Computer-assisted decision analysis in orthopedics

The Journal of Arthroplasty Vol. 15 No. 3 2000

Computer-Assisted Decision Analysis in Orthopedics Resurfacing the Patella in Total Knee Arthroplasty as an Example Philippe Zangger, MD* and Allan Detsky, MD, PhD-I-

Abstract: The purpose of the present study was to illustrate the use of computerassisted decision analysis in making decisions in the field of orthopaedic surgery, using the choice between resurfacing and not resurfacing the patella in total knee arthroplasty as an example. We used a decision analysis technique based on probability theory and on Bayesian logic, with the help of an especially developed computer software. The process involves building a decision tree, searching for probabilities and utilities in the literature, folding back the tree to compute the baseline result, and running sensitivity analyses. Our literature search provided 26 useful articles, only 3 of which were randomized controlled trials. In the baseline analysis, both options were rated similarly, with resurfacing the patella faring slightly better. Sensitivity analyses revealed that not resurfacing becomes the procedure of choice if the probability of postoperative anterior knee pain with an unresurfaced patella falls below i 4 % , or if the probability of having pain with a resurfaced patella rises above 8%, or if the utility of patellar implant failure falls below 80% of the utility of a perfect health state. Computer-assisted decision analysis is a promising, evidence-based tool to assist clinical decision making in orthopaedic surgery. However, its validity is limited by the poor quality of data found in the orthopaedic literature, especially the scarcity of randomized controlled trials. K e y w o r d s : decision analysis, knee prosthesis, patella.

Traditionally, clinicians make decisions by using their personal experience, their knowledge of the medical literature, and their intuition. With the advent of evidence-based medicine, decision analysis has emerged as an evidence-based tool to assist clinidans in making choices in controversial situations and to help

them generate treatment algorithms. Decision analysis was developed in marketing, where it is used to choose the most profitable option. It has been increasingly applied by clinidans and researchers in various medical specialties [1] and by health authorities in costeffectiveness studies of health care processes [2].

From the *H3pital Orthopddique de la Suisse Rornande, Centre Hospitalier Universitaire Vaudois, UniversiO, of Lausanne, Switzerland; and the y-Department of Medicine, The Toronto Hospital, University of Toronto, Ontario, Canada. Submitted November 18, 1997; accepted August 2, 1999. Benefits or funds were received in partial or total support of the research material described in this articIe from the Swiss Orthopaedic Society; the H6pital Orthop~dique de la Suisse Romande;

and the Centre HospitaIier Universitaire Vaudois, University of Lausanne, Switzerland. Reprint requests: Philippe Zangger, H6pital Orthop6dique de la Suisse Romantic, 4, Av. Pierre Decker, 1005 Lausanne, Switzerland. Copyright © 2000 by Churchill Livingstone ''~ 0883-5403/00/1503-0003510.00/0

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The first step in a decision analysis is to build a decision tree. At the base of the tree is the basal choice u n d e r consideration. All possible o u t c o m e s resulting f r o m the first choice are catalogued and entered into the tree structure as successive branches. Points at which branches are forming are n a m e d nodes. Each branch bears a specific probability of the corresponding o u t c o m e to occur. At the end of each b r a n c h is a terminal node, w h i c h represents a final health state. Each terminal n o d e bears a specific utility, w h i c h is the value of the corresponding health state in terms of patient preference. A set of rules for building sound decision trees have b e e n published by Detsky et al. [3-7]. Guidelines on h o w to appraise published decision analyses have also b e e n issued [81. In the second step, a careful review of the medical literature pertaining to the subject u n d e r scrutiny is carried out. In a meta-analytic m a n n e r , probabilities for each of the outcomes to occur are searched for, averaged, and entered into the tree. Patient preferences for a defined health state, c o m p a r e d with a state of perfect health, are referred to as utilities. They are a w a y of assigning health state a subjective value, w h i c h can be used m a t h e m a t i c a l l y by the software. Utilities m a y be derived f r o m surveys of patients having the condition u n d e r scrutiny or f r o m subgroups of the general p o p u l a t i o n [9]. They m a y also be estimated by clinicians or health care workers, based on clinical experience, current medical knowledge, or reviews of the literature. In a process t e r m e d folding back the tree, the software c o m p u t e s an expected o u t c o m e value for each of the m a i n options. The highest expected o u t c o m e value d e t e r m i n e s the baseline result of the analysis: One of the options is preferred by the model. In the third step, the m o d e l undergoes sensitivity analyses, in which, at turns, the value of each variable (probability or utility) is changed stepwise across the whole spectrum of values it m a y assume. As the variable reaches a certain threshold, the baseline result of the m o d e l changes w h e n the tree is folded back, indicating that the m o d e l is sensitive to a change in the variable u n d e r study. Using m o r e c o m p l e x algorithms, this t e c h n i q u e can be used to generate cost-effectiveness analyses. The p u r p o s e of the present study is to illustrate the process of decision analysis by an e x a m p l e from the field of orthopaedic surgery. Over the last 2 decades, total k n e e arlhroplasty (TKA) has b e c o m e one of the m o s t successful joint arthroplasties in the field of orthopaedic surgery, with good and excellent results in 90% of cases. Patellofemoral compli-

