How microsimulation translates outcome estimates to patient lifetime event occurrence in the setting of heart valve disease

Summary

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Treatment decisions in healthcare often carry lifelong consequences that can be challenging to foresee. As such, tools that visualize and estimate outcome after different lifetime treatment strategies are lacking and urgently needed to support clinical decision-making in the setting of rapidly evolving healthcare systems, with increasingly numerous potential treatments. In this regard, microsimulation models may prove to be valuable additions to current risk-prediction models. Notable advantages of microsimulation encompass input from multiple data sources, the ability to move beyond time-to-first-event analysis, accounting for multiple types of events and generating projections of lifelong outcomes. This review aims to clarify the concept of microsimulation, also known as individualized state-transition models, and help clinicians better understand its potential in clinical decision-making. A practical example of a patient with heart valve disease is used to illustrate key components of microsimulation models, such as health states, transition probabilities, input parameters (e.g. evidence-based risks of events) and various aspects of mortality. Finally, this review focuses on future efforts needed in microsimulation to allow for increasing patient-tailoring of the models by extending the general structure with patient-specific prediction models and translating them to meaningful, user-friendly tools that may be used by both clinician and patient to support clinical decision-making.

INTRODUCTION

Treatment decisions in healthcare often carry lifelong consequences. For example, a 55-year-old male with a bicuspid aortic valve, who has been under surveillance for 7 years, now presents with severe valvular stenosis with a peak velocity of 5.0 m/s and trivial regurgitation. He is asymptomatic with a normal left ventricular function, has no further comorbidities and leads an active lifestyle. According to the latest European guidelines, aortic valve replacement should be considered [1]. During decision-making, his surgical risk for the upcoming intervention as well as valve selection is contemplated upon. However, it is reasonable to already consider the consequences of this decision for the distant future. What are the consequences of treatment choices for this intervention, and how do they influence decision-making in future treatment decisions that this patient will face? What are the different lifetime treatment strategies for this individual patient, and is it possible to determine an optimal treatment strategy, if any?

Several risk-prediction models have been developed to estimate surgical risk, such as EuroSCORE II [2]. Not all are heart valve disease (HVD)-specific and are developed to predict short-term operative risks. Nevertheless, models that estimate consequences of lifetime patient trajectories for different treatment strategies are lacking and urgently needed because the initial treatment choice may impact future treatment choices later in life, especially with an ever-evolving palette of HVD treatment options [3, 4]. In this regard, ‘microsimulation’ models provide a useful tool [5], as microsimulation models are used to simulate the clinical pathway and health outcomes of individuals and populations over time, allowing for exploration of the potential impact of different treatment decisions.

In this way, microsimulation can help unravel the impact of a variety of decisions and guide which treatment(s) might be preferred in specific circumstances. This review aims to explain the concept and the mechanism of microsimulation using the example of patients requiring aortic valve intervention.

MICROSIMULATION CONCEPT

The microsimulation models discussed in this paper are part of the state-transition model family, in which members of a population are allocated to discrete health states, e.g. alive or dead. Transitions between health states at predetermined time intervals occur based on transition probabilities. On a population level, these models are called ‘state-transition’ cohort models [6], and they can provide projections of long-term outcomes before and after interventions in homogeneous cohorts. Microsimulation models are individualized state-transition models and differ from state-transition cohort models, in that they model all possible individual trajectories of heterogeneous individuals. Aggregating the outcomes of multiple individuals results in a particular distribution of an outcome of interest, e.g. valve-related complications such as endocarditis.

A major advantage of microsimulation is that it allows for ‘variability’ across individual trajectories. This makes it well-suited for supplementing clinical practice, where ‘variability’ tends to be the rule rather than the outlier. In the case of the 55-year-old male HVD patient, it is known that his lifetime risk of sudden, unexplained death is higher than that of a 55-year-old male in the general population, but, logically, not everyone with this diagnosis dies at once; there is variability in time of death and cause of death between individuals. It is also known that a heart valve intervention comes with risks but, fortunately, not everyone dies after a heart valve intervention. Accounting for this variability, when does (in general) the scale tip in favour of a certain decision for this particular patient? When should the asymptomatic 55-year-old male with a bicuspid aortic valve undergo an intervention, and what type of intervention, to ensure optimal outcome during a lifetime? And what are outcomes following different treatment approaches? It would be of tremendous value if thousands of virtual patients just like him/her existed and the different impacts of each different decision could be explained. This is precisely how microsimulation may help decision-making in daily practice.

