SIMULATING THE NEED FOR RENAL REPLACEMENT THERAPY CAPACITY

Anders L Nielsen1), Alok Kumar1), Philip Nielsen2), Susanne Petersen1)

1) University of the West Indies, Cave Hill, Barbados 2) Act-Consult, London, UKemail: anders.nielsen@cavehill.uwi.edu

1. KEYWORDSDiscrete Event Simulation, Kidney failure, Model building, Patient-centered simulation, Renal Replacement Therapy capacity, Health Care optimization.

2. ABSTRACTBarbados has experienced a rising burden of patients with end-stage renal failure (ESRF) and the burdens of a renal replacement therapy (RRT) on society are significant. We developed a patient-centered discrete event simulation (DES) model to simulate the needed RRT capacity fitted to local conditions. Two scenarios were analyzed. 1) What happens over the next 5 years if the present capacity is maintained assuming unchanged prevalence and incidence of ESRF? The simulation indicated that equilibrium with 300 patients receiving RRT will be reached during the next 5 years. This equilibrium is best explained by increased mortality due to rationing the dialysis time.2) What is the effect of improved predialysis treatment without resource limitations? The simulation indicates that one would expect a 19% increase in patients who survive the first year. In this scenario it means 387 patients’ years gained.

3. INTRODUCTIONHealth care systems worldwide have seen a rising burden of patients with Chronic Kidney Diseases (CKD) that for some unfortunately will progress to end-stage renal failure (ESRF) 1. When the patient reaches this stage the patient needs renal replacement therapy (RRT) to stay alive. Only three treatment modalities for RRT are available namely renal transplantation (TX) and two forms of dialysis, either peritonealdialysis (PD) or hemodialysis (HD). The prevalence of patients with CKD in a particular region is determined by one set of factors. An additional set of factors influence how many of the patients with CKD will ultimately progress to ESRF. The conditions that lead to the majority of CDK cases are obesity, diabetes and hypertension. But also race and comorbidities like HIV, hepatitis and lupus are other cofactors that define the number of patients that will need RRT and hence the health care resources needed.Regardless of which form of RRT the patient receives it is a chronic and costly treatment. The burden of RRT on society is significant and add to the already existing ‘health care

crisis’2. Consequently health care systems have to increase efficiency3. The challenge then becomes how to improve the outcomes for these patients within the given constraints? One has to evaluate many possible scenarios to find the most optimal ones. Obviously evaluations of different interventions call for tools that can be used assisting with the planning of future healthcare services to become more efficient.The aim of this paper is to share our considerations and experiences when building a patient-centered discrete event simulation (DES) model estimating the need for RRT capacity. The ultimate goal is to develop a tool that can contribute to the process of optimizing economic efficiency in healthcare systems offering RRT to its population.

4. METHODSWe used the ARENA® simulation software (V 13.5 from Rockwell Automation Technologies Inc., USA) to build our simulation model and run the simulations. Initially we used the free but limited student version due to economic constraints. However that forced us to think in terms of prototyping and building models that can be used as sub-models. Previously we have used a prototyping approach with success 4 and it is our experience that it is straight forward to build models that consist of many sub-models and eventually integrate them into one comprehensive bigger model. As literature reference database we use Refmann® (Version 12 from Thomson Reuters) and we have presently collected almost 800 references with clinical information relevant for building a RRT DES model.To keep a dynamic graphical overview of the associative relationships between the different clinical components we use PersonalBrain Pro® (Version 6 from TheBrain Technologies LP).

5. THE MODEL5.1. The Macro ModelOn the Macro level our simulation model assumes the same universal RRT model as originally presented by Davies & Roderick5. It basically deals with the flow within what we could call the ‘Chronic RRT-core’. Patients with ESRF in need of RRT enter the model based on known crude incidence rates. The model also simulates interaction between the three available treatment-modalities (PD, HD, TX) based on known transfer frequencies between the

modalities. There is by nature only one-way out of the model (i.e. death) determined by the crude mortality rates. The strengths of Davies & Roderick’ model5 is its simplicity and universality on the macro level. It only needs changing a few crude rates to refit the model to any country/region offering RRT services.

