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J Thorac Cardiovasc Surg 2007;134:702-709
© 2007 The American Association for Thoracic Surgery
Surgery for Acquired Cardiovascular Disease |
a Department of Cardio-thoracic Surgery, Erasmus University Medical Center, Rotterdam, The Netherlands
b Department of Public Health, Erasmus University Medical Center, Rotterdam, The Netherlands
c University of British Columbia, Vancouver, Canada
d Providence Health System, Portland, Ore.
Received for publication March 6, 2006; revisions received February 22, 2007; accepted for publication March 8, 2007. * Address for reprints: Martijn W. A. van Geldorp, MD, Department of Cardio-thoracic Surgery, Erasmus Medical Center, Room Bd 575, PO Box 2040, 3000 CA, Rotterdam, The Netherlands. (Email: m.vangeldorp{at}erasmusmc.nl).
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Abstract |
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 Top Abstract IntroductionMaterials and MethodsResultsDiscussionConclusionsReferences |
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Methods: By using a primary dataset containing 1847 patients and 14,429 patient-years, advantages and disadvantages of standard methods of outcome analysis are discussed, and the potential role of microsimulation is illustrated by means of a step-by-step explanation of building, testing, and using such a model.
Results: Total life expectancy, event-free life expectancy, and reoperation-free life expectancy for a 65-year-old male patient were 10.6 years, 9.2 years, and 9.8 years, respectively. Lifetime risk of reoperation due to structural valve deterioration was 13.3%.
Conclusions: Microsimulation is capable of providing accurate estimates of age-related life expectancy and lifetime risk of reoperation for patients who underwent aortic valve replacement with the Carpentier–Edwards supra-annular valve. It provides a useful tool to facilitate and optimize the choice for a specific heart valve prosthesis in a particular patient.
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Introduction |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionConclusionsReferences |
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and it is often not easy to translate these outcomes into the actual consequences for the patient who requires AVR.
We have previously developed an alternative method to study outcome after AVR that allows direct estimation of patient outcome after AVR: microsimulation.2 This method solves most of the methodologic limitations of standard outcomes analyses but does have several limitations of its own.
The goal of this article is to provide insight into microsimulation methodology and to give an overview of the advantages and disadvantages of microsimulation compared with standard methods of outcome analysis. This will be done by using primary data on outcome after AVR with the Carpentier–Edwards supra-annular valve (CE-SAV) prosthesis from a large single center in Canada.3 The following issues will be addressed:
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Materials and Methods |
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These operations were conducted from February 1982 through December 1999 at the affiliated teaching hospitals of the University of British Columbia in Canada, namely St Paul’s Hospital, Vancouver General Hospital, and the Royal Columbian Hospital.
The characteristics of the complete dataset (n = 1847) are summarized in Table 1. To calculate the input of the microsimulation model, 85 aortic valve rereplacements were excluded, resulting in 1762 remaining primary AVRs (see Table 1 for characteristics). Details of the occurrence of valve-related events and the associated mortality of these primary AVRs are given in Table 2. Valve-related events were defined according to the Society of Thoracic Surgeons/American Association for Thoracic Surgery Guidelines for Reporting Morbidity and Mortality after Cardiac Valvular Operations,4 with 2 modifications: transient ischemic attacks were not counted as neurologic events (to avoid recall bias), and structural valve deterioration (SVD) was only included if diagnosed either at reoperation or autopsy.
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can be explained by the use in the present study of a subset of 1762 patients and by differences in definition of SVD.
Standard Methods of Outcome Analysis
The Kaplan–Meier (KM) and actuarial methods are commonly used time-to-event models to estimate the survival of patients after AVR. The distribution of the time to death for currently alive patients is assumed to follow the pattern of those who have already died. These methods have now been extended to summarize valve-related events, such as SVD, that are not necessarily fatal. In Figure 1
the cumulative (actuarial) risk of reoperation for SVD calculated by using the KM method (the complement of cumulative freedom from reoperation for SVD) is displayed for the CE-SAV dataset. For estimating the lifetime risk of nonfatal events, the KM and actuarial methods assume noninformative censoring: they assume that the risk of dying and the risk of SVD are independent, which in fact is not true (patients with high risk of death have lower risk of SVD, and patients with low risk of death have a higher risk of having SVD at some time in their lives). The KM and actuarial methods therefore estimate the freedom from SVD by also censoring patients who have not yet experienced the event, including those who have died and will therefore never have the event. In doing so, they describe the risk of SVD for the patient based on the assumption of immortality, resulting in a higher probability of SVD than that actually had by the patient. This effect is magnified with advancing age of valve implantation and could serve to underestimate the benefits of biologic valve implantation. Therefore although the KM and actuarial methods are perfectly capable of analyzing fatal events, for describing competing events, their value is dubious because in clinical medicine the assumption of noninformative censoring can often not be guaranteed.
