The majority of the nearly 70 million traumatic injuries occurring annually in the United States involve the musculoskeletal system, amounting to approximately 6 million fractures, which consume a substantial share of the health-care expenditures for trauma1-6. The cost of musculoskeletal injuries is considerable in terms of both health-care resources and individual patient morbidity and quality-of-life impairment1,3,5,6. In 1995, it was reported that fracture care accounted for $24 billion of the nearly $150 billion per annum spent in the United States on musculoskeletal conditions2. Assuming that ~5% of fractures fail to heal, at an average per-patient cost of ~$15,000, the estimated annual cost of nonunion treatment in the United States is $4.5 billion. As more emphasis is placed on outcome-based reimbursements, methods to maximize cost-effective treatment of patients with ununited fractures become essential.
Barriers to fracture-healing include tobacco use, chronic illness, malnutrition, prior radiation, bone loss, comminuted and devascularized bone, impaired blood supply to the fracture site and local soft tissue, instability, and infection3,7,8. Advances in the understanding of the pathophysiology of fracture nonunion as well as technical improvements in bone reconstruction have been made in recent years; however, there is a lack of definitive evidence regarding the best treatment method or modality in most instances. Although general principles of nonunion treatment have been established, there is very wide variability in treatment among surgeons. Some surgeons use a particular technique routinely while others never use that treatment. This treatment variability is partially due to a lack of definitive evidence to guide treatment.
It has been difficult to develop approaches to the management of nonunions on the basis of definitive evidence derived from controlled clinical trials. Practical challenges and study design considerations make the performance of prospective, randomized, placebo-controlled, blinded trials in this setting impractical. In order to improve the evidence for treatment decisions, the best available evidence for evaluating and adopting treatment modalities for the management of nonunions must be obtained from large, well-characterized patient cohorts treated with a consistent therapeutic approach and then assessed for relevant clinical and functional outcomes.
Modalities in the form of applied mechanical energy have been increasingly studied for the treatment of nonunions. One such modality, extracorporeal shock wave therapy, appears to be a promising approach to this complex clinical problem on the basis of its safety and the mechanistic and treatment response data accumulated thus far9-19. We showed previously that data from a well-characterized study population consisting of patients with a complex clinical problem (nonunion of the tibial shaft treated with shock wave therapy) can be analyzed to determine factors significantly associated with the healing outcome18. The statistical method most commonly utilized to determine independent factors predictive of clinical outcome is logistic regression analysis. Regression models are trained individually for each outcome of interest. This approach allows the regression models to attain goodness of fit with the data, producing generally strong cross-validation statistics. However, logistic regression models are linear (fit to curvilinear space) and are sensitive to outliers and missing data. As a result, when confronted with incomplete and disorganized clinical information, which is common in clinical records, regression approaches can suffer from severely reduced accuracy20,21.
The Bayesian classification methodology and Bayesian belief network modeling are being utilized with increasing frequency in the field of surgery as they account effectively for data multidimensionality and uncertainty and have the ability to codify complex clinical problems into clear-cut, intuitive, predictive models. We have previously defined proof of principle with this analytical approach, showing how Bayesian belief network models can be used to analyze multifaceted clinical data and present the outcome estimates in a graphical, user-friendly output, enabling the clinician to assimilate complex high-dimensionality data sets into usable and individualized prognostic information22,23. The Bayesian belief network methodology incorporates all outcomes and covariates into a single network and, unlike logistic regression, maintains predictive accuracy and robustness in the face of incomplete clinical data. The predictions can then be tested prospectively to confirm their accuracy. In the current study, we assessed the feasibility of developing a clinically relevant probabilistic naïve (e.g., linear) Bayesian belief network model to estimate individualized, site-specific healing in patients with a refractory fracture nonunion treated with extracorporeal shock wave therapy.
