operative risk of staged bilateral knee arthroplasty is underestimated in retrospective studies

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The Journal of Arthroplasty Vol. 26 No. 8 2011

Operative Risk of Staged Bilateral KneeArthroplasty is Underestimated in

Retrospective Studies

Sunny Kim, PhD,* John P. Meehan, MD,* and Richard White, MD, FACPy

Abstract: To find a safer surgical option, a number of studies have compared postoperativecomplications after bilateral total knee arthroplasty vs staged total knee arthroplasty (STKA) bycontrasting postoperative complications collected retrospectively. However, we believe that acomparison based on retrospective studies could be biased. The purpose of this study was todemonstrate the misclassification bias associated with a retrospective study in comparing operativeoutcomes. Our analysis indicates that any conclusions based simply on retrospective analysis ofsubjects who successfully completed STKA is biased because it includes only cases that recoveredafter the first operation, rather than all of the patients who had planned STKA. In the absence of aprospective study to date, published studies should be interpreted with caution. Keywords:arthroplasty, TKA, operative risk, safety, complications.Published by Elsevier Inc.

Approximately 16.4% of the population 45 years andolder in the United States has symptomatic osteoarthritisof the knee [1]. When nonsurgical treatment modalitieshave proved unsuccessful, total knee arthroplasty (TKA)is considered [2]. Joint arthroplasty effectively provideimproved physical function as well as pain relief [3,4],and these surgical treatments have received widespreadacceptance. Nearly one half million primary kneearthroplasties were performed during 2006 in theUnited States [5], and the number of surgeries isincreasing at a steep rate [6-8].Total knee arthroplasty is one of the most successful

surgeries, but there are still risks of venous thrombosis,pulmonary embolism (PE), infection, bleeding, stroke,myocardial infarction, or even death. The most commoncomplication after TKA is venous thrombosis. Deep veinthrombosis (DVT) often causes delayed hospital dis-charge. It also exposes patients to prolonged anticoa-gulation and the potential risk of postthromboticsyndrome. Postthrombotic syndrome, involving pain,swelling, and skin changes in the affected extremity,

e *Department of Orthopaedic Surgery, University of California,yDepartment of Internal Medicine, University of California, Davis.ted May 25, 2010; accepted January 2, 2011.nflict of Interest statement associated with this article can beoi:10.1016/j.arth.2011.01.004.requests: Sunny Kim, PhD, Department of Orthopaedic860 Y Street, Suite 3800, Sacramento, CA 95817.ed by Elsevier Inc.403/2608-0014$36.00/0016/j.arth.2011.01.004

119

occurs in approximately 20% to 50% of patients within1 to 2 years of an episode of DVT [9]. The greatest risk ofDVT is its potential for life-threatening PE.In the absence of prophylaxis, TKA carries a risk of

DVT in 56% to 66% of patients [10,11] and sympto-matic PE in 1.9% [11]. Of the patients who receivedanticoagulant prophylaxis, the incidence of sympto-matic nonfatal venous thrombosis is 1.4% to 3.0% andthat of fatal PE is 0 to 0.12% [12,13]. Overall, mortalitywithin 1 year after primary TKA is approximately0.4%, and the median time to death is 9 days followingprimary TKA [13]. Among the Medicare population,the mortality during the 3 months after primary TKA is0.7% [14].Bilateral knee osteoarthritis is more prevalent than

unilateral knee osteoarthritis [15]. Surgical options forpatients with symptomatic bilateral knee osteoarthritisare (1) simultaneous bilateral TKA (BTKA) under 1anesthesia and (2) staged TKA (STKA) with 2 distinctoperations separated by a few days to years. Althoughthere is no consensus regarding the time intervalbetween 2 operations, most surgeons reported thatthey perform STKAwithin 1 year [16]. AmongMedicareenrollees in the United States, approximately 72% ofpatient who underwent STKA had 2 surgeries within ayear, and the remaining 28% had 2 surgeries between 1and 2 years apart [17]. Although it is possible thatpatients can have 2 operations during the samehospitalization [18,19], in most cases, the first kneesurgery (referred to as STKA-1 hereafter) is done duringone hospitalization and the contralateral knee surgery

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Postoperative Risk of Bilateral Knee Arthroplasty � Kim et al 1199

