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Paragraph: This study takes coronary artery bypass graft (CABG) surgical site infections (SSIs) as an example to examine whether a relationship exists between operation volumes and SSIs , when different SSIs case identification, definitions and categorization methods of operation volumes were implemented. METHODS: A population-based cross-sectional multilevel study was conducted. A total of 7,007 patients who received CABG surgery between 2006 and 2008 from19 medical centers in Taiwan were recruited. SSIs associated with CABG surgery were identified using International Classification of Diseases, 9th Revision, Clinical Modification (ICD-9 CM) codes and a Classification and Regression Trees (CART) model. Two definitions of surgeon and hospital operation volumes were used: (1) the cumulative CABG operation volumes within the study period; and (2) the cumulative CABG operation volumes in the previous one year before each CABG surgery. Operation volumes were further treated in three different ways: (1) a continuous variable; (2) a categorical variable based on the quartile; and (3) a data-driven categorical variable based on k-means clustering algorithm. Furthermore, subgroup analysis for comorbidities was also conducted. RESULTS: This study showed that hospital volumes were not significantly associated with SSIs, no matter which definitions or categorization methods of operation volume, or SSIs case identification approaches were used. On the contrary, the relationships between surgeon’s volumes varied. Most of the models demonstrated that the low-volume surgeons had higher risk than high-volume surgeons. CONCLUSION: Surgeon volumes were more important than hospital volumes in exploring the relationship between CABG operation volumes and SSIs in Taiwan. However, the relationships were not robust. Definitions and categorization methods of operation volume and correct identification of SSIs are important issues for future research. Text: data, which should use hierarchical models, may result in biased estimation of the variation and also lead to incorrect conclusions. SSIs following coronary artery bypass graft (CABG) procedures place a heavy burden on patients and healthcare systems. The total length of stay and expenditure for patients with SSIs after CABG surgery is significantly longer and higher than those without SSIs. [20, 21] In 2008, the Centers for Medicare & Medicaid of the United States of America implemented the "Never Event" policy, where hospitals would no longer receive higher payments for the additional costs associated with treating patients for certain healthcare-acquired infections, including those related to CABG. In view of the accuracy of SSIs identification and the heterogeneity of definition and categorization methods, no existing studies have used different infection case identification nor definitions and categorization methods of operation volume simultaneously to explore the relationship between operation volumes and infection. The current study takes CABG SSIs as an example  , given different SSI cases identification, operation volume definitions and categorization methods. This retrospective and cross-sectional study adopted a multilevel design to examine the relationships between provider volumes and SSIs after adjusting for patient-, surgeon-, and hospital-level covariates. We used data from the Taiwan National Health Insurance Research Database (NHIRD) from 2005 and 2008. The NHIRD, published by the Taiwan National Health Research Institute, includes all the original claims data and registration files for beneficiaries enrolled under the National Health Insurance (NHI) program. The database covers the 23 million Taiwanese enrollees (approximately 98% of the population) in the NHI program. It is a de-identified secondary database containing patient-level demographic and administrative information; however, treatment items are aggregated and without time-related and clinical information. The data is released for research purposes. The protocol for the study was approved by the Institutional Review Board of the National Taiwan University Hospital (protocol #201001027R). The dataset we used in this study was secondary data; all information was de-identified by data owners. In this study, we adopted the ICD-9-CM SSI codes (hereafter referred to as the ICD-9-CM based model) and the Classification and Regression Trees (CART) model, which was developed in our previous work [11] to identify SSI cases. As we mentioned above, the ICD-9-CM SSI codes were the most popular tool to identify the SSI cases in claims data. In the ICD-9-CM based model, SSI cases were divided into two categories: index hospitalization events and post-discharge events (i.e., SSIs that occurred within 1 year after discharge and required readmission to a hospital and/ or the use of ambulatory services). Following Wu et al [13] , this study adopted the secondary ICD-9-CM diagnosis codes for index hospitalization events (ICD-9-CM code: 996.03, 996.61, 996.72, and 998.5), and the primary and secondary diagnosis codes for post-discharge events (ICD-9-CM code: 038.0-038. 