Clinical Study Inclusion Criteria
Over a ten-year period (December 1998 through December 2008), 349 consecutive patients provided informed consent for, and were entered into, an institutional review board-approved prospective observational study in which they were treated with extracorporeal shock wave therapy for a fracture nonunion at any anatomic site. Patients were excluded if they had a bone defect of >5 mm (the distance between the two fracture fragments on a standardized anteroposterior or lateral radiograph exceeding 5 mm), an open growth plate or a malignant tumor in the treatment area, coagulopathy, or angulation or rotation requiring surgical correction; if they chose surgical intervention; if they were not a suitable candidate for regional or general anesthesia; if they had an active infection in the brain, spinal cord, or lung tissue or in the treatment area; and/or if they were pregnant. "Active or acute infection" was established as an exclusion criterion to avoid bacterial dissemination into the bloodstream. The inclusion criterion was a patient with a fracture nonunion referred after failure of previous therapy on the basis of the practice pattern of the referring orthopaedic surgeon. The study was a retrospective analysis of the data in this study population, which encompassed all patients with a fracture nonunion treated during the ten-year period.
Study Definitions
A fracture was defined as a break or disruption in the continuity of bone. A nonunion was defined, according to the U.S. Department of Health and Human Services criteria, as a fracture that has failed to show continuity of three of four cortices after surgical or nonsurgical treatment for six or more months from the time of the fracture-related injury, or has failed to demonstrate any radiographic change (improvement) for three consecutive months, and is associated with clinical findings consistent with a fracture nonunion (an inability to bear weight on the affected extremity, pain on palpation, or motion at the fracture site for three to six months or more following the incident traumatic event or the last surgical procedure). A treated nonunion in this study was one exposed to therapeutic extracorporeal shock wave therapy.
Assessment of Fracture-Healing
Clinical and radiographic criteria were used to assess healing of the fracture. Clinical criteria of fracture-healing included no pain on weight-bearing, palpation, or attempted manual bending of the fracture site and no movement of the fracture fragment at the fracture site. Imaging assessment included anteroposterior and lateral radiographs made at the time of the initial presentation and at one, three, and six months after the extracorporeal shock wave therapy. Reestablishment of cortical continuity of a minimum of three of four cortices defined fracture-healing. Stress radiography and/or CT scans were obtained if the adequacy of fracture-healing could not be assessed with radiography alone. Magnetic resonance imaging was not utilized in the study.
Fracture-healing was defined as (1) the ability of the patient to bear full weight on the affected limb (for a lower extremity nonunion), (2) the absence of pain or tenderness at the fracture site with manual bending or compression, and (3) reestablishment of cortical continuity on three of four cortices at the fracture site on radiographs and/or CT scans. Failure to meet the aforementioned criteria was considered to represent a persistent nonunion. Patients demonstrating clinical or radiographic improvement, but not complete healing, were categorized as "not healed."
Treatment of the Nonunion
Treatment of all of the nonunions included extracorporeal shock wave therapy. Shock waves were delivered to the nonunion site with the Orthowave 280 device (Tissue Regeneration Technologies, Woodstock, Georgia), with use of the regional or general anesthesia required for focused extracorporeal shock wave therapy as previously described18. Following shock wave therapy, the limb was immobilized much like a limb with an acute fracture. Typically, this is done with a plaster cast or customized orthosis. In cases where the nonunion was particularly mobile (>15° of motion apparent on stress fluoroscopy), an external fixator was also placed. Supplementary stabilization was not required in cases of rigidly fixed and internally stabilized fractures without signs of implant loosening. In this study, immobilization was accomplished with an orthosis (n = 36), a plaster cast (n = 187), or external fixation (n = 33).
Previous studies have suggested that initial acute fracture and nonunion healing begins with blood vessel growth into the fracture site15-17. Thus, we attempt to minimize micromovement at the nonunion site during the first three to four weeks following shock wave therapy in order to prevent microvessel disruption. Consequently, no weight-bearing on the affected lower extremity is allowed during that period of time. Prior to treatment, the patients were instructed about this postoperative restriction, as the analgesic effect of shock wave therapy immediately following treatment can contribute to a tendency for the patient to resume full weight-bearing on the affected extremity. The duration of immobilization (up to three months) was not standardized in this study, as the length of time that an affected limb was immobilized was an individualized, provider-driven decision based on the location of the fracture, the osseous gap at the fracture site, the stability of the fracture, the mechanical alignment of the extremity, and the presence or absence of infection.