(referred to as STKA-2 hereafter) is done during asubsequent hospitalization. The STKA is performedmore frequently than BTKA. Staged TKA was 2.1 timesmore frequent than BTKA in the United States [17]and 2.4 times more frequent in Ontario [16]. Comparedwith STKA, BTKA is a convenient option for patientsbecause it requires only 1 hospitalization and 1 recoveryprocess. In addition, from a Medicare's perspective,BTKA is less costly compared with STKA [20]. Thepatient “out-of -pocket” cost is also less for BTKAcomparedwith STKA [21]. From the health care system'sperspective, given the steeply increasing demand ofknee arthroplasty, BTKA can reduce some strain onhospitals and surgeons as well. Due to some benefitslisted above, BTKA surgeries are increasing steeply in theUnited States [22]. However, the safety of BTKAhas beenquestioned because BTKA requires longer operating timecompared with STKA-1 or STKA-2.To find a safer surgical option for patients with

bilateral knee osteoarthritis, a number of studies havecompared postoperative complications of BTKA vsSTKA based on retrospective analyses of medicalrecords. Although some studies have demonstrated nosignificant increase in complications after BTKA com-pared with STKA [23-25], or even compared withunilateral TKA (UTKA) [26-28], other studies includingmeta-analyses reported that the postoperative compli-cation is higher for BTKA compared with STKA [29,30].In either case, we believed that these study results basedon retrospective analyses of medical record may be

Plan at time of the first surgery (unknown)

Observed one year after the first surgery (known)

Unilateral

Unilateral

P(A)Change after the first surgery

P(A): Proportion of unilateral patients whafter the satisfactory surgery experience

P(B): Among patients who initially plannwith complications who did not pursue th

P(B)

Fig. 1. Direction of bias in comparing adverse

biased. Retrospective analysis of medical record fails toaccount for the patients who had planned STKA butwho never completed the second stage due to death ora serious postoperative complication after the firstoperation, leading to cancellation of the second STKA(consequently, misclassified as UTKA).The purpose of this study was to demonstrate the

misclassification bias in comparing postoperative com-plications. The issue of operative complications of kneearthroplasty is crucial in surgical treatment decisionmaking. We demonstrated that STKA always appearsto be safer than BTKA, even if the true proportion ofpostoperative complications were in fact the same.

Research MethodsTo demonstrate the bias, a mathematical derivation

and graphical presentation were developed. Patientswho changed the initial surgery plan independent ofpostoperative complication may not introduce systema-tic errors in comparing STKA and BTKA. However, ifpatients changed to receiving (or declining) STKA-2based on the presence (or absence) of postoperativecomplications after STKA-1, this systematic error in theSTKA group threatens the validity of the study. Thereare 2 major mechanisms of misclassifying patients intothe STKA group in retrospective studies (Fig. 1). First,patients who had serious complications after STKA-1tend to decline STKA-2 (dropout). For instance, aproportion of patients (denoted by P[B] in Fig. 1) whoexperienced major cardiac complications or stroke

Staged bilateral

Simultaneous bilateral

Staged bilateral

Simultaneous bilateral

o proceed to have the second surgery

ed SKA, the proportion of patients e second operation

outcomes after TKA in retrospective studies.

Table 1. Proportion of True and Observed PostoperativeComplications in the Population

Surgery Adverse Outcome No Adverse Outcome Total

Unilateral P11(P11 *) P12(P12 *) P1.(P1. *)Staged P21(P21 *) P22(P22 *) P2.(P2. *)Simultaneous P31 P32 P3.

1.00

* Corresponding observed proportions if observed and trueproportions are different.

1200 The Journal of Arthroplasty Vol. 26 No. 8 December 2011

decline STKA-2. In an extreme case, a patient who diesfrom complications of STKA-1 does not have a chance toundergo STKA-2 and thus would be misclassified intothe UTKA group despite the initial intention to undergoSTKA. Second, among patients with bilateral osteoar-thritis, we sometimes see a patient who initially plansUTKA but returns for contralateral TKA after having asuccessful first operation (denoted by P[A] in Fig. 1). Itseems that some patients focus on the other knee onlyafter the significantly more painful one has beenrepaired. Despite the initial intention to have UTKA,this patient would be misclassified as STKA in retro-spective studies.Table 1 shows the true proportion and its corresponding

observed proportion in parentheses. True proportion isthe portion of patients who experienced postoperative

complications among who had planned (or intended)UTKA, STKA, or BTKA. Observed proportion is theportion of patients who experienced postoperativecomplications among who actually completed UTKA,STKA, or BTKA. Consider the proportion of patients Pxy inTable 1. Let its row number be x (x = 1 if unilateral, x = 2 ifstaged, and x = 3 is simultaneous bilateral) and its columnnumber be y (y = 1 if patients experienced postoperativecomplication, and y = 2 if patients did not experiencepostoperative complication).The true probability P21 (row 2 column 1) is proportion