4 ) as the criteria for SSI identification, in order to avoid cases in which infection existed prior to hospitalization. If a case had an index hospitalization event or a post-discharge event, then he/ she will be identified as SSIs by the ICD-9-CM based model. In the CART model, we adopted the type of antibiotics, dose of cefazolin, length of stay, and number of vessels obstructed (as a proxy indicator of duration of operation) as the parameters to identify the SSIs, according to our previous findings. [11] In our previous work, we used the 2005-2008 National Health Insurance claims data and healthcare-associated infection surveillance data from two medical centers for model development and model verification. Infection cases based on surveillance were identified by infection control personnel if the patient met the Taiwan CDC's criteria, which are the same as those adopted in the U.S. CDC. They manually review medical records of all patients at risk for the specified healthcare-associated infection. The classification algorithms, the multivariable regression model, and the data mining model were adopted to develop alternative models based on surrogate indicators to identify cases of CABG SSIs and to compare the performance among these models and the ICD-9-CMbased model. For the classification algorithms, researchers build up several criteria, and if a case satisfies (or exceeds) a specific number of criteria, then it will be identified as a case of infection. For the multivariable regression model, researchers usually calculated a risk score by the logistic regression model, and the optimal cutoff point was determined according to the resulting receiver operating characteristic curve. Concerning the data mining approach, which is widely used for predicting and classifying objects, the characteristics are: automatic discovery of patterns, prediction of likely outcomes, creation of actionable information, and focus on large data sets and databases. The classification and regression tree (CART) model, which is the most popular approach as applied in our work, and the growing, stopping, and pruning of the tree were determined by Gini improvement measures. [22, 23] After referring to the literature and conferring with infectious disease specialists, we adopted the following seven parameters: type of antibiotic, doses of antibiotic, doses of cefazolin, use of second-line antibiotics, length of stay, and number of vessels obstructed. Additionally, cross-validation was also employed, where data from one medical center was used for model development, and another one was used for model validation. The results of our previous work revealed that the CART model offered better performance than that of the other identification models or the ICD-9-CM based model, especially in the positive predictive value (>70%), which was only found to be 20% in the ICD-9-CM based model. (Table 1 ) The findings also implied that the CART was a decidedly better tool for identifying cases of SSI in the Taiwan National Health Insurance database. Therefore, this study also adopted the CART model for identifying CABG SSIs. To ensure homogeneity, current study analyzed 7,007 patients from 19 medical centers in Taiwan who underwent CABG surgery (ICD-9-CM procedure codes 36.1x-36.2x) between 2006 and 2008. CABG patients under the age of 18 years or over 85 years were excluded in this study. A total of 302 cases were identified as SSIs by ICD-9-CM based model, and a total of 107 cases were identified as SSIs by CART model. In this study, we used the following two definitions to define operation volumes: (1) the cumulative operation volumes by each surgeon and hospital within the study period, which was the most common definition in the literature; and (2) following Yasunaga et al. 's study, [24] cumulative operation volumes by each surgeon and hospital in the previous one year for each surgery. However, our data was skewed, which did not follow a normal distribution. Therefore, we conducted the log transformations on operation volumes. The current work treated operation volumes in three different ways: (1) a continuous variable; (2) a categorical variable based on the first and the third quartile as cutoff points (the most common method to categorize service/ operation volumes) [25] [26] [27] [28] ; and (3) a data-driven categorical variable based on k-means clustering algorithm. This study categorized surgeon and hospital volumes into low, medium, and high volume groups by quartile method and kmeans clustering algorithm. In the quartile method, the cut-off value (transformed by logarithm) of the first quartile (<25%) for hospital volumes was 5.65, and the third quartile (>75%) was 6.43. In terms of surgeon volumes, the first quartile was 4.38, and the third was 5.35, when we used the cumulative operation volumes within the study period as the definition. While the definition changed, first quartile (<25%) for hospital volumes was 4.66, and the third quartile (>75%) was 5.31. In terms of surgeon volumes, the first quartile was 3.40, and the third was 4.32. K-means clustering is an unsupervised machine-learning algorithm introduced by MacQueen in 1960s. This method is not only a simple and very reliable method in categorization/ classification, but is also recognized as one of the top 10 algorithms in data mining. [29] This method has often been applied in many fields. [30] [31] [32] Yu and his colleagues even applied it to define the quality