KEY COMPONENTS

Microsimulation models are currently being used in several settings, such as the prediction of traffic flow, financial transactions or spread of pathogens [7–9]. Additionally, it is used for different health applications, such as the cost-effectiveness of prostate cancer or cervical cancer screening policies [10, 11]. As such, these models can have numerous configurations and may be difficult to grasp, but state-transition models in healthcare have several key components in common, namely: health states, transition probabilities, cycles and input parameters. To illustrate these concepts, a microsimulation model was constructed, in which patient outcome after aortic valve intervention is evaluated.

Health states

In essence, state-transition microsimulation models consider the probability of switching from one health state to another during a particular time interval. So, a priori, different health states should be defined. In most models, these health states will involve ‘dead’ and ‘alive’, but can become more complex. For instance, common health states resemble the health–sick–sicker–death model, in which the health states are categorized according to level of severity of a certain illness [12]. In the case of the HVD patient, the following health states were previously defined: alive after surgical aortic valve replacement, alive after transcatheter aortic valve replacement and dead. This is schematically displayed in Fig. 1. In this visualized model, the late outcomes of patients after aortic valve replacement are of interest [13].

Transition probabilities and cycles

Transition probabilities determine the probability of changing from one state to another during a given time period. These probabilities are coupled with the ‘cycles of’ the microsimulation model, which are sequential steps in time of a discrete time interval (e.g. 1 month or 1 year). At the beginning of each cycle, a hypothetical two-sided dice, analogous to a Bernoulli trial, is thrown for each individual and, depending on the magnitude of the transition probability, the dice will more likely land on the current health state or another health state (Fig. 2). In the total cohort, health state probabilities are averaged over time. Please note that, in this paper, only state-transition models using a cyclic pre-specified (discrete) time interval (e.g. 1 month or 1 year) are discussed. It is also possible to develop continuous microsimulation models by simulating time-to-event, considering time as a continuous variable [14].

Parameters and uncertainty

Parameters encompass all the numerical input the model requires to simulate patient lives, so the number of total cycles and transition probabilities are all parameters needed to run the model. In the example of the HVD model in Fig. 1, all the parameters specified in Table 1 are required. The source of parameter estimates can vary; one can use systematic reviews with meta-analyses and/or large patient-level databases to estimate (pooled) event rates/risks, which can be turned into transition probabilities.

Variability can occur on 2 levels. First, variability in outcomes between identical individuals, derived from the stochastic process of throwing dice (first-order uncertainty) occurs. This variability is higher if a small number of patients are simulated, and can be decreased by increasing the number of simulated patients [15, 16]. Furthermore, some degree of uncertainty is always present in the input parameters themselves (second-order uncertainty). In literature, this is illustrated by the 95% confidence interval, reflecting an underlying probability distribution. State-transition microsimulation models can consider the uncertainty in input parameters and incorporate its implications into the modelled outcomes. This is done in so-called probabilistic sensitivity analysis. Probabilistic sensitivity analysis is essentially re-running the microsimulation multiple times and remembering the outcome. Each time, a value for each input parameter is randomly drawn from its respective probability distribution. When this process is repeated numerous times, the resulting aggregated outcomes can be summarized into an outcome distribution, effectively capturing the associated uncertainty.

EVENT SIMULATION

The model presented in Fig. 1 represents a simplistic microsimulation model, and does not capture all the potential clinical pathways that patients may experience after aortic valve intervention. Therefore, development of a conceptual framework of different pathways that may affect transition between health states is needed. Building such a framework requires clinical knowledge and is best discussed in focus groups with clinicians [17]. This is done in a previously developed microsimulation model that incorporated all relevant clinical pathways after heart valve surgery (Fig. 3) [15]. These pathways rely on the event–consequence structure. At each cycle, a dice is thrown to determine if a patient undergoes an event, such as endocarditis (the ‘event’). The probability that the dice lands either on the side of the event or on the side of no event is based on the available literature or original patient data. If a patient has the event, a new dice is thrown to determine if the patient either dies, undergoes a reintervention or is treated conservatively. If the patient undergoes a reintervention, another dice is thrown to determine if the patient survives the reintervention. The potential snowball effect becomes immediately clear; if the probability that a patient develops endocarditis changes (for example by choosing another valve conduit) (Fig. 4), this impacts the occurrence of reintervention and reintervention-related mortality following the event.