cations, however, still account for m o s t revision operations after k n e e replacement [ 10-13]. W h e t h e r or not to resurface the patella during TKA remains a controversial issue [14-16]. Patellofemoral pain in unresurfaced patellae appears to occur m o r e frequently in patients with r h e u m a t o i d arthritis; in tall a n d h e a v y individuals; in association with lowsitting, unresurfaced patellae; and with advanced deformity or destruction of the articular surface of the patella. Patellofemoral m a l f u n c t i o n in resurfaced patellae m a y be related to i m p l a n t malposition, and a high rate of aseptic loosening has b e e n reported with metal-backed, u n c e m e n t e d patellar buttons. Reported revision operations after patellar c o m p o n e n t failure can be technically challenging and have a high rate of complications [17], and it is not clear w h e t h e r they result in a satisfactory outcome, particularly w h e n c o m p a r e d with secondary patellar resurfacing [18]. In the literature, there is evidence to support resurfacing the patella [10,19-25] as well as not resurfacing the patella [26,27]. Some authors have suggested guidelines on h o w to select patients for patellar resurfacing [28-33].

Material and Methods Question In TKA, should the patella be resurfaced or not?

Model Decision Tree. The decision tree is illustrated in Fig. 1. The m o d e l c o m p a r e s 2 strategic choices: to resurface the patella and not to resurface the patella. If a surgeon chooses the first branch of the tree, all patients undergo patellar resurfacing. After this, they m a y h a v e no pain or have s o m e a m o u n t of residual patellofemoral pain. In either of these 2 branches, the i m p l a n t m a y or m a y not fail. The most likely o u t c o m e s are that patients w h o h a v e no residual pain will also h a v e no implant failure and that patients w h o h a v e residual pain will h a v e implant failure. If a surgeon chooses the no resurfacing branch of the tree, the o u t c o m e is d e t e r m i n e d by the probability of patients having anterior k n e e pain (AKP). If this pain occurs, s y m p t o m s m a y be severe e n o u g h to w a r r a n t a secondary patellar resurfacing procedure. In this case, the o u t c o m e is a s s u m e d to be identical to the o u t c o m e of p r i m a r y patellar resurfacing except that it takes 2 operations to reach the same result, w h i c h is considered a disadvantage to the patient. If s y m p t o m s are not severe e n o u g h to w a r r a n t secondary patellar resurfacing, the final

Computer-Assisted Decision Analysis in Orthopedics • Implant failure Residual pain Patellar resurfac

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|No reoperation Nopatellar resu~acing No anterior knee pain

Fig. 1. Decision tree of the 2 approaches to total knee arthroplasty. After each node (O), different, mutually exclusive outcomes may occur, with probabilities gathered from the literature. At the end of each branch is a different health state with a utility value (eg, U1, U2), which, in this study, was estimated.

o u t c o m e is determined by the disadvantage for the patient to have residual pain after TKA. W h e n choosing the resurface branch, one trades the possibility of implant failure, which m a y require a difficult revision with an uncertain outcome, against the advantage of having no AKP. W h e n choosing the no resurface branch, one trades the risk of having AKP and possibly a second operation to relieve it against the guarantee to have no implant-related complication because there is no implant. Variables a n d Probabilities. Table 1 summarizes the variables and the probabilities that were used in the decision analysis. Probabilities were obtained from a survey of the literature. Baseline probabilities are the average of all values found. The range of