Outcomes
The Bayesian belief network was trained with use of a priori variables to estimate the probability of a persistent nonunion. The primary outcome was the presence or absence of a persistent nonunion at six months from the date of the first treatment with extracorporeal shock wave therapy.
Statistical Methods
The baseline characteristics of the subjects in the various groups were compared by using analysis of variance for continuous variables. Associations between healing outcomes and categorical factors included in the model on the basis of goodness of fit were studied with a contingency table analysis with use of a Fisher exact test (for contingency tables containing any cells with expected values of fewer than five patients) or the Pearson chi-square test as appropriate.
The objective of this study was to evaluate an established methodology, the Bayesian belief network, as a novel approach to aiding orthopaedic surgeons in clinical decision-making. In this instance, we sought to develop a model that could estimate the likelihood of a specific nonunion responding to extracorporeal shock wave therapy. The objective was to provide a statistically derived approach for the selection of patients for treatment with the modality. A Bayesian belief network is a graphical representation of conditional dependence between information features in a domain, which represents the hierarchy by which known factors can be used to estimate clinical outcomes. These outcomes are estimated with use of joint probability distributions, such that knowledge of the existence or likelihood of a given data point (such as the specific bone involved) informs the expected distribution of an outcome (such as the probability of union after treatment). Any amount of available evidence can be input into the network to calculate a specific estimate of outcome.
A naïve Bayesian belief network was trained to estimate the likelihood of fracture-healing six months after extracorporeal shock wave therapy. This model was developed with use of commercially available machine learning algorithms (FasterAnalytics; DecisionQ, Washington, DC), which automatically learn joint probabilities from the prior probabilities in the data24,25. For our Bayesian belief network model, we grouped the number of days between the injury and the first administration of extracorporeal shock wave therapy and the number of days between the injury and the surgery into three categories, each using equal probability density binning, a method for converting continuous distributions into normalized parametric distributions. Equal probability density binning creates ranges that segregate the data into groups of similar size. The equal probability ranges used for the number of days between the injury and the first treatment with extracorporeal shock wave therapy were 181 days or less, between 182 and 339 days, and more than 339 days. The equal probability ranges used for the time between the injury and the initial operative treatment were 0 days (the surgery performed on the day of the injury), one to 100 days, and more than 100 days. In order to develop the optimum Bayesian belief network model, a stepwise training process was used. Quantitative as well as qualitative assessments were carried out to optimize variable preparation and variable selection.
Cross-validation was performed on the final naïve Bayesian belief network model with use of a train-and-test cross-validation methodology to produce classification accuracy estimates. Tenfold cross-validation was performed by randomizing the data into ten unique "training" sets containing 90% of the data and ten corresponding "test" sets, each of which contained the remaining 10% of the data. Ten new naïve Bayesian belief network models were trained with use of the same parameters as those generated by the naïve model from the full data set. Once the test model was created with a training set, the matching test set was entered into the Bayesian belief network model, generating a case-specific prediction for each record for independent variables of interest. After development of the Bayesian belief network model, a receiver operating characteristic curve was plotted for each test to calculate classification accuracy. Receiver operating characteristic curves in this case are a graphical plot of sensitivity versus (1 - specificity) for the Bayesian belief network model at all of the various levels of discrimination threshold. The area under the receiver operating characteristic curve was then calculated, and this served as a metric of overall model quality.
Source of Funding
Funding for this study was provided by the Combat Wound Initiative Program, Walter Reed Medical Center, Washington, DC (a Henry M. Jackson Foundation for the Advancement of Military Medicine program).
The present study was conducted to determine the feasibility of developing a clinically useful probabilistic naïve Bayesian belief network model to estimate individualized, site-specific fracture-healing in a selected patient study population—one that had undergone extracorporeal shock wave therapy for a nonunion that had been refractory to surgical treatment and immobilization. Successful nonunion healing in this consecutive cohort encompassing all patients with a nonunion treated at a single center with the same shock wave device occurred 80% of the time within six months after the first treatment with the shock wave therapy. While healing outcome results have a significant relationship with all of the variables in our Bayesian belief network model, including the anatomic location of the nonunion, the number of bone-grafting procedures and/or intramedullary stabilization prior to extracorporeal shock wave therapy, and the number of shock wave treatments, the Bayesian belief network identified two covariates within the model that appear most predictive of fracture-healing. These covariates—the time to the first treatment with extracorporeal shock wave therapy following the fracture and the specific bone involved—dominate the model and appear to provide the bulk of the predictive power.
