Reply

Sir—We appreciate the opportunity to respond to some of the concerns raised by Saleh et al. [1] and Hanssen et al. [2] in their letters to Clinical Infectious Diseases. We created a mathematical model simulating competing management strategies for infection associated with hip prostheses in older people [3]. Models, including this one, can serve as a means to synthesize available data, help facilitate medical decision making, and identify important areas of uncertainty, which may in turn highlight important research questions [4]. Models are also easily modified, so that emerging data can be incorporated and novel strategies can be evaluated. In modeling, there is always a tension between an overly simplistic representation of reality, which provides little insight into real-world problems, and an overly realistic representation, which may be as chaotic and difficult to understand as the real world itself [5]. Nonetheless, we suggest that our model does provide helpful insights to clinicians dealing with this challenging issue. We agree with Saleh et al. [1] that rehabilitation with initial debridement and retention cannot be used to treat patients who present with loosened, nonfunctional prostheses, which is why we explicitly stated that our model should only be applied to instances in which loosening of the prosthesis has not occurred, as Hanssen et al. [2] point out. In this context, we identified the best available data for the probability estimates used in our model, including data from studies by coauthors of Saleh and Hanssen [6,7,8,9,10–11]. However, most data on prosthetic hip infection have been published in the form of case series, which are difficult to interpret because of likely publication bias (i.e., the preferential publication of series that demonstrate a method that appears effective) [12] and the lack of control patients. Even observational studies that present the outcomes of multiple surgical modalities (so that “control” interventions can be identified) are difficult to interpret because of confounding by indication [13]. With reference to prosthetic hip joint infection, such confounding is a result of the more aggressive surgical treatment of people with more robust health status (e.g., younger people, people without comorbid illnesses), who are expected to have a better outcome regardless of the management strategy used. Because of the limitations of available data, we explored the implications of the resulting uncertainty in a large number of “sensitivity analyses” [14]. This process involves varying the input data (e.g., rate of relapse after debridement) over plausible ranges to examine whether this changes the conclusions. We performed extensive sensitivity analyses on all data inputs used in the model, and a number of the concerns raised by Saleh et al. [1] can be addressed by simply examining the results of these analyses as presented in our article [3]. For example, for reasons outlined in our article, we restricted our analysis to data derived from studies of gram-positive aerobic organisms and estimated the annual rate of relapse after debridement and retention to be 30%. If the risk of relapse were to increase, as might occur with a gram-negative organism, the benefits of initial debridement and retention with regard to life expectancy would progressively decrease and costs would increase, making initial debridement a less attractive strategy. As we noted in our article, annual rates of relapse >60% after initial debridement would result in a decrease in life expectancy relative to initial exchange arthroplasty, because patients would undergo debridement only as a prelude to almost-immediate arthroplasty. Similarly, we examined the impact of decreasing relapse rates after 2-stage exchange arthroplasty in our article [3]. As we state in our discussion, rates of relapse after exchange arthroplasty as low as 0.6% annually would make initial debridement and retention an unattractive option for 65-year-old people, although it would remain cost-effective for frail 80-year-old individuals. We are certain that Clinical Infectious Diseases readers understand why we did not preferentially use data on infected knee arthroplasty to model prosthetic hip joint infections. We do agree with Saleh et al. [1] that average health utility values may not represent the health preferences of an individual patient. Individual health preferences may be influenced by a variety of factors, including baseline health status and risk preferences (e.g., risk-averse patients may wish to avoid major surgery even though the potential health benefits are great) [15, 16]. Again, we tested the sensitivity of our model to utility estimates for functional hip arthroplasty and resection arthroplasty by performing wide-ranging sensitivity analyses. We did not find evidence that changing utility values would have changed our conclusions. It should also be noted that the application of any clinical research finding to the care of individual patients is subject to such limitations; the applicability of findings despite these limitations is usually referred to as the “external validity” or “generalizability” of a study [17]. Whether or not our base-case utility values are generalizable, our sensitivity analyses covered a broad range of potential health preferences, which suggests that our results are likely to apply even to people with widely differing preferences with regard to future health states. Nonetheless, we agree that more work is needed to better quantify health preferences and attitudes toward risk among older people undergoing joint replacement surgery. Saleh et al. [1] also suggest that other strategies should have been included in our model. As noted above, mathematical models such as ours can be modified to incorporate novel strategies. As outlined in our article, we did not include the strategy of 1-stage exchange arthroplasty because the data available on relapse rates are limited; nonetheless, we can easily perform a threshold analysis [14] to evaluate the circumstances under which 1-stage arthroplasty would be preferable to initial debridement and retention. Figure 1 presents the incremental cost-effectiveness ratio of debridement and retention compared with 1-stage exchange arthroplasty. The incremental cost-effectiveness ratio is the relative cost of a 1-year gain in quality-adjusted life expectancy when initial debridement is performed. Because we do not have good data on the probability of relapse after 1-stage exchange, we have plotted the risk of relapse on the X-axis as the relative risk of relapse after 1-stage, as compared with 2-stage, exchange arthroplasty. Note that the annual probability of relapse