A clinically based discrete-event simulation of end-stage liver disease and the organ allocation process

The Spillover Effects of Extending Liver Transplantation to Patients with Colorectal Liver Metastases: A Discrete Event Simulation Analysis

BACKGROUND

Liver transplantation is an alternative treatment for patients with nonresectable colorectal cancer liver-only metastases (CRLM); however, the potential effects on wait-list time and life expectancy to other patients on the transplant waiting list have not been considered. We explored the potential effects of expanding liver transplantation eligibility to include patients with CRLM on wait-list time and life expectancy in Norway.

METHODS

We developed a discrete event simulation model to reflect the Norwegian liver transplantation waiting list process and included 2 groups: 1) patients currently eligible for liver transplantation and 2) CRLM patients. Under 2 alternative CRLM-patient transplant eligibility criteria, we simulated 2 strategies: 1) inclusion of only currently eligible patients (CRLM patients received standard-of-care palliative chemotherapy) and 2) expanding waiting list eligibility to include CRLM patients under 2 eligibility criteria. Model outcomes included median waiting list time, life expectancy, and total life-years.

RESULTS

For every additional CRLM patient listed per year, the overall median wait-list time, initially 52 d, increased by 8% to 11%. Adding 2 additional CRLM patients under the most restrictive eligibility criteria increased the CRLM patients' average life expectancy by 10.64 y and decreased the average life expectancy for currently eligible patients by 0.05 y. Under these assumptions, there was a net gain of 149.61 life-years over a 10-y programmatic period, which continued to increase under scenarios of adding 10 CRLM patients to the wait-list. Health gains were lower under less restrictive CRLM eligibility criteria. For example, adding 4 additional CRLM patients under the less restrictive eligibility criteria increased the CRLM patients' average life expectancy by 5.64 y and decreased the average life expectancy for currently eligible patients by 0.12 y. Under these assumptions, there was a net gain of 96.36 life-years over a 10-y programmatic period, which continued to increase up to 7 CRLM patients.

CONCLUSIONS

Our model-based analysis enabled the consideration of the potential effects of enlisting Norwegian CRLM patients for liver transplantation on wait-list time and life expectancy. Enlisting CRLM patients is expected to increase the total health effects, which supports the implementation of liver transplantation for CRLM patients in Norway.

HIGHLIGHTS

Given the Norwegian donor liver availability, adding patients with nonresectable colorectal cancer liver-only metastases (CRLM) to the liver transplantation waiting list had an overall modest, but varying, impact on total waiting list time.Survival gains for selected CRLM patients treated with liver transplantation would likely outweigh the losses incurred to patients listed currently.To improve the total life-years gained in the population, Norway should consider expanding the treatment options for CRLM patients to include liver transplantation.Other countries may also have an opportunity to gain total life-years by extending the waiting list eligibility criteria; however, country-specific analyses are required.

Impact of Allocation on Survival During Intermittent Chemotherapy Shortages: A Modeling Analysis

BACKGROUND

Intermittent shortages of chemotherapeutics used to treat curable malignancies are a worldwide problem that increases patient mortality. Although multiple strategies have been proposed for managing these shortages (eg, prioritizing patients by age, scarce treatment efficacy per volume, alternative treatment efficacy difference), critical clinical dilemmas arise when selecting a management strategy and understanding its impact.

PATIENTS AND METHODS

We developed a model to compare the impact of different allocation strategies on overall survival during intermittent chemotherapy shortages and tested it using vincristine, which was recently scarce for 9 months in the United States. Demographic and treatment data were abstracted from 1,689 previously treated patients in our tertiary-care system; alternatives were abstracted from NCCN Clinical Practice Guidelines in Oncology for each disease and survival probabilities from the studies cited therein. Modeled survival was validated using SEER data. Nine-month shortages were modeled for all possible supply levels. Pairwise differences in 3-year survival and risk reductions were calculated for each strategy compared with standard practice (first-come, first-served) for each 50-mg supply increment, as were supply thresholds above which each strategy maintained survival similar to scenarios without shortages.

RESULTS

A strategy prioritizing by higher vincristine efficacy per volume and greater alternative treatment efficacy difference performed best, improving survival significantly (P<.01) across 86.5% of possible shortages (relative risk reduction, 8.3%; 99% CI, 8.0-8.5) compared with standard practice. This strategy also maintained survival rates similar to a model without shortages until supply fell below 72.2% of the amount required to treat all patients, compared with 94.3% for standard practice.

CONCLUSIONS

During modeled vincristine shortages, prioritizing patients by higher efficacy per volume and alternative treatment efficacy difference significantly improved survival over standard practice. This approach can help optimize allocation as intermittent chemotherapy shortages continue to arise.

Model to Calculate Harms and Benefits of Early vs Delayed Liver Transplantation for Patients With Alcohol-Associated Hepatitis

BACKGROUND & AIMS

Early liver transplantation (without requiring a minimum period of sobriety) for severe alcohol-associated hepatitis (AH) is controversial: many centers delay eligibility until a specific period of sobriety (such as 6 months) has been achieved. To inform ongoing debate and policy, we modeled long-term outcomes of early vs delayed liver transplantation for patients with AH.

METHODS

We developed a mathematical model to simulate early vs delayed liver transplantation for patients with severe AH and different amounts of alcohol use after transplantation: abstinence, slip (alcohol use followed by sobriety), or sustained use. Mortality of patients before transplantation was determined by joint-effect model (based on Model for End-Stage Liver Disease [MELD] and Lille scores). We estimated life expectancies of patients receiving early vs delayed transplantation (6-month wait before placement on the waitlist) and life years lost attributable to alcohol use after receiving the liver transplant.

RESULTS

Patients offered early liver transplantation were estimated to have an average life expectancy of 6.55 life years, compared with an average life expectancy of 1.46 life years for patients offered delayed liver transplantation (4.49-fold increase). The net increase in life expectancy from offering early transplantation was highest for patients with Lille scores of 0.50-0.82 and MELD scores of 32 or more. Patients who were offered early transplantation and had no alcohol use afterward were predicted to survive 10.85 years compared with 3.62 years for patients with sustained alcohol use after transplantation (7.23 life years lost). Compared with delayed transplantation, early liver transplantation increased survival times in all simulated scenarios and combinations of Lille and MELD scores.

CONCLUSIONS

In a modeling study of assumed carefully selected patients with AH, early vs delayed liver transplantation (6 months of abstinence from alcohol before transplantation) increased survival times of patients, regardless of estimated risk of sustained alcohol use after transplantation. These findings support early liver transplantation for patients with severe AH. The net increase in life expectancy was maintained in all simulated extreme scenarios but should be confirmed in prospective studies. Sustained alcohol use after transplantation significantly reduced but did not eliminate the benefits of early transplantation. Strategies are needed to prevent and treat posttransplantation use of alcohol.

