In this study, a Markov model was implemented together with a probabilistic sensitivity analysis (PSA) to compare the costs of fish skin grafts with SOC for the treatment of DFUs. The Markov model is particularly well suited to simulate processes in which probabilities for future states depend, in some part, on the present state. The cost-effectiveness of clinical application in the present study was evaluated by following disease progression, QoL, and cost accumulation over time. The model divides a simulated patient cohort into 4 discrete health states, each of which is associated with a cost and a utility (ie, QoL) for a patient in that state. At regular intervals, or cycles, patients may transition from one health state to another, and the corresponding costs and utilities are calculated for the new distribution of health states.51 The model was constructed using MATLAB (MATLAB 2019a, The MathWorks, Inc.).
Data
The present analysis was based on data collected in both a physician practice and a hospital setting between January 1, 2014, and December 31, 2018. Part of the cohort used in this analysis was already published in a retrospective study in 2019 but with less stringent inclusion criteria.52 The local institutional review board, in collaboration with the American Health Network of Indianapolis, approved the collection and storage of non-identifying patient information used in this analysis in REDCap (Vanderbilt University).
The inclusion criteria captured 55 patients with diabetes over 18 years of age who had fish skin grafts applied to their full-thickness foot ulcerations (distal to the ankle malleoli; n = 59). The most common locations of the wounds were (in order from most to least common) the hallux, the plantar (mid)foot, sub-first metatarsal head, and the dorsal foot. The remaining locations included the heel, toes, lateral foot, metatarsophalangeal joints, and minor amputation sites.
The average size of the wounds was 3.7 cm2 (range, 0.05–26.4 cm2), and 48% of the wounds had a duration of more than 2 months at the beginning of treatment. Of the wounds included, 53% were Wagner grade 1, 37% were grade 2, and 10% were grade 3. Of the 59 wounds, 55 (93%) eventually healed after an average of 11.3 weeks (SD = 9.1 weeks); 3 patients underwent an amputation and 1 entered palliative care. The wounds received an average of 5.5 applications of fish skin. Average age of patients was 52 years (range, 45–88 years) and the male/female ratio was 1.8.
Patients were followed for 20 weeks after initial presentation, or until fully healed, amputation, or death. If a patient still had an active ulcer at 20 weeks, medical records were checked to determine whether that patient eventually healed, underwent an amputation, or died within 52 weeks after initial presentation. Wound healing was defined as complete wound epithelialization according to the treating physician. Patients were excluded if they had partial-thickness wounds, were not followed for 20 weeks after initial presentation, their status after 52 weeks was unknown, or if their fish skin graft treatment did not meet the recommended criteria set by the investigators. Those criteria included at least 5 applications of fish skin, or applications at least once every 4 weeks on average if the patient healed or underwent an amputation before the 20-week time point. Patients were instructed to offload with the Aircast boot and foam insert (Plastazote; Zotefoams) or surgical shoe and foam or custom insert. Total contact casting was not applied. Patients were not excluded if they missed appointments. Furthermore, infection, poor nutrition or circulation, and lack of adherence to offloading did not influence inclusion in the present study.
Time horizon
A time horizon of 52 weeks was chosen in order to include costs that were incurred beyond 20 weeks. Because the time horizon was so short, cost and utility were not discounted.
Cycle time
A cycle time of 1 week was chosen to reflect the recommended 1-week interval between fish skin graft applications, as described in the product instructions for use.
