Background {#Sec1}
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The burden of chronic obstructive pulmonary disease (COPD) continues to rise \[[@CR1], [@CR2]\], and in the United States, COPD remains the 4th leading cause of death as of 2017 \[[@CR3]\]. Exacerbations are common, and economic burdens from related hospitalizations are substantial \[[@CR4], [@CR5]\]. 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 \[[@CR6]\]. Efforts to understand and reduce readmission risk highly important to health systems. COPD patients have high burdens of various comorbid conditions \[[@CR7]--[@CR9]\], with multiple comorbidities associated with symptom burden, mortality, and hospital utilization \[[@CR10]--[@CR13]\]. COPD patients often meet the threshold of the "multimorbid" patient \[[@CR14]\].

The performance of risk adjustment measures in the HRRP remain debated \[[@CR15]\], 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 \[[@CR16]\]. The Charlson Comorbidity Index (CCI) predicts mortality in hospitalized patients \[[@CR17]--[@CR19]\]. Higher CCI scores correlate with mortality, risk of readmission, and lower likelihood of receiving appropriate COPD treatments \[[@CR20]\]. The Elixhauser Comorbidity Index (ECI) is an inventory of comorbidities \[[@CR21]\], later updated to predict mortality \[[@CR22], [@CR23]\] and readmission \[[@CR24]\]. Both the Charlson and Elixhauser indices have been associated with readmission outcomes in surgical conditions \[[@CR25]--[@CR27]\], psychiatric conditions \[[@CR28]\], and hospitalizations due to other medical conditions and procedures \[[@CR29]--[@CR31]\].

Previous studies show variance between these two indices' ability to discriminate important outcomes in the COPD population \[[@CR32]\]. 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.

Methods {#Sec2}
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Data source {#Sec3}
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We analyzed discharge records from January 2010 to December 2016 in a pooled, multiple cross-sectional analysis of the Nationwide Readmissions Database (NRD) \[[@CR33]\], 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 \[[@CR34]\]. 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 {#Sec4}
---------------------

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 \[[@CR35], [@CR36]\], 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 \[[@CR35], [@CR36]\].

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 \[[@CR37], [@CR38]\] 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 \[[@CR24], [@CR39], [@CR40]\]. 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 in-hospital events (e.g.*,* mechanical ventilation) using ICD codes. We estimated the proportion of within-hospital Medicaid patient-days by taking the number of patient-days 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](#MOESM1){ref-type="media"}).

Statistical analysis {#Sec5}
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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-discharge- and 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 \[[@CR41], [@CR42]\].

Sensitivity analysis {#Sec6}
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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 {#Sec7}
=======

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](#Tab1){ref-type="table"}, further stratified by hospital teaching status (Additional file [11](#MOESM11){ref-type="media"}) and urban/rural designation (Additional file [12](#MOESM12){ref-type="media"}). 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 post-acute care or with home health services and had longer lengths of stay (4.16 vs 3.67 days). Table 1Baseline patient-level characteristics of the aggregated cohort, comparing readmitted to non-readmitted patients in index staysOverall *N* = 1,662,983Not Readmitted *N* = 1,375,099Readmitted *N* = 287,884*P*Sex*, (N) %* Male41.1%40.8%42.8%\<.001 Female58.9%59.2%57.2%Age*, (N) Mean ± SD*68.0 ± 11.967.9 ± 11.968.7 ± 11.7\<.001Median household income by ZIP code*, (N) %* 1st Quartile37.1%37.0%37.5%\<.001 2nd Quartile26.7%26.8%26.4% 3rd Quartile20.9%20.9%20.8% 4th Quartile13.9%13.9%14.1% Missing1.4%1.4%1.4%^b^Patient geographic location*, (N) %* Central county metro area ≥ 1 M22.3%22.0%23.5%\<.001 Fringe county metro area ≥ 1 M24.6%24.4%25.5% County metro area 250,000--999,999 k20.8%20.9%20.4% County metro area 50,000--249,999 k10.3%10.4%10.1% Micropolitan area13.0%13.1%12.2% Non-metro/non-micropolitan (rural)9.0%9.1%8.3%^c^Primary Payer*, (N) %* Medicare (includes dual-eligible)70.4%69.6%74.3%\<.001 Medicaid12.0%11.8%13.0% Private insurance11.6%12.3%8.3% Self-pay3.1%3.4%1.9% Other, including no-charge2.9%3.0%2.4%Number of admissions each patient had over a year*, (N) Mean ± SD*2.50 ± 1.962.13 ± 1.604.31 ± 2.50\<.001Number hospitals where each patient received care over a year*, (N) Mean ± SD*1.33 ± 0.671.31 ± 0.641.44 ± 0.75\<.001Discharge disposition*, (N) %* Routine to home67.5%69.1%60.1%\<.001 Transfer to post-acute care13.1%12.4%16.3% Other0.7%0.7%0.8% Home with home health services18.7%17.8%22.8%^a^Length of Stay*, (N) Mean ± SD*3.75 ± 2.043.67 ± 1.964.16 ± 2.38\<.001Care intensity and complications*, (N) %* Use of non-invasive ventilation8.0%7.7%9.7%\<.001 Use of mechanical ventilation4.7%4.5%5.7%\<.001 Placement or presents of tracheostomy0.8%0.8%1.2%\<.001 Cardiac arrest0.2%0.2%0.3%\<.001 Performance of cardiopulmonary resuscitation0.1%0.1%0.2%\<.001Note: Unweighted N's displayed. Frequencies derived using weighted analysis. ^a^Geometric Mean and SD for log transformed variable presented ^b^N's 1,373,301 & 287,296; ^c^N's 1,372,214 & 287,362