OUTPUT OF MICROSIMULATION

Microsimulation-based outcomes are generally reported as lifetime risk estimates and mean (event-free) life expectancy [4, 13, 18]. After applying the probabilistic sensitivity analysis, these are reported along with a 95% credible interval. The interpretation of a credible interval differs from a 95% confidence interval. A 95% credible interval constitutes the interval within which an unobserved parameter (the outcome) will fall with 95% probability given the observed data (the input parameter). The 95% confidence interval denotes that in many repeated samples, 95% of the resulting intervals include the true parameter value.

EXTENSIONS OF MICROSIMULATION MODELS

In simple microsimulation models, a static transition probability to switch between health states may be assumed, but in clinical practice, such constant probabilities may not always be accurate. For instance, it is well-known that the hazard of a valve-related reintervention due to structural deterioration of a biological valve increases with time since the initial operation. Accordingly, transition probabilities should change over time—i.e. ‘time-varying’. It is also known that not every patient is equally prone to valve deterioration; for example in very young patients, bioprosthetic valve deterioration is more likely than in older patients. Hence, transition probabilities should be dependent upon individual patient characteristics—i.e. ‘patient-tailoring’ [15, 19, 20]. One of the major advantages of microsimulation is that the flexible structure of these models allows for several extensions that incorporate these concepts.

Time-varying transition probability

The transition probability between health states does not have to be constant over time. In microsimulation, it is possible to estimate time-varying transition probabilities based on the time-to-event data (such as freedom from reintervention curves). In this case, a parametric survival distribution can be fitted to the time-to-event data. Thereafter, the transition probability at every cycle is computed (Fig. 5).

Patient-tailoring

Prediction models, ideally based on large datasets, can be used to estimate patient-tailored transition probabilities, ensuring variation in transition probabilities for patients with specific characteristics. These can also be made hospital- or setting-specific, if the data allows for it. In other words, each unique set of patient characteristics is appointed its own dice. For example, the probability of dying within 30 days after an aortic valve intervention is determined by multiple patient-related and procedural factors. Old and frail patients and those with comorbidities have higher likelihoods of dying after an intervention, and an isolated aortic valve replacement carries a lower 30-day mortality risk than combined procedures. Patient-specific event probabilities may be estimated by a logistic regression model (e.g. the EuroSCORE II) and incorporated in the microsimulation model. This has been implemented in a previous microsimulation model of elderly patients undergoing aortic valve surgery [21]. This may be extended to late outcomes using survival models such as accelerated time failure models or Cox proportional hazard models. The predictions of these models may, yet again, be converted to transition probabilities for specific patient profiles, allowing for further optimization of the microsimulation model. Of course, recurrent events can also be implemented in the model. For example, by changing the transition probabilities for the next stroke after a previous stroke for individual patients.

DECONSTRUCTING MORTALITY

Not all patients with a certain disease will die because of it. For example, the HVD patient may die from other causes, such as cancer or a car accident. This kind of mortality is called the ‘matched-general-population mortality’, or ‘background mortality’. Clinically, this is important to consider, e.g. very old patients have high ‘background’ mortality, so surgery in these patient will probably not prolong life substantially and, hence, may not outweigh early mortality risks. Matched-general-population mortality of patients with HVD should be matched with the general population on at least age, sex and country of origin, because older patients are more likely to die within the next year compared to younger patients.

In previous microsimulation models regarding HVD [4, 13, 18, 22, 23], mortality has been deconstructed into 3 components: ‘matched general population mortality’, ‘valve event-related mortality’ (mortality directly due to heart valve-related events, e.g. reintervention or endocarditis) and ‘excess mortality’. Excess mortality is the additional mortality observed in HVD patients that is not explained by matched-general-population mortality and valve event-related mortality. Clinically, this may be due to, for example, left ventricular dysfunction associated with chronic HVD [24]. As such, excess mortality is calculated by subtracting the matched-general-population mortality and valve event-related mortality from the observed mortality in HVD patients (Fig. 6).