Health states and transition probabilities
The present Markov model was built using 4 health states: DFU, Healed, Amputated, and Death (Figure 2). All patients started with DFUs from the beginning of the first cycle (week 1). For each cycle of the model, new health-state distributions were generated. During the first cycle, a patient with a DFU remained in the same state (ie, with an active DFU), healed, underwent amputation, or died. Those who had remained in the same, or initial, state (DFU) faced the same risks in the subsequent cycles. Of those who had healed or received an amputation, the patients either remained in those states (ie, healed or amputated) or passed away. The Death state was immutable. Each state transition was determined by applying the transition probabilities shown in Table 1.53,55-57 For each cycle, the number of patients in each state was calculated as the sum of those who remained in the state and those who joined the state, subtracting those who left the state. As data for the rates of recurrence for the retrospective cohort were not available, and in order to simplify the model, recurrence (ie, Healed to DFU) was not included. Probabilities for transition between model states were based on literature or retrospective data on the cohort treated with fish skin (Table 1).53,55-57 Since the majority of published DFU studies reported healing at 20 weeks, and the vast majority of DFU-related amputations occur within the first 20 weeks, the present authors created separate transition probability matrices for both the SOC and fish skin cohorts for weeks 1 to 20 and weeks 21 to 52.53
The most appropriate approach when creating a multi-state model with competing risks is to convert the probabilities for events over time, such as annual probabilities, to the transition probabilities for a series of shorter time periods by performing an eigendecomposition on the original probability.54 Weekly rates of healing in the fish skin-treated cohort were calculated directly from the retrospective data on 55 fish skin-treated patients included in this analysis using the healing probabilities from weeks 1 to 20 and weeks 21 to 52 and then applied the equation pn= 1-(1-p)1/n, where pn was the adjusted weekly rate and p was the probability of healing at week n using the previously mentioned MATLAB program.51 The healing probability was higher during weeks 1 to 20 than weeks 21 to 52 by a factor of 3.6, reflecting the challenging nature of the remaining wounds. As a comparable retrospective SOC cohort was not available, the present authors used baseline data from the patient cohort treated with fish skin upon presentation to predict their probability of healing by week 20 if they had received SOC instead of fish skin treatment using an equation created by Margolis et al.55 This equation predicts the probability of healing at 20 weeks of SOC treatment based on the Wagner grade, size, and age of the wound at presentation, factors which were all known for the retrospective fish skin treated cohort.55 The healing probability for the SOC cohort for weeks 21 to 52 was extrapolated by adjusting the probability from weeks 1 to 20 with the same factor as the reduction of healing that was observed for fish skin treatment (ie, 3.6). The transition probability for amputation was obtained from a 2005 paper by Margolis et al,53 which reported a total of 6.72% amputations (n = 1653), where 96% of these amputations occurred during the first 4 months of care. To more accurately represent this amputation probability in the present model, the authors approximated that 96% of amputations occurred during weeks 1 to 20 and the remaining 4% during weeks 21 to 52. These probabilities were used to perform the eigendecomposition for both time frames, and the resulting weekly rates were applied to both cohorts. Mortality rates for the Healed state were derived from an Agency for Healthcare Research and Quality study that analyzed mortality among patients with a DFU or lower extremity amputation.56 These rates were converted to reflect the probability of mortality for weeks 1 to 20, and 21 to 52, prior to eigendecomposition. The same mortality rates were applied to both the SOC and fish skin cohorts (Table 1).53,55-57 The hazard ratio was calculated as the ratio of the weekly healing probabilities of the fish skin cohort to SOC cohort at weeks 1 to 20, and weeks 21 to 52.
