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  • A Markov model with a cycle length of one year was used to simulate the longevity of the knee prosthesis brands over the patients’ lifetime [14]. This model is adapted from a published evaluation of alternative types of total hip replacement, as failure of the prosthesis is the primary concern for both hip and knee replacement [15]. For each brand, costs and outcomes were estimated for a hypothetical cohort of patients who enter the model at the time of the primary TKR (Fig 1). After the primary replacement, patients face a possibility of immediate post-operative mortality, and then annual probabilities of revision of the TKR and mortality. Patients requiring revision move to the ‘Revision’ state. After successful recuperation patients then transit to the ‘Revised TKR’ state. Figure data removed from full text. Figure identifier and caption: 10.1371/journal.pone.0150074.g001 Markov model of TKR Time spent in health states after primary and revision TKR was weighted for QOL and summed over 45 cycles to estimate life expectancy in terms of quality-adjusted life years (QALYs). Lifetime costs from a health care perspective were calculated by summing the cost of the primary TKR and any subsequent revision procedure. We tested whether the model’s main assumptions (see Box 1) were robust to alternative assumptions in sensitivity analyses. Box 1. Main assumptions underlying the Markov model of the cost effectiveness analysis.Patients enter the model at the time they have the TKR. The model assumes that the post-operative QOL observed at six months, applies from when the patients enter the model, and to subsequent model cycles in the TKR health state.The differences observed in QOL across prosthesis types six months after TKR is maintained for the lifetime, subject to the decline in QOL with increasing age, and the possibility that the TKR fails.The approach to estimate the effect of prosthesis type on QOL has fully addressed confounding.Deterioration of the prosthesis does not affect QOL adversely unless the prosthesis is revised.All failed prostheses are revised.The effect of prosthesis failure on QOL is estimated from the QOL observed before surgery in those who had a revision, and is applied for one year post revision.The approach to extrapolate prosthesis survival beyond the observed data accurately predicts the long term probability of prosthesis survival.The costs of revising the TKR are same for each prosthesis brand.QOL during and after revision is the same whether or not the revision was undertaken due to sepsis. We used individual patient data from the English National PROMs Programme [13], linked to records from the NJR [11] and the English Hospital Episode Statistics (HES) database [16] to estimate the effect of TKR brand on post-operative QOL and length of stay (LOS). QOL in the primary TKR state was parameterised using post-operative data after primary TKR. QOL in the revision state was parameterised using pre-operative data after revision TKR. QOL in the revised TKR state was parameterised using post-operative data after revision TKR. We estimated revision rates by prosthesis brand using NJR data. Re-revision rates and mortality were estimated from HES data. QOL, pre-operative characteristics and prosthesis type: Data from the National PROMs Programme included patients who had an elective TKR between August 2008 and July 2012 [13]. This programme collects patient-reported comorbidities and QOL immediately before the TKR and QOL six month thereafter. The Oxford Knee Score (OKS) is a 12-item disease-specific instrument which generates scores ranging from 0 (worst health status) to 48 (best health status) [17]. The EQ-5D-3L is a generic instrument which generates health profiles using five dimensions (mobility, self-care, usual activities, pain and discomfort, anxiety and depression) and three levels (no problems, some problems, severe problems) [18]. These profiles were combined with health state preference values from the UK general population, to give EQ-5D-3L utility index scores on a scale anchored at 0 (death), and 1 (perfect health) [19]. We accessed pre-operative PROMs records for 158 799 patients aged 55 to 84 years, and subsequently included 105 637 patients whose record could be linked to NJR and HES records. The NJR provided data on prosthesis type, diagnosis (osteoarthritis or other), body mass index (BMI), and American Society of Anesthesiologists (ASA) grade [20]. HES provided data on socioeconomic deprivation derived from the patient’s postcode as the Index of Multiple Deprivation (IMD) [21]. We excluded patients who had missing data on prosthesis brand, those who had any diagnosis other than osteoarthritis or an ASA grade worse than 3; and those who received a cementless prosthesis component or a non-standard surgical procedure such as a bone-graft. The resulting sample of 53 126 patients was used to estimate LOS and QOL six months after TKR. These QOL estimates were applied to patients in the primary TKR health state in the initial cycle and each subsequent cycle. After each cycle of the Markov model we reduced QOL in each health state to reflect the effect of aging. The magnitude of the reduction increased with age (for example the reduction was 0.004 in QOL tariff at age 70) reflecting the curvilinear relationship observed in a large UK observational study [22]. For the health state representing the year in which patients had a TKR revised, QOL and LOS was taken from pre-operative data for 6 128 patients whose TKR was a revision. For subsequent years, QOL was taken from the 3 912 patients who had responded to outcome questionnaires six months after the revision surgery. Rates of revision and re-revision: The annual revision rates after a primary TKR according to prosthesis brand were estimated from NJR data. We accessed 265 910 records of patients who had a primary, unilateral TKR between 1 April 2003 and 1 March 2012, who were aged between 55 and 84, who had a primary diagnosis of osteoarthritis, and who received treatment in an NHS hospital or treatment centre. Records for 239 945 patients were available for analysis after applying the same exclusion criteria we applied to the PROMs data. The data contained 3 148 linked revisions recorded in the NJR (593 PFC Sigma, 392 AGC Biomet,129 Nexgen, 112 Genesis 2, 74 Triathlon, and 1 848 other brands). Maximum observation periods varied by brand from 11.1 years for the PFC Sigma to 6.7 years for the Triathlon. Re-revision rates were estimated from the records of 54 134 patients with a revision recorded in HES between April 1997 and March 2012, after linking initial and subsequent revisions on the same knee. Operative mortality after TKR was estimated