Summarizing, mortality in microsimulation consists of several components that are aggregated in a transition probability of death during each cycle. This process accounts for the matched-general-population mortality and excess mortality, as well as occurrence of valve-related events and their potentially lethal consequences, again these are based on literature or original patient data.

APPLICATION OF MICROSIMULATION IN CARDIOVASCULAR RESEARCH

Microsimulation has been increasingly applied in cardiovascular research, but absolute numbers remain low. As an illustrative example, a simple PubMed search consisting of: ‘microsimulation’ AND ‘cardiovascular’, conducted on 23 March 2023, yielded 254 results starting from 1999. Strikingly, 54% of the publications were published in the last 5 years, from 2018 to 2022, underscoring that microsimulation has recently gained an increasing amount of attention in the field of cardiovascular research.

A large diversity of applications is found across the studies. One-hundred and forty articles (55%) have focused on costs modelling and cost-effectiveness studies in cardiovascular disease, mainly in the setting of lifestyle interventions or medication prescription and associated effects [25–27]. Several studies have focused on modelling of lifetime outcomes after coronary artery bypass surgery or heart valve surgery [4, 18, 22, 23, 28, 29].

As value-driven healthcare is increasingly practiced, demand for data regarding quality-of-life and patient-reported outcome measures (PROMS) has likewise increased. To accommodate this, the concept of quality-adjusted life years and PROMS has already been integrated into some microsimulation models [15, 21].

ADVANTAGES OF MICROSIMULATION

Microsimulation’s full potential is yet to be unleashed in clinical outcome modelling for lifetime decision-making in cardiac disease. Awareness of the possibilities and advantages of microsimulation is essential to facilitate increased application of these models in clinical research. Advantages include:

1. In times of increasing numbers of large registries and a growing body of literature, microsimulation is one of the few approaches that allows for utilization of different data sources as input.

2. Individual patient lifetimes are simulated; enabling patients and clinicians to look beyond the 1st intervention or event, in multiple types of events. Moreover, microsimulation can demonstrate cost-effectiveness of a particular lifetime strategy [15, 30].

3. There is vast potential for patient-tailoring.

4. It opens an opportunity for so-called ‘scenario analyses’. Due to the aforementioned snowball effect, it is useful to model what will most likely happen in the long term if different choices are made. For example, in the HVD patient, choosing for watchful waiting versus immediate intervention, and in case of an intervention, choosing a mechanical versus biological valve substitute.

5. The output of microsimulation models is easy to visualize and interpret (e.g. lifetime risks and life expectancy) and clinically useful to both patients and clinicians.

6. In microsimulation, opposed to some artificial intelligence-based algorithms, microsimulation is not a ‘black box’. Insight into all stages of the modelling process—i.e. model input, assumptions and output—can be obtained. This ensures transparency regarding the generation of outcome estimates.

CURRENT LIMITATIONS AND FUTURE PERSPECTIVES

An important limitation of microsimulation models includes the fact that the process of building and employing a microsimulation model is time-consuming, limiting its application. Moreover, appropriate input data are not always available. The limited use of microsimulation models may also partly be because current microsimulation models do not sufficiently consider individual patient characteristics and therefore provide a picture that is too general, which can only be applied at the level of a population. To develop microsimulation models that are more valuable in clinical practice, efforts should be made to increase patient-tailoring of transition probabilities. Like all statistical models, low quality of the input data begets low quality of the output of the model. Finally, awareness among clinicians regarding the existence, validity and potential of microsimulation models can be expanded.

Traditional statistical models are commonly used, but novel machine learning and predictive artificial intelligence algorithms are on the rise [31, 32]. These machine learning algorithms and predictive artificial intelligence algorithms may yield better patient-specific estimates of events, and may be integrated as extensions of microsimulation.

Additionally, in HVD, many decisions are not made based on a single measurement but on successive measures over time (e.g. repeated echocardiograms of valve dysfunction). Extending patient-tailoring based upon models that use repeated measures within such microsimulation models may prove of additional benefit in patient-tailoring of transition probabilities.

