A decision analytic model to estimate cost-effectiveness was developed using a Markov process. Four plausible competing allocation options were compared to the current kidney allocation option (Table 1). They are: allocating the best 20% of KDRI donor kidneys to the best 20% of EPTS recipients (option 1); allocating the worst 20% of KDRI donor kidneys to the worst 20% of EPTS recipients (option 2); allocating the youngest 25% of donor kidneys to the youngest 25% of recipients (option 3), which resembles Canadian allocation system; and, allocating the oldest 25% of donor kidneys to the oldest 25% of recipients (option 4) both of which resemble the Eurotransplant allocation system.

## Target population

The study population was Australian CKD patients who were waitlisted for a kidney transplant. Data from the Australia and New Zealand Dialysis and Transplant Registry (ANZDATA)(17) were used. ANZDATA collects and reports the incidence, prevalence and outcome of dialysis treatment and kidney transplantation for all patients with end stage kidney disease treated with kidney replacement therapy across Australia and New Zealand, including the private sector. Activities of the registry have been granted full ethics approval by the Royal Adelaide Hospital Human Research Ethics Committee (reference number: HREC/17/RAH/408 R20170927, approval date: 28/11/2017).

## Model structure

The Markov model (Figure 1) was developed using TreeAge Pro 2019 (TreeAge Software, Inc., Williamstown, MA) to estimate the incremental costs and incremental quality-adjusted life years (QALY) associated with each donor organ allocation option. The model structure and assumptions used were validated by a systematic review(18) and by two clinical experts involved in kidney transplantation care in Australia.

For each option modelled patients may experience four health states: waitlisted, transplant, post graft-failure dialysis and death. The cohort starts at the “wait list” health state and patients in the cohort will be in this health state until they are transplanted or until die. The probability of being transplanted is different in each of the allocation options (Table 2). When a patient transitions to the “transplant” health state they can experience either graft failure or death, or continuing successful transplantation. It was assumed that once a graft fails patients will not be wait-listed for another transplant, thus, the patient will either remain on dialysis or die while on dialysis.

The measure of health benefits or the effectiveness of each allocation option are quality adjusted life years. The perspective of the analysis was that of the healthcare payer. Both future costs and QALY were discounted at an annual rate of 5%, as recommended by the Medical Services Advisory Committee’s Technical Guidelines, Australia(19).

## Data sources

The costs of a transplant were taken from the report “The economic impact of end-stage kidney disease in Australia - Projections to 2020” by Kidney Health Australia in 2010 (20). The cost during the first year of deceased donor kidney transplantation was AUD $81,549. This included costs of the surgery, hospitalization, specialist consultations, immunosuppressive therapy and other drugs, as well as cost of the donor surgery. From year two onwards the annual cost for follow-up management which included immunosuppressive therapy, other drugs and non-drug follow-up costs was AUD $11,770 per year (20).

Dialysis costs were taken from the New South Wales Dialysis Costing Study (2008). The total dialysis cost included costs directly related to dialysis, such as nursing, allied health, dialysis fluid and consumables and depreciation costs, as well as ongoing CKD management costs, such as pharmacy, pathology and medical costs. Of the dialysis patients, 81% are on haemodialysis and the remainder are on peritoneal dialysis. Of the haemodialysis patients 68% are undergoing in-centre haemodialysis, 11% are on home haemodialysis and the remainder are undergoing haemodialysis at satellite centres(21). The final dialysis cost of AUD $69,089 was calculated as a blend of all the dialysis modalities, proportionate to the different dialysis modalities practiced in Australia. All costs were converted to 2018 values.

Utility scores for different health states for Australian CKD patients are not available. Instead we took utility values for the transplant and dialysis states from a systematic review and meta-analysis (22). The authors reviewed 190 studies reporting more than 300 utilities in more than 56,000 patients. The utility score for the transplant health state was estimated to be 0.82 (95% CI 0.74 to 0.90), while that of a dialysis health state was 0.70 (95% CI 0.62 to 0.78).

Two separate data sets were created to calculate the transition probabilities. The first dataset set was created by linking patients who were implanted with deceased donor kidneys (1st graft) between 1st January 2007 and 31st December 2017 in Australia to the waitlisted patient information dataset using a unique patient identification number provided by ANZDATA. The final dataset included those who were transplanted as well as those who were waitlisted but not transplanted during the study period. Furthermore, transplanted patients’ EPTS score and the KDPI of implanted organs were available. Both variables have been validated in Australian kidney transplant populations as valid measures of recipient and donor quality respectively (23, 24). The probability of transplant and mortality while on waitlist and the probability of mortality and graft failure after transplantation was calculated in the first dataset population. The second dataset was created by linking CKD patients who started hemodialysis or peritoneal dialysis between 1st January 2007 and 31st December 2016, to transplant and waitlist patient information datasets. The probability of mortality while on dialysis after graft failure was calculated in the second dataset.