Hospital characteristics and aggregated sub-cohort readmission rates by hospital type are found in Table [2](#Tab2){ref-type="table"}. 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 higher proportions of Medicaid patients had higher unadjusted readmission rates. There was significant temporal variation in readmission rates both within individual years and across the entire study period, shown in Fig. [1](#Fig1){ref-type="fig"}. Distribution of comorbid conditions are shown in Table [3](#Tab3){ref-type="table"}. Readmitted patients had significantly higher mean CCI (2.41 vs. 2.10) and ECI (20.5 vs. 16.3) scores. The distribution of the composite Charlson and Elixhauser scores is shown in Fig. [2](#Fig2){ref-type="fig"}. Comorbid conditions were higher across all observed Charlson domains for the readmitted, with the exception of connective tissue diseases. The most pronounced differences were for congestive heart failure (34.8% of readmitted versus 26.1% of non-readmitted) and advanced diabetes (18.1% vs. 13.1%). In Elixhauser categories, readmitted patients had higher proportions of all comorbid conditions with the exception of hypertension, most pronounced for congestive heart failure (34% vs. 25.4%), renal failure (17.2% vs. 12.3%), and iron deficiency anemias (19.9% vs. 14.4%). Average comorbidity scores within for both indices increased over the study period (Additional file [2](#MOESM2){ref-type="media"}). Table 2Baseline characteristics of hospitals included in pooled cohortCohort ProportionReadmission Rate*P*Hospital ownership/control*, (N) %* Government, non-federal16.1%16.8%\<.001 Private, non-profit62.9%17.2% Private, for-profit21.0%17.4%Hospital teaching status*, (N) %* Metro, non-teaching44.2%17.3%\<.001 Metro, teaching30.0%17.6% Non-metro, non-teaching25.8%15.9%Hospital geographic location*, (N) %* Large metro area ≥ 1 M43.7%17.9%\<.001 Small metro area \< 1 M30.5%16.8% Micropolitan area15.3%16.0% Non-metro/non-micropolitan (rural)10.5%15.5%Hospital bed size*, (N) %* Small26.6%16.5%\<.001 Medium32.3%17.1% Large41.1%17.4%Hospital total all-cause annual discharges*, (N) Mean ± SD*6296 ± 6425Quartiles of Hospital total all-cause annual discharges*, (N) %* 1st Quartile (≤ 8971)59.1%16.4%\<.001 2nd Quartile (8972 -- 15,406)20.9%17.5% 3rd Quartile (15,407 -- 24,534)12.9%17.7% 4th Quartile (≥24,535)7.1%18.0%COPD Discharges*, (N) Mean ± SD*161 ± 133COPD Discharge Quartiles 1st Quartile (≤ 122)48.5%15.8%\<.001 2nd Quartile (123--205)24.1%17.0% 3rd Quartile (206--322)17.0%17.6% 4th Quartile (≥ 323)10.4%18.0%Proportion of Medicaid patient days*, (N) Mean ± SD*0.171 ± 0.112Medicaid Proportion Quartiles*, (N) %* 1st Quartile (≤ 10.6%)31.5%16.9%\<.001 2nd Quartile (10.6--16.1%)25.1%17.2% 3rd Quartile (16.1--23.9%)22.9%17.3% 4th Quartile (≥ 23.9%)20.5%17.6%Note: Unweighted frequencies displayed for cohort proportions. Weighted frequencies for Sub-Strata readmission rates presented. *P* values are for between hospital characteristic differences in readmission rates Fig. 1Readmission rates, aggregated within-year by quarter (**a**) and month (**b**), and across-years by quarter (**c**) and month (**d**) Table 3Baseline comorbidity characteristics of the aggregated cohort, comparing readmitted to non-readmitted patients in index stays for the Charlson and Elixhauser IndicesOverall (1,622,983)Not Readmitted (1,375,099)Readmitted (287,884)*P*Charlson Index Composite2.16 ± 1.432.10 ± 1.392.41 ± 1.57\<.001Charlson Index Grouping Index Score = 142.7%44.2%35.5%\<.001 Index Score = 227.6%27.5%27.8% Index Score ≥ 329.7%28.3%36.8%Charlson Component Comorbidities *Neurologic/Psychiatric*  Cerebrovascular disease3.1%3.0%3.5%\<.001  Dementia1.8%1.8%1.9%0.041  Hemiplegia/paraplegia0.3%0.3%0.3%\<.001*Cardiovascular* Congestive heart failure27.6%26.1%34.8%\<.001 Peripheral vascular disease5.6%5.4%6.2%\<.001 Myocardial infarction7.8%7.6%8.9%\<.001*Respiratory* Chronic pulmonary disease100.0%100.0%100.0%--*Gastrointestinal* Peptic ulcer disease0.8%0.8%0.9%\<.001 Mild liver disease2.2%2.1%2.4%\<.001 Moderate or severe liver disease0.2%0.1%0.2%\<.001*Renal/Electrolyte Disorders* Moderate or severe renal disease14.0%13.1%18.1%\<.001*Infectious Disease* HIV/AIDS0.2%0.2%0.3%\<.001*Hematologic/Oncology* Malignancy (any type)3.4%3.2%4.4%\<.001 Metastatic solid tumor1.1%1.0%1.7%\<.001*Rheumatologic and Musculoskeletal* Connective tissue disease2.2%2.2%2.2%0.131*Endocrine* Diabetes mellitus16.5%16.4%17.0%\<.001 Diabetes mellitus w/end-organ damage2.1%2.0%2.6%\<.001Elixhauser Index Composite17.0 ± 15.016.3 ± 14.720.5 ± 16.0\<.001Elixhauser Comorbidity Domain Count3.99 ± 1.843.92 ± 1.814.37 ± 1.91\<.001Elixhauser Component Comorbidities*Neurologic/Psychiatric* Paralysis1.3%1.2%1.5%\<.001 Other neurologic disorders8.6%8.3%9.8%\<.001 Alcohol abuse4.5%4.5%4.7%\<.001 Drug abuse3.6%3.5%4.2%\<.001 Psychoses6.3%6.1%7.6%\<.001 Depression16.9%16.7%17.8%\<.001*Cardiovascular* Congestive heart failure26.9%25.4%34.0%\<.001 Peripheral vascular disease7.9%7.7%9.2%\<.001 Valvular Heart Disease6.5%6.2%7.5%\<.001 Hypertension54.1%54.5%52.2%\<.001*Respiratory* Chronic pulmonary disease100.0%100.0%100.0%-- Pulmonary circulation disorders7.9%7.6%9.8%\<.001*Gastrointestinal* Peptic ulcer disease0.1%0.1%0.2%\<.001 Liver disease2.4%2.3%2.8%\<.001*Renal/Electrolyte Disorders* Renal Failure13.1%12.3%17.2%\<.001 Fluid and electrolyte disorders28.0%27.4%30.9%\<.001*Infectious Disease* HIV/AIDS0.2%0.2%0.3%\<.001*Hematologic/Oncology* Solid tumor without metastasis3.4%3.1%4.6%\<.001 Metastatic cancer1.1%1.0%1.7%\<.001 Lymphoma0.5%0.5%0.6%\<.001 Coagulopathy3.2%3.1%3.8%\<.001 Blood loss anemia0.4%0.3%0.5%\<.001 Deficiency anemia15.4%14.4%19.9%\<.001*Rheumatologic and Musculoskeletal* Rheumatoid arthritis and collagen vascular disorders3.3%3.3%3.5%\<.001*Endocrine* Diabetes mellitus (uncomplicated)26.3%25.8%28.4%\<.001 Diabetes mellitus (complicated)6.0%5.7%7.3%\<.001 Hypothyroidism13.7%13.6%14.0%\<.001 Obesity19.1%19.0%19.6%\<.001 Weight loss4.6%4.5%5.4%\<.001Note: Unweighted N's displayed. Frequencies derived using weighted analysis Fig. 2Charlson (**a**) and Elixhauser (**b**) distributions between readmitted and not readmitted patient stays