of patients who experienced complications among thosewho intended STKA even if patients could not berecovered after the STKA-1. This true probability of anadverse event is unknown to researchers conductingretrospective studies because of a lack of information onintent-to-treat (ITT). Initial treatment plan is typicallyunknown when researchers do not have access tooriginal charts. The probability of P21 is an observedproportion of patients who experienced complicationsafter STKA-1 or STKA-2 among those who completedboth STKA-1 and STKA-2. Because we have no basis tobelieve otherwise, the true probabilities of adverseevents after STKA-1 and STKA-2 were assumed to bethe same, for simplicity. To address 2 objectives of thestudy, a mathematical derivation and graphical presen-tation were used.

ResultsBias in Estimating in Postoperative Risk After STKATo calculate the bias in the observed proportion of complications among patients who underwent STKA, the

proportions of true and observed complications were compared. For the observed proportion of complications forSTKA (P21*), the denominator and numerator can be defined as follows.Denominator for P21* (total number of observed patients with STKA).Let N denote the total number of knee arthroplasty procedures performed. As shown in Fig. 1, let P(A) be the

proportion of UTKA patients who changed plans and had contralateral TKA after satisfactory UTKA. Let P(B) be theproportion of patients with complications who did not complete the initially planned STKA-2. The total number ofobserved patients who finished STKA is as follows.

N × P2:½ � + NP1:P12P Að Þ½ � − NP2: × 0:5P21 × P Bð Þ½ �

The first term is the total number of patients who planned STKA. The second term is the number of patients whochanged plans after satisfactory UTKA and instead also underwent STKA-2. The third term is the number of patientswho declined STKA-2 due to complications from STKA-1.Numerator for P21* (total number of patient with complication among observed STKA groups).

NP2: × 0:5P21½ � − NP2: × 0:5P21 × P Bð Þ½ � + denominator × 0:5P21

The first term is the total number of patients who experienced complications after STKA-1 among those whoinitially planned STKA. The second term is the number of patients who declined STKA-2 due to complications fromSTKA-1; therefore, these patients were not classified into the STKA group in retrospective studies. The third term isthe number of patients who experienced complications after STKA-2.P21* (observed proportion of patients with complications among those who finished STKA).


For the observed proportion of complications from STKA, the denominator and numerator can be definedas follows.

P214 =NP2: × 0:5P21½ � + NP2: − NP2: × 0:5P21 × P Bð Þð Þ + NP1:P12P Að Þð Þ½ � × 0:5P21 − NP2: × 0:5P21 × P Bð Þ½ �

NP2: − NP2: × 0:5P21 × P Bð Þ½ � + NP1:P12P Að Þ½ �

We canceled out the total number of knee arthroplasties performed (denoted as N) in both the numerator anddenominator of the equation.

P214 =P2: × 0:5P21½ � − P2: × 0:5P21 × P Bð Þ½ � + P2: − P2: × 0:5P21 × P Bð Þ½ � + P1:P12P Að Þ½ �½ � × 0:5P21

P2:½ � − P2: × 0:5P21 × P Bð Þ½ � + P1:P12P Að Þ½ �

Mathematically, we were able to show that the function of bias, f(x) = P21*–P21 is always negative within the validrange of P21, which is between 0 and 1. If f(x) = 0, then no bias exist. Because the bias is always negative for allpossible ranges of P21, this supports that P21* always underestimates P21. Therefore, the observed proportion ofcomplications after STKA is always smaller than the true proportion of complications after STKA (that is, P21* b P21).Details of mathematical solution will be available from the corresponding author upon request.

II. Simulation of Bias in Prevalence of Complication After STKA

Bias in Comparing Postoperative Complications Between BTKA and STKAWe calculated the observed proportion of complications (P21*) for the probable range of other parameters. In this

simulation, the true postoperative complications value was set to be the same for BTKA and STKA. Becausepostoperative complications for BTKA and STKA were the same, the true odds ratio should be 1.

True Odds Ratio =Odds of complication for STKAOdds of complication for BTKA

=

P21P22:

� �

P31P32

� � = 1

However, if P21* is underestimated (= less than P21), then the observed odds ratio should be less than 1.