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these values is also specified. The probability of having AKP ranges from 5% in some studies to 29% in others. In this analysis, we have used a value of 18%, w h i c h represents the arithmetical m e a n of these values. Similarly, we used a value of 5% for the probability of having residual pain with a resurfaced patella, 7% for the probability of undergoing secondary patellar resurfacing in the presence of AKP, and 88% for the probability of the patellar implant failing w h e n causing residual pain. Utilities. We used the concept of utility to assess the value that patients place on the health states at the end of the decision tree. Utility theory bases decision making on the expression of patient preferences for a given health state. These expressions m a y be estimated, or measured, by asking patients about which option they w o u l d prefer in a situation of uncertainty. Usually, numerical expressions for utilities originate from a comparison b e t w e e n health states, in which the optimal o u t c o m e in each branch is given a value of 1.0. In this study, for instance, having AKP with an unresurfaced patella has a utility value of 0.7, compared with the optimal situation, in which not resurfacing the patella has led to a complete pain relief. For negative p h e n o m ena, such as the disadvantage of implant failure, the concept of disutility is used, and its value is subtracted rather than multiplied. In Table 2, the utilities are listed in order of decreasing value. The best outcomes are having no pain and no implant failure with a resurfaced patella or having no AKP with an unresurfaced patella. The worse o u t c o m e is to have had no patellar resurfacing, which resulted in severe AKP that required a secondary resurfacing, followed by implant failure. To have had the patella resurfaced in the first place and then to have implant failure appears slightly better. In this decision analysis, utilities were estimated, based on current knowledge and personal experience. The different health states, their expressions, and values are summarized in Table 2. The results of patellar

Table 1. Variables and Probabilities Variable Probability of AKP when patella is not resurfaced Probability of pain when patella is resurfaced Probability of a second operation for AKP in unresurfaced patellae Probability of the patellar impIant being loose when there is pain

Baseline Probability*

Ranget

References

.1787 .0543 .6684 .8813

.0577-.2900 .0244-.I205 .2857-1.0000 .6250-I.0000

26, I1,17,22,23,30,32,33 15,24,25,34,35 11,17,22,23,26,30,34,35 11,17,22,26,30

AKP,anterior knee pain. *Baseline probabilities are average of estimates from published studies. tRanges are based on highest and lowest estimates from published studies.

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Table 2. Utilities in the Decision Tree Health State No AKP, patella not rcsurfaced No pain, patella resurfaced Moderate AKP, no reoperation Severe AKP, reoperation, no residual pain, no loosening No pain, patella resurfaced, loosening Pain, patella resurlaced, no loosening Severe AKP, reoperation, residual pain, no loosening Severe AKR reoperation, no residual pain, loosening Pain, patella resurfaced, loosening Severe AKP, reoperation, residual pain, loosening

Estimated Value 1.00

1.00 0.80 0.70 0.70 0.70 0.56 0.50 0.40 0.26

defined as the point at which both t r e a t m e n t options appear to h a v e the same potential value. A b o v e and below this threshold, the baseline result of the decision analysis changes from 1 option to the other. This variability allows one to estimate the a m o u n t of uncertainty in the baseline result. For example, if the probability of having AKP rises > 1 4 % , which m a y be the case in specific groups of patients, such as patients with r h e u m a t o i d arthritis, the r e c o m m e n d e d option changes from no patellar resurfacing to patellar resurfacing. This type of analysis m a y be conducted as a 1 - w a y sensitivity analysis, in which only 1 variable at a time is changed, or as 2 - w a y or 3-way sensitivity analyses, in which 2 or 3 variables are changed at a time.

AKP, anterior knee pain.

Results implant revision surgery w e r e a s s u m e d to be worse t h a n those of secondary patellar resurfacing. This a s s u m p t i o n is supported by s o m e published data [18], but it is largely a m a t t e r of controversy.

Baseline Result The result of the decision analysis is s u m m a r i z e d in Table 3. Resurfacing the patella has the highest expected utility (0.96442) using the baseline variables in Table 1, and it is the preferred approach.

Analytic Strategies Baseline Analysis. We used the decision analysis software SMALLTREE (J. P. Hollenberg, MD, Roslyn, NY) to conduct the analyses, based on the values listed in Table 1. The expected utility of a particular b r a n c h is a weighted average of the utility associated with all possible o u t c o m e s of that branch. For each branch, the expected utility value is comp u t e d by multiplying probabilities times utilities, in a process k n o w n as folding back the decision tree. For example, the patellar resurfacing b r a n c h in Fig. 1 is associated with 4 possible outcomes: having residual pain caused by a failed implant, having residual pain with a sound implant, having no residual pain but an underlying failed implant, and having no residual pain with a sound in]plant. The expected utilities of these b r a n c h e s are 0.55, 0.80, 0.75, and 1.00. Sensitivity Analyses. Using the software, the value of each probability or utility was varied across its entire possible range, to d e t e r m i n e threshold values. The threshold point in decision making is

Table 3. Result of the Decision Tree* Expected utility PateIlar resurfacing No patellar resurfacing *Choose: resurface.