5.2. The module ‘Chronic HD’For socio-economic reasons the main RRT modality used in Barbados is HD. Accordingly the model was fitted to simulate the HD modality more accurately (for an overview of our final model see Figure 1). The macro model by Davies & Roderick5 does not simulate each single HD session and the model among other things does not take into consideration what happens when the number of patients in need of HD exceeds the present capacity. Hence the HD modality in the macro model was expanded with the sub-module ‘Chronic HD’ where each single HD session is simulated. For more than four decades, the standard worldwide schedule for hemodialysis has continued to be three sessions a week, largely owing to logistic and cost concerns6 The module simulates conventional thrice-weekly hemodialysis sessions of 2.5 to 4.0 hours7 duration, with median set to 3 Figure 1 Model overview

hours. The simulated facility has 24 HD machines (likelihood of break down included) and they operate on a double shift schedule six days a week. We have at present not expanded the model with the option of the patients receiving more frequent HD sessions than thrice weekly as the evidence of benefits with more than thrice-weekly HD sessions is conflicting6-8. If the numbers of persons in need of RRT exceed the available slots some patients already on HD are reduced to receive only 4 hours HD twice weekly. As many patients as needed are put on reduced HD to free slots for the new patients. If capacity is maximized by using the 2 times 4 hour HD regimen using all allocated resources, no new patients are accepted. The 2 times weekly regimen carries a price in terms of increased mortality and morbidity compared to the longer 3 times weekly option hence the model incorporates different mortality and morbidity for the two treatments9. If slots become available the model accepts patients transferred from other RRT modalities as first priority, new patients as second priority and finally as third priority patients on 2 times weekly HD are increased to 3 times weekly.

The sub-module ‘Chronic HD’ (see Figure 1) is further divided in three sub-modules. The first step is that the model checks the existing capacity (see Figure 2). If there is a slot available for HD 3 times weekly the patient is transferred to the sub-module ‘HD 3 times weekly’ (See Figure 3). If there are no slots available the patient is transferred to the sub-module ‘HD 2 times weekly’ (see Figure 4). The reason for this construction is of cause the difference in mortalities and morbidities and we want to keep track of which weekdays the patients receive HD.

Figure 2 Submodel checks capacity

Figure 3 HD three times a week

Figure 4 HD two times a week

5.3. The module “In need waiting for HD”As a consequence of the occurrence of cases where no HD slot is available a sub-module had to be added simulating patients with immediate need for RRT but waiting for

treatment. This is mathematically a straightforward module (see Figure 5). If the patient does not receive dialysis (i.e. accepted by the Acute HD module) within a short time frame the outcome is death (i.e. the item exists in the model only while alive and in queue).

Figure 5 In need of HD but waiting.

5.4. The module ‘Acute HD’It is well known that mortality and morbidity are higher during the first three months on HD10. An issue not addressed by the ‘chronic HD’-core module since it does not specifically simulate the first 3-months on HD. The added ‘Acute HD’ module simulates the increased mortality and morbidity that is found during the first 3 months. The sub-module is similar to the ‘chronic HD’ sub-module but with increased mortality rate. A rate that in simple terms is dependent on how stigmatized the patients are and the existence of comorbidities.

5.5. EntryMeeting a number of KDOQI guideline goals at dialysis initiation is independently associated with survival during the first year of dialysis treatment. These goals are primarily related to three issues: That the patient has a permanent vascular access before starting on HD, has the CKD related anemia well treated and has a good nutritional status11, 12. The model therefore has 4 entry points. One called ‘timely referrals’ for patients who have been prepared and are ready for HD meeting all three goals. They enter directly into the sub-module ‘Chronic HD’ as they have no initial increased mortality. The second entry point is the ‘late referrals’ for the patients who meet two goals. The third is the ‘known not ready’ for patients who only meet one goal and the fourth entry point the ‘acute’ for the ones who has no preparation at all (not shown in Figure 1). Unfortunately most of our patients fit the ‘acute’ category. The entry points are modeled with increased mortality risk initially and the patients are forwarded to the ‘in need waiting for HD’ module except for ‘timely referrals’ as already mentioned they go directly to the ‘chronic – HD’ module.

