Cost-Effectiveness of Five Commonly Used Prosthesis Brands for Total Knee Replacement in the UK: A Study Using the NJR Dataset

Background There is a lack of evidence on the effectiveness or cost-effectiveness of alternative brands of prosthesis for total knee replacement (TKR). We compared patient-reported outcomes, revision rates, and costs, and estimated the relative cost-effectiveness of five frequently used cemented brands of unconstrained prostheses with fixed bearings (PFC Sigma, AGC Biomet, Nexgen, Genesis 2, and Triathlon). Methods We used data from three national databases for patients who had a TKR between 2003 and 2012, to estimate the effect of prosthesis brand on post-operative quality of life (QOL) (EQ-5D-3L) in 53 126 patients at six months. We compared TKR revision rates by brand over 10 years for 239 945 patients. We used a fully probabilistic Markov model to estimate lifetime costs and quality-adjusted life years (QALYs), incremental cost effectiveness ratios (ICERs), and the probability that each prosthesis brand is the most cost effective at alternative thresholds of willingness-to-pay for a QALY gain. Findings Revision rates were lowest with the Nexgen and PFC Sigma (2.5% after 10 years in 70-year-old women). Average lifetime costs were lowest with the AGC Biomet (£9 538); mean post-operative QOL was highest with the Nexgen, which was the most cost-effective brand across all patient subgroups. For example, for 70-year-old men and women, the ICERs for the Nexgen compared to the AGC Biomet were £2 300 per QALY. At realistic cost per QALY thresholds (£10 000 to £30 000), the probabilities that the Nexgen is the most cost-effective brand are about 98%. These results were robust to alternative modelling assumptions. Conclusions AGC Biomet prostheses are the least costly cemented unconstrained fixed brand for TKR but Nexgen prostheses lead to improved patient outcomes, at low additional cost. These results suggest that Nexgen should be considered as a first choice prosthesis for patients with osteoarthritis who require a TKR.


Section 2: Multiple imputation of missing data
Missing pre-operative data in the linked PROMs-HES-NJR dataset was generally below 10% with the exception of BMI (67%). Missing post-operative data ranged from 17-24% and arose predominantly from missing questionnaires. Missing data was imputed using Chained Equations (ICE command in Stata). 10 The MI equations included all variables which entered the regression models for LOS and QOL, including agebrand and sex-brand interaction terms which were included in a sensitivity analysis of post-operative QOL. Preand post-operative EQ-5D-3L responses were specified using dichotomous variables to indicate a level two or three response to each of the five dimensions. This approach utilised the information available from partially complete EQ-5D-3L responses. Pre-operative EQ-5D-3L tariff scores, specified using fractional polynomials as they appeared in the regression models for QOL and LOS, were also included. We further included ethnicity, total number of diagnosis (ICD) codes in HES, duration of symptoms, measures of overall health (such as the EQ-5D-3L Visual Analogue Scale), and measures of satisfaction with surgery. Ordered categorical data, including quintiles of IMD and EQ-5D visual analogue scale responses, were imputed using ordered logistic regression. Oxford knee scores were imputed using predicted mean matching to allow for the truncation and skew of the distribution. Post-operative LOS and the total number of ICD-9 codes in HES were log transformed to reduce skew. Twenty imputations were undertaken.
QOL and LOS before and after imputation are illustrated in Table 1 below. Post-operative EQ-5D-3L index scores were lower after imputation by a similar amount across all five TKR brands (0.01 QALYs).

Section 3: Analysis of QOL after primary TKR and before and after revision TKR
Linear Regression was used to estimate post-operative QOL by brand after primary TKR and adjusting for differences in patient and provider characteristics. The analysis adjusted for ASA grade, BMI, disability, type of hospital, comorbidities, IMD, EQ-5D-3L pre-score, OHS pre-score, patella replacement, surgical position (medial parapatellar or not), age and sex. Model fit, was assessed by Akaike's Information Criteria (AIC). 11 Fractional polynomials were used to specify the relationship of the dependent variable to pre-operative EQ-5D-3L tariff and pre-operative OKS. 12 Fractional polynomial forms of age and BMI were investigated, but rejected in favour of a linear specification of BMI and a quadratic specification of age, as the latter, simpler specifications yielded regression models with equivalent fit. The model was used to predict QOL for the six subgroups (men and women aged 60, 70 and 80) and for each of the five TKR brands assuming mean values from the relevant subgroup population for the dependent variables.

Extrapolation of QOL gains
The health state tariffs for each health state in the model were reduced with each cycle to reflect the impact of age on QOL. The adjustment utilised the regression model of the impact of age on QOL reported by Brazier and Ara, and based on a large sample of UK data. 13 In this model the impact of age is curvilinear; QOL drops at an increasing rate with advancing age. The yearly decrement for patients aged 70 is 0.004QALYs.

Health State tariffs during and after revision
The PROMs data included 6 769 patients undergoing a revision TKR of which 6 128 were 55 or over. Of these patients, 5761 had a pre-operative EQ-5D-3L tariff score and 3 912 had a post-operative EQ-5D-3L tariff score.
Linear regression of scores prior to surgery generated QOL tariffs for the Markov state 'Revision' as a function of age and sex. Likewise, the QOL tariff for the Markov state 'revised TKR' was parameterised as a function of age and sex using EQ-5D-3L tariff scores following revision surgery.