Multi-level logistic regression models were fitted separately for the Charlson Index and the Elixhauser Index and compared (Table [4](#Tab4){ref-type="table"}). 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 hospital-adjusted (Model 3) estimates in their original scaling are found in Additional file [3](#MOESM3){ref-type="media"} (CCI) and Additional file [4](#MOESM4){ref-type="media"} (ECI). Table 4Multilevel logistic regression model for Charlson (left) and Elixhauser (right) Indices, adjusted for patient and hospital factors with random intercepts for hospital clustersModel InfoCharlson IndexElixhauser Index N1,658,3721,658,372 LL-1,683,418.10-1,677,856.30 df4141 AIC3,366,918.303,355,794.50 BIC3,367,423.503,356,299.80PredictorsOR (95% CI)*P*OR (95% CI)*P*Comorbidity Index *(per ½ SD)*1.09 (1.09, 1.09)\<.0011.13 (1.12, 1.13)\<.001Year *(ref = 2010)* *2011*1.00 (0.97, 1.02)0.6730.99 (0.97, 1.01)0.484 *2012*0.96 (0.94, 0.98)\<.0010.95 (0.93, 0.97)\<.001 *2013*0.93 (0.91, 0.95)\<.0010.91 (0.89, 0.93)\<.001 *2014*0.92 (0.90, 0.94)\<.0010.89 (0.87, 0.91)\<.001 *2015*0.88 (0.86, 0.90)\<.0010.86 (0.84, 0.88)\<.001 *2016*0.87 (0.85, 0.89)\<.0010.85 (0.83, 0.87)\<.001Quarter *(ref = 1st)* *2nd Quarter*0.97 (0.96, 0.98)\<.0010.97 (0.95, 0.98)\<.001 *3rd Quarter*1.01 (1.00, 1.02)0.1671.00 (0.99, 1.02)0.778 *4th Quarter*0.99 (0.98, 1.01)0.2770.99 (0.97, 1.00)0.086Sex *(ref = male)* *Female*0.92 (0.91, 0.93)\<.0010.92 (0.91, 0.92)\<.001Age *(per 10 year)*0.97 (0.97, 0.98)\<.0010.98 (0.98, 0.99)\<.001Income Quartile *(ref = 1st)* *2nd Quartile*0.98 (0.97, 0.99)0.0030.98 (0.97, 1.00)0.009 *3rd Quartile*0.97 (0.95, 0.98)\<.0010.97 (0.96, 0.99)\<.001 *4th Quartile*0.94 (0.93, 0.96)\<.0010.95 (0.93, 0.97)\<.001 *Missing*0.97 (0.93, 1.00)0.0830.97 (0.93, 1.01)0.136Payer *(ref = Medicare)* *Medicaid*1.08 (1.06, 1.10)\<.0011.08 (1.06, 1.09)\<.001 *Private*0.69 (0.68, 0.71)\<.0010.71 (0.70, 0.73)\<.001 *Self-Pay*0.62 (0.60, 0.64)\<.0010.63 (0.61, 0.65)\<.001 *Other/No Charge*0.79 (0.77, 0.82)\<.0010.80 (0.77, 0.82)\<.001Disposition *(ref = Routine to home)* *Post-acute care*1.30 (1.28, 1.32)\<.0011.21 (1.19, 1.23)\<.001 *Home Health*1.35 (1.33, 1.37)\<.0011.30 (1.28, 1.32)\<.001 *Other*1.13 (1.06, 1.20)\<.0011.07 (1.00, 1.14)0.038Length of Stay *(per day)*1.02 (1.02, 1.02)\<.0011.01 (1.01, 1.01)\<.001Care intensity *(ref = No)* *Non-invasive ventilation*1.16 (1.14, 1.18)\<.0011.08 (1.06, 1.10)\<.001 *Mechanical ventilation*0.95 (0.92, 0.97)\<.0010.82 (0.79, 0.84)\<.001 *Tracheostomy*1.02 (0.97, 1.09)0.4251.04 (0.99, 1.11)0.133 *Cardiac arrest*0.82 (0.74, 0.91)\<.0010.81 (0.74, 0.90)\<.001 *CPR*1.08 (0.95, 1.24)0.2421.09 (0.95, 1.24)0.21Hospital ownership *(ref = government)* *Private, non-profit*0.99 (0.98, 1.01)0.4370.98 (0.96, 1.00)0.022 *Private, for-profit*1.04 (1.01, 1.06)\<.0011.03 (1.01, 1.06)0.002Hospital teaching status *(ref = Non-teaching)* *Teaching Hospital*1.01 (0.99, 1.02)0.4231.00 (0.98, 1.01)0.902Hospital location *(ref = Large metro area)* *Small metro area*0.94 (0.92, 0.95)\<.0010.93 (0.92, 0.95)\<.001 *Micropolitan area*0.89 (0.87, 0.91)\<.0010.90 (0.88, 0.92)\<.001 *Rural*0.87 (0.84, 0.90)\<.0010.89 (0.86, 0.92)\<.001Hospital Bed Size *(ref = Small)* *Medium*1.01 (0.99, 1.03)0.1741.01 (0.99, 1.03)0.389 *Large*1.02 (1.00, 1.04)0.041.01 (0.99, 1.03)0.407Annual Discharge (per 10 k)1.01 (1.00, 1.02)0.131.01 (1.00, 1.02)0.012Proportion of Medicaid patient days per 10%1.00 (1.00, 1.01)0.5311.00 (0.99, 1.01)0.872