from HES data. We did not find any difference in operative mortality across prostheses brands (p>0.4) after adjusting for potential confounders (age, sex, ASA grade, BMI, funding source and date of surgery), and therefore we applied the same probabilities of death across all prosthesis brands. Annual mortality according to age and sex was taken from general population data, after using HES data to adjust for the “healthy patient” effect, to recognise that patients who have undergone joint replacement for osteoarthritis have a lower mortality than observed in the general population [23]. The healthy patient effect was largest for older patients (relative risk of dying was 0.3 for males aged 80 in the year after surgery) and decayed exponentially to a relative risk of 1.0 over the decade following surgery. All costs are reported in British pounds (1 British pound ≈ 1.60 US dollars ≈ 1.20 euros) according to 2011–12 prices. The unit cost of each prosthesis brand was taken from the average prices paid by a mid-size NHS provider (including all components and instrumentation) to reflect discounts negotiated on list prices: £1 835 for PFC Sigma, £1 150 for AGC Biomet, £1 676 for Nexgen, £1 294 for Genesis 2, and £1 325 for Triathlon (Lewis P. NHS SupplyChain. Personal Communication). Unit costs of the operating theatre for a primary TKR (£2 022) and a hospital bed day (£332) were based on data from a recent RCT carried out in the UK [24]. The unit costs of revisions (£8 429) recognised that more resources are used than for primary surgery [24]. Statistical analysis to provide input parameters for the cost-effectiveness model: QOL after primary TKR and revision: We estimated QOL following primary TKR according to prosthesis brand using linear regression to adjust for observed differences in pre-operative patient and provider characteristics between the comparison groups. We adjusted for the following differences in case mix: age, sex, comorbidities, BMI, disability, ASA grade, IMD, patella replacement, surgical position, pre-operative EQ-5D-3L and OKS scores. To avoid attributing differences arising from surgeon or hospital factors to prosthesis brand, we also adjusted for provider characteristics (surgeon experience [senior surgeon or not], and hospital type [specialist treatment centre or general hospital]). We applied fractional polynomials to continuous variables where they provided an improvement in model fit over linear or quadratic functions [25]. We then predicted post-operative QOL by prosthesis brand separately for men and women in three different age groups (60, 70 and 80 years). QOL in the year during which revision TKR took place, and in subsequent years after revision was predicted according to age and sex using linear regression. Of the 53 126 patients included in the QOL analysis 17% were missing post-operative PROMs. Most other data items were missing for less than 10% of the sample. Multiple imputation using chained equations was applied to pre- and post-operative data to impute missing responses [26]. Twenty imputations were undertaken and results across these imputations were combined by Rubin’s rules [27]. Rate of revision and re-revision: Annual revision rates were predicted from NJR data for each prosthesis brand after adjusting for differences between the comparison groups. We adjusted for differences in case mix (age, sex, ASA grade, BMI, patella replacement, antibiotic cement) and provider characteristics (surgeon experience, and hospital type). We used a restricted cubic spline regression model to capture the underlying variation in revision rates over time, without imposing a pre-specified relationship, and to allow extrapolation of revision rates beyond the observation period [28]. To meet the requirements of the Markov model, re-revision rates were estimated from HES data with a piece-wise constant survival regression model which differentiated revision rates at only one time point: the first year versus all subsequent years. For men and women aged 60, 70 and 80, the cost-effectiveness model reported revision rates, costs related to TKR, and QALYs for patients with the average pre-operative characteristics for each subgroup. A recommended annual discount rate of 3.5% was applied to both costs and outcomes to reflect societal time preferences [29]. We report the incremental costs per QALY, and the probability that each prosthesis brand is the most cost-effective. We recognised sampling uncertainty in the estimation of the model parameters by undertaking a probabilistic analysis. Model results are reported after averaging across 1 000 simulations in which each model parameter was sampled from the appropriate probability distribution. For each brand of TKR, we calculated the net monetary benefit by multiplying total lifetime QALYs by society’s willingness-to-pay for a QALY gain and subtracting from this the total lifetime cost. The calculation was repeated with alternative levels of willingness-to-pay for a QALY gain (from £0 to £50 000). We calculated cost-effectiveness acceptability frontiers to report the brand with the highest mean net monetary benefit (most cost-effective on average) and the proportion of simulations for which this brand had the highest net monetary benefit (recognising sampling variation), at different levels of willingness-to-pay for a QALY gain [30]. We tested whether the results were robust to alternative assumptions about post-operative QOL, revision rates and costs across brands. First, we assumed that differences in post-operative QOL between prosthesis brands were only maintained for one year after TKR, rather than until a revision or death. Second, we considered an alternative form of linear regression model to estimate post-operative QOL across TKR brands by including interaction terms between prosthesis brand and both age and sex. Third, in the linear regression model that estimated the effect of brand on post-operative QOL, rather than including a single continuous variable for the baseline EQ-5D-3L, we specified categorical variables for each health state dimension. Fourth, we considered an alternative form of the regression model used for the prediction of revision rates by using a piece-wise constant rather than a restricted cubic spline hazard function. Fifth, we applied the same prosthesis cost to each brand. The Markov model was built in Excel; statistical analysis to parameterize the model was undertaken in STATA version 11. The study is exempt UK NREC approval as it involved analysis of existing datasets of anonymised data for service evaluation. Approvals for the use of HES data were obtained as part of the standard Hospital Episode Statistics approval process.
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