Section 4: Quantifying LOS following primary and revision TKR
Linear regression was used to estimate differences in LOS after primary TKR by brand after investigation revealed the data was only moderately skewed. We adjusted for ASA grade, BMI, home environment (living alone or not), disability, type of hospital, comorbidities, IMD, EQ-5D-3L pre-score, OHS pre-score, patella replacement, surgical position (medial parapatellar or not), age and sex. After adjustment for patient and provider characteristics LOS varied by 0.5 days across brands with the AGC Biomet associated with the shortest LOS. We found very similar results using a Generalised Linear Model which assumed a Gamma distribution for LOS. The linear regression model was used to predict LOS for the six subgroups (men and women aged 60, 70 and 80) and for each of the five TKR brands assuming mean values from the relevant subgroup population for the dependent variables.
Linear regression was also used to model LOS after revision TKR as a function of age and sex. The model utilised the data on revision TKR in the linked PROMs-HES-NJR data.

Section 5: Analysis of primary revision rates
There are multiple causes of TKR revisions including infection, surgical errors during primary TKR and failure or loosening of components. The relative importance of these causes varies with time since surgery. The resulting overall hazard function is poorly approximated by a simple monotonic function with respect to time.
Consequently, we chose to use restricted cubic splines to model the log cumulative hazard. 14 This technique is well documented and provides a flexible approach to modelling event data.
A restricted cubic spline model was fitted to the NJR data. It adjusted for ASA grade (classified as 1, 2 or other), BMI (classified as <30; 30 to 35; >35), patella replacement, surgical position (medial parapatellar or not); use of antibiotic cement; surgeon grade (consultant level or not), hospital type (general or specialist orthopaedic centre), age and sex. Patients with missing BMI data were assumed to have a BMI below 30. Model fit was judged by AIC. Optimal fit was obtained using the hazard scale with four degrees of freedom (three internal knots) for the baseline hazard and allowing a time dependent effect of age (one degree of freedom). The model allowed prediction of revision rates within the observed period after adjustment for casemix and extrapolation of revision rates beyond the observed period. occurring on the same knee were linked using pseudo-anonymised patient identifiers and laterality codes. We assumed the earliest revision recorded on a knee was the first revision and the next procedure was a re-revision.
Further operations were not considered. The resulting data had a mean follow-up time of 4.2 years and consisted of 52 660 patients of which 9 978 underwent re-revisions. Preliminary analysis showed a higher re-revision rate in the first year following surgery. The data was modelled using a piece-wise constant hazard function with a single boundary at one year. 15 The resulting hazard was constant with respect to time after the first year but varied with patient age. The overall revision risk fell as patients aged. Probabilities over a range of ages are tabulated below (table 2). The probability of re-revision in the first year was applied to patients in the revision state and an event resulted in patients remaining in this state to undergo a further revision in the following cycle.
The probability of re-revision in subsequent years was applied to patients in the revised TKR state and an event resulted in transition to the revision state.

Men Women
Age

Section 8: Parameterisation of sampling uncertainty
The Markov model was fully probabilistic. Sampling uncertainty around each of the parameters was incorporated by specifying each parameter as a random variable with mean and variance derived from the regression model used in its estimation. Each coefficient in the respective regression models was assumed to follow a normal distribution, and correlation of the uncertainty around coefficient estimates was captured by applying the Cholesky decomposition of the covariance-correlation matrix. 19

Analysis of QOL after primary TKR using an alternative linear regression model
In the base case analysis, the regression model used to estimate post-operative QOL by brand included preoperative EQ-5D-3L specified as the tariff score. In a sensitivity analysis we applied an alternative regression model for post-operative QOL in which pre-operative QOL entered the model using dichotomous variables to identify a response at level 2 or level 3 on each of the five dimensions of the instrument (ten dummies in total).

Assuming the same cost for all prosthesis brands
To investigate the impact of primary prosthesis costs on the results we ran a sensitivity analysis in which all prostheses were assumed to cost the same as the PFC Sigma.

Extrapolating revision rates using a Piece-wise Constant model
The Restricted Cubic Spline model used to extrapolate revision rates by brand in the base case, was replaced with a Piece-wise Constant model. 20 The model specified intervals at the end of years 1,2,3,4 and 5, effectively allowing the baseline hazard to change at these intervals according to the data. Dummies specified for the years 1 through 5 were interacted with each of the five brands (25 interaction terms in total). The resulting model allowed hazard rates to vary each year for the first five years and by brand. Revision rates beyond five years were assumed constant across brands and constant with respect to time. Revision rates still varied according to age and sex. The model included the same dependent variables as those specified in the Restricted Cubic Spline model used in the base case.

Allowing interactions between subgroup and brand in the estimation of post-operative QOL
The regression model used in the base case to predict post-operative QOL by brand did not include interaction terms for age and sex with the dichotomous variables identifying brand, as their inclusion did not lead to an improvement in model fit. A regression model which included these interactions was used to predict postoperative QOL in a sensitivity analysis.

Assuming differences in QOL by TKR brand are maintained for one year only
Differences in QOL in the primary TKR state according to brand were applied for the first cycle (year) only. In subsequent cycles the QOL tariff for patients with a PFC Sigma (for the relevant subgroup) was applied to all patients in the primary TKR state regardless of brand fitted. The adjustment to QOL tariffs in each health state due to aging remained as in the base case.