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 \[[@CR41], [@CR42]\]. 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](#MOESM5){ref-type="media"} and Additional file [6](#MOESM6){ref-type="media"}). 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](#MOESM7){ref-type="media"} for CCI and Additional file [8](#MOESM8){ref-type="media"} 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](#MOESM9){ref-type="media"}) 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](#MOESM10){ref-type="media"}). Of notable difference, the effects of discharge disposition and care intensity diminished, likely demonstrating some collinearity between these factors and comorbidity.

Discussion {#Sec8}
==========

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 \[[@CR20]\], 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 \[[@CR32]\], 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 \[[@CR43], [@CR44]\], 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 \[[@CR45]--[@CR48]\], 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 \[[@CR49]\], 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 \[[@CR50]\]. 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 \[[@CR51]\]. 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 {#Sec9}
------------------------------------

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 \[[@CR52]\]. 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 \[[@CR34]\].

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 {#Sec10}
==========

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.

Supplementary information
=========================

 {#Sec11}

**Additional file 1.** Supplemental Methods Appendix. **Additional file 2:** **Figure S1.** Trend of mean Charlson and Elixhauser Index scores over time. **Additional file 3: Table S1.** Multilevel Logistic Regression models of Readmission using Charlson Index using Hospital Level random intercept. **Additional file 4: Table S2.** Multilevel Logistic Regression models of Readmission using Elixhauser Index using Hospital Level random intercept. **Additional file 5: Table S3.** Charlson and Elixhauser Indices (with 95% CI) over time per 1/2 standard deviation increase. **Additional file 6: Figure S2.** Changes in Charlson and Elixhauser Indices (with 95% CI) overtime per 1/2 standard deviation increase. **Additional file 7: Table S4.** Multilevel Logistic Regression models of Readmission using Charlson Index using Hospital Level random intercept (age 18 and older). **Additional file 8: Table S5.** Multilevel Logistic Regression models of Readmission using Elixhauser Index using Hospital Level random intercept (age 18 and older). **Additional file 9: Table S6.** Multilevel Logistic Regression models of Readmission using only the covariates as predictor with Hospital Level random intercept. **Additional file 10: Table S7.** Comparisons between covariate-only and comorbidity index models. **Additional file 11: Table S8.** Pooled cohort characteristics of patients, stratified by hospital teaching status. **Additional file 12: Table S9.** Pooled cohort characteristics of patients, stratified by urban/rural hospital location designation.

