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Ann Thorac Surg 2003;75:1372-1376
© 2003 The Society of Thoracic Surgeons
a Department of Cardio-Thoracic Surgery, Erasmus University Medical Center, Rotterdam, The Netherlands
b Providence Health System, Portland, Oregon, USA
* Address reprint requests to Dr Takkenberg, Department of Cardio-Thoracic Surgery, Bd162, Erasmus University Medical Center Rotterdam, PO Box 2040, 3000CA Rotterdam, The Netherlands
e-mail: takkenberg{at}thch.azr.nl
Which valve substitute would you prefer to implant in a 63-year-old male patient? And which valve substitute would in your opinion be best for a 36-year-old female patient? It can be quite complicated to predict prognosis after implantation of a certain aortic valve substitute in the individual patient who requires aortic valve replacement. Multiple interrelated factors (patient, physician, and prosthesis related) affect outcome after aortic valve replacement. Published clinical experiences provide information on outcome after aortic valve replacement on a group level. By applying standard parametric and semiparametric models for risk factor assessment, it is possible to identify factors that may influence long-term outcome in that particular patient group. One can translate this to the outcome in the individual patient by inserting his or her risk factors into the equation for the model. Although feasible, it is often not an easy task because it necessitates integration of information on many interrelated factors that simultaneously play a role. Simulation techniques may provide a useful adjunct to standard methods because they allow modeling of complex outcome paths resulting from many simultaneous risks.
Recently, several authors reported on the use of simulation techniques to predict outcome after aortic valve replacement and to support prosthetic valve choice [1–4]. These studies use a complex and mostly unknown methodology, and are therefore often difficult to interpret.
This report focuses on the microsimulation method that is used in the article in this issue [5] by Takkenberg and colleagues on outcome after aortic root replacement with cryopreserved allografts. The background and structure of the aortic valve replacement model will be described, the steps that are taken during one simulation cycle will be illustrated, and the advantages and disadvantages using this methodology will be highlighted.
Background and structure of the microsimulation model
Simulation methodologies emerged from the field of operational research. The best known example of a simulation program is the flight simulator used in the aviation industry to simulate flights and train pilots.
The two types of simulation models that are currently used to model outcome after aortic valve replacement are the Markov state-transition model and the microsimulation model. Both models are state-transition models and based on the same principle: patients who undergo aortic valve replacement can enter a number of discrete health states over time, and transition occurs from one health state to another according to transition probabilities. Although the basic assumptions of the Markov and the microsimulation model are similar, there are a few important differences between the models: using the Markov model a virtual population is followed over time (at population or "macro" level), whereas the microsimulation model allows simulation of the life histories of individual patients (at patient or "micro" level). Also, in the Markov model time is divided into intervals during which events may or may not occur, with microsimulation the time to next event is estimated based on the probability distribution of that event. Finally, the Markov model has no memory, ie, it assumes that subjects in a particular state are a homogeneous group without variability, while microsimulation allows adjusting of hazards for the individual patient depending on prior events (for example, increasing operative mortality with each reoperation).
To date, microsimulation techniques have been used sporadically in clinical medicine studies. A PubMed search (National Library of Medicine, Bethesda, MD) for the term "microsimulation" dated July 6, 2002 resulted in 63 publications that are mainly related to health economics, for example the cost-effectiveness of screening programs. A schematic representation of the basic principle of the microsimulation model is illustrated in Figure 1. After aortic valve replacement the patient can either die as a result of the procedure or stay alive. If the patient stays alive, he or she is at risk for developing valve-related events for the remainder of life. If the patient experiences a valve-related event, he or she may die due to the event (immediately or as a result of reoperation) or stay alive (with or without reoperation). Eventually the patient will either die due to valve-related causes or to other mortality categories. "Other mortality" includes the mortality that is observed in the general population and, in addition, excess mortality that is observed in patients after aortic valve replacement in comparison to the general population and cannot be explained by valve-related events [6–8]. Important causes of this excess mortality are largely unknown but are most likely due to increased occurrence rates of cardiac death and sudden unexplained and unexpected death in patients after aortic valve replacement compared with the general population. Underreporting of valve-related events is probably also a component of excess mortality.
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In order to make predictions using microsimulation it is necessary to obtain real-life estimates of the occurrence of valve-related events after aortic valve replacement and the effect they have on prognosis. In other words, the limited clinical evidence from real-life practice is used to feed the model with information on outcome after aortic valve replacement. Currently, the aortic valve replacement microsimulation model is fed by pooled complication rates from systematic literature reviews and primary data on outcome after aortic valve replacement.
Microsimulation step by step
Figure 2 represents the microsimulation of one life history of a 40-year-old male individual in a population of 40-year-old males requiring aortic valve replacement. A number of steps can be discriminated:
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First, it is randomly determined whether the patient will survive the operation. Operative mortality is dependent on the age of the patient and of the valve type that is implanted. Let’s assume that the patient survives the operation. Next, the real microsimulation process begins.
Step 2
From the general population life-table for 40-year-old males, the age of death is randomly drawn and adjusted for excess mortality after aortic valve replacement by applying an age- and gender-specific hazard ratio to the general population life-table. The random draw in this example results in death at the age of 75, if no valve-related events interfere.
