Predictive Models to Assess Risk of Extended Length of Stay in Adults with Spinal Deformity and Lumbar Degenerative Pathology: Development and Internal Validation

failure, and academic institution). A cutoff of 0.18 for eLOS yielded a sensitivity of 77% and specificity of 68%. Conclusions. This predictive model can facilitate identification of adults at risk for eLOS following elective multi-level lumbar/thoracolumbar spinal instrumented fusions for ASD. With a fair diagnostic accuracy, the predictive calculator will ideally enable clinicians to improve preoperative planning, guide patient expectations, enable optimization of modifiable risk factors, facilitate appropriate discharge planning, stratify financial risk, and accurately identify patients who may represent high-cost outliers. Future prospective studies that validate this risk assessment tool on external datasets would be valuable.


Introduction
Adult spinal deformity (ASD) is a highly prevalent condition with a definitive negative impact on health-related quality of life [1,2]. Such patients have greater functional limitations and pain than patients with other chronic conditions, even when compared with age-matched controls [3,4]. When expectant management and physical therapy fails to provide relief, elective surgical intervention can be pursued [5]. While surgical intervention can provide considerable benefit, post-operative recovery after ASD operations is arduous, frought with complications, and often requires extended hospital stays, and rehabilitation [6][7][8].
Measurement of eLOS can serve as a composite reflection of the postoperative course for ASD patients, with extended stay associated with increased risk of hospital-acquired infections, medical complications, and readmissions [9][10][11]. The resulting retention of patients in post-acute care settings can result in significant administrative challenges due to the ensuing disruption of patient flow and bed shortages, limiting access to care [12]. Furthermore, eLOS has also been identified as one of the top predictors of catastrophic costs, of over $100,000 for ASD patients [13]. Hence, there exists a significant interest in predicting which patients will have eLOS following surgery for ASD.
While numerous studies have identified independent risk factors associated with eLOS, few are specific to ASD patients, major discrepancies exist on importance of selected risk factors [14][15][16]. Additionally, assessment of risk through a combination of many significant variables, each with respective odds ratio or relative risk, can make preoperative evaluation difficult. Therefore, a need exists for a method to rapidly predict patients at risk for eLOS in the preoperative setting. Thus, the goal of this study is to develop a machine learning model to pre-operatively estimate the likelihood of eLOS for patients with elective multi-level lumbar/thoracolumbar spinal instrumented fusions for spinal deformity.

Source of Data
Data were acquired retrospectively on ASD patients from state-level inpatient database hosted by the Healthcare cost and Utilization Project (HCUP) [17]. Data were derived from both public and private healthcare institutions in the states of California, Florida, Nebraska, New York, North Carolina, and Utah from the period of 2005-2013. No patient identifiers were gathered throughout data collection.
Data included patient demographic variables, comorbidities, operative information, and LOS measured in days for each patient.

Participants, Sample Size, and Missing Data
Inclusion criteria were ASD patients with age ≥50 years undergoing elective multi-level spine fusions ( levels) to the lumbar or thoracolumbar regions (Figure 1). Cases of malignancy, trauma, or infection were excluded. Patients with unknown LOS, discharge against medical advice, or missing data were also excluded. Inclusion and exclusion criteria were applied by utilization of International Classification of Diseases, Volumes 9 codes (ICD-9) [18].

Predictors and Outcomes
The primary outcome was whether a patient had eLOS, defined as >7 days.

Statistical Analysis
Chi-Square and Fisher's exact tests were used for univariate analysis to determine the association between predictor variables and an eLOS, with generation of odds ratios and corresponding 95% confidence intervals (CI), and p-values. P-values <0.05 were considered statistically significant. Multivariate analyses were then conducted on all significant variables through binary logistic regression.

Development and Validation of Predictive Models
In development of machine learning models, the cohorts were separated into 80% To create a clinically applicable tool with estimation of predictive probability of eLOS, beta coefficients for the simplified logistic model were determined. In addition to AUC, model characteristics such as sensitivity, specificity, positive predictive value, and negative predictive value were calculated at varying thresholds.

Software/Tools Used
MATLAB version 2020b was used to conduct all statistical analyses and predictive model development [20].

Saturated Model Development
Data from 80% of patients the cohort (n=7,093) were used to train the machine learning models with validation on 20% (n=1,773). All significant variables from multivariate analysis were used in the development of the saturated logistic regression predictive model (AUC=0.77, 95% CI: 0.74-0.80). The ROC is displayed in Figure 2.    Table 3).

Model Interpretation
The aim of this study was to develop a machine learning model to pre-operatively predict eLOS in patients undergoing elective multi-level lumbar or thoracolumbar instrumented fusion for a diagnosis of ASD. The model created utilized six essential pre-operative patient variables (combined anterior and posterior approaches, thoracic+lumbar regions, >8 instrumented/fused levels, malnutrition, congestive heart failure, academic institution) and produced a diagnostic AUC of 0.76, with a sensitivity of 77% and specificity of 68% at a selected threshold of 0.18.
Given that the saturated logistic model utilizing all significant variables had an AUC of 0.77, the goal was met in creation of a simplified pre-operative model that kept diagnostic accuracy. With the provided beta coefficients, clinicians can easily utilize the model pre-operatively within the clinical setting to facilitate rapid risk assessment.
Overall, the associations determined between significant predictive variables and eLOS agree with the literature. For example, male sex has been widely associated with reduced LOS and lower readmission rates in patients undergoing surgery for lumbar degenerative pathology [21,22]. Combined anterior and posterior approaches, surgery to both lumbar and thoracic regions, and a greater number of fused interspaces (≥8) have been proven to increase chances postoperative infection risk, medical complications, and LOS in ASD patients [23][24][25][26]. Certain comorbidities, such as CHF, renal disease, malnutrition, and osteoporosis, have been well documented as significant mortality risks following elective spine surgery [27][28][29][30]. While the association between alcohol use disorder and poor perioperative outcome is mixed for ASD

