Comparing the Influence of Heterogeneity on Model Outcomes in Individual-Level and Cohort Simulations: An Exploratory Simulation Study

Abstract

Introduction

When developing health economic simulation models, individual-level and cohort state-transition model types are commonly used. However, heterogeneity and the extent to which it is taken into account is thought to affect simulation outcomes differently in individual-level and cohort simulations, even when model structures are identical.

Objective

This study aimed to investigate the conditions under which the use of different model types may lead to different outcomes and therefore potentially different policy decisions.

Methods

A microsimulation model was used to reflect an individual-level simulation, simulating patient characteristics and, artificially, a cohort-level simulation of identical patients, using the exact same model structure. Four scenarios were analyzed: heterogeneity in age (scenario 1) influencing progression and recovery probabilities when on treatment, heterogeneity in sex (scenario 2) influencing progression and recovery probabilities when on treatment, combined heterogeneity in age and sex (scenario 3) influencing progression and recovery probabilities when on treatment, and heterogeneity in age when including age-dependent all-cause mortality (scenario 4). In every scenario, heterogeneity impact was varied, and health state occupancy, incremental costs, incremental effects, and the net monetary benefit of treatment versus no treatment were compared between the individual-level and cohort simulations.

Results

When introducing heterogeneity in age, sex, and age and sex combined, all scenarios showed differences between outcomes of individual-level and cohort simulations. However, these differences did not change the cost-effectiveness conclusions. When age influenced only age-dependent mortality, there were differences between the outcomes for the individual-level and cohort simulations when heterogeneity in age was introduced.

Conclusion

Patient heterogeneity can affect the outcomes of individual and cohort simulations differently, but reflecting more heterogeneity does not necessarily increase differences in simulation outcomes. However, age-dependent mortality affected analytic outcomes differently, suggesting a need for caution when developing cohort models if age is heterogeneous.

Supplementary Information

The online version contains supplementary material available at 10.1007/s40273-025-01547-3.

Key Points for Decision Makers

How heterogeneity may affect individual-level and cohort state-transition model outcomes, and their differences, is not yet fully known.

This study compared the influence of heterogeneity on individual-level and cohort simulation outcomes while ensuring model structures were the same. This ensured that observed differences were the result of heterogeneity and not other factors.

Results showed that patient heterogeneity can affect the outcomes of individual-level and cohort simulations differently, especially when age-dependent mortality is involved. This suggests a need for caution when developing and interpreting results from a cohort simulation if age is heterogeneous.

Introduction

In health economic evaluations, simulation models are commonly developed to evaluate the (long-term) impact of diagnostic procedures, disease management, and treatment strategies [1]. There are many different model types, of which individual-level state-transition models and cohort state-transition models are most often used [1]. Cohort simulation (Csim) models are relatively simple models that may require limited development efforts [1]. In Csim models, cohorts move through health states as one, whereas subgroup analysis and additional health states may be used to reflect differences within the cohort [1]. However, these model types become incomprehensible when too many health states or subgroups are included [2]. In an individual-level simulation (ILsim) model, also called microsimulation, characteristics are assigned to every individual to create a heterogeneous patient population within the model, allowing characteristics such as comorbidities, age, and sex to be taken into account [1]. In addition, microsimulations allow for patient history, such as medical events or treatments, to be tracked and taken into account. Although ILsim approaches can reflect the patient population in more detail, these models are often more complex and more difficult to understand and require more development time and resources than Csim models [3, 4]. Guidelines state that simplicity is essential in a simulation model, but if treatment effectiveness can differ for patients with differing characteristics, this should be included in the cost-effectiveness analysis [5–7]. Consequently, the decision to develop an ILsim model or a Csim model can be crucial. Furthermore, there is no complete understanding of the impact of this choice on simulation outcomes. [4, 8]

In simulation models, there is often a non-linear relationship between input parameters and output values [9]. ILsims and Csims may reflect non-linearity in different ways, even when the underlying model structure is identical [10, 11]. How this difference may lead to differences in outcomes is unclear, but it is likely influenced by the extent to which patient heterogeneity is present and taken into account [12–14]. In non-linear simulation models, comprehensively reflecting heterogeneity may lead to different outcomes than would ignoring it (i.e., considering only an homogeneous population) or reflecting only part of the heterogeneity [15, 16]. In particular, regarding heterogeneous individuals’ characteristics with a skewed distribution, the use of mean values across individuals (simulating identical individuals as one cohort) rather than the full distribution (on an individual level) may affect model outcomes [17]. Therefore, the degree to which patient heterogeneity can be and is taken into account could significantly affect simulation outcomes.