after 2-stage exchange was 3.5% in our original article. The incremental cost-effectiveness ratio of initial debridement and retention compared with 1-stage exchange arthroplasty. QALY, quality-adjusted life-year. It can be seen that, when 1-stage exchange arthroplasty has a relapse rate equivalent to that associated with 2-stage exchange, 1-stage exchange “dominates” initial debridement and retention. In other words, 1-stage exchange provides greater quality-adjusted life expectancy and also costs less than initial debridement and retention. As the relative risk of relapse with 1-stage arthroplasty increases beyond 1.2, initial debridement becomes a more favorable strategy with regard to quality-adjusted life expectancy, but a large increase in cost is required for these gains to be achieved. When the relative risk of relapse with 1-stage exchange is higher than 1.4, initial debridement and retention is a strategy that could be considered to be cost-effective, in comparison with other commonly used health care interventions. This analysis highlights the importance of future clinical studies comparing 1- and 2-stage exchange arthroplasty. Similarly, Saleh et al. [1] suggest that we should have included the possibility of performing multiple 2-stage exchange arthroplasties in our model, rather than forcing people with repeated instances of infection to make a transition to a resection arthroplasty health state. We performed analyses in which relapsed infections could be treated with a second, third, or even fourth exchange arthroplasty. For reasons outlined below, the survival advantage associated with initial debridement and retention persisted, regardless of the number of future exchange arthroplasties permitted. However, the costs associated with the initial exchange arthroplasty strategy increased more than those associated with initial debridement and retention, leading to increasingly favorable cost-effectiveness ratios for initial debridement as the number of allowed exchanges increased (figure 2). Therefore, rather than “introduc[ing] bias against the 2-stage outcome,” as Saleh et al. [1] suggest, the strategies used in our model likely led to underestimation of the cost-effectiveness of initial debridement. The incremental cost-effectiveness ratio of initial debridement and retention compared with 1 or more 2-stage exchange arthroplasties. QALY, quality-adjusted life-year. Saleh et al. [1] are puzzled by one of the most important insights provided by our model. How, they ask, can delaying exchange arthroplasty by performing initial debridement increase life expectancy, when most people who survive long enough will ultimately require exchange arthroplasty? Understanding this apparent paradox requires recognition of the fact that competing mortality (i.e., death due to other causes) is included in the model. For example, in figure 3, we present the hypothetical survival curves for 2 therapeutic strategies in a cohort of 65-year-old people. The solid line represents a strategy similar to our exchange arthroplasty strategy, in which a highly effective surgery is associated with a high operative mortality rate. The dashed line represents a strategy similar to our initial debridement strategy, in which a less effective surgery with a 3-fold lower operative mortality rate is used initially; relapse is expected 5 years after the initial surgery, at which time surviving patients undergo the more effective but riskier procedure. The background “competing mortality” rate is 10% per year. It can be seen that the initial survival rate is greater among people subjected to the less risky, less effective surgery. Five years after the initial operation, relapse occurs, and these people undergo the riskier but more effective procedure. At this point, the survival curves cross, indicating that a smaller proportion of patients who were initially subjected to the less risky procedure survive at 6 years after the original surgery. Nonetheless, when the surgery associated with less morbidity is performed first, some people die of competing causes of mortality, rather than as a result of operative complications. As a result, the expected survival time (the area under the survival curves [18]) is greater among those who initially underwent the less risky procedure. In this highly simplified example, the area under the survival curve is 15.9 years for people who initially undergo highly effective but risky surgery and 16.3 years among people who initially undergo a less effective but less risky surgery. Hypothetical survival curves for 2 therapeutic strategies. Solid line, highly effective initial surgery with high mortality; dashed line, less effective initial surgery with lower mortality. As competing mortality and the operative mortality associated with the more aggressive procedure increase, the survival benefits associated with less-aggressive initial management also increase. This is more than a math trick! Many physicians and surgeons understand this intuitively, and it forms the probabilistic basis for the less aggressive surgical management often practiced with frail elderly patients. As clinicians, we agree with the contention of Saleh et al. [1] that these difficult decisions should be made “by the experienced clinician, not by a health maintenance organization accountant with an algorithm,” and this was one of the factors that motivated us to create this model. It should be noted that it was projected that the appropriate use of debridement and retention, as described in our article, would increase costs, and so would not be appealing to people focused only on financial resources. Our point is that it is projected that this relatively small increase in cost would provide health benefits (i.e., greater quality-adjusted life expectancy) at a rate that compares favorably to that associated with many currently available health-related interventions. We are surprised at the implicit suggestion that cost is not a parameter that needs to be considered when clinical practices are assessed. Resource constraints and financial pressures have become common in health care; if Saleh et al. [1] practice in settings where such constraints are absent, they are fortunate indeed. We conclude by agreeing with Hanssen et al. [2] that the use of modeling is not a substitute for well-designed randomized, controlled trials. These have been rare in the field of orthopedic infectious diseases but are badly needed. Until data from such trials become more widely available, we hope that our model will serve as an aid to decision making for clinicians involved in the management of these challenging infections.

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