The present study considered a decision-analytic model-based CUA of TKR in patients of various age groups with OA knee in India with different severities and accounting for multiple scenarios using the provider’s perspective. A Markov model was the chosen methodology for this purpose as it can model the risk of recurrent events in a straightforward fashion as compared with other decision analytic methods; this is because in TKR, the ‘expiry’ of prostheses leads to ‘recurrence’ of the problem, often necessitating re-surgery [22].

We assume the earliest average age of OA knee becoming severe enough to warrant TKR would be 50 years and the lifespan of the implant to be around 20 years [23]. The clinical severity of OA knee is commonly and universally measured with the Kellgren–Lawrence (KL) scale, with the severity ranging between grades 1 (least severe) to 4 (most severe).

TKR is effective for grade 4 OA, but delaying surgery until this advanced stage can severely compromise quality of life due to increased pain and functional limitations. Early TKR, before reaching grade 4, results in better outcomes, including reduced pain, improved function, and quicker recovery. Thus, it is advisable to consider TKR at earlier stages such as KL grade 3 and sometimes KL grade 2 to preserve quality of life and achieve better overall results.

2.1 Markov Model

Two basic Markov models were developed for TKR and non-surgical management (Figs 1 and 2) using Excel. In both models, the states were represented by oval shapes, and the transition between the states was shown by the arrows. The loops indicated the possibility of remaining in a particular state in successive cycles.

Fig. 1

Markov model for non-surgical management of osteoarthritis of the knee (OA Knee)

Fig. 2

Markov model for intervention (total knee replacement). ASM age-specific mortality, OA Knee osteoarthritis of the knee, TKR total knee replacement

The first model, meant for non-surgical management, consisted of four states: OA knee grade 2, OA knee grade 3, and OA knee grade 4, all-cause death (Fig. 1). The second model meant for the TKR arm (Fig. 2) consisted of seven states: ‘OA knee undergoing TKR’, ‘improved OA knee’, ‘early failure post-TKR’, ‘late-failure post-TKR’, ‘systemic complication post-TKR’, ‘all-cause death’, and ‘death due to TKR-related systemic complications’. The transition probability, health utility values, and cost matrices (also called Markov trace) of both models are presented in the supplementary tables (Supplementary Table 1 and Supplementary Table 2, see electronic supplementary material [ESM]).

The stopping rule in the model was either the expiry period of the prosthesis, which was assumed to be 20 years, or the death of all patients, which was assumed to be at 100 years considering different scenarios mentioned in section 2.4 [24]. Therefore, each Markov model had 20-year cycles while the cycle for non-surgical management remains constant throughout.

2.2 Data Inputs

Estimates of transition probabilities and health utility values of each Markov state were identified and synthesized from existing literature and the models were populated with those values (Figs. 1 and 2). The sources of the individual parameters are detailed in the following subsections [25]. The transition probability and utility values were derived from other countries in the absence of India-specific values, hence, we presumed that the input parameters may differ in the Indian setting.

2.2.1 Transition Probabilities

The non-surgical arm consisted of four states and 16 possible transitions between these states. However, it is assumed that patients do not recover from the progressive disease of OA knee with conservative management, hence, transitions (in this case improvement) from grade 4 to grade 3 or grade 2 of OA knee were not considered. Therefore, we extracted eight transition probabilities (see Fig. 1 and Supplementary Table 1 in the ESM). Similarly, the TKR intervention arm consisted of seven states and 49 possible transitions in these health states. As explained earlier, out of the 49 possible transitions, 12 transition probabilities were synthesized (see Fig. 2 and Supplementary Table 2 in the ESM). The value of the other 37 transition probabilities was zero because of the theoretical impossibility of their transitions.

The transition probabilities were informed by published literature. Specifically, Elmallah et al. [26] provided rates for systemic complications and TKR-related mortality, Azad et al. [27] contributed age-specific all-cause mortality data, and Losina et al. [28] provided early and late failure probabilities. Certain probabilities, such as improvement after TKR and transitions from the improved state, were calculated. Recovery probabilities for early failure and complications were based on reasonable assumptions, as detailed in Supplementary Table 1 and Supplementary Table 2 (see ESM).

2.2.2 Health Utility Values

The health utility value (HUV) of OA knee was 0.69 based on existing evidence. Patients who died had an HUV of 0. Patients who experienced systemic complications had an HUV of 0.61. HUV for those with early and late failure TKR was 0.51 (Table 1). Lastly, the HUV for the post-TKR improved state was allocated to be 0.90 [23, 28,29,30].

Table 1 HUV value for each state of OA knee2.3 Costing Data

The costs of TKR, revision TKR, and treatment of systemic complications post-TKR were extracted from the National Health System Cost Database 2014–15 (Supplementary Table 3, see ESM). The cost per outpatient department (OPD) visit for non-surgical management of OA knee was obtained from the National Health System Cost Database 2014–15 [37]. The implant cost is estimated at 54,000 Indian National Rupees (INR), while the hospitalization and surgery costs amount to INR 30,000 [15]. All cost values were inflated to 2020–21 based on the CPI (Consumer Price Index) health inflation rate [39]. The TKR intervention arm involved substantial costs: INR 117,041 (USD 1565.40) for TKR, 1.5 times the cost of TKR for revision TKR [37], and INR 692 (USD 9.25) for treatment of systemic complications post-TKR. The cost per OPD visit for symptoms of OA knee was INR 324 (USD 4.33) and it was assumed that the patient required two visits per year as this represents the minimum number of visits required. Utilizing the minimum values ensures a conservative and realistic approach in the assessment, providing a baseline that can be reliably achieved and sustained. So, the non-surgical treatment has a fixed cost in each annual cycle (2 × INR 324 = INR 648). Hence, the cost obtained from secondary data was used to calculate the total cost. Total QALYs of treatment for both arms was calculated through the Markov model by using quality-of-life data obtained from literature. Further, the total cost and total QALYs were discounted at 3% to adjust it to the present value [40].

