The decision tree and sensitivity analysis were constructed and performed using TreeAge Pro (Williamstown, MA, USA). The decision tree modeled a hypothetical clinical scenario of a patient who presents 3 weeks after a cementless primary THA with a deep periprosthetic joint infection. From the root node (diagnosis of periprosthetic infection), three treatment options were available: open I & D with modular femoral head and acetabular liner exchange, a one-stage revision arthroplasty with removal and immediate reimplantation of all components, or a two-stage exchange revision arthroplasty (Fig. ).
Fig. 1 The decision tree is shown. The initial decision occurs at the root node (first decision point) at the left side of the tree where one of three treatment options is selected. Based on the chance (probability [prob]) of this treatment resulting in a specific (more ...)
The model assumed that success of a given procedure was a period greater than 2 years without additional surgery for treating the infection, with or without long-term suppressive antibiotics. If the patient initially was treated with an open débridement and this failed, the model assumed the patient would undergo a two-stage exchange [12
]. If the two-stage exchange failed, the patient would undergo a second two-stage exchange. If the initial treatment is a one-stage exchange and this treatment failed, then the patient would undergo one subsequent two-stage exchange. If the initial treatment was a two-stage exchange and this failed, the patient would undergo one subsequent two-stage exchange. In this algorithm, the patient would have the possibility of undergoing a maximum of two resections and reimplantations; two two-stage exchanges after an initial open débridement, one two-stage exchange after a failed one-stage exchange, or a second two-stage exchange after a failed initial two-stage exchange. If the two subsequent two-stage exchange arthroplasties failed, the treatment was defined as a failure and we assumed the patient would undergo a resection arthroplasty without reimplantation of any components [22
The probability of obtaining an infection-free, functioning THA after any of the specified procedures was based on previously published studies (Table ). Crockarell et al. [8
] found débridement and prosthesis retention after an infected THA controlled infection 18% of the time. They further identified patients who had the procedure performed within 2 weeks of the primary THA and found the rate of infection control was slightly greater, at 24%, the rate we used in our model.
Some studies [5
] report the ability of a one-stage exchange to control infection using a cemented THA and antibiotic cement, where it appears infection control rates are predicated on the use of antibiotic cement and thus local delivery of antibiotics. In the scenario modeled in our study, the revisions were performed with cementless implants and thus local antibiotic delivery via bone cement would not be available. We identified two studies in which this scenario was reported. First, Tsukayama et al. [34
] reviewed their patients with infected THAs and identified a cohort that had revision THAs with a cementless component for presumed aseptic loosening. Some of these patients were later determined to have septic loosening based on intraoperative cultures taken at the time of the revision surgery and were treated with intravenous antibiotics and no additional surgery. These patients effectively had a cementless revision THA in the face of infection without the need for additional treatment for infection in 93% of cases. Winkler et al. [35
] reported a novel technique of a one-stage exchange for infection combined with the use antibiotic-impregnated allograft bone. They reported a 92% infection control rate at a minimum 2-year followup. Based on these two studies, we assumed a 93% success rate for a one-stage exchange with cementless components. Cementless revision THA after two-stage exchange for an infected THA with an intervening antibiotic cement spacer (a two-stage exchange) has been investigated by several groups with similar infection control rates of 92% [10
], the value used in this study.
Pagnano et al. [22
] reported infection control was successful in three of five patients undergoing a second two-stage exchange, therefore we assumed the success rate of a second two-stage exchange was 60% when performed after a failed two-stage exchange. We identified no series reporting the effectiveness of a two-stage exchange after a failed open débridement or failed one-stage exchange. For these two scenarios, we assumed the effectiveness of a two-stage exchange after an open débridement or one-stage exchange to control the infection was the same as that of an initial treatment of two-stage exchange.
