The Risk Factors and Predictive Nomogram for Length Of Stay More than 14 Days in Undergoing TKA Patients: A Secondary Analysis Based on a Cohort Study in Singapore

Objective: The aim was to explore the risk factors and establish a predictive nomogram of length of stay (LOS) more than 14 days in a undergoing Total knee arthroplasty (TKA) cohort . Methods: We used the raw data, a retrospective cohort study of 2622 patients undergoing TKA in Singapore, for secondary analysis. The LASSO regression was used to optimize feature selection for the LOS more than 14 days. The Multivariable logistic regression analysis was applied to build a predicting nomogram by using the feature selected in the LASSO regression model. In order to evaluate the prediction ability of the model, we calculated the C-index. Simultaneously, the ROC curve, the Calibration curve and the DCA curve was draw to assess the model. Finally, we used 1000 times bootstrap method to verify the accuracy of the model.


Introduction
Total knee arthroplasty (TKA) is one of the most common orthopedic surgeries, Studies have shown that over time, the prevalence rate has increased signi cantly and shifted to a younger age, and the prevalence rate in women is higher than that in men 1 .The TKA was mainly used for the treatment of pain, mobility limitation and joint deformity caused by osteoarthritis, rheumatoid arthritis and knee trauma 2 . It can help patients restore knee joint function and signi cantly improve the quality of life of patients 3 .The increased life expectancy and the aging population have led to a dramatic increase in the number of patients with knee disorders, and total knee arthroplasty (TKA) is currently the most important and effective treatment for severe knee disorders, the demand for TKA will increase dramatically in the coming years 4,5 . It is estimated that more than 700,000 TKA surgeries are performed in the United States every year, and this number will increase to nearly 3.5 million by 2030. Therefore, it is inevitable to perform TKA in an economical and effective way 6 .
The associated costs of surgical procedures, inpatient care, rehabilitation, and postoperative care have increased substantially due to enhanced intra -and perioperative management 7 . Meanwhile, as the epidemic of new coronary pneumonia spread, there was an obvious decline in the global economy, and the Medical insurance expenditure increased signi cantly. Some countries have removed the TKA from the List of Medicare Outpatient Payment System Rules 8 . The focus of reducing hospitalization cost is to reduce Length Of Stay(LOS). The shortening LOS will increase the turnover rate of inpatients, reduce medical costs and reduce the medical burden of the society 9 .
In addition, TKA surgery may be accompanied by serious complications, which will adversely affect the prognosis of patients and increase the possibility of disability and death 10 . However, the longer LOS is a risk factor for the postoperative complications. It is particularly important to reduce postoperative complications such as postoperative infection, thromboembolism, postoperative delirium and cognitive dysfunction 11 . Therefore, how to determine the factors of LOS , reduce the incidence of surgical complications, decress hospitalization expenses and save medical resources are the problems,which should be solved by the doctors .The purpose of this study was to explore the risk factors and establish a predictive nomogram of length of stay (LOS) more than 14 days in a undergoing Total knee arthroplasty (TKA) .

Patients Dates
Our study is a secondary analysis based on a single-center retrospective cohort study in Singapore.
Patients who underwent TKA at Singapore General Hospital from January 2013 to June 2014 were selected 12 . We download the raw data uploaded by Abdullah et al at the"DATADRYAD"web site (www.datadryad.org). Abdullah et al have authorized the ownership of the original data to the datadryad Web site; therefore, we could utilize these data for secondary analysis on a different hypothesis without violating the authors'rights.
The study was approved by the Ethics Committee of the A liated Hospital of Qingdao University. The Ethics Committee particularly approved that informed consent was not required because of being approved by the"DATADRYAD"Web site (www.datadryad.org) and data were analyzed anonymously.The ethics committee waived the requirement for informed consent from all patients.