Implications
A critical implication of the pre-operative predictive model is the potential to predict financial risk. The relation between eLOS and costs of care is significant and represents a driving factor behind the need for accurate pre-operative assessment. For example, for spine deformity patients, a single additional day in the hospital can incur over $10,000 in insurance charges and over $5,000 in hospital costs, accompanied with significant associated financial risks of returning to the operating room within 90 days [37]. Moreover, the direct cost per day in the hospital is significantly greater than that of a post-acute care rehabilitation facility [38,39]. Of note, while a portion of patients require an eLOS due need for management of perioperative complications, a substantial amount of eLOS patients reside longer in the hospital due to delays in the discharge transfer process to a rehabilitation or skilled nursing facility [40]. Thus, such patients represent cost outliers as they incur high costs associated with both eLOS and rehabilitation.
Under reimbursement models such as Bundled Payments for Care Improvement Initiative (BPCI), where reimbursement is fixed for the duration of care, eLOS can cause catastrophic financial loss and inability for the hospital to sustain surgical spine care [41][42][43]. Ensuring financial viability of elective surgeries is important to ensure that hospital systems can continue to operate. Therefore, a key utility of the predictive calculator derived in this study is to stratify financial risk and accurately identify patients who may represent high-cost outliers.
Usage of the predictive calculator to predict patients at risk of eLOS may also aid in alleviating hospital bed shortages and therefore improve patient access to care [12].
Administrative teams may establish an acceptable predictive model risk tolerance depending on the hospital's typical space availability. The predictive calculator threshold can be changed depending on the most recent occupancy of the post-acute care unit and the acceptable risk tolerance as determined by the healthcare team. With the predictive calculator in hand, clinicians can ensure greater transparency with patients, better manage post-operative expectations, and have additional tools in the shared-decision making process on the risks and benefits of surgery [44].

Strengths and Limitations
A key strength of this study is that it utilizes a large cohort size with patients from multiple healthcare institutions in different states within the United States while retaining a sufficient granularity of patient information. The usage of large sample size in training the models is critical for robust machine learning and predictive model development [36].
Moreover, application of inclusion criteria to focus only on elective procedures for ASD provides a reasonable control against confounding conditions, which few prior studies have done. The predictive model only utilized six variables, with retention of diagnostic accuracy when compared to the fully saturated model, and is preferable to other models that require every single feature of the patient's risk profile. The resulting predictive calculator, with corresponding beta coefficients, can be easily applied in the clinical setting to rapidly facilitate pre-operative identification of adult patients at risk for eLOS following spinal deformity surgery.
Future prospective studies that validate the risk assessment tool on an external dataset would be valuable. As additional data become available, the relative contribution of each variable to the prediction of eLOS can be modified for improved accuracy. Delays in the referral process to a post-operative care facility due to administrative barriers can also result in eLOS [35]. Unfortunately, identification of patients with a prolonged discharge referral process was not feasible in this study, as the dataset does not allow one to assess and/or differentiate between reasons for an eLOS (i.e. secondary to additional postoperative management needed vs. complication vs. waiting for transfer to rehabilitation/SNF). Of note, eLOS and discharge disposition were interdependent outcomes, as discharge location was significant for eLOS on univariate analysis. However, discharge disposition was not factored into the predictive model development because the primary goal of this study was to utilize only variables available pre-operatively.
We also acknowledge that since the composition of our cohort is dependent on the accuracy of the ICD codes queried, it is possible that patients with purely degenerative pathology were treated in this cohort. Also unavailable were information on the prevalence of individual diagnoses and granular information on etiologies of the ASD patients that comprised our cohort.
Furthermore, we realize that information on the patient's condition prior to surgery, such as ambulatory status, neurological function, pre-operative narcotic usage, and pre-operative living situation, can influence eLOS, and were not utilized in this study. While more granular data with additional risk factors may be attained from a single institution, building a predictive model from one institution with a more limited patient cohort size would likely be overly specific to that singular location and lack broader generalizability. The predictive model we have presented is the first to utilize high-volume patient data from multiple healthcare institutions for ASD patients specifically, and hence represents a foundational tool that can be improved in the future as more granular patient data become available.

Conclusion
In this study of 8,866 ASD patients, a predictive calculator was created that can facilitate pre-operative identification of adults at risk for eLOS following elective multi-level lumbar/thoracolumbar spinal instrumented fusions for ASD. The predictive calculator built utilized six essential pre-operative predictors (surgical approach, surgical region, levels fused, malnutrition, congestive heart failure, and institution type). With a diagnostic AUC of 0.76, this predictive calculator will ideally enable clinicians to improve pre-operative planning, guide patient expectations, enable optimization of modifiable risk factors, facilitate appropriate discharge planning, stratify financial risk, and accurately identify patients who may represent high-cost outliers. Future prospective studies that validate this risk assessment tool on external datasets would be valuable.      * COPD = chronic obstructive pulmonary disease; CHF = congestive heart failure; MI = myocardial infarction.