Decision modelling for economic evaluation of liver transplantation

As the gap between a shortage of organs and the immense demand for liver grafts persists, every available donor liver needs to be optimized for utility, urgency and equity. To overcome this challenge, decision modelling might allow us to gather evidence from previous studies as well as compare the costs and consequences of alternative options. For public health policy and clinical intervention assessment, it is a potentially powerful tool. The most commonly used types of decision analytical models include decision trees, the Markov model, microsimulation, discrete event simulation and the system dynamic model. Analytic models could support decision makers in the field of liver transplantation when facing specific problems by synthesizing evidence, comprising all relevant options, generalizing results to other contexts, extending the time horizon and exploring the uncertainty. For modeling studies of economic evaluation for transplantation, understanding the current nature of the disease is crucial, as well as the selection of appropriate modelling techniques. The quality and availability of data is another key element for the selection and development of decision analytical models. In addition, good practice guidelines should be complied, which is important for standardization and comparability between economic outputs.

Simulating the Outcome of Heart Allocation Policies Using Deep Neural Networks

We created a system to simulate the heart allocation process in a transplant queue, using a discrete event model and a neural network algorithm, which we named the Lund Deep Learning Transplant Algorithm (LuDeLTA). LuDeLTA is utilized to predict the survival of the patients both in the queue and after transplant. We tried four different allocation policies: wait time, clinical rules and allocating the patients using either LuDeLTA or The International Heart Transplant Survival Algorithm (IHTSA) model. Both IHTSA and LuDeLTA were used to evaluate the results. The predicted mean survival for allocating according to wait time was about 4,300 days, clinical rules 4,300 days and using neural networks 4,700 days.

Simulation model of the relationship between cesarean section rates and labor duration

Cesarean delivery is the most common major abdominal surgery in many parts of the world, and it accounts for nearly one-third of births in the United States. For a patient who requires a C-section, allowing prolonged labor is not recommended because of the increased risk of infection. However, for a patient who is capable of a successful vaginal delivery, performing an unnecessary C-section can have a substantial adverse impact on the patient's future health. We develop two stochastic simulation models of the delivery process for women in labor; and our objectives are (i) to represent the natural progression of labor and thereby gain insights concerning the duration of labor as it depends on the dilation state for induced, augmented, and spontaneous labors; and (ii) to evaluate the Friedman curve and other labor-progression rules, including their impact on the C-section rate and on the rates of maternal and fetal complications. To use a shifted lognormal distribution for modeling the duration of labor in each dilation state and for each type of labor, we formulate a percentile-matching procedure that requires three estimated quantiles of each distribution as reported in the literature. Based on results generated by both simulation models, we concluded that for singleton births by nulliparous women with no prior complications, labor duration longer than two hours (i.e., the time limit for labor arrest based on the Friedman curve) should be allowed in each dilation state; furthermore, the allowed labor duration should be a function of dilation state.

Transplanting hepatitis C virus-positive livers into hepatitis C virus-negative patients with preemptive antiviral treatment: A modeling study

Under current guidelines, hepatitis C virus (HCV)-positive livers are not transplanted into HCV-negative recipients because of adverse posttransplant outcomes associated with allograft HCV infection. However, HCV can now be cured post-LT (liver transplant) using direct-acting antivirals (DAAs) with >90% success; therefore, HCV-negative patients on the LT waiting list may benefit from accepting HCV-positive organs with preemptive treatment. Our objective was to evaluate whether and in which HCV-negative patients the potential benefit of accepting an HCV-positive (i.e., viremic) organ outweighed the risks associated with HCV allograft infection. We developed a Markov-based mathematical model that simulated a virtual trial of HCV-negative patients on the LT waiting list to compare long-term outcomes in patients: (1) willing to accept any (HCV-negative or HCV-positive) liver versus (2) those willing to accept only HCV-negative livers. Patients receiving HCV-positive livers were treated preemptively with 12 weeks of DAA therapy and had a higher risk of graft failure than those receiving HCV-negative livers. The model incorporated data from published studies and the United Network for Organ Sharing (UNOS). We found that accepting any liver regardless of HCV status versus accepting only HCV-negative livers resulted in an increase in life expectancy when Model for End-Stage Liver Disease (MELD) was ≥20, and the benefit was highest at MELD 28 (0.172 additional life-years). The magnitude of clinical benefit was greater in UNOS regions with higher HCV-positive donor organ rates, that is, Regions 1, 2, 3, 10, and 11. Sensitivity analysis demonstrated that model outcomes were robust.

CONCLUSION

Transplanting HCV-positive livers into HCV-negative patients with preemptive DAA therapy could improve patient survival on the LT waiting list. Our analysis can help inform clinical trials and minimize patient harm. (Hepatology 2018;67:2085-2095).

Using time-varying models to estimate post-transplant survival in pediatric liver transplant recipients

PURPOSE

To distinguish clinical factors that have time-varying (as opposed to constant) impact upon patient and graft survival among pediatric liver transplant recipients.

METHODS

Using national data from 2002 through 2013, we examined potential clinical and demographic covariates using Gray's piecewise constant time-varying coefficients (TVC) models. For both patient and graft survival, we estimated univariable and multivariable Gray's TVC, retaining significant covariates based on backward selection. We then estimated the same specification using traditional Cox proportional hazards (PH) models and compared our findings.

RESULTS

For patient survival, covariates included recipient diagnosis, age, race/ethnicity, ventilator support, encephalopathy, creatinine levels, use of living donor, and donor age. Only the effects of recipient diagnosis and donor age were constant; effects of other covariates varied over time. We retained identical covariates in the graft survival model but found several differences in their impact.

CONCLUSION

The flexibility afforded by Gray's TVC estimation methods identify several covariates that do not satisfy constant proportionality assumptions of the Cox PH model. Incorporating better survival estimates is critical for improving risk prediction tools used by the transplant community to inform organ allocation decisions.

A systematic literature review of operational research methods for modelling patient flow and outcomes within community healthcare and other settings

An ambition of healthcare policy has been to move more acute services into community settings. This systematic literature review presents analysis of published operational research methods for modelling patient flow within community healthcare, and for modelling the combination of patient flow and outcomes in all settings. Assessed for inclusion at three levels - with the references from included papers also assessed - 25 "Patient flow within community care", 23 "Patient flow and outcomes" papers and 5 papers within the intersection are included for review. Comparisons are made between each paper's setting, definition of states, factors considered to influence flow, output measures and implementation of results. Common complexities and characteristics of community service models are discussed with directions for future work suggested. We found that in developing patient flow models for community services that use outcomes, transplant waiting list may have transferable benefits.

Cost Effectiveness of Pre- vs Post-Liver Transplant Hepatitis C Treatment With Direct-Acting Antivirals

BACKGROUND & AIMS

Oral direct-acting antivirals (DAAs) for hepatitis C virus (HCV) treatment offer new hope to both pre- and post-liver transplant (LT) patients. However, whether to treat HCV patients before vs after LT is not clear because treatment can improve liver function but could reduce the chance of receiving an LT while on the waiting list. Our objective was to evaluate the cost effectiveness of pre-LT vs post-LT HCV treatment with oral DAAs in decompensated cirrhotic patients on the LT waiting list.