Cross-validation studies comparing different modelling approaches, including Csim and ILsim approaches, could provide some insight as to when specific modelling approaches may be preferred. Previous studies have shown that individual-level models could allow for more factors to be considered and potentially result in more accurate outcomes, but most concluded that further research is needed to further improve guidance on model selection [18, 19]. Also, because compared model structures were not identical, it was impossible to determine how exactly heterogeneity influenced simulation model outcomes. Therefore, this study investigated the conditions under which, regarding heterogeneity type and extent, ILsims may provide different outcomes than would simulating identical individuals in a Csim, using a single model structure and analysis framework.

Methods

To compare the outcomes of ILsims and Csims, an existing microsimulation model was adjusted to create a single model that can be used to implement both an ILsim and a Csim based on the exact same model structure. To maintain this same model structure, we simplified the definition of a Csim to the simulation of identical individuals, without including health states or subgroup analyses to reflect individual differences. The model used in this study was an adjusted version of the DARTH microsimulation implementation of the Sick–Sicker model [20]. The Sick–Sicker model has a 30-year time horizon with yearly cycles comparing two strategies: treatment and no treatment. The model consists of four health states, as shown in Fig. 1 in the electronic supplementary material (ESM): healthy (H), sick (S1), sicker (S2), and dead (D). Briefly, patients can transition from healthy to sick, from sick to sicker, and from all health states to dead. When on treatment, patients can also recover from sick to healthy. Treatment also influences the probability of progression from sick to sicker. Krijkamp et al. [20] describes this model structure in more detail. To compare the outcomes of ILsims and Csims, this model was adjusted to implement both based on a single model structure. In Csims, subgroups and additional health states can be used to reflect heterogeneity, but these were not included in this study. To maintain identical model structures, this study used simplified definitions of ILsims and Csims to determine the impact of heterogeneity on simulating the cohort as a single entity (Csim), or simulating individuals (ILsim). The use of a single model structure eliminated the impact of potential differences in model structure, model coding, parameter values, among others, on simulation outcomes, between the ILsim and Csim. This ensured that any observed differences in outcomes were only due to the nature (granularity) of the model: ILsim or Csim. The model always simulated on an individual level but provided the option to simulate a cohort by completely ignoring any patient-level heterogeneity, effectively simulating a perfectly homogeneous cohort. Namely, in the Csim, separate individuals were still simulated; however, the means of all parameters (from the distributions used in the ILsim) were assigned to every individual, so all individuals were identical, and no heterogeneity was present (see Fig. 1).

Fig. 1.

Schematic overview of the cohort and individual-level simulation using the same model structure. On the left (cohort simulation), all individuals included in the model are the same with an age of 50 years. On the right (individual-level simulation), all individuals have their own characteristics such as age and sex. These influence input parameters in the model such as recovery (p.S1H) in scenarios 1.1, 1.3, 2.1, 2.3, and 3, progression (p.S1S2) in scenarios 1.2, 1.3, 2.2, 2.3, and 3, and all-cause mortality (p.HD) in scenario 4

Furthermore, to minimize first-order uncertainty, 1,000,000 individuals were simulated in all analyses, effectively having the ILsim outcomes converge to the Csim outcomes when not including any heterogeneity, through simulation of identical individuals. To ensure results were indeed comparable, ILsim and Csim were first simulated without introducing heterogeneity (scenario 0).

Base model

To introduce heterogeneity in the simulations, options for incorporating age- and sex-dependent progression probability and recovery probability were included, as well as age-dependent all-cause mortality. All model input parameters are presented in Tables 1 and 2 in the ESM.

Table 1.