Transition probabilities of current practice were calculated from the first dataset. Then this was divided into overlapping subsets of data (option 1 to 4) for the purpose of the modelling. Note that data not conforming to the criteria of a particular hypothetical allocation option (table 1) were excluded from a subset.

Three transition probabilities were calculated from each of the dataset populations:

- the annual probability of being transplanted from all waitlisted patients (Figure 1; P1)
- the annual probability of graft failure following transplant (Figure 1; P2)
- the annual probability of mortality following transplant (Figure 1; P3)

Weibull regression was used to calculate above three probabilities based on its visual (parametric function fits well to the non-parametric function(25)) and statistical fit (based on Akaike and Bayesian information criterion (AIC, BIC)(26)) to the observed data. The Weibull distribution assumes that the baseline hazard is time-dependent, thus it allows the baseline hazard to increase or decrease over time at a different rate(27). Age was considered a co-variate in the model. Lambda (λ), Gamma (ϒ) and beta coefficient of age were used to calculate the time-dependant probabilities (Table 1). Age was considered 50 for the analysis.

Fixed transition probabilities were calculated for mortality while waitlisted (Figure 1; P4) and mortality while on dialysis after graft failure (Figure 1; P5). These two probabilities were assumed to be the same for all five allocation options.

Fixed transition probabilities were calculated as follows; initially, cumulative incidence and standard error of the cumulative incidence were calculated for each of the transition probabilities. Then the cumulative incidences were first converted to rates and then to annual transition probabilities using following formulas (28).

The quality of the data used to inform model parameters was determined using the modified hierarchies of data sources for economic analyses (29). The quality of data sources range from 1 to 6 with the highest quality of evidence ranked 1.

## Model evaluation

The outcomes of change to costs and change to QALY for each option were tested in a simulated cohort of 1,000 patients for a 20-year time horizon. As the cohort transitions through different health states according to the calculated transition probabilities, both costs and utility are accumulated and aggregated at the end of 20 years to yield total costs and QALYs. The Incremental Cost Effectiveness Ratio (ICER) was calculated using:

An intervention is considered cost-effective if the ICER is less than the chosen Wiliness to pay (WTP) threshold. The WTP for a marginal QALY for Australia, based on life satisfaction as an indicator of utility to estimate the WTP value, is in a range between AUD 42,000 to AUD 67,000 (30). A different threshold of AUD 28,000 was proposed recently (31) and this reflects the opportunity cost of additional healthcare expenditures under a constrained budget. For this analysis we used AUD28,000, and then conducted scenario analyses with thresholds of AUD 42,000 and AUD 67,000.

## Cost effectiveness analysis - Sensitivity analyses

Probabilistic sensitivity analyse (PSA) was performed to capture the uncertainty of the parameters used in the model and their effects on cost-effectiveness (32). PSA was performed using the Monte Carlo simulation method with 20,000 iterations. In PSA, the input parameters for costs, utilities and transition probabilities were defined as probability distributions to reflect the range of parameter uncertainty (Table 2). Since the cost data are not expected to be skewed, uniform distribution was used.

Net monetary benefit (NMB), which represents the difference between economic value of health benefits and the change in costs, was used to evaluate the sensitivity of the cost-effectiveness results. The equation is:

NMB can be calculated either as an absolute parameter for a single option (eg: intervention) without any comparison or as an incremental parameter as indicated below (33).

The average incremental NMB across 20,000 iterations was calculated for each pair of options compared (each allocation method versus current practice) in the analysis. A positive incremental NMB indicates a cost-effective decision and choosing anything else would incur an opportunity cost. The allocation option with the highest incremental NMB is the most cost-effective allocation strategy, compared to current practice, for Australia and choosing anything else would incur an opportunity cost. The probability of error in this decision was computed. The proportion of iterations in which an allocation method returns the highest NMB, compared to the current method, represents the probability that the particular option is the optimal decision. One minus this proportion (probability of error) indicates the probability that the allocation method does not yield the highest NMB compared to the current practice, thus the decision is incorrect(34).