METHODS

We used a validated mathematical model that simulated a virtual trial comparing long-term clinical and cost outcomes of pre-LT vs post-LT HCV treatment with oral DAAs. Model parameters were estimated from United Network for Organ Sharing data, SOLAR-1 and 2 trials, and published studies. For each strategy, we estimated the quality-adjusted life-year, life expectancy, cost, and the incremental cost-effectiveness ratio.

RESULTS

For lower MELD scores, quality-adjusted life-years were higher with pre-LT HCV treatment compared with post-LT treatment. Pre-LT HCV treatment was cost saving in patients with MELD scores of 15 or less, and cost effective in patients with MELD scores of 16 to 21. In contrast, post-LT HCV treatment was cost effective in patients with MELD scores of 22 to 29 and cost saving if MELD scores were 30 or higher. Results varied by drug prices and by United Network for Organ Sharing regions.

CONCLUSIONS

For cirrhotic patients awaiting LT, pre-LT HCV treatment with DAAs is cost effective/saving in patients with MELD scores of 21 or lower, whereas post-LT HCV treatment is cost effective/saving in patients with MELD scores of 22 or higher.

Dynamic transmission models for economic analysis applied to health care-associated infections: A review of the literature

BACKGROUND

Cost-effectiveness analyses are an important methodology in assessing whether a health care technology is suitable for widespread adoption. Common models used by economists, such as decision trees and Markov models, are appropriate for noninfectious diseases where treatment and exposure are independent. Diseases whose treatment and exposure are dependent require dynamic models to incorporate the nonlinear transmission effect. Two different types of models are often used for dynamic cost-effectiveness analyses: compartmental models and individual models. In this methodology-focused literature review, we describe each model type and summarize the literature associated with each using the example of health care-associated infections (HAIs).

METHODS

We conducted a review of the literature to identify dynamic cost-effectiveness analyses that examined interventions to prevent or treat HAIs. To be included in the review, studies needed to have each of 3 necessary components: involve economics, such as cost-effectiveness analysis and evidence of economic theory, use a dynamic transmission model, and examine HAIs.

RESULTS

Of the 9 articles published between 2005 and 2016 that met criteria to be included in our study, 3 used compartmental models and 6 used individual models.

CONCLUSIONS

Very few published studies exist that use dynamic transmission models to conduct economic analyses related to HAIs and even fewer studies have used these models to perform cost-effectiveness analyses.

Using decision modeling to guide drug allocation during a shortage

BACKGROUND

Drug shortages require clinical teams to decide how to allocate drugs in limited supply among their patients. Ethical frameworks are invaluable for promoting rational approaches to drug distribution, but gaps remain between ethical theory and clinical application. The goal of this work was to explore how decision modeling could supplement ethical frameworks to inform drug distribution from the perspective of a clinical team.

PROCEDURE

We created a hypothetical pediatric oncology clinic with a limited supply of 50,000 mg of methotrexate (MTX) and 21 patients due for treatment on one of six regimens. We constructed a simple decision analytic model to compare the effectiveness of MTX in milligrams per life year saved for each regimen. The robustness of the model was tested under various conditions including alternative drug effectiveness and time horizons. Effects on outcomes and distribution by substituting alternative dosing were explored for each regimen.

RESULTS

Prescribed therapy for this group of patients required 108,791 mg MTX. Two regimens for three patients required ≥20,000 mg/m² . If distributed in order of arrival, only seven patients could receive full treatment. If distributed in order of efficiency, 19 patients could receive treatment. If less effective regimens were substituted, 20 patients could receive treatment. The primary driver of efficiency was dose per square meter.

CONCLUSIONS

In this hypothetical drug shortage, no allocation scenario exists that does not result in a worse outcome for some patients. Evidence of drug efficacy affected the decisions to substitute alternative treatments. First-come-first-served allocation resulted in fewer patients receiving treatment than allocation based on efficiency.

Efficient and Fair Heart Allocation Policies for Transplantation

Background: The optimal allocation of limited donated hearts to patients on the waiting list is one of the top priorities in heart transplantation management. We developed a simulation model of the US waiting list for heart transplantation to investigate the potential impacts of allocation policies on several outcomes such as pre- and posttransplant mortality. Methods: We used data from the United Network for Organ Sharing (UNOS) and the Scientific Registry of Transplant Recipient (SRTR) to simulate the heart allocation system. The model is validated by comparing the outcomes of the simulation with historical data. We also adapted fairness schemes studied in welfare economics to provide a framework to assess the fairness of allocation policies for transplantation. We considered three allocation policies, each a modification to the current UNOS allocation policy, and analyzed their performance via simulation. The first policy broadens the geographical allocation zones, the second modifies the health status order for receiving hearts, and the third prioritizes patients according to their waiting time. Results: Our results showed that the allocation policy similar to the current UNOS practice except that it aggregates the three immediate geographical allocation zones, improves the health outcomes, and is “closer” to an optimal fair policy compared to all other policies considered in this study. Specifically, this policy could have saved 319 total deaths (out of 3738 deaths) during the 2006 to 2014 time horizon, in average. This policy slightly differs from the current UNOS allocation policy and allows for easy implementation. Conclusion: We developed a model to compare the outcomes of heart allocation policies. Combining the three immediate geographical zones in the current allocation algorithm could potentially reduce mortality rate and is closer to an optimal fair policy.

Optimal timing of hepatitis C treatment for patients on the liver transplant waiting list

The availability of oral direct-acting antivirals has altered the hepatitis C virus (HCV) treatment paradigm for both pre-liver transplant (LT) and post-LT patients. There is a perceived trade-off between pre-LT versus post-LT treatment of HCV-treatment may improve liver function but potentially decrease the likelihood of a necessary LT. Our objective was to identify LT-eligible patients with decompensated cirrhosis who would benefit (and not benefit) from pre-LT treatment based on their Model for End-Stage Liver Disease (MELD) scores. We simulated a virtual trial comparing long-term outcomes of pre-LT versus post-LT HCV treatment with oral direct-acting antivirals for patients with MELD scores between 10 and 40. We developed a Markov-based microsimulation model, which simulated the life course of patients on the transplant waiting list and after LT. Simulation of LT integrated data from recent trials of oral direct-acting antivirals (SOLAR 1 and 2), the United Network for Organ Sharing (UNOS), and other studies. The outcomes of the model included life expectancy, 1-year and 5-year patient survival, and mortality. Model-predicted patient survival was validated with UNOS data. We found that, at the national level, treating HCV before LT increased life expectancy if MELD was ≤27 but could decrease life expectancy at higher MELD scores. Depending on the UNOS region, the threshold MELD score to treat HCV pre-LT varied between 23 and 27 and was lower for UNOS regions 3, 10, and 11 and higher for regions 1, 2, 4, 5, 8, and 9. Sensitivity analysis showed that the thresholds were stable.