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This method takes into consideration the competing risk of death, it excludes future events attributed to already deceased patients, and it therefore calculates the percentage of patients who will experience an event before they die, answering the more pertinent question of the lifetime risk of the event.1,7-9 As is shown in Figure 1, the cumulative actuarial risk of reoperation for SVD (7.0% at 15 years) is higher than the actual patient risk of reoperation for SVD (4.3% at 15 years).
The guidelines for reporting morbidity and mortality after cardiac valve operations have also incorporated the actual method.4 Except for the cumulative incidence estimation, competing risk analyses in general do have the disadvantage of assuming that the competing events are independent. However, occurrence of an event (or reintervention) might alter the subsequent survival time and alter the risk of reoccurrence of the event.
An advantage of the KM method and the cumulative incidence method is that they can be performed with standard statistical software and that they give a valid general impression of outcome in patient populations after valve replacement. However, there are several limitations to these methods. In both KM and cumulative incidence analysis, an event can only occur once in the same patient. After the occurrence of an event, the patient is excluded from the analysis. Furthermore, although the KM and cumulative incidence analyses permit any hazard function, whereas the parametric exponential method requires a constant hazard, neither of these models take into account that event risk might change over time and might change after occurrence of events.
Simulation Methods
To obtain optimal insight into outcome after valve replacement in a particular population, ideally all patients should be followed over time until everybody has died, and all events (not only the first) that took place over time should be analyzed. In real life, the former is usually not a realistic option and the latter is difficult and time-consuming to achieve by using standard methods of outcome analysis. Simulation methods offer a complementary tool to standard methods of outcome analysis by simulating the lives of virtual patients until death and taking into account all complications that might occur over time (including repeating events and changing hazards over time, with the occurrence of prior events, or both).
The two types of simulation models that have been used to model patient outcomes after AVR are the Markov state-transition model and the microsimulation model.2,10 The Markov model creates a virtual population of patients that is followed over different time intervals until all patients have died. At each time interval, a transition from one health state to the other can occur, depending on predefined operative mortality estimates, occurrence rates of valve-related events and their consequences (death or reoperation), and the probability of dying of other non–valve related causes. Events can occur repeatedly over time, and hazards can change with each time interval, but it is hard to change hazards after the occurrence of an event by using a Markov model.
A microsimulation model is a computer model that simulates a representative population but at the level of the individual: the micro level. The remaining life (until death) of a single patient with a particular age and sex after AVR with a given valve type is simulated. It takes into account the morbidity and mortality that the patient might experience according to predefined estimates of operative mortality, event occurrence and their consequences (death or reoperation), and the probability of dying of other non–valve related causes. By repeating this simulation multiple times (eg, 10,000 times), a virtual patient population is generated, consisting of identical patients with all possible outcomes after AVR. A detailed account of the microsimulation structure and methodology has been given previously.2,11
We used the AVR microsimulation model, designed at our institution, to provide insight into the age- and sex-related life expectancy (LE) and lifetime risks of valve-related events after AVR with the CE-SAV bioprosthesis because it has several advantages over the Markov model. First, the microsimulation model allows simulation of the individual life histories of patients, starting directly after AVR and ending with the death of the patient (follow-up does not end at the event), rather than following a virtual population over time. By simulating multiple times, the lives of identical virtual patients, all possible competing events that might occur during the remainder of life, and the time to occurrence of these events can be studied. Then, by using this virtual closed-cohort dataset, the average prognosis (including the lifetime risk of SVD and of other valve-related events) of an individual patient with these characteristics can be calculated. Furthermore, unlike the Markov model, in which time is divided in intervals during which an event might or might not occur, the microsimulation model estimates the time to the next event based on the occurrence probability of that event. Finally, the microsimulation model allows for adjustment of event occurrence rates with time or based on the occurrence of prior events (eg, operative mortality increases with age and with each successive reoperation).
Building a Microsimulation Model
Figure 2
shows the general structure of the microsimulation model, including and itemizing the information that is needed to start building the model.
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Operative mortality was estimated as 2.6% for a 40-year-old man, increasing with an odds ratio of 1.034 for age (per year). For a 69-year-old man, operative mortality would be 6.6%. The real operative mortality derived from the CE-SAV dataset for primary AVR (mean age 69 years) was 5.0%.