5.6. The ‘Start up’ moduleInitially the model did not behave as expected. We had very few on HD and hardly any mortality during the first ½ year and then it suddenly rose significantly. We had made the

classic mistake of omitting a run-in period13. We then finally added a module that feeds the current stock of patients into the model during the first week of simulation. 5.7. The PD ModuleWe have added a PD module. At present we have very few patients on PD simply because the social environment does not facilitate the use of PD as a viable RRT option. And the few put on PD generally after a short time is transferred from PD to HD on medical grounds, but the underlying cause is primarily cultural-social-economical.

6. RESULTS6.1. What is the present capacity?Simulation of the model was performed with 1000 replications of a 5 year period. With the initial number of patients on HD (approximately 200 in 2010) and the initial rate of admissions, the simulation predicted a larger capacity than perceived by the staff. The simulation indicated that the capacity was only utilized to 80.2 % of its scheduled capacity. Organizational and cultural barriers are believed to be major contributors to the non-optimal use of the resources.

Average Avg min Avg Max Worst case scenario #

New Patients with ESRF

300 196 424 424

Died waiting for HD

3.5 0 20 0

Died first 3 months on HD

84 11 138 11

Died on Chronic HD

223 136 304 136

Total 5 year gain -11 49 -38 277Net yearly gain --2 9.8 -8 55# is inversed worst case scenario i.e. number of incoming maximized, number of death minimized. Table 1: Results from five years simulations

The simulation reached a steady state with a population on RRT of approximately 300. However it also showed the possibilities of peaks where the current resources would not meet demand, as seen by the fact the average maximum for patients dying while waiting for treatment is 20 [see Table1].On the one hand from a patient perspective this steady state situation is unacceptable. It is reached because some patients die waiting for HD while others die because they do not receive sufficient treatment (the ones on twice weekly HD). On the other hand from a health care system perspective it can be claimed that with the current allocated resources at least 300 patients will receive some treatment. However such ethical dilemmas can never be solved using simulation – we can only contribute to the quest to become more efficient.

6.2. What if predialysis treatment is improved? An additional question is what happens if we have increased resources (i.e. no patients die waiting and all patients are on trice weekly HD) and at the same time improve the predialysis treatment so that a larger percentage of patients will enter the model with the label ‘timely referrals’. For details of such an intervention see Table 2.

Model group No of criteria met

Mortality hazard ratios (95% confidence intervals)

Percent of new patient ( N yearly = 70)

Pre-inter-vention

Post-inter-vention

Timely referrals 3 0.34(0.30 -0.39)

5 % 60 %

Known not ready

2 0.53(0.51 -0.56)

10 % 25 %

Late referrals 1 0.81(0.80 -0.83)

25 % 10 %

Acute referrals 0 1 60 % 5 %

Table 2 Improved predialysis treatment

With the changes in the referrals (i.e. post interventions data) the simulation is repeated over 5 years with 500 iterations. The utility of the HD machines is initially 64% (see Figure 6). In year one in both the pre- and post-interventions scenarios the system needs to work at its present maximum allocative efficiency (Usage 66.5% = two full shifts). It is very unlikely that the initial capacity is sufficient after year one. (The minimum average usage is 66.8%, average is 71.0% and maximum usage is 75.2%).

Figure 6 HD Machine utility before and after improvement to pre-dialysis treatment

Five year after the intervention on average 38.7 more patients will have survived the first year on RRT. That is an increase of 19.4% in patients who survive the first year With an average life expectancy of 10 years on HD the intervention therefore is predicted to gain 387 years of life. It means that one year after the intervention has been implemented; on average 9.67 additional patients annually will survive the first year of RRT.

7. DISCUSSION7.1. Why choose DESWhy choose DES? Literature reviews reveal that simulations are the prominent method used for planning and system/resource utilization projects in health care 14, 15.Four characteristics have to be reflected in the model. First it deals with individual patients. Secondly the model has to be a Non-Markovian since the future (e.g. survival on HD) for the individuals is conditionally dependent of the past (e.g. the patient is diabetic), given the present (i.e. the patient has reached ESRF). Thirdly the individuals belong to different discrete-states (i.e. different disease stages modified by different comorbidities) and finally the model examines interactions with the environment (e.g. availability of resources such as staff and equipment and/or available treatment modalities). Applying the taxonomy proposed by Brennan et al. 16 suggests that DES is an optimal method.