Observed Odds Ratio� =Odds of complication for STKAOdds of complication for BTKA

=

P214P22:

� �

P314P32

� � b1

To demonstrate the bias for various ranges of P(A) and P(B) in Fig. 1, we calculated the odds ratio using the truecomplication rate of 1%, which is approximately the incidence of infection when antibiotic prophylaxis was used[31]. Among US Medicare enrollees who had an index TKA, approximately 78%were UTKA, 15% were STKA, and7% were BTKA [17]. Therefore, we used P1. = 0.78, P2. = 0.15, and P3. = 0.07 in our simulation.Fig. 2 demonstrates the bias in odds ratio in comparing complications between STKA and BTKA. The complication

rate used was 1%, which is approximately the infection incidence rate. In this simulation, the percentage of UTKApatients who had surgery on the other knee after satisfactory UTKA ranged from 1% to 25%. The percentage ofpatients with complications who declined STKA-2 ranged from 10% to 50%. The probability of P(A) played asignificant role in distorting the true odds ratio. Although the true odds ratio was set as 1 in this simulation, theobserved odds ratio ranged from 0.90 to 0.56 for 0.01 b P(A) b 0.25 and 0.1 b P(B) b 0.5 (Fig. 2). As shown in Table 2,if 10% of UTKA patients changed plans and had contralateral surgery after satisfactory UTKA (P(A) = 0.1) and a halfof patients who experienced infection did not complete the initially planned STKA-2 (P(B) = 0.5), the odds ofinfection for STKA compared with BTKA appeared to be 0.61 when the true odds ratio was set as 1. Therefore, STKAappeared to be safer than BTKA when the actual infection risk was the same in our simulated data.We repeated the same simulation with a complication rate of 2.5%, which is approximately the symptomatic

nonfatal DVT incidence after TKA. Because the postoperative risk is higher, the bias was slightly larger. Regardless,the conclusion was almost the same; the observed odds ratio ranged from 0.89 to 0.54 for 0.01 b P(A) b 0.25 and0.1 b P(B) b 0.5 (Table 2). In an extreme case if a patient died from complications of STKA-1, then P(B) plays asignificant role in distorting the true odds ratio in comparing mortality (Table 2). Patients died after STKA-1 cannotnot have a chance to undergo STKA-2; therefore, P(B) is always equal to 1.0. As shown in Table 2, the odds of deathfor STKA appeared to be half compared with BTKA even if the actual mortality was the same in our simulated data.

Fig. 2. Observed odds ratio for postoperative complications between STKA and BTKA when the true odds ratio was set to 1.


CommentsWe illustrated the source of misclassification bias in

comparing postoperative complications between BTKAand STKA. We also demonstrated that in retrospectiveanalyses of medical records, the operative risk of STKAappeared to be lower than it truly is. A number ofpublished studies have reported that BTKA has a higherrisk of serious cardiac complications, pulmonary com-plications, and mortality [29,30]. However, our researchsuggests that study results based on retrospectiveanalysis without considering the initial treatment planare biased because STKA patients who had adverseoutcomes are less likely to be identified in the STKAgroup; therefore, STKA appears to be a safer procedurethan it truly is (conversely, the risk of BTKA isoverstated). This type of bias is well recognized inprospective clinical trials; therefore, an ITT analysis isused to avoid a misleading conclusion [32]. Intent-to-treat analysis in prospective clinical trials is based on theinitial treatment intent rather the treatment eventuallyadministered. In most retrospective studies, however,ITT is unknown, and this lack of information could leadto misclassifying patients into the wrong treatmentgroup. Therefore, if a patient was dropped from theinitial treatment plan, this is a more serious validity issuein retrospective studies because the patient can be

classified into another treatment group that was neverintended. Many studies compared the operative riskbetween BTKA and STKA [17,19,23-26,29,30,33,34].However, to our knowledge, no published study hasadjusted for this misclassification bias. The study resultsbased on biased data may not offer adequate guidelinesfor patient care. In the absence of a prospective study,published studies should be interpreted with caution.Without P(A) and P(B) estimates, we are unable to

estimate the amount of bias in published studies.However, our simulation results help us to understandthe previous study on the risk of mortality, which isseemingly counterintuitive; a study reported that theproportion of mortality within 30 days after UTKA istwice compared with that of STKA-2 (0.29% after UTKAand 0.14%-0.15% after STKA-2) [30]. We posit that thisphenomenon is due to the fact that STKA-2 groupincludes only patients who were able to be recoveredafter the first operation. The safety of BTKAs remainscontroversial. A meta-analysis reported that the oddsratios for mortality following BTKA is 2.24, and it issignificantly higher than STKA [29]. However, as shownin our simulation, the odds of death for BTKA inretrospective studies appeared to be 2 times largercompared with STKA, even if the actual mortality wasthe same in our simulated data. The elevated risk of

Table 2. Observed Odds Ratios for Selected PostoperativeComplications Between Staged Knee Arthroplasties andSimultaneous Knee Arthroplasties When the True OddsRatio Was Set to 1