Estimates of occurrence rates of valve-related events
The estimates of occurrence rates of valve-related events are derived from the primary dataset described earlier (patients with primary AVR only) and are depicted in Table 2. Assuming a constant hazard over time, weighted mean estimates of linearized annual occurrence rates were calculated for valve thrombosis, thromboembolism, endocarditis, and nonstructural dysfunction, respectively. The occurrence of hemorrhage was modeled as an age-dependent hazard of 0.076, with an age-dependent mortality of 0.034.12
A reoperation because of SVD is more relevant to the patient than the occurrence of SVD without consequences.7 Furthermore, the onset and severity of SVD is difficult to measure. Hence SVD was defined as "reoperation caused by SVD" or "SVD confirmed by means of autopsy." The cumulative risk of SVD in a bioprosthesis decreases with increasing age of the patient at valve implantation and increases subexponentially with elapsing time since implantation.13 Grunkemeier and colleagues14 have shown that the Weibull distribution, a generalization of the exponential distribution, was efficient in summarizing SVD in biologic valves.15 However, they stressed that at least 12 years of follow-up are needed to provide reliable estimates.14 We used primary data on the CE-SAV bioprosthesis, with a 20-year follow-up, as described in the previous section, to calculate the parameters of the Weibull distributions.3 The value of the scale (
) parameter of the Weibull model, fitted to represent SVD depends on age: + e
2.2240+0.0154*Age. The shape parameter (ß) was estimated at 3.316. With the resulting age-dependent Weibull distributions for reoperation caused by SVD, median time to reoperation caused by SVD in the supra-annular valves was 19.2 (range 18.0–20.5), 22.4 (range 20.5–24.6), and 26.2 years (range 23.1–29.7), respectively for 55-, 65-, and 75-year-old male patients.
Mortality risk associated with each valve-related event
The estimates of mortality risk associated with each valve-related event are derived from the primary dataset described earlier and are depicted in Table 2.
Reoperation risk associated with each valve-related event
The estimates of reoperation risk associated with each valve-related event are derived from the primary dataset described earlier and are depicted in Table 2.
Mortality risk associated with each reoperation
The estimates of reoperative mortality risk were also obtained from the previous meta-analysis discussed above.11 For each first and following reoperation in a single patient, the operative mortality of 1.5% was increased, with an odds ratio of 1.7. The mean age of the patients undergoing reoperation in the CE–SAV dataset was 53 years, and therefore the expected reoperative mortality in the dataset would be as follows: 2.7% + 1.034(53-40) + 1.7 = 5.9%. Again, this reoperative mortality was comparable with the observed reoperative mortality in the CE–SAV dataset, which was 5.4%.
Estimate of mortality risk caused by other factors (mortality risk of general population plus excess mortality)
The mortality of a patient after valve replacement is composed of the mortality of the general population, the operative mortality, the valve-related mortality, and an excess mortality. This excess mortality cannot be explained by valve-related events but is due to mortality associated with underlying valve pathology, left ventricular function, increased occurrence of sudden unexpected unexplained death, and the underreporting of valve-related events, respectively.16-18 The model calculates patient outcomes by superimposing the morbidity and mortality estimates of valve-related events on the other components of patient mortality.
The mortality of the general population was incorporated into the model by means of the life table of the relevant age- and sex-matched population, American male subjects in this analysis.19 The excess mortality, not accounted for by the valve-related events, was represented by age- and sex-specific hazard ratios. These hazard ratios have previously been estimated by approximating age- and sex-specific survival curves produced by the model, which contained background morbidity and mortality caused by valve-related events to the corresponding empiric curves obtained from data on stented porcine bioprostheses that contained all 3 components of patient mortality.20,21 The hazard ratios were 2.9, 1.8, 1.2, and 0.8 for male patients aged 45, 55, 65, and 75 years, respectively.16 The LE of a 65-year-old patient, for example, was estimated at 10.6 years. This corresponds to a 10-year survival of 50%, which is comparable with survival in other reports.22-24 However, it is in contrast to an LE of 13.8 years for a 65-year-old male patient in the relevant general population, which translates to a 78% relative LE for the patient. The relative LE of a 65-year-old hypothetical patient who is immune from valve-related events and from operative mortality was about 90%. In the latter instance, the excess mortality of the patient might be related to underlying valve pathology, left ventricular residual hypertrophy, and functional abnormality.
Kvidal and colleagues,17 who investigated this excess mortality after heart valve replacement, described an increasing excess hazard during follow-up and a decreasing excess hazard with advancing age of implantation. This supports a "multiplicative" excess mortality, which was a structural assumption in our model. The use of an "additive" model might overestimate LE estimates, especially in patients younger than 70 years.
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Testing a Microsimulation Model
Validation
There are 2 types of validation: internal and external validation. Internal validation tests whether the results of the microsimulation model correspond to the outcome in the dataset from which the model was derived. For example, observed survival in the CE-SAV dataset was 27% at 15 years, whereas this was 21% by using the microsimulation model for a 69-year-old patient (mean age of the CE-SAV population). Furthermore, observed actual freedom from all-cause reoperation in the dataset was 86% at 15 years, whereas this was 82% for a 69-year-old patient by using microsimulation.