Since there is a relatively small volume of literature on what constitutes good practice and it is not prescriptive about every aspect of decision modeling Sculpher et al.17 suggest the analysts provide explicit and comprehensive justification of their methods instead, and allow the user of the model to make an informed judgment about the relevance, coherence and usefulness of the analysis. Banks and Chwif’s 18

proposed to describe the process using seven categories: Data Collection, Model Building, Verification and Validation, Analysis, Simulation Graphics, Managing the Simulation Process, and Human Factors, Knowledge and Abilities. Only Data Collection, Model Building, Analysis, and Human Factors, Knowledge and Abilities are of special interest for our project.

7.2. Data collection

7.2.1. Data format - Applying clinical risks to the model

Data is often in the wrong format, collected as discrete data rather than continuous data 18. Sod’s law of data collection says that the data available is never quite exactly the data you want because it was originally collected for a purpose different from your simulation study 18. In the medical literature clinical evidence is often found in reported randomized trials and systematic reviews and they generally

report on dichotomous outcomes (such as death versus survival)19 . Binary variables are easily modeled in a DES – it is either state A or state B – so the converting of clinical evidence into DES-models seems straight forward. The task for the modeler is the same as the physician faces. For the physician the question is how is data from literature interpreted and converted into meaningful advice for the individual patient 20. For the modeler the task is to translate the data from literature into probabilities determining the fate of the entity.When building simulation models in the medical domain the modeler needs to extract knowledge from several studies that have reported on the same outcomes and that is where things starts to be a little complicated for the modeler. The outcomes can be reported using several different terminologies including hazard ratios, absolute risks, relative risks, risk ratios and odds ratios. Our literature database at present consists of 251 publications describing a clinical investigation relevant for the model. The number of different probability terms used in the publications is shown in Table 3. Note that 185 of the publications only use a single term but 66 use a combination of terms. Absolute Risk (AR), Relative Risk or Risk Ratio (RR) values can be directly applied to a DES model but in our case they only represent a quarter of the 251 publications. For the remaining three quarters of publications using Hazard ratio (HR), Kaplan-Meier (KM) and Odds Ratio (OR) the challenge for the modeler is to convert the data into probabilities that can be applied to the model.

AR RR RR OR HR KM SumAbsolute risk (AR) 1 4 0 0 1 0 6Relative risk (RR) 4 37 2 7 3 2 55Risk ratio (RR) 0 2 1 1 0 0 4Odds Ratio (OR) 0 7 1 36 6 0 50Hazard ratio (HR) 1 3 0 6 93 7 110Kaplan-Meier (KM)

0 2 0 0 7 17 26

Sum 6 55 4 50 110

26 251

Table 3 Method used to describe risk in the literature database.

7.2.2. Hazard RatioSurvival is often reported at intervals as Hazard ratio (HR), i.e. as discrete data even though they in reality represent a continuous dataset. HR is a measure of how often a particular event happens in one group compared to how often it happens in another group, over time (t). HR is the most complicated to convert to the model since it is a measure of Relative Risk - also called Risk Ratio- (RR) over t. Hence it is used not only to describe the total number of events, but their timing as well. The HR equals a weighted

RR over the entire duration of a study and is often derived from a time-to-event curve or Kaplan-Meier plot 21. Especially two problems related to HR need to be mentioned. First the timing of events may not be evenly distributed over time throughout the study period and many studies report only a single HR averaged over the duration of the study’s follow up 22. The challenge for the modeler is to subdivide t into smaller intervals that make sense. If a Kaplan-Meier plot is presented in a publication a feasible way is to read the values from the Kaplan-Meier plot at the required intervals. In our literature database only 7 of 110 (see Table 1) describing HR’s presented a Kaplan-Meier plot, therefore the only other option is to have a medical expert estimating the characteristics of the HR-function over time. Secondly the period-specific HR has a built-in selection bias. To describe this bias, consider that the (discrete-time) hazard during period t is defined as the risk of the outcome during period t among those who reached period t free of the outcome 22. Thus the hazard ratio must be interpreted judiciously especially in settings where the duration of events or the disease are the primary efficacy variables 23.