The probability of a positive healing result deteriorates significantly with the time to the shock wave therapy following the injury12,14,18,27. When more than eleven months (339 days) have elapsed between the injury and the extracorporeal shock wave therapy, nonunion healing rates are significantly lower than those observed when extracorporeal shock wave therapy is administered earlier in the course of the fracture nonunion. The anatomic region (specifically, the affected bone) is also an independent predictor of healing following extracorporeal shock wave therapy. However, there is an important interaction between these two clinical variables in terms of their effect on the six-month healing results. The inference table (Table II) demonstrates the likelihood of fracture-healing at six months and underscores this conditional dependence of these two a priori variables, anatomic region and days between the injury and the extracorporeal shock wave therapy. Although healing is the most likely outcome in all cases, the effect time (from the time of injury to the extracorporeal shock wave therapy) differs according to the specific bone affected. Unlike the case in linear models, in Bayesian models predictive variables are not exclusively positive or negative predictors. In particular, nonunions of the foot tend to heal at a very high rate regardless of the time between the injury and the shock wave therapy. In the study population, all twenty-eight foot fracture nonunions healed, including five with lag times of 1995 days (five and a half years), 1131 days, 801 days, 752 days, and 728 days between the injury and the first treatment with extracorporeal shock wave therapy. Conversely, the time between the fracture and the shock wave therapy has a pronounced effect on the Bayesian belief network model estimate of healing of a femoral shaft nonunion. The estimated likelihood of a femoral shaft nonunion healing at six months drops from 79% to 63% when the time between the injury and the first treatment with extracorporeal shock wave therapy increases from =181 to >339 days. A similar pattern emerges for nonunion of the hand, with a 77% healing estimate when shock waves are administered within 181 days after the injury but a healing rate of only 59% when the first treatment with extracorporeal shock wave therapy is delayed for >339 days. The effect of a time lag between the injury and the first treatment with extracorporeal shock wave therapy on nonunion healing retains significance even when the data are restricted to patient subsets with femoral shaft and hand fractures (at a 90% significance level). Because of sample-size limitations, we were unable to conduct statistical testing on the relationship between the number of days until the first treatment with extracorporeal shock wave therapy and the healing outcome for the humerus or ulna. Another potential limitation is the bias associated with the stringent definition of fracture-healing used in this study, which required that all of three criteria be met: (1) an ability to bear full weight on the affected limb (for lower-extremity nonunions), (2) the absence of pain or tenderness at the fracture site, and (3) reestablishment of cortical continuity of three of four cortices at the fracture site as seen radiographically.
We believe that our study demonstrates the potential utility of Bayesian belief network classification models not only for selecting patients for extracorporeal shock wave therapy, but, perhaps more importantly, also to identify candidates for other novel or established therapeutic modalities. The Bayesian classification methodology is designed to be inherently robust and tolerant of heterogeneous and incomplete data sets, while presenting graphical feedback to the user, which allows the clinician not only to receive a case-specific estimate of outcome, but also to understand how the estimate is derived28. We believe that this is a superior paradigm for support of clinical decision-making as it allows the clinician to interact with the system in an intuitive manner and also to make informed decisions with statistical guidance, rather than making decisions on the basis of black-box algorithms.
Note: The authors acknowledge the significant contributions of Drs. Andreas Fischer, Andreas Sailler, and Ender Karradas from the AUVA-Trauma Center in Meidling, Vienna. Their diligent care of this patient population was critical to the work presented herein. They also acknowledge Tiffany Felix and Fred Gage for their invaluable assistance supported in part by the Henry M. Jackson Foundation for the Advancement of Military Medicine. They are grateful to the members and staff of the Combat Wound Initiative Program and the AUVA-Trauma Center for their consistent support of this collaborative research effort.