AHRQ

:   Agency for Healthcare Research and Quality

CCI

:   Charlson comorbidity index

CMS

:   Centers for Medicare and Medicaid Services

COPD

:   chronic obstructive pulmonary disease

ECI

:   Elixhauser comorbidity index

HCUP

:   Healthcare Cost and Utilization Project

HRRP

:   Hospital Readmissions Reduction Program

ICD

:   International Classification of Diseases

NRD

:   Nationwide Readmissions Database

SD

:   Standard deviation

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Michael K. Ong and Carol M. Mangione are co-senior authors

Supplementary information
=========================

**Supplementary information** accompanies this paper at 10.1186/s12913-019-4549-4.

The authors would like to acknowledge the mentorship of Dr. Igor Barjaktarevic and Dr. Christopher B. Cooper and the intellectual contributions of Dr. Tara Russell, Dr. Stefan Richter, and Ms. Petra Rasmussen.

The paper is derived from the PhD dissertation research in the field of health policy and management of the first/corresponding author. RGB and NJJ had full access to all of the data in the study and take responsibility for the integrity of the data and accuracy of the analysis. RGB, NJJ, GFK, SMD, MKO, and CMM contributed to the conception and design of the study. RGB, NJJ, GFK, SMD, MKO, and CMM contributed to the drafting of the manuscript. All of the authors listed above approved this version of the manuscript to be published.

This research was supported in part by the University of California at Los Angeles (UCLA) Clinical and Translational Science Institute (CTSI), National Institutes of Health (NIH) National Center for Advancing Translational Science (NCATS) Grant Number UL1TR001881, and the UCLA Joyce and Saul Brandman Fund for Pulmonary Research.

RGB received a loan repayment award from NIH National Heart, Lung, and Blood Institute (NHLBI) Grant Number L30HL134025 and was supported by NIH/NCATS UCLA CTSI Grant Number TL1TR001883--01, as well as the UCLA Specialty Training for Advanced Research (STAR) program.

CMM received support from the UCLA Resource Centers for Minority Aging Research Center for Health Improvement of Minority Elderly under National Institutes of Health NIH/National Institute on Aging (NIA) under Grant P30AG021684 and from the NIH/NCATS UCLA CTSI under Grant UL1TR001881. CMM holds the Barbara A. Levey and Gerald S. Levey Endowed Chair in Medicine, which partially supported her work. The funding source played no role in the study design, data collection, analysis or interpretation, or the writing of the manuscript. The researchers retained complete independence in the conduct of the study.

The datasets generated and/or analyzed during the current study are available in the Agency for Healthcare Research and Quality's Healthcare Utilization Project repository, available online at <https://www.hcup-us.ahrq.gov/nrdoverview.jsp>. A full list of partner organizations providing data for the Nationwide Readmission Database can be found at <https://www.hcup-us.ahrq.gov/db/hcupdatapartners.jsp>.

The study was reviewed and determined to be exempt from oversight based on its use of deidentified, publicly-available data by the University of California, Los Angeles Institutional Review Board (IRB\# 18--001208).

Not applicable.

RGB received personal consulting fees from GlaxoSmithKline, not related to this work.

NJJ reports nothing to disclose.

GFK reports nothing to disclose.

SMD is a member of the scientific advisory boards of Johnson & Johnson Lung Cancer Initiative, T-cure Bioscience, Cynvenio Biosystems, and EarlyDx, Inc., not related to this work.

MKO reports nothing to disclose.

CMM is a member of the United States Preventive Services Task Force (USPSTF). This article does not necessarily represent the views and policies of the USPSTF.

RGB, MKO, and SMD are employed as part-time physicians and researchers by the Veterans Health Administration This article does not necessarily represent the views and policies of the Department of Veterans Affairs.