CONCLUSION

Our findings suggest that the optimal MELD threshold below which decompensated cirrhosis patients should receive HCV treatment while awaiting LT is between 23 and 27, depending on the UNOS region. (Hepatology 2017;65:777-788).

A Simulation Model to Estimate the Cost and Effectiveness of Alternative Dialysis Initiation Strategies

Background. Patients with end-stage renal disease (ESRD) require dialysis to maintain survival. The optimal timing of dialysis initiation in terms of cost-effectiveness has not been established.

Methods . We developed a simulation model of individuals progressing towards ESRD and requiring dialysis. It can be used to analyze dialysis strategies and scenarios. It was embedded in an optimization frame worked to derive improved strategies.

Results. Actual (historical) and simulated survival curves and hospitalization rates were virtually indistinguishable. The model overestimated transplantation costs (10%) but it was related to confounding by Medicare coverage. To assess the model's robustness, we examined several dialysis strategies while input parameters were perturbed. Under all 38 scenarios, relative rankings remained unchanged. An improved policy for a hypothetical patient was derived using an optimization algorithm.

Conclusion. The model produces reliable results and is robust. It enables the cost-effetiveness analysis of dialysis strategies.

Gerrymandering for Justice: Redistricting U.S. Liver Allocation

U.S. organ allocation policy sequesters livers from deceased donors within arbitrary geographic boundaries, frustrating the intent of those who wish to offer the livers to transplant candidates based on medical urgency. We used a zero-one integer program to partition 58 donor service areas into between four and eight sharing districts that minimize the disparity in liver availability among districts. Because the integer program necessarily suppressed clinically significant differences among patients and organs, we tested the optimized district maps with a discrete-event simulation tool that represents liver allocation at a per-person, per-organ level of detail. In April 2014, the liver committee of the Organ Procurement and Transplantation Network (OPTN) decided in a unanimous vote of 22-0-0 to write a policy proposal based on our eight-district and four-district maps. The OPTN board of directors could implement the policy after the proposal and public-comment period.Redistricting liver allocation would save hundreds of lives over the next five years and would attenuate the serious geographic inequity in liver transplant offers.

Predicting Liver Transplant Capacity Using Discrete Event Simulation

The number of liver transplants (LTs) performed in the US increased until 2006 but has since declined despite an ongoing increase in demand. This decline may be due in part to decreased donor liver quality and increasing discard of poor-quality livers. We constructed a discrete event simulation (DES) model informed by current donor characteristics to predict future LT trends through the year 2030. The data source for our model is the United Network for Organ Sharing database, which contains patient-level information on all organ transplants performed in the US. Previous analysis showed that liver discard is increasing and that discarded organs are more often from donors who are older, are obese, have diabetes, and donated after cardiac death. Given that the prevalence of these factors is increasing, the DES model quantifies the reduction in the number of LTs performed through 2030. In addition, the model estimatesthe total number of future donors needed to maintain the current volume of LTs and the effect of a hypothetical scenario of improved reperfusion technology.We also forecast the number of patients on the waiting list and compare this with the estimated number of LTs to illustrate the impact that decreased LTs will have on patients needing transplants. By altering assumptions about the future donor pool, this model can be used to develop policy interventions to prevent a further decline in this lifesaving therapy. To our knowledge, there are no similar predictive models of future LT use based on epidemiological trends.

Declining liver graft quality threatens the future of liver transplantation in the United States

National liver transplantation (LT) volume has declined since 2006, in part because of worsening donor organ quality. Trends that degrade organ quality are expected to continue over the next 2 decades. We used the United Network for Organ Sharing (UNOS) database to inform a 20-year discrete event simulation estimating LT volume from 2010 to 2030. Data to inform the model were obtained from deceased organ donors between 2000 and 2009. If donor liver utilization practices remain constant, utilization will fall from 78% to 44% by 2030, resulting in 2230 fewer LTs. If transplant centers increase their risk tolerance for marginal grafts, utilization would decrease to 48%. The institution of "opt-out" organ donation policies to increase the donor pool would still result in 1380 to 1866 fewer transplants. Ex vivo perfusion techniques that increase the use of marginal donor livers may stabilize LT volume. Otherwise, the number of LTs in the United States will decrease substantially over the next 15 years. In conclusion, the transplant community will need to accept inferior grafts and potentially worse posttransplant outcomes and/or develop new strategies for increasing organ donation and utilization in order to maintain the number of LTs at the current level.

Comparison of listing strategies for allosensitized heart transplant candidates requiring transplant at high urgency: a decision model analysis

Allosensitized children who require a negative prospective crossmatch have a high risk of death awaiting heart transplantation. Accepting the first suitable organ offer, regardless of the possibility of a positive crossmatch, would improve waitlist outcomes but it is unclear whether it would result in improved survival at all times after listing, including posttransplant. We created a Markov decision model to compare survival after listing with a requirement for a negative prospective donor cell crossmatch (WAIT) versus acceptance of the first suitable offer (TAKE). Model parameters were derived from registry data on status 1A (highest urgency) pediatric heart transplant listings. We assumed no possibility of a positive crossmatch in the WAIT strategy and a base-case probability of a positive crossmatch in the TAKE strategy of 47%, as estimated from cohort data. Under base-case assumptions, TAKE showed an incremental survival benefit of 1.4 years over WAIT. In multiple sensitivity analyses, including variation of the probability of a positive crossmatch from 10% to 100%, TAKE was consistently favored. While model input data were less well suited to comparing survival when awaiting transplantation across a negative virtual crossmatch, our analysis suggests that taking the first suitable organ offer under these circumstances is also favored.

D-MELD risk capping improves post-transplant and overall mortality under markov microsimulation

AIM: To hypothesize that the product of calculated Model for End-Stage Liver Disease score excluding exception points and donor age (D-MELD) risk capping ± Rule 14 could improve post liver transplant and overall survival after listing.

METHODS: Probabilities derived from the United Network for Organ Sharing database between 2002 and 2004 were used to simulate potential outcomes for all patients listed for transplantation. The Markov simulation was then modified by screening matches using a 1200 or 1600 D-MELD risk cap ± allowing transplants for Model for End-Stage Liver Disease (MELD) ≤ 14 (Rule 14). The differential impact of the rule changes was assessed.

RESULTS: The Markov simulation accurately reproduced overall and post transplant survival. A 1200 D-MELD risk cap improved post-transplant survival. Both the 1200 and 1600 risk caps improved overall survival for waitlisted patients. The addition of Rule 14 further improved post transplant and overall survival by redistribution of donor livers to recipients in higher MELD subgroups. The mechanism for improved overall and post-transplant survival after listing was due to shifting a larger percentage of transplants to the moderate MELD score subgroup (MELD 15-29) while also ensuring that high MELD recipients have livers of high quality to achieve excellent post transplant survival.