Sensitivity Analyses O n e - W a y Sensitivity Analyses. O n e - w a y sensitivity analyses (Fig. 2) indicates that resurfacing the patella is the preferred option as long as the incidence of AKP in the no resurfacing branch is >0.14, while keeping all o t h e r variables constant. Similarly, Fig. 3 depicts a 1-way sensitivity analysis in w h i c h the probability of pain with a resurfaced patella is

Threshold: 0.1393

1.0

Expected utility

0.7446

Value 0.96442 0.95436

0.2

0.4

0.6

0.8

1.0

Probability of having antedor knee pain with an unresurfaced patella

Fig. 2. O n e - w a y sensitivity analysis of t h e i n c i d e n c e of

anterior knee pain versus its expected utility for each treatment strategy.

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Discussion

Threshold: 0.0808 J 1.0

Expected utility

0.5625

i 0.2

I

I

I

0.4

0.6

0.8

",J 1.0

Probability of pain with a resurfaced patella

Fig. 3. One-way sensitivity analysis of the probability of pain with a resurfaced patella versus its expected utility for each treatment strategy.

changed: The preferred option is to resurface the patella as long as this probability remains <0.08. TWo-Way S e n s i t i v i t y Analysis. Figure 4 plots the incidence of AKP against the disutility of having a loose implant, w h e n both are varied at the same time. Points located on the curve represent values of these 2 variables in which the expected utility is equal for both t r e a t m e n t options. For values located above and to the left of the curve, the preferred option is to resurface the patella, and the reverse is true for values located to the right and b e l o w the curve.

The baseline result of this model shows that, using the available data, there is no significant difference b e t w e e n patellar resurfacing and no patellar resurfacing. Each choice appears to h a v e advantages and disadvantages, w h i c h are balanced w h e n all aspects of 1 option are c o m p a r e d with all aspects of the other. Sensitivity analyses show that the m o d e l is sensitive to changes in the probability of having AKP with an u n r e s u r f a c e d patella, in the probability of having pain with a resurfaced patella, and in the subjective value of having a loose patellar implant. The reliability of this m o d e l is influenced to a great extent by the quality of the data. In our case, the validity of most of the probability values retrieved f r o m the literature is highly questionable. In only a few studies were all patients carefully accounted for, outcomes accurately described, and proportions given in a usable m a n n e r . Only 3 of these studies [25,34,35] w e r e randomized, controlled trials, and perhaps o u r study should h a v e included only these. Because this study was t h o u g h t of as an illustration of decision analysis, we chose to use as m u c h data as possible, accepting lowerquality data to enrich the analysis and trigger discussion. Utilities were estimated by the authors. In s o m e medical fields, utility values h a v e b e e n derived from patient groups or f r o m the general population and have b e e n published. We w e r e not able to find any such reports in the orthopaedic literature.

Conclusion 1.0

resurfacing

Threshold of the probability of having anterior knee pain (pAKP)

0.05

I

I

I

I 1.0

Probabdlty of residual pain with an unresurfaced patella (pPain)

Fig. 4. Two-way sensitivity analysis varying the incidence of anterior knee pain against the disutility of implant failure. © represents the value used in our example. The dotted rectangle indicates the range of values found in the literature for pAKP and pPain. This area depicts the part of uncertainty in the model.

Computer-assisted decision analysis m a y help orthopaedic surgeons in m a k i n g decisions. This type of analysis does not substitute clinical j u d g m e n t or personal experience, but it m a y provide an evidencebased aid in controversial issues. The e x a m p l e chosen here illustrates that considerable efforts m u s t still be m a d e to raise the quality level of the orthopaedic literature, by refining clinical trial m e t h odology and extending the use of validated o u t c o m e m e a s u r e s . Further research combining decision analysis and orthopaedic surgery m a y include the p u b l i c a t i o n of p a t i e n t - d e r i v e d or p o p u l a t i o n derived utilities for the m o s t c o m m o n health states e n c o u n t e r e d in this field.

Acknowledgment We t h a n k Dr Earl R. Bogoch for reviewing the manuscript.

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