A utility in a decision-tree analysis is a number between 0 and 1 used to describe the preference of the final outcome of any given pathway through the tree. In our model, the utilities after treatment of an infected THA reflected the estimated final health state defined as health-related quality of life and were based on a quality-of-life database compiled by the Institute for Clinical Research and Health Policy Studies [12
]. Disutility refers to a number, often deducted from the final utility value (termed disutility toll), that estimates the negative impact an undesirable event may have on the final utility, in this case quality-adjusted life years. We defined this undesirable event as repeat surgery for treating the infection. In our model, a disutility toll was one deduction from the final quality-adjusted life year value after any reoperation (and more than one deduction for more than one reoperation). Failure of one of the three initial treatments and subsequent reoperation resulted in a second deduction (disutility toll) that further reduced the final utility value. By deducting from the final utility of any given path in the model we attempted to account for disability incurred from reoperation and generally lower health-related quality of life after multiple surgeries on the same hip. The disutility after an open débridement was assumed to be −0.1, a value similar to that used after undergoing a primary THA [6
]. The disutility at the time of planned reimplantation during a two-stage exchange was estimated to be −0.2, twice the value of primary THA to account for two operations and an intervening period of an antibiotic spacer. The value assigned to a one-stage exchange was assumed to be between these two values and set in this model to be −0.15 (Table ).
Although no studies evaluate the utilities for the specific final health states in this model, the value reported from the largest series in the Clinical Research and Health Policy Studies database for an uncomplicated primary THA was 0.86 [24
]. Because repeat surgery to treat infection leads to a lower quality of life than an uncomplicated THA (ie, because of a repeat procedure, time of treatment, loss of income), a disutility toll was applied to the final quality-of-life estimate to account for this additional treatment. We assumed the final utility after a successful open débridement was approximately the same as that for an uncomplicated THA (0.86) but because of the repeat surgery, a disutility toll of 0.1 was subtracted from the quality-of-life estimate of an uncomplicated THA (to account for the morbidity of a second procedure). Thus, the estimate of utility (quality of life) after a débridement for THA infection was 0.86 (utility of an uncomplicated THA) minus 0.1 (disutility toll for débridement procedure), or 0.76. The quality-of-life value estimate for a patient undergoing a revision THA is reportedly 0.82 [32
]. We found no studies that specifically reported utility values of one-stage exchanges as compared with two-stage exchanges. In our model, the utility after a one-stage or two-stage revision THA for sepsis was assigned the value of 0.82. We assumed a two-stage exchange would lead to an ultimate lower quality of life than a one-stage exchange owing to a second operation and interval without a formal hip prosthesis. We accounted for this difference in the final quality-of-life outcome estimates between one-stage and two-stage exchanges in the disutility toll subtracted from the final quality-adjusted life year estimate after each procedure. The utility of a resection arthroplasty was estimated to be 0.60 [11
] (Table ).
The initial analysis for a decision tree is to determine the pathway that leads to the greatest expected outcome (utility) based on the initial estimates of each parameter (utilities, probabilities, disutilities) in the tree. This is accomplished by folding back the decision tree, where, working from right to left along the branches of the tree, the utility at each branch is multiplied by its respective probability. The sum of these products along each branch that yields the highest number then will predict the pathway with the highest chance of achieving the most desirable outcome.
Because uncertainty exists in many estimates used in decision analysis, a technique termed sensitivity analysis uses a numerical calculation to evaluate the effect that these uncertainties might have on the decision-analysis outcome. First, a plausible clinical range of each of the parameters used in the model is determined. The probability rates of success of each of the initial and subsequent treatment options were analyzed over a large range (0%–99%). The wide range of probabilities for these parameters was used in an attempt to mitigate any potential bias from the variance reported in the small number of studies reporting these rates. Sensitivity analysis is used repeatedly to reevaluate the decision tree as each model parameter is varied over the plausible range to determine if a change in that parameter could change the product of the analysis. In a one-way sensitivity analysis, one variable is changed over the estimated range while all other parameters are held constant. The value of the parameter that leads to a change (if one exists in the plausible range of values) of the optimal pathway through the decision tree is recorded as a threshold value. If varying more than one parameter leads to a different optimal pathway, a multiple-way sensitivity analysis is performed where those variables are compared to estimate which variable might have the most influence on the product of the model.