CONCLUSION: A 1200 D-MELD risk cap + Rule 14 provided the greatest overall benefit primarily by focusing liver transplantation towards the moderate MELD recipient.

Accept/decline decision module for the liver simulated allocation model

Simulated allocation models (SAMs) are used to evaluate organ allocation policies. An important component of SAMs is a module that decides whether each potential recipient will accept an offered organ. The objective of this study was to develop and test accept-or-decline classifiers based on several machine-learning methods in an effort to improve the SAM for liver allocation. Feature selection and imbalance correction methods were tested and best approaches identified for application to organ transplant data. Then, we used 2011 liver match-run data to compare classifiers based on logistic regression, support vector machines, boosting, classification and regression trees, and Random Forests. Finally, because the accept-or-decline module will be embedded in a simulation model, we also developed an evaluation tool for comparing performance of predictors, which we call sample-path accuracy. The Random Forest method resulted in the smallest overall error rate, and boosting techniques had greater accuracy when both sensitivity and specificity were simultaneously considered important. Our comparisons show that no method dominates all others on all performance measures of interest. A logistic regression-based classifier is easy to implement and allows for pinpointing the contribution of each feature toward the probability of acceptance. Other methods we tested did not have a similar interpretation. The Scientific Registry of Transplant Recipients decided to use the logistic regression-based accept-decline decision module in the next generation of liver SAM.

An agent-based simulation model to study accountable care organizations

Creating accountable care organizations (ACOs) has been widely discussed as a strategy to control rapidly rising healthcare costs and improve quality of care; however, building an effective ACO is a complex process involving multiple stakeholders (payers, providers, patients) with their own interests. Also, implementation of an ACO is costly in terms of time and money. Immature design could cause safety hazards. Therefore, there is a need for analytical model-based decision-support tools that can predict the outcomes of different strategies to facilitate ACO design and implementation. In this study, an agent-based simulation model was developed to study ACOs that considers payers, healthcare providers, and patients as agents under the shared saving payment model of care for congestive heart failure (CHF), one of the most expensive causes of sometimes preventable hospitalizations. The agent-based simulation model has identified the critical determinants for the payment model design that can motivate provider behavior changes to achieve maximum financial and quality outcomes of an ACO. The results show nonlinear provider behavior change patterns corresponding to changes in payment model designs. The outcomes vary by providers with different quality or financial priorities, and are most sensitive to the cost-effectiveness of CHF interventions that an ACO implements. This study demonstrates an increasingly important method to construct a healthcare system analytics model that can help inform health policy and healthcare management decisions. The study also points out that the likely success of an ACO is interdependent with payment model design, provider characteristics, and cost and effectiveness of healthcare interventions.

Redesigning Organ Allocation Boundaries for Liver Transplantation in the United States

Geographic disparities in access to and outcomes in transplantation have been a persistent problem widely discussed by transplant researchers and the transplant community. One of the alleged causes of disparities in the United States is administratively determined organ allocation boundaries that limit organ sharing across regions. This paper applies mathematical programming to construct alternative liver allocation boundaries that achieve more geographic equity in access to transplants than the current system. The performance of the optimal boundaries were evaluated and compared to that of current allocation system using discrete event simulation.

Applying Discrete Event Simulation (DES) in Healthcare

This paper highlights the opportunities and challenges of applying Discrete Event Simulation (DES) to support capacity planning of a network of outpatient facilities. Despite an abundance of studies using simulation techniques to examine the operation and performance of outpatient clinics, the problem of capacity allocation and planning of medical services within a network of outpatient healthcare facilities appears to be underexplored. Here, a case study of a health insurance provider that operates a network of six outpatient medical facilities in the US is used to illustrate and explore the synthesizing and adaptive, yet parsimonious nature of using DES methodology for network design and capacity planning. Results of this case study demonstrate that significant performance improvements for the network operator can be achieved with applying DES method to support the network facility capacity planning process.

Center-level utilization of kidney paired donation

With many multicenter consortia and a United Network for Organ Sharing program, participation in kidney paired donation (KPD) has become mainstream in the United States and should be feasible for any center that performs live donor kidney transplantation (LDKT). Lack of participation in KPD may significantly disadvantage patients with incompatible donors. To explore utilization of this modality, we analyzed adjusted center-specific KPD rates based on casemix of adult LDKT-eligible patients at 207 centers between 2006 and 2011 using SRTR data. From 2006 to 2008, KPD transplants became more evenly distributed across centers, but from 2008 to 2011 the distribution remained unchanged (Gini coefficient = 0.91 for 2006, 0.76 for 2008 and 0.77 for 2011), showing an unfortunate stall in dissemination. At the 10% of centers with the highest KPD rates, 9.9-38.5% of LDKTs occurred through KPD during 2009-2011; if all centers adopted KPD at rates observed in the very high-KPD centers, the number of KPD transplants per year would increase by a factor of 3.2 (from 494 to 1593). Broader implementation of KPD across a wide number of centers is crucial to properly serve transplant candidates with healthy but incompatible live donors.

Conceptualizing a model: a report of the ISPOR-SMDM Modeling Good Research Practices Task Force-2

The appropriate development of a model begins with understanding the problem that is being represented. The aim of this article is to provide a series of consensus-based best practices regarding the process of model conceptualization. For the purpose of this series of papers, the authors consider the development of models whose purpose is to inform medical decisions and health-related resource allocation questions. They specifically divide the conceptualization process into two distinct components: the conceptualization of the problem, which converts knowledge of the health care process or decision into a representation of the problem, followed by the conceptualization of the model itself, which matches the attributes and characteristics of a particular modeling type to the needs of the problem being represented. Recommendations are made regarding the structure of the modeling team, agreement on the statement of the problem, the structure, perspective and target population of the model, and the interventions and outcomes represented. Best practices relating to the specific characteristics of model structure, and which characteristics of the problem might be most easily represented in a specific modeling method, are presented. Each section contains a number of recommendations that were iterated among the authors, as well as the wider modeling taskforce, jointly set up by the International Society for Pharmacoeconomics and Outcomes Research and the Society for Medical Decision Making.

Conceptualizing a model: a report of the ISPOR-SMDM Modeling Good Research Practices Task Force--2

The appropriate development of a model begins with understanding the problem that is being represented. The aim of this article was to provide a series of consensus-based best practices regarding the process of model conceptualization. For the purpose of this series of articles, we consider the development of models whose purpose is to inform medical decisions and health-related resource allocation questions. We specifically divide the conceptualization process into two distinct components: the conceptualization of the problem, which converts knowledge of the health care process or decision into a representation of the problem, followed by the conceptualization of the model itself, which matches the attributes and characteristics of a particular modeling type with the needs of the problem being represented. Recommendations are made regarding the structure of the modeling team, agreement on the statement of the problem, the structure, perspective, and target population of the model, and the interventions and outcomes represented. Best practices relating to the specific characteristics of model structure and which characteristics of the problem might be most easily represented in a specific modeling method are presented. Each section contains a number of recommendations that were iterated among the authors, as well as among the wider modeling taskforce, jointly set up by the International Society for Pharmacoeconomics and Outcomes Research and the Society for Medical Decision Making.