Types of Complication

Infection

P(B)

0.10 0.20 0.30 0.40 0.50 1.00

P(A) 0.01 0.90 0.85 0.81 0.76 0.72 0.490.05 0.78 0.75 0.72 0.68 0.65 0.490.10 0.70 0.68 0.66 0.63 0.61 0.490.15 0.66 0.64 0.62 0.60 0.58 0.490.20 0.63 0.62 0.60 0.58 0.57 0.490.25 0.61 0.60 0.58 0.57 0.56 0.49

Symptomatic Nonfatal DVT

P(B)

0.10 0.20 0.30 0.40 0.50 1.00

P(A) 0.01 0.89 0.84 0.80 0.75 0.71 0.470.05 0.77 0.74 0.70 0.67 0.64 0.470.10 0.69 0.67 0.64 0.62 0.60 0.470.15 0.65 0.63 0.61 0.59 0.57 0.470.20 0.62 0.60 0.59 0.57 0.55 0.470.25 0.60 0.58 0.57 0.56 0.54 0.47

Death

P(B)

0.10 0.20 0.30 0.40 0.50 1.00

P(A) 0.01 * * * * * 0.490.05 * * * * * 0.490.10 * * * * * 0.490.15 * * * * * 0.490.20 * * * * * 0.490.25 * * * * * 0.49

* Not applicable.Odds ratios are underestimated due to a lack of ITT information. P(A):proportion of unilateral patients who proceed to have the contralateralsurgery after the satisfactory surgery experience. P(B): the proportionof patients with complications who did not pursue the contralateraloperation among who initially planned staged knee arthroplasties.


mortality associated with BTKA in previous studiescould be, in part, due to the misclassification bias.To our knowledge, there are no published prospective

studies that considered an initial surgery plan. In aneffort to overcome difficulty in identifying the STKAgroup, some studies compared the relative risk betweenBTKA and STKA by assuming that the risk of STKA istwice that of UTKA [30,34]. However this approach isbased on the improbable assumption that STKA andUTKA patients are comparable. Obesity is more stronglyassociated with bilateral osteoarthritis of the knee thanwith unilateral osteoarthritis [15]. Knee injury is astronger predictor for unilateral OA. Therefore, patientswith bilateral OA are likely to have an elevated risk ofcardiovascular complications compared with patientswith unilateral OA.Our study should be interpreted within the limitations

of a simulated study. Because the percentage of patients

failing to return for the STKA-2 after experiencingadverse events after STKA-1 is unknown, we performedsimulations with a wide range of probabilities. Althoughwe demonstrated that the postoperative risk after BTKAwas overstated, the exact amount of bias remainselusive. In our simulation, we did not consider patientcharacteristics. In general, older patients or high-riskpatients are more likely to undergo STKA than BTKAbecause studies support the hypothesis that patients80 years or older who undergo BTKA are at increasedrisk [35,36]. Appropriate patient selection may be thekey for a favorable surgical outcome, but this is beyondthe scope of our study. The bias in retrospective analysisof medical records exists, regardless of whether thepatients are at high or low risk.As a future research, identification of subgroups with

favorable prognosis for BTKA or STKA would be a goodguideline in clinical practice. We believe that the relativerisk between frequency and time length of operationdepends on a patient's characteristics and comorbidcondition. Some patients may experience more severepostoperative complications after BTKA than otherpatients, depending on their age, sex, or comorbidcondition [24,33,36]. Due to the absence of anyprospective study, heterogeneity of treatment is notwell understood either [37]. Further prospective studieswould help identify the patient characteristics associatedwith favorable outcomes after BTKA or STKA.

ConclusionAlthough the safety of BTKA remains controversial, in

general, BTKA has been believed to be riskier thanSTKA. However, our study demonstrated that therelative risk of the BTKA is overstated. Our studysuggested that conclusions based on retrospectivestudies could be biased because the surgical plan at thetime of the first surgery and the surgery eventuallyperformed are not always the same in knee osteoarthri-tis patients. Intent-to-treat is unknown in most retro-spective studies. The information gap on the relativepostoperative complications between BTKA and STKA islargely due to the absence of a prospective study. Thisstudy calls for a prospective follow-up study forcomparative effectiveness research, which is importantfor clinicians and patients to decide the best treatment.

AcknowledgmentThe authors wish to thank Drs Betty Guo and Jeffrey

Elias at the UC Davis Clinical and Translational ScienceCenter for editorial advice.

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operative risk of staged bilateral knee arthroplasty is underestimated in retrospective studies

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