2.4 Different Scenarios and Age Groups

Given that the lifespan of the implant used in TKR is 20 years, we could envision three different scenarios, each representing different combinations of TKR, repeat TKR (up to two repeats), and non-surgical management. Also, as the average age of onset of OA knee of sufficient severity (KL grade 2 onwards) where TKR may be applied is 50 years, we decided to model the outcomes starting with three different cohorts, the starting age of which were 50, 60 and 70 years, respectively, as others have done [15]. Table 2 describes the possibility of three different scenarios for the TKR arm.

Table 2 Scenarios based on the expiry of the implant2.5 Sensitivity Analysis

All three sets of input variables, transition probability, health utility values, and cost, were selected from either published literature or national repository; however, these values had variations, in particular, the price varied between the different types of implants. Also, these values were bounded by upper and lower limits of their uncertainty intervals (95% confidence intervals in most cases). To capture this variation of input values, we conducted a univariate deterministic sensitivity analysis (DSA) and a probabilistic sensitivity analysis as commonly carried out in such circumstances. This usually compares different input variables at a fixed variation level. The cost of different types of implants ranged between INR 55,000 (USD 735.61) and INR 77,000 (USD 1029.86): INR 54,720 (USD 731.87) for cobalt chromium; INR 56,490 for high flexibility implants; and INR 76,600 (USD 1024.51) for zirconium and titanium [41]. A 50% increase in the cost of TKR (INR 175,561 or USD 2348.09) would include the cost of TKR involving any one of the different types of TKR implants. Therefore, the sensitivity analysis of different input variables of both TKR and non-surgical arms was estimated based on 50% variation (see Supplementary Tables 1, 2, 3, 4, 5 in the ESM).

The probabilistic sensitivity analysis (PSA) involved assigning probability distributions to each input parameter. Where possible, normal distributions were used for continuous variables and beta distributions were applied for probability values, ensuring the variability and uncertainty inherent in these parameters were adequately represented. The PSA was conducted through Monte Carlo simulations, with 1000 iterations performed to simulate the joint uncertainty across all input variables. This process allows for the exploration of a wide range of potential outcomes, reflecting the combined uncertainty in the model parameters.

2.6 Cost-Effectiveness Plane

The cost-effectiveness plane presents the incremental cost-effectiveness ratio (ICER) values of different scenarios and grades vis-à-vis different thresholds. The per-capita GDP of India was INR 128,829 at current price in 2020–21. Normally, three times the per-capita GDP is assumed to be the willingness-to-pay (WTP) threshold value. Anything less than one per capita GDP is considered highly cost effective, which is often attributed to the Commission on Macroeconomics and WHO guidelines on Choosing Interventions that are Cost Effective (WHO-CHOICE) [42]. The ICERs derived from sensitivity analyses were also presented through the cost-effectiveness plane (we present only the ICER with the highest increase from DSA estimates).

2.7 Budget Impact Analysis

Given the limited resources and competitive priorities within health, TKR, which is found to be cost effective, and can be considered by the government or not, needs a rigorous discussion. Therefore, we undertook a budget impact analysis to understand the resource requirement for TKR and whether the new intervention is affordable. We considered the provider’s perspective where the health system will invest to meet expenses for TKR and the total time period is 5 years as this time frame can encompass the progression of the disease, potential changes in treatment frequency, and associated costs, providing a comprehensive view of the financial burden. Additionally, it balances capturing long-term costs and benefits with manageable uncertainty levels, ensuring that stakeholders have a realistic and actionable understanding of the economic impact, which is critical for effective decision making and ensuring sustainable healthcare funding. For the BIA, we have assumed different scenarios here without accounting for discount.

To estimate the burden of TKR in the population, we begin with the total population, which is 143.01 crores (1 crore [cr] = 10 million). We focus on the subset of the population aged 50 years and above, as they are more likely to require TKR. The proportion of this age group within the total population is 19.07%. Next, we consider the prevalence rate of TKR among this specific age group, which is 14.77%. To calculate the estimated number of individuals in the population who might require TKR, we multiply the total population by the proportion of the population aged 50 years and above and then by the TKR prevalence rate within this age group. The calculation is as follows:

Total population (143.01 cr) × proportion of population aged 50 years and above (19.07%) × TKR prevalence rate among those aged 50 years and above (14.77%) = 4.77 cr.

Scenario 1: The government may not bear the expenses of the entire population requiring TKR and may cover up to 40% of the population who are vulnerable. This 40% vulnerable population is decided as per the Ayushman Bharat-Pradhan Mantri Jan Arogya Yojana (ABPMJAY) eligibility criteria. The PM-JAY initiative is a comprehensive effort to address healthcare needs across prevention, promotion, and ambulatory care at secondary and tertiary levels. The ambitious goal is to provide coverage to approximately 50 cr (500 million) beneficiaries, representing around 40% of India's poor and vulnerable population. This expansive program aims to enhance healthcare access and financial protection for a significant portion of the country's underprivileged and marginalized communities [43].

Scenario 2: The government covers the expenses of the entire population who are recommended TKR surgery.

Scenario 3: We have also attempted to understand the share of TKR expenditure in the National Health Mission (NHM) budget considering the cost of 40% of the vulnerable population to be covered under NHM, like scenario 1.