Step 3
Next, for all valve-related events the virtual age at which they will take place is calculated by randomly drawing the age at which each valve-related event would take place from the distribution of the duration until each valve-related event, starting at the time of primary valve surgery. This distribution can be based on linearized occurrence rates but also on hazard estimates that change over time (for example, the hazard for structural valve deterioration of tissue valves increases with time). The valve-related event with the earliest age of occurrence is considered to be the first event that really happens. The probability of immediate mortality due to the event is used to randomly determine whether the patient will die of the event or not. In the first case the simulation of this patient ends, in the latter case the simulation goes on and the time to the next event is determined. If the distributions of time until events are affected by the event that just occurred, new random times until event are drawn from the adapted distributions. Again the event with the earliest time of occurrence will be the one that really occurs. This process continues until the patient either dies from a valve-related event, or the estimated age of death has been reached, which is 75 years in this example. Of note, it is very well possible that the patient dies without experiencing valve-related events.
Step 4
This simulation cycle is repeated for a large number of random 40-year-old male patients (for example 10,000 or 100,000), and thus a virtual population of 40-year-old males with all possible outcomes after aortic valve replacement is created. From this population average estimates of outcome can be calculated, for example event-free life expectancy, total life expectancy, and lifetime event risk.
The more patients are simulated, the more precise the estimates of outcome become because random noise disappears. This phenomenon is also illustrated in Figure 3, which depicts a known distribution, in this example an exponential distribution for mortality with a hazard of 3% per year (dotted line). From this known distribution four random samples of time to death are drawn, with sample sizes of 5, 15, 35, and 100 patients. Figure 3 reveals that by increasing the sample size of random draws the empirical distribution function will more and more approach the true distribution function.
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The example in Figure 2 indicates that microsimulation is not only capable of taking in account life expectancy of the patient, changing hazards over time, and allowing events to occur repeatedly over time; the microstimulation adjusts hazards depending on events that occurred in the past. In addition, it allows detailed insight into the life history of each virtual patient, including the duration of the event-free period, the total number of years lived, and the numbers of each of the events per patient. Standard statistical techniques for outcome analysis also address each of these issues individually. The added value of microsimulation is that it integrates these multiple, complex, and interrelated factors that determine outcome after aortic valve replacement.
The three major disadvantages of the microsimulation model are the following: (1) it is a simplification of real life; (2) it requires several assumptions regarding mortality after aortic valve replacement and the occurrence of valve-related events; and (3) it is limited by the quality of the input.
By structuring the clinical problem, simplification of reality cannot be avoided. To date, the microsimulation model only considers age and gender when calculating prognosis, although a number of other factors are also important determinants of outcome, for example the need for concomitant coronary artery surgery, etiology of the aortic valve disease, heart rhythm, and left ventricular function. Therefore, it is yet unable to make predictions taking in account all these important additional risk factors. These risk factors should and, ultimately, will be integrated into the microsimulation model to give more precise patient-specific estimates. However, by enabling us to make age- and gender-specific estimates of outcome, the microsimulation model is already helping us to get some rudimentary insights into overall patient prognosis.
Several assumptions are necessary when using microsimulation. First of all an excess mortality hazard after aortic valve replacement is assumed. As explained above this is done because the additional mortality that is observed after aortic valve replacement can only in part be explained by valve-related events. The causes of this additional mortality are probably related to the heart valve disease, associated with myocardial muscle abnormalities, and increased risk of heart rhythm disturbances. Future research should be aimed at improving knowledge on these causes of excess mortality. Also, several assumptions are made with regard to the occurrence of valve-related events. For example the hazard for thromboembolism is constant with time and patient age, although in fact there is evidence that with age this hazard increases. However, this hazard also increases in the general population and, therefore, is implemented in the background mortality of the model that is based on the general population. Further studies are necessary to study the true relation between thromboembolism, time, and patient age.
The quality of the input of the model is the third potential limitation to a microsimulation model. Because most of the input of the model is currently obtained from pooled reported clinical evidence, the quality of the input may be adversely affected by heterogeneity between the studies and publication bias. Also, the estimated hazards obtained from current clinical evidence that are entered into the aortic valve replacement microsimulation model all carry some uncertainty. For example, the structural valve failure hazard for bioprostheses and allografts varies with patient age. Empirical data on this subject are scarce and have a limited follow-up. This results in a considerable degree of uncertainty regarding this parameter. By means of sensitivity analysis one can investigate the magnitude of the effect that this uncertainty may have on the outcome of the microsimulation model.
Conclusions
Is microsimulation a valid tool for prediction of outcome after aortic valve replacement? The methodology is only as good as the assumptions that define the model, and the available reported evidence from which the parameters of the model are estimated. An advantage of this method is that it is easy to change the input of the model as new evidence on outcomes after aortic valve replacement becomes available. Ideally, this methodology could eventually be individualized to the patient sitting across the table in the doctor’s office deciding what the most appropriate valve substitute is in his or her particular clinical situation. Microsimulation and associated simulation techniques have the potential to become an additional dynamic source of insight into the prognosis after aortic valve replacement.
References
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