Comparative effectiveness of donation after cardiac death versus donation after brain death liver transplantation: Recognizing who can benefit

Due to organ scarcity and wait-list mortality, transplantation of donation after cardiac death (DCD) livers has increased. However, the group of patients benefiting from DCD liver transplantation is unknown. We studied the comparative effectiveness of DCD versus donation after brain death (DBD) liver transplantation. A Markov model was constructed to compare undergoing DCD transplantation with remaining on the wait-list until death or DBD liver transplantation. Differences in life years, quality-adjusted life years (QALYs), and costs according to candidate Model for End-Stage Liver Disease (MELD) score were considered. A separate model for hepatocellular carcinoma (HCC) patients with and without MELD exception points was constructed. For patients with a MELD score <15, DCD transplantation resulted in greater costs and reduced effectiveness. Patients with a MELD score of 15 to 20 experienced an improvement in effectiveness (0.07 QALYs) with DCD liver transplantation, but the incremental cost-effectiveness ratio (ICER) was >$2,000,000/QALY. Patients with MELD scores of 21 to 30 (0.25 QALYs) and >30 (0.83 QALYs) also benefited from DCD transplantation with ICERs of $478,222/QALY and $120,144/QALY, respectively. Sensitivity analyses demonstrated stable results for MELD scores <15 and >20, but the preferred strategy for the MELD 15 to 20 category was uncertain. DCD transplantation was associated with increased costs and reduced survival for HCC patients with exception points but led to improved survival (0.26 QALYs) at a cost of $392,067/QALY for patients without exception points. In conclusion, DCD liver transplantation results in inferior survival for patients with a MELD score <15 and HCC patients receiving MELD exception points, but provides a survival benefit to patients with a MELD score >20 and to HCC patients without MELD exception points.

Optimization of PSA screening policies: a comparison of the patient and societal perspectives

OBJECTIVE

To estimate the benefit of PSA-based screening for prostate cancer from the patient and societal perspectives.

METHOD

A partially observable Markov decision process model was used to optimize PSA screening decisions. Age-specific prostate cancer incidence rates and the mortality rates from prostate cancer and competing causes were considered. The model trades off the potential benefit of early detection with the cost of screening and loss of patient quality of life due to screening and treatment. PSA testing and biopsy decisions are made based on the patient's probability of having prostate cancer. Probabilities are inferred based on the patient's complete PSA history using Bayesian updating.

DATA SOURCES

The results of all PSA tests and biopsies done in Olmsted County, Minnesota, from 1993 to 2005 (11,872 men and 50,589 PSA test results).

OUTCOME MEASURES

Patients' perspective: to maximize expected quality-adjusted life years (QALYs); societal perspective: to maximize the expected monetary value based on societal willingness to pay for QALYs and the cost of PSA testing, prostate biopsies, and treatment.

RESULTS

From the patient perspective, the optimal policy recommends stopping PSA testing and biopsy at age 76. From the societal perspective, the stopping age is 71. The expected incremental benefit of optimal screening over the traditional guideline of annual PSA screening with threshold 4.0 ng/mL for biopsy is estimated to be 0.165 QALYs per person from the patient perspective and 0.161 QALYs per person from the societal perspective. PSA screening based on traditional guidelines is found to be worse than no screening at all.

CONCLUSIONS

PSA testing done with traditional guidelines underperforms and therefore underestimates the potential benefit of screening. Optimal screening guidelines differ significantly depending on the perspective of the decision maker.

The Effect of Race, Sex, and Insurance Status on Time-to-Listing Decisions for Liver Transplantation

Fair allocation of organs to candidates listed for transplantation is fundamental to organ-donation policies. Processes leading to listing decisions are neither regulated nor understood. We explored whether patient characteristics affected timeliness of listing using population-based data on 144,507 adults hospitalized with liver-related disease in Pennsylvania. We linked hospitalizations to other secondary data and found 3,071 listed for transplants, 1,537 received transplants, and 57,020 died. Among candidates, 61% (n = 1,879) and 85.5% (n = 2,626) were listed within 1 and 3 years of diagnosis; 26.7% (n = 1,130) and 95% (n = 1,468) of recipients were transplanted within 1 and 3 years of listing. Using competing-risks models, we found few overall differences by sex, but both black patients and those insured by Medicare and Medicaid (combined) waited longer before being listed. Patients with combined Medicare and Medicaid insurance, as well as those with Medicaid alone, were also more likely to die without ever being listed. Once listed, the time to transplant was slightly longer for women, but it did not differ by race/ethnicity or insurance. The early time period from diagnosis to listing for liver transplantation reveals unwanted variation related to demographics that jeopardizes overall fairness of organ allocation and needs to be further explored.

Tutorial in medical decision modeling incorporating waiting lines and queues using discrete event simulation

In most decision-analytic models in health care, it is assumed that there is treatment without delay and availability of all required resources. Therefore, waiting times caused by limited resources and their impact on treatment effects and costs often remain unconsidered. Queuing theory enables mathematical analysis and the derivation of several performance measures of queuing systems. Nevertheless, an analytical approach with closed formulas is not always possible. Therefore, simulation techniques are used to evaluate systems that include queuing or waiting, for example, discrete event simulation. To include queuing in decision-analytic models requires a basic knowledge of queuing theory and of the underlying interrelationships. This tutorial introduces queuing theory. Analysts and decision-makers get an understanding of queue characteristics, modeling features, and its strength. Conceptual issues are covered, but the emphasis is on practical issues like modeling the arrival of patients. The treatment of coronary artery disease with percutaneous coronary intervention including stent placement serves as an illustrative queuing example. Discrete event simulation is applied to explicitly model resource capacities, to incorporate waiting lines and queues in the decision-analytic modeling example.

Sociodemographic differences in early access to liver transplantation services

The question of whether health care inequities occur before patients with end-stage liver disease (ESLD) are waitlisted for transplantation has not previously been assessed. To determine the impact of gender, race and insurance on access to transplantation, we linked Pennsylvania sources of data regarding adult patients discharged from nongovernmental hospitals from 1994 to 2001. We followed the patients through 2003 and linked information to records from five centers responsible for 95% of liver transplants in Pennsylvania during this period. Using multinomial logistic regressions, we estimated probabilities that patients would undergo transplant evaluation, transplant waitlisting and transplantation itself. Of the 144,507 patients in the study, 4361 (3.0%) underwent transplant evaluation. Of those evaluated, 3071 (70.4%) were waitlisted. Of those waitlisted, 1537 (50.0%) received a transplant. Overall, 57,020 (39.5%) died during the study period. Patients were less likely to undergo evaluation, waitlisting and transplantation if they were women, black and lacked commercial insurance (p < 0.001 each). Differences were more pronounced for early stages (evaluation and listing) than for the transplantation stage (in which national oversight and review occur). For early management and treatment decisions of patients with ESLD to be better understood, more comprehensive data concerning referral and listing practices are needed.