7.2.3. Risk and odds ratioClinicians find it difficult to understand odds and odds ratios as measures of association, although they may be comfortable with the parallel concepts of risk and risk ratios. Although both the risk ratios and odds ratios are perfectly valid ways of describing a treatment effect, it is important to note that they are not the same measures, cannot be used interchangeably and should not be confused. For treatment that increases the chance of an event, the odds ratio will be larger than the risk ratio. For interventions that reduce the chance of an event, the odds ratio will be smaller than the risk ratio. Thus if an odds ratio is misinterpreted as a risk ratio it will lead to an overestimation of the intervention. Unfortunately, this error and interpretation is quite common in published reports on individual studies and systematic reviews 24. The bottom line is: When calculations have been based on odds ratios the modeler has to transform the findings to the concept of risk.

7.3. Model buildingWe create first a conceptual model prior to the implementation of the computerized model using PersonalBrain Pro®. A conceptual model is an abstraction of the real system that is being studied. The conceptual model consists of 18:1) Assumptions on system components.

2) Structural assumptions that define the interactions between system components. These are expressed by means of natural language and diagrams and 3) Input parameters and data assumptions.

It is recommended that model structure should be as simple as possible and only with complexity level as needed 14, 18. The single dominate error in logic modeling is to incorporate excessive details 25. In addition the model should be consistent with the stated decision problem and it should be based on theory of the diseases and not just defined by data availability or health service inputs alone 16. Therefore the model described in this paper is simple but complex enough to reflect the dynamics and characteristics of patients with ESRF as well as the interactions between the patients and the health care system that provide the services the patients need to stay alive. 7.4. AnalysisOur simulation model has most features common with a ‘push system’ and few features common with a ‘pull system’A push system has external arrivals at some arrival rate (i.e. entities are pushed into the system such as patients categorized as ‘late arrivals’). A pull system demands entities to feed it (i.e. entities are pulled into the system such as patients categorized as ‘timely referrals’). Obviously the kidney model is mainly a push system. Patients need dialyses when they do - but ‘timely referrals’ can be argued to attain some features of the pull system. 18

7.5. Human factors (Knowledge and abilities)The most critical component for a simulation project is not software. Neither is it hardware. It is ‘human ware’. Beware of the SINSFIT principle: Simulation is no substitute for intelligent thinking 18.As Banks stresses the key to successful models is the human ware. A team with members whose qualifications and competences are complementary to each other is an asset. The combination of expertise on kidney diseases, research interpretations, public health, human behavior, system and interactive analysis and software programming definitely facilitated the development of our model.

7.6. Ethical issues.During the development of the Chronic HD module it became clear that during certain periods the need for HD exceed the capacity provided using trice weekly HD sessions. We had to investigate how the situations were de facto handled when demand exceeded the capacity since no formal policy existed and we found no “hidden capacity". It became evident that an informal priority setting/rationing took place. In order to make capacity available for new

patients the amount of HD given to patients already in the program was reduced. This informal priority setting had to be incorporated into the model (see Figure 2 Submodelchecks capacity). One could argue that it hereby became an explicit priority setting (i.e. a described rule) at least in the model.

This example serves as a reminder of the fact that the process of building DES models not only might aid in future planning but also is a tool to clarify which processes really take place in the organization. We will argue that this case once again shows that DES can be a valuable tool when optimizing complex adaptive healthcare systems4.

8. CONCLUSIONWe have presented a patient-centered Discrete Event Simulation model that simulates the need for Renal Replacement Therapy capacity. The model simulates each individual dialysis session and it assigns different mortalities to the individual patient groups. The model has been used to illustrate two scenarios. The first scenario simulates the number of patients that the system can maximally cope with over a five year period with unchanged resources. It shows that with a rationing procedure put in place (i.e. decreased dialysis) the mortality increases and hence a new steady state level is reached. The second scenario simulates the consequences of an intervention aimed at improving pre-dialysis treatment without resource limitations. It shows a significant number of years of survival gained if this intervention was introduced.We have highlighted the crossroads that we have encountered and the considerations and decisions that the team had to handle. In this process it was an asset having team members with qualifications and competences in different domains. Despite the barriers and the complexity we still argue that it is possible to build relatively simple models that can be used in the processes aiming at optimizing health care systems.