External validation tests whether a model also performs satisfactorily for patients other than the ones from whose data the model was derived. Figure E1
displays the age- and sex-specific survival results of the model with corresponding survival curves for the Carpentier–Edwards standard bioprosthesis (Edwards Lifesciences LLC, Irvine, Calif). This dataset was obtained from the Providence Health System in Portland, Oregon.25 The survival outputs of the microsimulation model for 55- and 65-year-old male patients compared favorably with the corresponding curves of the Carpentier–Edwards standard Portland experience through 25 years after implantation: the 10-year-survival of a 55- and 65-year-old male patient was, respectively, 64% and 50% in the model versus 65% and 53% in the Portland dataset. However, the model showed a slight overestimation of mortality for 75-year-old male subjects compared with the Portland dataset: the 10-year-survival was 32% in the model versus 40% in the Portland dataset. Patients who undergo an operation in this age group do not strictly represent the average patient in this age group who actually requires AVR. In fact, they represent a selection of relatively healthier patients with a relatively better LE. Systematic variations in the patient profile, too, especially in the older age groups, might result in these differences between model output and comparison data.
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It ignores interactions between different parameters and can therefore underestimate the level of uncertainty. Multivariate sensitivity analysis would be preferred, but then also the distributions of the parameters have to be known, which in our study is not yet possible. For this reason, we performed one-way sensitivity analysis, and variation of the estimates by their 95% confidence intervals yielded only very small changes in the long-term outcomes. Therefore we defined larger ranges by increasing and decreasing the baseline estimates by 25%. The resulting LE and EFLE of a 65-year-old male patient for a plausible range of valve-related events and additional mortality is given in Table 3. It shows that variation in the hazard ratio representing excess mortality had the most pronounced effect on both LE and EFLE, and it underscores the importance of the excess mortality on the outcomes of patients after AVR.
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Discussion |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionConclusionsReferences |
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Second, the current simulation model is based on certain structural assumptions regarding mortality and morbidity after AVR. For example, a constant hazard was assumed for the valve-related events other than SVD. Certain hazards of complications, such as hazard of bleeding, will not be constant over time but will increase with advancing age or have a high-risk and a lower-risk phase, such as endocarditis. Therefore, in our model there is an age-dependent risk and age-dependent mortality for "bleeding." The model does not have a 2-period risk for endocarditis because we do not have access yet to primary datasets to support these changing hazards over time. Furthermore, sudden unexpected unexplained death is incorporated in the excess mortality because gaining insight into this determinant remains difficult.27
The third limitation is the fact that the quality of the model, as in any model, is directly dependent on the quality of the input. Especially for input in simulation models, high-quality data are essential. Most of the model input is obtained from meta-analysis of earlier published studies, largely with a retrospective design, which are generally known to underestimate the incidence of (valve-related) events. Furthermore, heterogeneity between the studies and possible publication bias can diminish the quality of the model input.
Finally, another disadvantage is the fact that the microsimulation software is not yet available in standard statistical software packages. However, the computer program, along with an extensive manual to get started with microsimulation, is available at www.cardiothoracicresearch.nl.
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Conclusions |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionConclusionsReferences |
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that microsimulation is capable of translating valve performance into patient outcome by providing age-related LE and risk of reoperation for patients who underwent AVR with the CE-SAV bioprosthesis. These estimates of patient outcome might be used to compare the patient lifetime risk of reoperation with the CE-SAV bioprosthesis with the pericardial valves and with newer bioprostheses in a comparable patient population. This study also showed that microsimulation has several disadvantages and limitations that need to be considered carefully and dealt with systematically when attempting to perform simulation studies.
In conclusion, microsimulation can be a quick, accurate, and useful tool to assess patient outcome after AVR with a specific prosthetic heart valve. Outcomes after implantation of different prosthetic heart valves can easily be compared to facilitate and optimize the choice of specific heart valve prostheses for both physician and patient.
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Footnotes |
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References |
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This article has been cited by other articles:
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  M. W.A. van Geldorp, M. van Gameren, A. P. Kappetein, B. Arabkhani, L. E. de Groot-de Laat, J. J.M. Takkenberg, and A. J.J.C. Bogers Therapeutic decisions for patients with symptomatic severe aortic stenosis: room for improvement? Eur. J. Cardiothorac. Surg., June 1, 2009; 35(6): 953 - 957. [Abstract] [Full Text] [PDF]
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 M. W.A. van Geldorp, W.R. Eric Jamieson, A. P. Kappetein, J. Ye, G. J. Fradet, M. J.C. Eijkemans, G. L. Grunkemeier, A. J.J.C. Bogers, and J. J.M. Takkenberg Patient outcome after aortic valve replacement with a mechanical or biological prosthesis: Weighing lifetime anticoagulant-related event risk against reoperation risk J. Thorac. Cardiovasc. Surg., April 1, 2009; 137(4): 881 - 886. [Abstract] [Full Text] [PDF]
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