Statistical analysis
Statistical analysis was performed using R software (version 3.1.1; https://www.R-project.org). Chisquared tests (categorical variables) and one-way analysis of variance or K-W test (continuous variables of a normal distribution or skewed distribution) were appropriately performed to verify signi cant differences between different groups.
We used R package "glmnet" for doing lasso regression analysis.Lasso regression can perform variable screening and complexity adjustment while tting the generalized linear model. Variable screening refers to not putting all variables into the model for tting, but selectively putting variables into the model to get better performance parameters. Complexity adjustment is to avoid over tting by controlling the complexity of the model through a series of parameters.Finally, we got the result of lasso's regression. All potential predictors were applied to develop a cohort model that predicted the risk of LOS more than 14 days.
Multivariate Logistic regression analysis was used to establish the prediction model combining the minimum absolute contraction and the selected features in the selection operator regression model. The accuracy of the prediction model was evaluated by the ROC curve. A decision curve analysis was performed by quantifying the net bene t at different threshold probabilities in the TKA cohort to determine the clinical usefulness of LOS more than 14 days risk nomogram. Furthermore, the calibration curves and decision curve analysis (DCA) curves were established for the assessment of the nomograms.
C-index, which is the consistency index, is used to evaluate the prediction ability of the model. We use 1000 bootstrap times to verify the accuracy of the model. There is a random sample put back in the original data, and the sample size remains unchanged. The obtained sample is called bootstrap sample.

Results
The Demographic characteristics of patients Finally, 2622 patients who underwent TKA from January 2013 to June 2014,a retrospective cohort, were included in the study. 2622 patients(96.19%) were hospitalized for less than 14 days, however, 100 patients(3.81%) were hospitalized for more than 14 days.In Table 1, the proportion of patients with advanced age (≥ 70 years) was higher in the prolonged LOS group than in patients with normal LOS (< 70 years), and the difference was statistically signi cant (P≤0.001).There were no signi cant differences in BMI, race, and sex distribution between the 2 groups.However, patients in the LOS extended group had a high ASA score (p≤0.001), a long operation time (p≤0.001), a high ratio of bilateral knee replacement (p≤0.001), a high incidence of anemia and diabetes (p≤0.001), a history of cough (p≤0.001), a high risk of transfusion during operation (p≤0.001), repeated operation (p≤0.001) during hospitalization, and general anesthesia (p≤0.001).

The Feature Risk Foctors Selection
This study was based on data on demographic, disease, and treatment characteristics of 2622 patients undergoing knee replacement in the cohort. 17 features were reduced to ten potential predictors on TKA patients in the cohort (Figure1 A and B) and were with nonzero coe cients in the LASSO regression model, as shown in Figure 1.These characteristics included Age, ASA Status, type of anaesthesia, operation duration, procedure description, DM, IHD, CHF, day of operation and blood transfusion ( Table   2).

The Development of Nomogram for LOS More Than 14 Days
We developed a model containing the above 10 independent predictors and expressed them as a nomogram ( Figure2).

The Validation of Prediction Nomogram
The ROC curve shows that the rosette has high predictive performance, and its AUC is 0.797 (Figure3).This shows that the prediction model has strong prediction ability. The calibration curves used to predict LOS more than 14 days risk nomogram in knee patients in this study cohort showed good consistency (Figure4). Similarly, the calibration curve also shows that the prediction ability of the model is strong.
To quantify the discrimination performance of the LOA more than 14 days nomogram, C-index was measured. The C-index for the prediction nomogram was 0.797 (95% CI: 0.755-0.839) for the cohort.The C-index is 0.763 through 1000 times bootstrapping validation. The DCA of LOS more than 14 days indicated that this nomogram can serve as an excellent diagnostic tool for patients undergoing TKA( Figure 5).

