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Simulation models to predict outcome after aortic valve replacement

Advances in transcatheter aortic valve replacement have led to the consideration of tissue aortic valve replacement in younger patients. Part of this enthusiasm is the presumption that younger patients would have more flexibility in future treatment options, such as a primary surgical aortic valve replacement followed later by transcatheter aortic valve replacement(s) (valve-in-valve), vice versa, or other permutations. We created a microsimulation model using published longevity of tissue valves to predict the outcomes of patients after primary tissue surgical aortic valve replacement.

The model calculated survival by incorporating annual mortality (Social Security Administration) and mortality from re-replacements (Society of Thoracic Surgeons) in patients with surgical aortic valve replacement. Freedom from reoperation for structural valve degeneration incorporated best published data to determine the annual risk of re-replacement for structural valve degeneration based on implant duration and stratified by patient age. A constant rate of re-replacement for nonstructural valve degeneration indications was also incorporated. Each simulation was performed for 50,000 individuals. Kaplan–Meier curves were generated to represent survival. All simulations were run within the MATLAB environment (The MathWorks, Inc, Natick, Mass).

Earlier decades of life at primary surgical aortic valve replacement were associated with higher incidences of re-replacements and especially multiple re-replacements. For those patients receiving a primary tissue surgical aortic valve replacement at age 50 years, 57.2% will require a second valve, 18.0% will require a third valve, and 1.6% will require a fourth valve with average operative mortalities of 2.9%, 4.8%, and 7.3%, respectively. A 50-year-old patient at primary surgical aortic valve replacement has a 13.1% chance of re-replacement before turning 60 years of age.

Microsimulation incorporates changing hazards to estimate the risk of aortic valve re-replacement in patients undergoing tissue surgical aortic valve replacement and may be a starting point for patient education and health care economic planning.

Although the results of aortic valve replacement with different valve prostheses are well documented in terms of survival, the risks of (valve-related) events are less well explored.

We used a dataset of 3934 patients who underwent aortic valve replacement with either a bioprosthesis (73%) or a mechanical prosthesis (27%) between 1982 and 2003 to simulate the outcome of patients after aortic valve replacement with either valve type. With the use of microsimulation, we compared total age and gender-specific life expectancy, event-free life expectancy, reoperation-free life expectancy, lifetime risks of reoperation, and valve-related events for both valve types.

The total follow-up was 26,467 patient-years. The mean follow-up was 6.1 years in the biological arm and 8.5 years in the mechanical arm. The mean age at implantation was 70 and 58 years for biological and mechanical prostheses, respectively, and the percentage of concomitant coronary artery bypass grafting was 47% and 28%, respectively. For a 60-year-old man, simulated life expectancy in years for biological versus mechanical prostheses was 11.9 versus 12.2, event-free life expectancy was 9.8 versus 9.3, and reoperation-free life expectancy was 10.5 versus 11.9. Lifetime risk of reoperation was 25% versus 3%. Lifetime risk of bleeding was 12% versus 41%.

Even for patients aged 60 years, event-free life expectancy is better with a bioprosthesis. Although the chance of reoperation is higher, the lifetime risk of bleeding is lower compared with a mechanical prosthesis. Comparing lifetime event risks between different types of valve prostheses provides more insight into patient outcome after aortic valve replacement and aids patient selection and counseling.

Numerous reports have been published documenting the results of aortic valve replacement. It is often not easy to translate these outcomes involving the condition of the valve into the actual consequences for the patient. We previously developed an alternative method to study outcome after aortic valve replacement that allows direct estimation of patient outcome after aortic valve replacement: microsimulation modeling. The goal of this article is to provide insight into microsimulation methodology and to give an overview of the advantages and disadvantages of simulation methods (in particular microsimulation) in comparison with standard methods of outcome analysis.

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.

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%.

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.

The probability of a type of failure that is not inevitable, but can be precluded by other events such as death, is given by the cumulative incidence function. In cardiac research articles, it has become known as the actual probability, in contrast to the actuarial methods of estimation, usually implemented by the Kaplan-Meier (KM) estimate. Unlike cumulative incidence, KM attempts to predict what the latent failure probability would be if death were eliminated. To do this, the KM method assumes that the risk of dying and the risk of failure are independent. But this assumption is not true for many cardiac applications in which the risks of failure and death are negatively correlated (ie, patients with a higher risk of dying have a lower risk of failure, and patients with a lower risk of death have a higher risk of failure, which is a condition called informative censoring).

Recent editorials in two cardiac journals have promoted the use of the KM method (actuarial estimate) for competing risk events (specifically for heart valve performance) and criticized the use of the cumulative incidence (actual) estimates. This report has two aims: to explain the difference between these two estimates and to show why the KM is generally not appropriate. In the process we will rely on alternative representations of the KM estimator (using redistribution to the right and inverse probability weighting) to explain the difference between the two estimates and to show how it may be possible to adjust KM to overcome the informative censoring.

The second-generation Carpentier-Edwards pericardial valve (Edwards Lifesciences LLC, Irvine, CA) is widely used for aortic valve replacement. However, knowledge on the long-term outcomes of patients after valve implantation is incomplete. We used microsimulation to calculate the long-term outcome of any given patient after aortic valve replacement with the Carpentier-Edwards pericardial valve.

A meta-analysis of 8 reports on aortic valve replacement with the Carpentier-Edwards pericardial valve (2,685 patients; 12,250 patient years) was used to estimate the hazards of valve-related events other than structural valvular deterioration. Structural valvular deterioration was described by age-dependent Weibull curves calculated from 18-year follow-up, premarket approval, Carpentier-Edwards pericardial primary data. These estimates provided the input data for the parameters of the microsimulation model, which was then used to calculate the outcomes of patients of different ages after valve implantation. The model estimates of survival were validated using two external data sets.

The Weibull analysis estimated a median time to reoperation for structural valvular deterioration ranging from 18.1 years for a 55-year-old male to 23.2 years for a 75-year-old male. For a 65-year-old male, microsimulation calculated a life expectancy and event-free life expectancy of 10.8 and 9.1 years, respectively. The lifetime risk of at least one valve-related event was 38% and that of reoperation due to structural valvular deterioration 17%, respectively, for this patient. The model estimates of survival showed good agreement with external data.

Microsimulation provides detailed insight into the long-term prognosis of patients after aortic valve replacement. The Carpentier-Edwards pericardial valve performs satisfactorily and offers a low lifetime risk of reoperation due to structural valvular deterioration, especially for elderly patients requiring aortic valve replacement.