Readmissions Reduction Program. Our aim is to compare these two indices' ability to quantify comorbidity and its contribution to readmission risk in COPD.

Data source
We analyzed discharge records from January 2010 to December 2016 in a pooled, multiple cross-sectional analysis of the Nationwide Readmissions Database (NRD) [33], a nationally representative sample of all-payer discharges from acute care hospitals across multiple states. Because the NRD does not allow for an individual patient to be linked across years, qualifying index discharges were restricted to stays occurring in February through November, as we could not identify whether January stays were actually readmissions from the prior December or follow December index stays into the next January. We restricted to patients who were residents of the state in which they were admitted to avoid loss to follow up when crossing state lines. Sample weights provided with the dataset were applied to calculate national estimates, compensating for under-sampled patient and hospital characteristics [34]. In the analyses that follow, raw numbers indicate the actual observations, while reported percentages and models utilize the sample weights to provide a population estimate.

Variable construction
We defined an index hospitalization as one where the patient was discharged alive, excluding transfer to other acute care hospitals and discharges against medical advice, occurring at least 30 days since another hospitalization. A COPD stay was defined by principal diagnosis of COPD exacerbation or principal diagnosis of respiratory failure and secondary diagnosis of COPD [35,36], excluding cases involving lung transplantation. We included all index discharges from the NRD for patients aged ≥40 years with a qualifying COPD diagnosis admitted to a hospital with at least 25 such discharges over the months outlined above for each given year. We defined readmission as return to any hospital for any diagnosis within 30 days of discharge, excluding certain conditions granted exemption from the HRRP (e.g., childbirth, organ transplantation, or chemotherapy). These definitions were constructed to be aligned with published HRRP methodology [35,36].
Most variables of interest were included in the original dataset; however, we derived several others. The Charlson and Elixhauser comorbidity scores were calculated using ICD codes and Diagnosis Related Groups, using adaptations of published macros [37,38] to recode individual ICD codes for each diagnosis into the respective comorbidity index categories and calculate weighted scores using the coding schemata outlined by the original comorbidity index publications [24,39,40]. We used diagnoses at the time of the index discharge due to limitations of the dataset to identify patients only within each year, precluding a look-back period. We constructed indicators for inhospital events (e.g., mechanical ventilation) using ICD codes. We estimated the proportion of within-hospital Medicaid patient-days by taking the number of patientdays paid by Medicaid divided by total patient-days each year. We tabulated the number of hospitals visited and admissions within a year to characterize utilization patterns.
Hospital volume for all-cause and COPD-specific discharges were tabulated. Additional details on database structure and variable definitions in the online supplemental methods appendix, where a full list of provided and derived covariates can be found (Additional file 1).

Statistical analysis
Summary statistics were calculated at the patient level, comparing the readmitted and non-readmitted. Continuous variables were compared using Welch's t-test (i.e., unequal variance), while categorical variables were compared using Chi-squared tests. Readmission rates were aggregated for population estimates by year, quarter, and month. Readmission rates for hospital sub-strata of interest were calculated, with differences across categories estimated by Chi-squared tests. Adjusted readmission odds were estimated using a two-level, mixed-effects logistic regression model with random intercepts assigned at the hospital cluster level using complete case analysis. A threshold of 10% missingness for variables of interest was set a priori to determine the necessity for use of imputation, which was not reached for any variable included in this analysis. We fit separate, parallel models for the Charlson and the Elixhauser indices as primary predictor, with fixed effects for year, patient-dischargeand hospital-level covariates consistent across both models. Comparison of the two models was made using Akaike and Bayesian information criteria, where lower values of the information criterion signify models of better fit [41,42].

Sensitivity analysis
We tested the stability of our estimates over time by refitting the model for individual years. We analyzed a liberalized age cutoff to ≥18 years, having initially favored an older age cutoff given the paucity of COPD in younger patients and concern that these observations may represent miscoding. All analyses were performed in Stata version 15.1 (StataCorp, College Station, TX) with weighted estimates reported using patient level survey weights for national representativeness.