Improving outcomes in state AIDS drug assistance programs

BACKGROUND

State AIDS Drug Assistance Programs (ADAPs) provide antiretroviral medications to patients with no access to medications. Resource constraints limit the ability of many ADAPs to meet demand for services.

OBJECTIVE

To determine ADAP eligibility criteria that minimize morbidity and mortality and contain costs.

METHODS

We used Discrete Event Simulation to model the progression of HIV-infected patients and track the utilization of an ADAP. Outcomes included 5-year mortality and incidence of first opportunistic infection or death and time to starting antiretroviral therapy (ART). We compared expected outcomes for 2 policies: (1) first-come first-served (FCFS) eligibility for all with CD4 count <or=350/microL (current standard) and (2) CD4 count prioritized eligibility for those with CD4 counts below a defined threshold.

RESULTS

In the base case, prioritizing patients with CD4 counts <or=250/microL led to lower 5-year mortality than FCFS eligibility (2.77 vs. 3.27 deaths per 1,000 person-months) and to a lower incidence of first opportunistic infection or death (5.55 vs. 6.98 events per 1,000 person-months). CD4-based eligibility reduced the time to starting ART for patients with CD4 counts <or=200/microL. In sensitivity analyses, CD4-based eligibility consistently led to lower morbidity and mortality than FCFS eligibility.

CONCLUSION

When resources are limited, programs that provide ART can improve outcomes by prioritizing patients with low CD4 counts.

Discrete-event simulation applied to analysis of waiting lists. Evaluation of a prioritization system for cataract surgery

OBJECTIVES

To outline the methods used to build a discrete-event simulation model for use in decision-making in the context of waiting list management strategies for cataract surgery by comparing a waiting list prioritization system with the routinely used first-in, first-out (FIFO) discipline.

METHODS

The setting was the Spanish health system. The model reproduced the process of cataract, from incidence of need of surgery (meeting indication criteria), through demand, inclusion on a waiting list, and surgery. "Nonexpressed Need" represented the population that, even with need, would not be included on a waiting list. Parameters were estimated from administrative data and research databases. The impact of introducing a prioritization system on the waiting list compared with the FIFO system was assessed. For all patients entering the waiting list, the main outcome variable was waiting time weighted by priority score. A sensitivity analysis with different scenarios of mean waiting time was used to compare the two alternatives.

RESULTS

The prioritization system shortened waiting time (weighted by priority score) by 1.55 months (95% CI: 1.47 to 1.62) compared with the FIFO system. This difference was statistically significant for all scenarios (which were defined from a waiting time of 4 months to 24 months under the FIFO system). A tendency to greater time savings in scenarios with longer waiting times was observed.

CONCLUSIONS

Discrete-event simulation is useful in decision-making when assessing health services. Introducing a waiting list prioritization system produced greater benefit than allocating surgery by waiting time only. Use of the simulation model would allow the impact of proposed policies to reduce waiting lists or assign resources more efficiently to be tested.

Beyond utilitarianism: a method for analyzing competing ethical principles in a decision analysis of liver transplantation

BACKGROUND

The utilitarian foundation of decision analysis limits its usefulness for many social policy decisions. In this study, the authors examine a method to incorporate competing ethical principles in a decision analysis of liver transplantation for a patient with acute liver failure (ALF).

METHODS

A Markov model was constructed to compare the benefit of transplantation for a patient with ALF versus the harm caused to other patients on the waiting list and to determine the lowest acceptable 5-y posttransplant survival for the ALF patient. The weighting of the ALF patient and other patients was then adjusted using a multiattribute variable incorporating utilitarianism, urgency, and other principles such as fair chances.

RESULTS

In the base-case analysis, the strategy of transplanting the ALF patient resulted in a 0.8% increase in the risk of death and a utility loss of 7.8 quality-adjusted days of life for each of the other patients on the waiting list. These harms cumulatively outweighed the benefit of transplantation for an ALF patient having a posttransplant survival of less than 48% at 5 y. However, the threshold for an acceptable posttransplant survival for the ALF patient ranged from 25% to 56% at 5 y, depending on the ethical principles involved.

DISCUSSION

The results of the decision analysis vary depending on the ethical perspective. This study demonstrates how competing ethical principles can be numerically incorporated in a decision analysis.

A novel model measuring the harm of transplanting hepatocellular carcinoma exceeding Milan criteria

No empirical studies have defined the posttransplant survival that would justify expansion of the Milan criteria for liver transplantation of hepatocellular carcinoma. We created a Markov model comparing the survival benefit of transplantation for a patient with >Milan HCC, versus the harm caused to other patients on the waiting list. In the base-case analysis, the strategy of transplanting the patient with >Milan HCC resulted in a 44% increased risk of death and a utility loss of 3 quality-adjusted years of life across the pre- and posttransplant periods for a nationally representative cohort of patients on the waiting list. This harm outweighed the benefit of transplantation for a patient with >Milan HCC having a 5-year posttransplant survival of less than 61%. This survival threshold was most sensitive to geographic variations in organ shortage, with the threshold varying from 25% (Region 3) to >72% (Regions 1, 5, 7 and 9). In conclusion, expansion of the Milan criteria will require demonstrating high survival rates for the newly eligible patients-approximately 61% at 5 years after transplantation. In regions with less severe organ shortage, a more aggressive approach to transplanting these patients may be justified.

Use of dynamic microsimulation to predict disease progression in patients with pneumonia-related sepsis

Introduction

Sepsis is the leading cause of death in critically ill patients and often affects individuals with community-acquired pneumonia. To overcome the limitations of earlier mathematical models used to describe sepsis and predict outcomes, we designed an empirically based Monte Carlo model that simulates the progression of sepsis in hospitalized patients over a 30-day period.

Methods

The model simulates changing health over time, as represented by the Sepsis-related Organ Failure Assessment (SOFA) score, as a function of a patient's previous health state and length of hospital stay. We used data from patients enrolled in the GenIMS (Genetic and Inflammatory Markers of Sepsis) study to calibrate the model, and tested the model's ability to predict deaths, discharges, and daily SOFA scores over time using different algorithms to estimate the natural history of sepsis. We evaluated the stability of the methods using bootstrap sampling techniques.

Results

Of the 1,888 patients originally enrolled, most were elderly (mean age 67.77 years) and white (80.72%). About half (47.98%) were female. Most were relatively ill, with a mean Acute Physiology and Chronic Health Evaluation III score of 56 and Pneumonia Severity Index score of 73.5. The model's estimates of the daily pattern of deaths, discharges, and SOFA scores over time were not statistically different from the actual pattern when information about how long patients had been ill was included in the model (P = 0.91 to 0.98 for discharges; P = 0.26 to 0.68 for deaths). However, model estimates of these patterns were different from the actual pattern when the model did not include data on the duration of illness (P < 0.001 for discharges; P = 0.001 to 0.040 for deaths). Model results were stable to bootstrap validation.