Overview of the performed scenario analyses

Scenario n	Independent parameter (heterogeneity)	Effect of parameter	Description
0	–	–	Control scenario to ensure outcomes between individual and cohort simulations are identical when no heterogeneity is introduced
1.1	Age	Age-dependent probability of recovery when on treatment (p.S1H)	The probability of recovery when on treatment depends on the age of the individual. The age of every individual is sampled, with an increasing age distribution over simulation runs. The higher the patient’s age, the lower the probability of recovery
1.2	Age	Age-dependent probability of progression when on treatment (p.S1S2)	The probability of progression when on treatment is adjusted based on the age of the individual. The age of every individual is sampled, with an increasing age distribution over simulation runs. The higher the patient’s age, the higher the probability of progression
1.3	Age	Age-dependent probability of recovery and progression when on treatment (p.S1H and p.S1S2)	The probability of recovery and progression when on treatment is adjusted based on the age of the individual. The age of every individual is sampled, with an increasing age distribution over simulation runs. The higher the patient’s age, the lower the probability of recovery and the higher the probability of progression
2.1	Sex	Sex-dependent probability of recovery when on treatment (p.S1H)	The probability of recovery when on treatment depends on the sex of the individual. When an individual is female, the effectiveness of the treatment is reduced, with an increasing probability of being female over simulation runs
2.2	Sex	Sex-dependent probability of progression when on treatment (p.S1S2)	The probability of progression when on treatment depends on the sex of the individual. When an individual is female, the effectiveness of the treatment is reduced, with an increasing probability of being female over simulation runs
2.3	Sex	Sex-dependent probability of recovery and progression when on treatment (p.S1H and p.S1S2)	The probability of progression when on treatment depends on the sex of the individual. When an individual is female, the effectiveness of the treatment is reduced, with an increasing probability of being female over simulation runs
3	Age and sex	Age- and sex-dependent probability of recovery and progression when on treatment (p.S1H and p.S1S2)	The probability of progression and recovery when on treatment is adjusted based on the age and sex of the individual. The age of every individual is sampled, with an increasing age distribution over simulation runs. When an individual is female, the effectiveness of the treatment is reduced, with an increasing probability of being female over simulation runs
4	Age-dependent mortality	Age-dependent all-cause mortality	The probability of death due to all-cause mortality depends on the age of the individual. The age of every individual is sampled, with an increasing age distribution over simulation runs

Table 2.

Mean net monetary benefit of 25 iterations of all runs for every scenario

Scenario	Runa	Scenario description	Incremental NMB individual	Incremental NMB cohort	Incremental NMB difference (%)
0	–		34,530	34,530	0 (0)
1.1	1	Heterogeneity in age influencing the probability of recovery when on treatment	− 20,534	− 19,058	− 1476 (8)
	2		− 34,244	− 29,240	− 5004 (17)
1.2	1	Heterogeneity in age influencing the probability of progression when on treatment	− 168,420	− 170,728	2308 (1)
	2		− 171,991	− 182,999	11,008 (6)
1.3	1	Heterogeneity in age influencing the probability of recovery and progression when on treatment	− 253,170	− 259,626	6456 (2)
	2		− 264,638	− 285,394	20,757 (7)
2.1	1	Influence of sex on the probability of recovery when on treatment	13,781	12,903	878 (7)
	2		7978	7165	813 (11)
2.2	1	Influence of sex on the probability of progression when on treatment	− 73,709	− 105,445	31,736 (30)
	2		− 105,471	− 128,475	23,004 (18)
2.3	1	Influence of sex on the probability of recovery and progression when on treatment	− 104,966	− 132,688	27,722 (21)
	2		− 145,537	− 162,747	17,210 (11)
3	1	Heterogeneity in age and sex on the probability of recovery and progression when on treatment	− 307,289	− 311,027	3738 (1)
	2		− 326,911	− 337,254	10,343 (3)
4	1	Heterogeneity in age on the probability of dying of all-cause mortality	20,110	23,379	− 3269 (14)
	2		9215	17,084	− 7869 (46)

A hypothetical disease model was used in this study, so incremental NMB values do not represent any real-world case values

^aWithin the scenarios, heterogeneity in age and sex was introduced in two gradations, run 1 (moderate heterogeneity) and run 2 (substantial heterogeneity)

NMB, net monetary benefit for a willingness-to-pay threshold of €50,000

Scenarios

Multiple scenarios were simulated in which age and sex influenced various parameters, as presented in Table 1. Within these scenarios, heterogeneity in age and sex was introduced in two gradations for every scenario: moderate (run 1) and substantial (run 2). Figure 2 in the ESM shows the distributions used to introduce heterogeneity in age for run 1 (Fig. A) and run 2 (Fig. B). For heterogeneity in sex, the probability of being female was increased over the simulation runs, first to 65% in run 1, then by 80% in run 2, as shown in Table 1 in the ESM. In the scenarios, age and/or sex influenced different input parameters. For every scenario, incremental cost, incremental effects, and net monetary benefit (NMB) were compared between ILsim and Csim simulations. The NMB of treatment versus no treatment was determined for all ILsim and Csim simulations with a willingness to pay (WTP) of €50,000 per quality-adjusted life-year, which is the middle of the three WTP thresholds applied in the Netherlands [21]. See Fig. 1 for a schematic overview of the comparison. In addition, Markov traces were studied. All scenarios and analyses were performed using R (version 4.2.1, the R Foundation for Statistical Computing, Vienna, Austria) [22]. All scenarios were performed 25 times to check for convergence of results. Computational constraints meant that no probabilistic sensitivity analysis was performed.