Results
A total of 1,622,983 index COPD admissions (weighted effective sample N = 3,743,164) occurred during the seven-year study period, 17.2% of which were readmitted within 30 days of discharge. Patient characteristics are found in Table 1, further stratified by hospital teaching status (Additional file 11) and urban/rural designation (Additional file 12). There were proportionally fewer readmissions among women than men. Readmitted patients were older (68.7 vs 67.9 years). Medicare and Medicaid patients had higher proportions of readmissions than private insurance or self-pay status. Readmitted patients were more frequently discharged to postacute care or with home health services and had longer lengths of stay (4.16 vs 3.67 days). Hospital characteristics and aggregated sub-cohort readmission rates by hospital type are found in Table 2.
In keeping with previous studies, teaching hospitals had higher readmission rates (17.7%) than non-teaching hospitals. For-profit hospitals had a higher readmission rate (17.5%) when compared to governmental (16.8%) and non-profit (17.3%) facilities. Hospitals with Multi-level logistic regression models were fitted separately for the Charlson Index and the Elixhauser Index and compared (Table 4). To standardize comparisons between the models, the comorbidity indices were scaled by their distributions, such that an odds ratio was calculated for a change of one-half standard deviation (SD) in score. In our adjusted models, a 1/2 SD change in the Charlson score (~1.5 points) was associated with a 9% increase in readmission odds while a 1/2 SD change in the Elixhauser score (~7.5 points) portended a 13% increase in readmission odds. The unadjusted (Model 1), patient-adjusted (Model 2), and patient-and hospitaladjusted (Model 3) estimates in their original scaling are found in Additional file 3 (CCI) and Additional file 4 (ECI).
Women had lower odds than men and readmission odds decreased with increases in age. In both models, Medicaid patients had higher readmission odds and the privately insured had lower odds compared to Medicare. Hospital proportion of Medicaid patient-days did not correlate with readmission odds. Compared to routine discharges home, those with transfers to post-acute care and home with home health services had significantly higher readmission odds. Each day increase in length of stay portended slightly higher readmission odds. Smaller but significant effects were observed for hospital location, while hospital teaching status, volume of discharges. The effect sizes for covariates were similar for both comorbidity models. To compare the fit of the two models, we employed the Akaike (AIC) and Bayesian (BIC) information criteria, which deal with the balance between goodness-of-fit and parsimony of any given model [41,42]. In our analysis, the Elixhauser model had a lower AIC (3,355,795 vs. 3,366,918) and BIC (3, 356,300 vs, 3,367,434) than the Charlson, demonstrating better fit.
In the sensitivity analyses, the odds ratios for comorbidity indices did not vary significantly across  time (Additional file 5 and Additional file 6). When we evaluated whether our original age restriction to patients ≥40 years old had any significant influence on the models, we found no substantial changes in our estimates by expanding to all adults ≥18 years old (Additional file 7 for CCI and Additional file 8 for ECI). We also evaluated whether the presence of the comorbidity index substantially changed the estimates of the covariates by fitting an additional model without the comorbidity indices (Additional file 9) which showed small changes in effect sizes, but no sign changes between the reduced and original models, with better fit in our original model (Additional file 10). Of notable difference, the effects of discharge disposition and care intensity diminished, likely demonstrating some collinearity between these factors and comorbidity.