of CABG care, and to explore the relationship among patient's income status, the level of quality of care, and inpatient mortality. [33] The main idea of this method is to partition observed data points into k non-overlapping clusters by minimizing the within-group sum of squares. Each point is assigned to the mean of its cluster using the Euclidian distance. Firstly, k cluster centers were randomly generated. Previous studies usually divided surgeons and hospitals into low-, medium-, and high-volume groups; therefore, we also predetermined the surgeon and hospital service volumes into 3 groups (k = 3). Then, participants were assigned to the cluster with the shortest distance to these cluster centers. Finally, the cluster centers were recomputed using the new cluster assignment and these steps would be iterated until convergence was achieved. [34] The cut-off values of hospital volumes were 5.21 and 5.69, and for surgeon's volumes were 2.40 and 4.38 respectively, when cumulative operation volumes within the study period was used as the definition. Likewise, when cumulative operation volumes before each surgery was used as definition, the cut-off values were 4.11 and 4.89 for hospital volumes, and 2.64 and 3.91 for surgeon's volumes. All cutoff values were transformed by logarithm. The results of k-means clustering are demonstrated in Figs 1-4. As the results show, the operation volumes were divided into three groups separately. In addition to surgeon and hospital volumes and SSI, we collected patient-, surgeon-, and hospital-level data. Firstly, patient-level variables included age, gender, length of ICU stay, number of vessels obstructed that were involved in the surgical operation, and the presence of important underlying diseases (e.g. diabetes mellitus, chronic obstructive pulmonary disease (COPD), heart failure, renal failure and renal insufficiency, which were associated with SSI). [13] Secondly, the surgeon-level variables included age and gender. Thirdly, the hospital-level variables included hospital ownership and geographic location. All statistical analyses of volume-infection relationship were performed using SAS (version 9.2, SAS Institution Inc., Cary, NC, USA). In statistical testing, a two-sided p value 0.05 was considered statistically significant. The distributional properties of continuous variables were expressed by mean ± standard deviation (SD), whereas categorical variables were presented by frequency and percentage. In univariate analysis, the potential three-level predictors of SSI were examined using chi-square test or two-sample t-test as appropriate. Next, to account for the correlations within surgeon (level-2) and hospital (level-3), multivariate analysis was conducted by fitting mixed-effects logistic regression models to each patient's data for estimating the effects of three-level predictors on the probability of post-operational SSI. Furthermore, subgroup analysis for comorbidities was also conducted. Table 2 shows that there were 7,007 patients with CABG performed by 199 surgeons in 19 hospitals during 2006-2008 in Taiwan. The majority of patients were male (77.5%), and the mean age of patients was 65.3 years. The average ICU stay was 6.05 days, the mean level of number of vessels obstructed was around 1.6, while 51.8% of patients had diabetes mellitus, 33.3% had heart failure, 14.1% had renal failure and renal insufficiency, and 22.0% had COPD. Three hundred and two patients (4.31%) were identified as having the ICD-9-CM SSI codes. However, identification by the CART model only revealed 107 infection cases, and 94 cases were identified in both models. Most cases received CABG surgery by male surgeons, with a mean age of 45.0 years, and the surgeon's average operation volumes within the study period was 151.64, while the average operation volumes before surgery was 52.18. More than half of the cases were performed with CABG in not-for-profit hospitals, and the hospitals' average operation volumes within the study period was 473.60, while the average operation volumes before each surgery was 158.79. Moreover, most of patients received their surgeries by high-volume surgeons and hospitals, when k-means algorithm was used for categorization, regardless of which definition of operation volumes were used. Table 3 shows the results of multilevel mixed-effect models, with the SSIs being identified by ICD-9-CM codes, and the operation volumes defined as the cumulative volumes within the study period. The results of Model 1 (continuous) reveal that the surgeon's volumes were negatively associated with SSIs, while hospital's volumes were not associated with surgical site infection SSIs. Model 2 (quartile) suggests that low-volume surgeons had higher SSI risk (OR = 2.220, p-value = 0.022) than high-volume surgeons. There were also no associations between hospital's operation volumes and SSIs. Model 3 (k-means) shows that the association did not exist between hospital's/ surgeon's volumes and SSIs. Table 4 displays the results of multilevel mixed-effect models, in which the SSIs were identified by the CART model, and the operation volumes were also defined as the cumulative volumes within the study period.

Question: What is the purpose of this research study?
to examine whether a relationship exists between operation volumes and SSIs