Fig. 2.

Markov traces of the no-treatment arm (control) of cohort and individual-level simulation when including age-dependent mortality (scenario 4). A The Markov trace when no heterogeneity in age is present (scenario 0), B The Markov trace for run 1 (moderate heterogeneity) of scenario 4, and C the Markov trace for run 2 (substantial heterogeneity) of scenario 4.

Scenario 1: Age-dependent treatment effect In the first scenario, age influenced the probability of recovery (scenario 1.1), the probability of progression (scenario 1.2), and the probability of recovery and progression (scenario 1.3). In these scenarios, the higher the patient’s age, the lower the treatment effect, meaning the higher the age, the lower the recovery probability and the higher the progression probability.

Scenario 2: Sex-dependent treatment effect In the second scenario, sex influenced the probability of progression (scenario 2.1), followed by the probability of recovery (scenario 2.2), and, finally, the probability of both progression and recovery (scenario 2.3). In these scenarios, being female was associated with a decreased probability of recovery and increased probability of progression.

Scenario 3: Age- and sex-dependent treatment effect In scenario three, the influence of age and sex were both applied, combining their effect on input parameters.

Scenario 4: Age-dependent mortality Mortality does not increase linearly with age, so the mortality risk at the mean age of a population may not be the same as the mean mortality risk based on all individuals’ age-dependent mortality risks. Therefore, a constant age-independent mortality risk was used in previous scenarios to isolate the effect of the heterogeneity in these scenarios on the outcomes. Because age-dependent mortality is usually included in both ILsim and, using mean age, in Csim, this was included in scenario 4. These risks were applied per individual in the ILsim based on their individually sampled age and applied based on the individuals’ mean age in the Csim (assigned to all individuals). The age-dependent mortality risk was based on Dutch all-cause mortality data [23]. For the age starting at which mortality data are no longer available (108 years), the mortality risk was set to 1 to ensure no individuals lived past this age. All age-dependent mortality probabilities are shown in Table 2 in the ESM. Finally, we used the health state occupancy in the ILsim to calculate the average mortality risk per cycle. This cycle-specific average mortality risk was then applied to all individuals in the Csim to evaluate how using time-dependent instead of age-dependent mortality risks influenced the difference between ILsim and Csim outcomes.

Funding Statement

No external funding was received for this study.

Results

When running all scenarios 25 times (iterations) with 1,000,000 individuals, results remained stable. Table 2 shows the NMBs of treatment versus no treatment based on the ILsims and Csims and their difference. For more detailed results, Table 3 in the ESM shows the incremental costs and mean incremental effects of treatment versus no treatment in all scenarios for the ILsim and Csim.

Scenario 0 When no heterogeneity was introduced, both ILsim and Csim resulted in an incremental cost of €39,995 and an incremental effect of 1.49 quality-adjusted life-years, resulting in an NMB of €34,530. Figure 3 in the ESM shows the incremental costs and effects of all iterations in scenario 0.

Scenario 1: Age-dependent treatment effect When age influenced the probability of recovery on treatment (scenario 1.1), incremental costs were higher in the ILsim, whereas incremental effects did not differ between ILsim and Csim, resulting in a lower treatment NMB in the ILsim than in the Csim. In scenario 1.2, incremental costs were consistently lower and incremental effects were higher in the ILsim when increasing heterogeneity, resulting in an increased NMB in the ILsim compared with the Csim.

When age influenced both recovery and progression on treatment, the results were similar to those in scenario 1.2, where only progression was influenced. Overall, most differences in incremental costs, incremental effects, and NMB between ILsim and Csim were minor; only increasing the heterogeneity in the scenarios resulted in a difference of incremental effects and NMB of >10% (see Table 2 and Table 2 in the ESM).

Scenario 2: Sex-dependent treatment effect When sex influenced the probability of recovery on treatment (scenario 2.1), the results from the ILsim and Csim showed only minor differences. Differences were larger when there was an influence on the probability of progression on treatment (scenario 2.2), with consistently lower costs and higher effects in the ILsim, resulting in increased NMBs in the ILsim compared with the Csim. When these two scenarios were combined in scenario 2.3, the difference observed in scenario 2.2 remained. The difference in incremental effects and NMB between ILsim and Csim often exceeded 10% and even reached >20%.