Discussion
In this large, all-payer, population study of those admitted COPD exacerbations, we examined the contributions of comorbidity and key patient and hospital factors to risk for 30-day rehospitalization. Escalating degrees of comorbidity were associated with significantly higher odds of 30-day readmission even after controlling for other patient and hospital factors in both the Charlson and Elixhauser models. This is in line with previously published work in the Veterans Affairs population showing that higher Charlson scores were associated with higher risk of readmissions [20], and a new finding for use of the Elixhauser model in COPD. While the comparison of comorbidity indices has been previously published with regard to predicting COPD exacerbations and hospitalizations [32], our findings showing the comparison of two widely-used candidate comorbidity indices to predict readmissions is novel. In this comparison, the Elixhauser Comorbidity Index performed slightly better, with the inclusion of more comorbidity parameters giving a better model fit. While previous studies of Medicare patients for other HRRP conditions have not shown socioeconomic status to be consistently correlated with readmission outcomes [43,44], our study showed that patients who lived in higher income neighborhoods had progressively lower adjusted readmission odds. Furthermore, while other studies in these populations have raised concern about higher readmission burdens in hospitals serving lower-income patients [45][46][47][48], our study did not show a significant correlation between adjusted readmission odds and proportion of hospital Medicaid patient-days. Our methodology did not allow for exact approximation of Disproportionate Share Hospital estimates due to lack of information on supplemental security income [49], and using Medicaid as a proxy may underrepresent the burdens on safety-net hospitals. These findings may be at odds with the arguments for need for additional adjustments for socioeconomic factors, but given the proxies used to measure income status in this study, it is difficult to draw a definitive conclusion from these data.
In sensitivity analyses, we found that including comorbidity scores improved upon models simply using patient demographic and hospital characteristics. This is unsurprising, given the rich detail that comorbidity information adds. The fact that comorbidity scores increased with time may reflect coding practice changes, as health systems include additional comorbid conditions in their discharge diagnoses to increase the severity reflected in coding schema for Diagnosis Related Grouping, or to mitigate readmission penalties by shoring up risk categorization [50]. It is possible that transition to electronic health records under the Affordable Care Act's Meaningful Use provisions let to more precise coding of diagnoses, though our data source does not allow for this delineation. In addition, more diagnoses (25 per record 2010-13, 30 in 2014, and 35 in 2015-16) are included in the later years of the dataset, which has been associated with up-coding of severity in Medicare analyses [51]. Regardless, our estimates for readmission odds were stable across time despite the decreases in readmission rates and the increases in coded comorbidity and transition from ICD-9 to ICD-10.

Limitations and residual confounding
Inconsistent coding of comorbid conditions at the time of hospital discharge may hinder our ability to truly model the breadth of comorbidity in our study. We were also limited by the structure of the database, using pooled cross-sectional data instead of a true longitudinal sample, further limited by the database's inability to identify the same patient or hospital across years. As such, there were likely some cases where a patient was measured more than once but not identified as such. While some degree of auto-correlation is possible from our approach, the large sample size was felt to adequately compensate for this. The same is true of repeated visits from the same patient within a year introducing additional  correlation between readmissions resulting in potentially overly narrow confidence intervals. The NRD as a data source contains some inherent limitations, including the absence of a race variable and the coding of income by medians at ZIP-centers rather than being patient-reported [52]. Inability to track a patient across state lines may lead to under-reporting of readmissions. Furthermore, not all states are included in the database, however provided sampling weights were used to compensate for otherwise underrepresented patient and hospital types [34]. Within these limitations, however, our approach fills in important gaps in the currently published literature. By including an all-payer sample, we are able to better understand the patient milieu beyond the Medicare population, where most previous studies have been done. The sample is nationally representative and covers all community hospital discharges within the study period across a wide range of states. Use of such a broad patient population enables insights not previously afforded by individual health system or payer populations.

Conclusion
In a large, national, all-payer sample of COPD hospitalizations, comorbidities are frequent and play a substantial role in the 30-day readmission risk. Between two available comorbidity scoring systems, the Elixhauser Comorbidity Index provides better model fit when compared to the Charlson Comorbidity Index and should be favored for future analyses of this type. Using comorbidity in risk adjustment tools may provide policy makers with additional insight into how best to correct for the multimorbid patient when assessing penalties. In addition, health systems seeking to improve their delivery methods could use such a scoring system to better understand their own distribution of comorbidities in order to develop programs tailored to their individual patient populations. Further study of the differential influence of these comorbid conditions on outcomes and the mitigating effects of care delivery by integrated practice units to address multimorbidity is warranted.