Future efforts should focus on modelling multiple interventions over a lifetime, considering all possible treatment options as the index procedure while keeping in mind the possibility of a 2nd or even 3rd intervention later in life. For example, a patient with aortic valve disease may 1st undergo a mechanical valve replacement followed by a bioprosthetic 3rd replacement and a valve-in-valve transcatheter aortic valve replacement over a lifetime. Another lifetime trajectory might be that of an aortic valve repair followed by a Ross procedure, ending with a bioprosthetic aortic valve replacement. Such microsimulation-based outcome projections of not only each individual procedure but of a lifetime trajectory of treatments can be used to aid decision-making for HVD patients. Of note, surgical and non-surgical interventions may be preceded by a strategy of watchful waiting. Initiatives such as the Heart Valve Society’s medical arm registry [33] might contribute to generating microsimulation models of the natural course of HVD, to provide patient-tailored recommendations on whether to intervene or not, additional to the timing of intervention.

In the setting of a shared decision-making process, it is important to know on which outcomes clinical decisions should be based, or in other words: which outcomes matter most to each patient? These might include more quality-of-life-related outcomes as measured by PROMs. International initiatives such as the International Consortium for Health Outcomes Measurement (ICHOM) HVD or heart failure standard set may aid in identifying these outcomes [34]. Nevertheless, shared decision-making can ultimately only be achieved by distilling individual patient goals, values and preferences while considering the patient’s unique clinical situation and, the best available medical evidence [35]. Although currently no valid individualized risk-prediction models that account for measures difficult to quantify, e.g. lifestyle habits or medical adherence exist, should they become available, these can be integrated into future microsimulation models.

Another important challenge to address is the fact that most microsimulation models are not user-friendly. After all, most models only exist as code in programming languages [20, 36, 37]. Therefore, now that extended microsimulation models are under development by experts, further translation of these models to easy-to-use tools for both patients and clinicians may prove valuable in increasing their utility in multidisciplinary team meetings, patient consultations and shared decision-making.

SOFTWARE

A vast repertoire of programming languages and corresponding software interfaces is available to perform microsimulation. Microsimulation analyses within the field of HVD-related research are most commonly carried out using the R programming language and R Studio software (R statistical software, version 4.2.2, R Development Core Team, R Foundation for Statistical Computing, Vienna, Austria). Tutorials in R also have been published [20]. Microsimulation models used in other fields of medical research, e.g. by the National Cancer institute Cancer Intervention and Surveillance Modelling Network, are written in a variety of languages ranging from Delphi, JAVA, Fortran, C/C++, Python to R. The choice of programming language and interface is often a matter of usability, preference and habit.

CONCLUSIONS

In this review, the general structure, clinical applications and potential extensions of microsimulation models are discussed. For microsimulation models to be used as decision tools in clinical decision-making, efforts should be focused on increasing patient-tailoring by extending the general structure with patient-specific prediction models, and development towards meaningful, user-friendly tools.

ACKNOWLEDGEMENTS

This work was not previously presented or published.

FUNDING

All authors currently receive no research funding for this project.

Conflict of interest: none declared.

DATA AVAILABILITY

No new data were generated or analysed in support of this research.

Author contributions

Maximiliaan L. Notenboom: Conceptualization; Investigation; Methodology; Project administration; Visualization; Writing—original draft; Writing—review and editing. Reda Rhellab: Conceptualization; Investigation; Methodology; Project administration; Visualization; Writing—original draft; Writing—review and editing. Jonathan R.G. Etnel: Conceptualization; Investigation; Methodology; Project administration; Supervision; Visualization; Writing—review and editing. Simone A. Huygens: Conceptualization; Investigation; Methodology; Software; Supervision; Visualization; Writing—review and editing. Jesper Hjortnaes: Conceptualization; Investigation; Methodology; Supervision; Visualization; Writing—review and editing. Jolanda Kluin: Conceptualization; Investigation; Methodology; Resources; Supervision; Visualization; Writing—review and editing. Johanna J.M. Takkenberg: Conceptualization; Investigation; Methodology; Resources; Supervision; Visualization; Writing—review and editing. Kevin M. Veen: Conceptualization; Investigation; Methodology; Supervision; Visualization; Writing—original draft; Writing—review and editing.

Reviewer information

European Journal of Cardio-Thoracic Surgery thanks Jose G. Fragata, Gary L. Grunkemeier and Armin Zittermann for their contribution to the peer review process of this article.

REFERENCES

ABBREVIATIONS

ABBREVIATIONS
 
• HVD

  Heart valve disease

 
• ICHOM

  International Consortium for Health Outcomes Measurement

 
• PROMS

  Patient-reported outcome measures

Author notes