Reference List

1. Meguid El NA, Bello AK. Chronic kidney disease: the global challenge. Lancet 2005;365(9456):331-340.

2. Goldsmith JC. The new health-cost crisis. Harv Bus Rev 2001;79(10):20-21.

3. WHO. World Report on Knowledge for Better Health - Strengthening Health Systems. Geneva,Switzerland: World Health Organization, 2004

4. Lassen Nielsen A, Hilwig H, Kissoon N, Teelucksingh S. Discrete event simulation as a tool in

optimization of a professional complex adaptive system. Stud Health Technol Inform 2008;136:247-252.

5. Davies R, Roderick P. Predicting the future demand for renal replacement therapy in England using simulation modelling. Nephrol Dial Transplant 1997;12(12):2512-2516.

6. Himmelfarb J, Ikizler TA. Hemodialysis. New England Journal of Medicine 2010;363(19):1833-1845.

7. Chertow GM, Levin NW, Beck GJ et al. In-Center Hemodialysis Six Times per Week versus Three Times per Week. New England Journal of Medicine 2010;363(24):2287-2300.

8. Wheeler DC, Caplin B. New Observational Data Demonstrate that Mortality Is Lower in Patients Receiving More Frequent Dialysis. Journal of the American Society of Nephrology 2012.

9. Saran R, Bragg-Gresham JL, Levin NW et al. Longer treatment time and slower ultrafiltration in hemodialysis: associations with reduced mortality in the DOPPS. Kidney Int 2006;69(7):1222-1228.

10. Winkelmayer WC, Owen WF, Levin R, Avorn J. A Propensity Analysis of Late Versus Early Nephrologist Referral and Mortality on Dialysis. Journal of the American Society of Nephrology 2003;14(2):486-492.

11. Slinin Y, Guo H, Gilbertson DT et al. Meeting KDOQI guideline goals at hemodialysis initiation and survival during the first year. Clin J Am Soc Nephrol 2010;5(9):1574-1581.

12. Roubicek C, Brunet P, Huiart L et al. Timing of nephrology referral: influence on mortality and morbidity. Am J Kidney Dis 2000;36(1):35-41.

13. Kelton WD, Sadowski RP, Sturrock DT. Simulation with Arena. 4 ed. New York: McGraw-Hill; 2007.

14. Jun JB, Jacobson SH, Swisher JR. Application of Discrete-Event Simulation in Health Care Clinics: A Survey. The Journal of the Operational Research Society 1999;50(2):109.

15. Brailsford SC, Harper PR, Patel B, Pitt M. An analysis of the academic literature on simulation and

modelling in health care. J of Sim 2009;2009(3):130-140.

16. Brennan A, Chick SE, Davies R. A taxonomy of model structures for economic evaluation of health technologies. Health Econ 2006;15(12):1295-1310.

17. Sculpher M, Fenwick E, Claxton K. Assessing quality in decision analytic cost-effectiveness models. A suggested framework and example of application. Pharmacoeconomics 2000;17(5):461-477.

18. Banks J, Chwif L. Warning about simulation. Journal of simulation 2011;2011(5):279-291.

19. Scott I. Interpreting risks and ratios in therapy trials. Aust Prescr 2008;31:12-16.

20. Roderick PJ. Assessing the impact of chronic kidney disease on individuals and populations: use of relative and absolute measures. Nephrol Dial Transplant 2012.

21. Boslaugh S, Watters PA. Statistics in a nutshell. 1 ed. Cambridge: O'Reilly; 2008.

22. Hernan MA. The hazards of hazard ratios. Epidemiology 2010;21(1):13-15.

23. Spruance SL, Reid JE, Grace M, Samore M. Hazard ratio in clinical trials. Antimicrob Agents Chemother 2004;48(8):2787-2792.

24. Center for Reviews and Dissemination. Systematic Reviews. CRD's guidance for undertaking reviews in healthcare. CRD, University of York; 2009.

25. Schmeiser BW. Some Myths and Common Errors in Simulation Experiments. Proceedings of the 2001 Winter Simulation Conference 2012;39-46.