Costs
The present authors sought to identify the likely costs associated with SOC clinical treatments for patients with DFUs, including extremity amputations. Given the paucity of financial data in the medical literature, a medical literature review was conducted in order to identify all papers that contained such data through a search of PubMed for articles published between January 2000 to June 2018. After a thorough review, it was decided to exclude papers whose financial data was particularly dated (ie, before 2000) and may not reflect current methods the US health care system accounts for spending on products and services associated with wound care. Additionally, any papers that did not identify the perspective of the financial data that were collected (eg, payer or provider) or the payment regimen under which it was collected (eg, commercial insurance, managed care, self-pay, Medicare) or were not broadly representative of the entire US population (ie, only commercial insurance, only managed care, or only Medicare, etc.) were excluded. Ultimately, focus was placed on a large study by Carls et al.58 Study data were derived from the Thomson Reuters MarketScan Research Database, 2005 to 2008.58 The database contained the fully adjudicated health insurance claims from 14 522 commercial enrollees and 17 127 Medicare enrollees with DFUs. The claims included inpatient medical, outpatient medical, and outpatient pharmacy costs. The weekly cost for patients with DFUs (without an amputation) was calculated to be $389.85 in July 2008. This figure was then updated for this analysis to the estimated weekly cost as of July 2019 using the US Bureau of Labor Statistics inflation calculator.57 The calculated weekly cost was $454.72 in 2019 dollars. From the same database, the total cost for patients with DFUs and amputations was assessed to be $65 427.65 when updated into 2019 dollars, which included surgical costs as well as postoperative care.58,59 The same costs of amputation were applied for both cohorts. The total cost of fish skin treatment was calculated as the cost for current SOC with the addition of the weekly cost of the fish skin application. The price for the treatment was based on the average sales price of the fish skin graft per square centimeter in 2019, which was $46.98. That average cost was calculated for the retrospective cohort by estimating and averaging the appropriate product size required for a full coverage of each wound with fish skin at presentation. Even though the average wound area would reduce over time as a result of healing, the average cost of fish skin was not reduced over time to reflect this. This was done to simplify the model. However, as a result, the treatment price will be overestimated over time. That cost of the graft was averaged for all patients and applied as a weekly cost, even though the frequency of treatments in the retrospective cohorts was only about once every 2.2 weeks. The estimated average weekly cost of fish skin was $252.40. As most of the other costs of wound care with fish skin would be the same as for SOC, the weekly cost of fish skin was simply added to the $454.72 weekly cost of SOC, giving a total weekly cost of $707.12 for fish skin treatment. For the model, the treatment costs for both cohorts were calculated by multiplying the proportion of the cohorts residing in each health state during each cycle by the weekly cost associated with that health state and summed over 52 weeks to obtain the total cost for the time horizon. The total cost of amputation was applied at the time of amputation. No costs were incurred for those in the Death state.
Quality-adjusted life-years
The QALYs for both cohorts were calculated for each cycle using utility variables obtained from the literature and the health-state distributions (Table 2).60,61 The decrement of utility values for active ulcers and amputations were subtracted from the utility value of type 2 diabetes without complications in order to obtain utilities for the states DFU and Amputated.
Probabilistic sensitivity analysis
Since calculating an output from the present Markov model from predetermined input variables would give a deterministic result, the present authors sought to examine what would happen to the model if those input variables fluctuated, thereby reflecting their natural uncertainty. Thus, a PSA using a Monte Carlo simulation was performed to incorporate that input-variable uncertainty. The model inputs were varied, and the simulation iteratively outputted new calculations. A total of 10 000 iterations were performed.
During random sampling, a seed was set for reproducibility purposes, which created a dummy dataset that allowed a comparison of fish skin graft application with SOC in terms of incremental cost (accumulated cost of fish skin graft therapy—accumulated cost of SOC) and incremental effectiveness (accumulated utility fish skin graft therapy—accumulated utility of SOC). During each iteration of the PSA, model values were drawn randomly based on the following parameter distributions: cost was assumed to have a gamma distribution because cost parameters are positive and skewed; utility variables were given a beta distribution because beta distributions take values from 0 to 1; and hazard ratios were given normal distributions.62
For sensitivity analysis, the present authors sought to include standard deviation values for costs. While standard deviation values for costs can be obtained from the retrospective data, this information was not available for SOC and amputations in the referenced work by Carls et al.58 However, great variability in cost was observed between different sources and publications for treatment of DFUs as well as for minor versus major limb amputations.57,63-66 To assess model robustness and account for such uncertainties, all costs were varied by 50% for sensitivity analysis, standard error (SE) for beta distribution of utility values was estimated from confidence intervals reported in the literature (Table 2), and SE of hazard ratio values was estimated from healing probabilities of the retrospective data and SOC cohorts using the equation (SE)= √(1/E1+1/E2), where E1 and E2 are the proportions healed within each cohort.60,61