Scenario 3: Age- and sex-dependent treatment effect In scenario 3, where age and sex both influenced recovery and progression probabilities, ILsim consistently resulted in lower incremental costs and higher incremental effects. These differences increased with more heterogeneity but remained below 10%. All observed differences in incremental costs, effects, and NMBs were small.

Scenario 4: Age-dependent mortality Figure 2 shows the Markov traces with increasing heterogeneity in age, showing the isolated effect of the age-dependent mortality when (A) no heterogeneity in age was present and (B and C) when increasing amounts of heterogeneity in age were present. These graphs show that more individuals transitioned to the dead state when heterogeneity in age across individuals increased (i.e., when the range of simulated ages increased). In the ILsim, more individuals transitioned to the dead state earlier, resulting in fewer individuals in the healthy, sick, and sicker states in later cycles. When comparing the NMB from ILsim and Csim, solely including heterogeneity in age and thereby age-dependent mortality resulted in a difference of >20%.

When using the cycle-specific (i.e., time-dependent) average mortality risk as observed in the ILsim (i.e., the proportion of individuals dying per cycle) as cycle-specific mortality risks in the Csim, the outcomes of the ILsim and Csim were very similar. Figure 4 in the ESM shows the health state occupancy of the ILsim and Csim when including high heterogeneity in age.

Discussion

In this simulation study, the conditions under which individual-level state-transition models may provide different outcomes than cohort state-transition models were studied. The results showed differences between ILsim and Csim outcomes across the simulated scenarios. However, these did not result in a different cost-effectiveness decision for the applied WTP of €50,000. Noticeably, most differences were observed in effect outcomes. In this study, the input parameters affected by age and sex were transition probabilities, so these indirectly influenced both the cost and the effect outcomes. However, the extent of this effect depended not only on the effect on these probabilities but also on the cost and utility values assigned to each health state in the model. The particular cost and utility values (Table 1 in the ESM) applied in our simulation study resulted in larger differences in health outcomes than costs between the different scenarios. We also implemented a scenario in which health state costs and utility under treatment depended on age. This scenario did not result in relevant differences between ILsim and Csim results (data not shown). Observed differences in NMB did not increase with increased heterogeneity per se, which might indicate that it is difficult to predict when heterogeneity may lead to substantial differences in ILsim and Csim outcomes. Therefore, if heterogeneity is present, ignoring this heterogeneity by simulating identical individuals in Csims can skew model outcomes. When including age-dependent mortality, differences between ILsim outcomes and Csim outcomes increased substantially. This suggests that, even heterogeneity in factors unrelated to the disease or treatment itself can affect model outcomes. Therefore, Csims and ILsims do not represent a population with heterogeneous age in the same way, and the implementation of age-dependent mortality may lead to biased outcomes when performing Csims implementing only average patient age.

Although not many studies are available for direct comparison, some cross-validation studies found substantial differences in costs and effects resulting from ILsims and Csims [18, 19]. However, given the nature of these studies, the cause of the observed differences could not be directly linked to patient heterogeneity. Also, no previous study has determined the (separate) effect of age-dependent all-cause mortality, as cross-validation studies either do not include it or do not specify how it was implemented.

This study has some limitations. Heterogeneity was introduced only in age and sex. Although these are simple heterogeneity factors often present in health economic evaluations, there are more aspects where heterogeneity may be of interest, such as genetic make up, comorbidities, medical history, and many others. We did not include other patient characteristics, but our results did indicate that, when a patient characteristic influences a transition probability, it could result in different outcomes between the ILsim and the Csim, which would likely also be the case for other patient characteristics, such as comorbidities. In addition, we only included age-dependent all-cause mortality, not sex- and age-dependent all-cause mortality. Although this could mean we underestimated the effect of heterogeneity, the results also showed that the impact of heterogeneity was unpredictable. Also, due to the set age limit of 108 years, the duration of the lifetime time horizon may differ between ILsim and Csim when introducing heterogeneity in age and including age-dependent mortality risks. However, given that 99.9% of simulated individuals die before reaching the maximum age of 108 years, we do not expect this age limit and the resulting time horizon to have any impact on the observed results. No probabilistic analyses were performed in this study because of the high computational burden of such analyses in ILsim in combination with the large number of simulated patients and scenarios. In this simulation, specific values for costs and effects were used. Although these values did not result in a difference in NMB that would influence decision-making, the use of different input values might result in differences that do, as illustrated by the sometimes-large differences in NMB resulting from both simulation types. The use of fictitious values for costs and effects may have resulted in implausible NMB values. However, we do not see this as a major limitation, given this is a proof-of-concept study without an actual disease or treatment, focusing on differences between simulation approaches rather than actual numerical outcomes. Lastly, in this study, we focused on the influence of patient heterogeneity when determining net benefits for the total population. Although reflecting patient heterogeneity can also allow stratified decision-making, that is, investigating for which particular patient groups treatments are cost effective and for which they are not, this was not the aim of this study.