Discussion
The aim of our study was to develop and validate a LOS more than 14 days risk prediction model for TKA patients. The risk factors were Age, ASA status, type of anesthesia, operation duration, procedure description, DM, IHD, CHF, day of operation and blood transfusion.Ultimately, We built the nomogram using the above risk factors for LOS more than 14 days in TKA patients. The Nomogram transforms the complex regression equation into a visual graph, which makes the results of the prediction model more readable and convenient for patient evaluation. Because of the intuitive and easy to understand characteristic of nomogram, it has gradually been paid more and more attention and applied in medical research and clinical practice.
In the risk prediction nomogram with LOS more than 14 days in this study, the highest independent predictor score was blood transfusion, many studies have come to the same conclusion, and the transfusion rate was directly related to LOS [13][14][15] . Autologous blood transfusion is often required when the blood loss is between 1000-1500 ml. research shows that the total blood loss after TKA may be as high as 2000 ml, and the proportion of blood transfusion may be as high as 67% 16, 17 . In a cohort of 228,316 TKA patients at 922 hospitals, the mean predicted probability of TKA transfusion was 7.9%, with 60% (95% CI, 36%-87%) patients with LOS more than 3 days 13 . In a cross-sectional study of 4,544,999 patients who received TKA between January 2000 and December 2009, blood transfusion were associated inhospital mortality, LOS increased by 0.71±0.01 days 14 . In addition, Danninger et al. 15 showed a signi cantly higher rate of major complications in patients receiving transfusion (19.1% vs 11.2%, P<0.0001), the mean length of hospital stay was signi cantly increased.
Our study found that the date of operation was a major factor in predicting the risk of LOS more than 14 days after blood transfusion. Similarly, studies demonstrated that operation procedure or factors related to doctors-nurses provide clinically relevant improvement in explaining length of stay in addition to patient-related risk factors 8 . In a prospective cohort study of 4,509 patients who underwent initial TKA at four hospitals between January 1, 2016 and September 30, 2017, surgery later in the day predicted a longer hospital stay, with patients who had surgery on Friday having a signi cantly longer LOS than patients who had surgery on Monday 8 . Our study showed that the risk prediction scores of operations on Monday, Tuesday and Friday were much higher than those on Thursday. The length of hospital stay was related to the date of operation. Possible reasons for this result include patients from different countries, surgical hospital system, doctors' mood and doctors' preferences.
This study found that the greater the variety of comorbid diseases, that is, the higher the comorbidity index, and the longer the hospital stay. Swain et al. 18 showed that 67% of patients with osteoarthritis had at least one other chronic condition, 20% more than those without osteoarthritis. The results of this study suggest that co-morbidity CHF, DM, and IHD are independent predictors of LOS more than 14 days. Similarly, some previous studies suggested that the TKA patients with comorbidities had prolonged LOS [19][20][21][22][23] . Higuera et al. 22 showed that chronic heart failure was associated with longer hospital stays and increased rates of major postoperative complications in TKA patients. In a study of 15,321 TKA patients, 18.2% had a medical comorbidity DM, with a 300% increase in overall mortality. Belmont et al. 23 found that DM was an independent predictor of hospitalization of 4 days or more.
ASA status was also particularly important for predicting LOS more than 14 days of risk. Consistent with previous literature, ASA-status more than 3 is an independent risk factor for prolonged LOS and increased postoperative complications 23,24 .The predicted risk score of bilateral total knee arthroplasty is higher than that of unilateral TKA, probably because bilateral patients suffer more blood loss, more severe hypotension, and more cardiac, respiratory, and neurological complications than unilateral patients 25,26 . In this study, it was suggested that patients undergoing knee revision were also predictors of LOS more than 14 days of risk, and that revision arthroplasty was associated with longer hospital stays and higher rates of complications and mortality, similar to results con rmed in previous studies 27,28 .
The type of anesthesia also played an important role in predicting the risk of LOS more than 14 days. In both primary and revised TKA patients, general anesthesia was associated with an increased risk of postoperative complications, such as thromboembolism and surgical incision infection, as well as increased the LOS, blood transfusion rates, postoperative opioid consumption, and surgical time, compared with epidural or spinal anesthesia [29][30][31][32][33] .In addition, age and operation duration were independent predictors of LOS more than 14 days risk, similar to previous nding 23,34 .Limitations of this study include: as the included cases excluded patients with GA combined with RA and other anesthesia methods, the results of this study cannot be used to predict the risk of this population.
There are still some limitations in our study. Firstly, this study is a retrospective study, using clinical data from a single center. Therefore, there may be differences in treatment strategies, race, and so on. Second, because of differences in healthcare Settings and practices, predictive models developed in one country are unlikely to be directly applicable in another country, requiring external validation and updating of the predictive performance of models in other new patient. Finally, there may be some in uencing factors not included in this paper, including patient income, medical expenses, medical insurance, hospital location, etc. Potential factors not included may also have some in uence on the results.

Conclusion
We based on the variables, including age, ASA status, type of anesthesia, operation duration, procedure description, DM, IHD, CHF, day of operation and blood transfusion, established the risk prediction model of LOS more than 14 days in undergoing TKA patients. We found that the model had good predictive ability. Clinicians can use the model for hospitalized patients to reduce the length of hospital stay, reduce complications, and save medical resources. 33. Pugely, A. J., Martin, C. T., Gao, Y., Mendoza-Lattes, S. & Callaghan, J. J. Differences in short-term complications between spinal and general anesthesia for primary total knee arthroplasty.   Figure 1 Demographic and clinical feature selection using the LASSO binary logistic regression model.   The ROC curves of the LOS more than 14 days in Undergoing TKA Patients.

Figure 4
The Calibration curves of LOS More Than 14 days in Undergoing TKA Patients.