Conclusion

An empiric simulation model of sepsis can predict complex longitudinal patterns in the progression of sepsis, most accurately by models that contain data representing both organ-system levels of and duration of illness. This work supports the incorporation into mathematical models of disease of the clinical intuition that the history of disease in an individual matters, and represents an advance over several prior simulation models that assume a constant rate of disease progression.

Shortening the timeline of pediatric phase I trials: the rolling six design

PURPOSE

To shorten the study conduct timeline of pediatric phase I oncology trials by employing a novel trial design.

METHODS

A comparison of the traditional 3 + 3 patients per cohort, phase I trial design with a novel, rolling six design was performed by using discrete event simulation. The rolling six design allows for accrual of two to six patients concurrently onto a dose level based on the number of patients currently enrolled and evaluable, the number experiencing dose-limiting toxicity (DLT), and the number still at risk of developing a DLT. Clinical trial simulations (n = 1,000) were based on historical data and were performed using SAS 9.1.3 (SAS Institute, Cary, NC). Study timelines and patient numbers were determined for each design, and safety was assessed as a function of the number of DLTs observed.

RESULTS

In twelve completed historical studies, the median time to study completion was 452 days (range, 220 to 606 days); number of evaluable participants enrolled was 22 (range, 11 to 33), and DLTs occurring per study was three (range, 0 to 5). In 1,000 study simulations, in which the average time to new patient accrual was 10 days, the average +/- standard deviation (SD) time to study completion was 294 +/- 75 days for the rolling six design versus 350 +/- 84 days for the 3 + 3 design, whereas the number of DLTs per study was the same (average +/- SD, 3.3 +/- 1.1 v 3.2 +/- 1.1 for the rolling six and 3 + 3 designs, respectively).

CONCLUSION

The rolling six design may significantly decrease the duration of pediatric phase I studies without increasing the risk of toxicity. The design will be tested prospectively in upcoming Children's Oncology Group phase I trials.

Assessing emerging technologies—The case of organ replacement technologies: Volume, durability, cost

Objectives:The aim of this study was to estimate thresholds for production volume, durability, and cost of care for the cost-effective adoption of liver organ replacement technologies (ORTs).

Methods:We constructed a discrete-event simulation model of the liver allocation system in the United States. The model was calibrated against UNOS data (1994–2000). Into this model, we introduced ORTs with varying durability (time to failure), cost of care, and production volume. Primary outputs of interest were time to 5 percent reduction in the waiting list and time to 5 percent increase in expected transplant volume.

Results:Model output for both calibration and validation phases closely matched published data: waiting list length (±2 percent), number of transplants (±2 percent), deaths while waiting (±5 percent), and time to transplant (±11 percent). Reducing the waiting list was dependent on both ORT durability and production volume. The longer the durability, the less production volume needed to reduce the waiting list and vice versa. However, below 250 ORT/year, durability needed to be >2 years for any significant change to be seen in the waiting list. For base-case costs, all ORT production volume and durability scenarios result in more transplants per year at less total cost of care/patient than the current system. ORTs remain cost saving until manufacturing costs are >5 times base-case costs, production is less 500 ORT/year, and durability <6 months.

Conclusions:Although there remain many technical challenges to overcome, as long as ORTs can meet these threshold criteria, they have the potential of transforming the world of end-stage liver disease.

Estimating the rate of accumulating drug resistance mutations in the HIV genome

OBJECTIVE

HIV mutation accumulation has great implications for pharmacoeconomics and clinical care, yet scarcity of data has hindered its representation in decision analytic models. Our objective is to determine the accuracy with which mutation accumulation and other unmeasured parameters could be estimated during model calibration.

METHODS

We used a second-order Monte Carlo simulation of HIV natural history that had been calibrated by varying two unmeasured parameters (mutation accrual rate and probability of adherence) to minimize differences between estimated and observed clinical outcomes (time to treatment failure and survival). We compared these estimated values first with only those results that had been already published at the time of model calibration, and second including results that were published after model calibration.

RESULTS

The value for mutation accrual rate assigned during calibration was 0.014 mutations per month for antiretroviral-naïve patients, at the lower bound of the results for nine heterogeneous studies published at the time of calibration (pooled 95% confidence interval [CI] 0.014-0.039 mutations per month). In contrast, this estimate accurately anticipated results from 11 larger and more homogeneous studies published after calibration (pooled 95% CI for antiretroviral-naïve patients, 0.012-0.015 mutations per month). The value for probability of adherence assigned during calibration (75%) was also within the range of published results (pooled 95% CI 62-76%).

CONCLUSION

Estimates for unobserved parameters derived during model calibration were not only within the range of clinical observations, but anticipated with accuracy clinical results that were not yet available. It may be feasible to use models to estimate unobserved parameters.

A new organ transplantation location-allocation policy: a case study of Italy

In this paper, we propose a location model for the optimal organization of transplant system. Instead of simulation approach, which is typical when facing many health care applications, our approach is distinctively based on a mathematical programming formulation of the relevant problem. In particular, we focus on the critical role of time in transplantation process as well as on a spatial distribution of transplant centers. The allocation of transplantable organs across regions with the objective of attaining regional equity in health care, is the aim of this paper. Our model differs from previous modeling approaches in that it considers the nationwide reorganization of the transplant system, identifying system barriers that may impair equity and efficiency. The demolition of these barriers may leads on a reduction of waiting lists and of wasted organs. We provide the basic structure and the properties of the model, and validate it on a real case study. The experimental validation of the model demonstrates the effectiveness and robustness of our proposal.

Incorporating biological natural history in simulation models: empirical estimates of the progression of end-stage liver disease

OBJECTIVE

To develop an empiric natural-history model that can predict quantitative changes in the laboratory values and clinical characteristics of patients with end-stage liver disease (ESLD), to be used to calibrate an individual microsimulation model.

METHODS

The authors report the development of a stochastic model that uses cubic splines to interpolate between observed laboratory values over time in a cohort of 1997 patients with ESLD awaiting liver transplantation at the University of Pittsburgh Medical Center. The splines were recursively sampled to provide a stochastic, quantitative natural history of each candidate's disease.

RESULTS

The model was able to simulate the types of erratic disease trajectories that occur in individual patients and was able to preserve the statistical properties of the natural history of ESLD in cohorts of real patients. Moreover, the model was able to predict pretransplant survival rates (87% at 1 year), which were statistically similar to rates observed in the authors' local cohort (92%).

CONCLUSIONS

Cubic splines can be used to generate quantitative natural histories for individual patients with ESLD and may be useful for developing clinically robust microsimulation models of other diseases.