Our study shows that heterogeneity can influence outcomes differently in ILsims and Csims. Assuming that the ILsim outcomes are more accurate than the Csim outcomes because individuals’ characteristics and their influence can be reflected more accurately implies that Csims might not always provide accurate cost and effect estimates when heterogeneity is present in the target population. Also, the finding that including all-cause mortality based on mean age in Csims produced outcomes deviating from those with all-cause mortality based on individuals’ age in ILsims has important implications. This suggests a need for caution when developing Csims if patient age is heterogenous and known and that, if possible, creating an ILsim would be advised. Fortunately, given computational advances and the increase in guidance and examples for developing ILsim, their development is more feasible and less challenging than in the past. Although our study suggests the need for caution when developing Csims when heterogeneity is present, there are some considerations to take into account regarding different model structures. First, it is important to note that models vary in complexity and that the influence of heterogeneity may vary with model complexity. For example, when simulating individuals over a short time horizon of 5 or 10 years, or in cases where disease-specific mortality is high, the impact of how all-cause mortality is incorporated may be limited. However, many jurisdictions require all (un)intended consequences of interventions to be included in the analysis. This typically requires applying a lifetime time horizon, which increases the relevance of correctly reflecting all-cause mortality [7]. Ultimately, the difference in outcomes between Csim and ILsim approaches cannot be assessed a priori, and the most suitable and feasible approach may depend on the practical context.

Second, in this study we looked at ILsims and Csims, but such simulations can be performed with different model types. For example, discrete-event simulations (DES) simulate at an individual level but allow for more flexibility and heterogeneity than state-transition models [24]. Graves et al. [25] showed a comparison between a Markov model, microsimulation, and DES but did not include patient heterogeneity and applied mortality risks based on mean age. Given that, in general, non-linearity is incorporated in different ways in models simulating at the cohort level than in models simulating at the individual level, heterogeneity can be expected to have a different impact on outcomes for these approaches, regardless of the actual model structure and type.

Third, in this study, we reflected a cohort model by simulating identical individual patients. This approach ensured that any differences between the ILsim and the Csim were attributable solely to patient heterogeneity rather than to other factors. As we simulated a very large number of identical individuals, thereby removing all first-order uncertainty, we consider these findings to be directly applicable to actual cohort models (Markov models without microsimulation). However, in cohort state-transition models, heterogeneity can also be reflected through subgroup analyses or by including additional health states. Including such approaches in a Csim will be easier than switching from a Csim to an ILsim. A modeling approach is often chosen at the start, and not all software environments would easily support switching to simulating individuals at a later time, making it quite important to identify the best modeling approach before starting model development.

Conclusion

Heterogeneity can result in different simulation outcomes when using an ILsim compared with a Csim. However, more heterogeneity does not always result in larger differences in outcomes between these simulation model types. If heterogeneity is present, it is therefore difficult to determine in advance whether an ILsim could result in other more accurate outcomes than a Csim. Furthermore, the use of mean patient age in Csim to determine all-cause mortality risk did not accurately reflect survival in a population with heterogeneous age, which is quite common in health economic analyses. Consequently, in general, the presence of patient heterogeneity should favor the development of ILsims, and results from Csims in this context should be interpreted with caution.

Supplementary Information

Below is the link to the electronic supplementary material.

Funding

No financial support was provided for this study, ensuring the authors’ independence in designing the study, interpreting the data, and writing and publishing the report.

Declarations

Conflicts of Interest

The authors have no conflicts of interest.

Availability of Data and Materials

The data underlying this article are available in the article and its ESM.

Ethics Approval

Not applicable.

Author Contributions

All authors made substantial contributions to the conception, design, analysis, and interpretation of the paper and have approved the manuscript.