A Dynamic Microsimulation Model for Ageing and Health in England: The English Future Elderly Model

In the United Kingdom (UK), life expectancy at birth has increased over the last 40 years. In 1981 male period life expectancy was 70.9 while for females this figure was 76.9. In 2018 this had risen to 79.3 and 82.9 respectively, with projected rises to 85.4 and 88 in 2061 (ONS, 2019a). The potential impact and implications of an ageing population in the UK has received considerable attention, for example the UK Government Foresight Future of an Ageing Population project which took a wide-ranging and multi-method approach across multiple domains, including housing, health and the impacts of technology and design (G. O. for Science, 2016).

These improvements in life expectancy are to be celebrated, however an ageing population will increase the strain on critical systems such as health and social care provision. This demographic shift will also have a wide-ranging impact on the rest of society. For example having a larger proportion of the population in retirement (relative to those in work) means lower tax revenue to fund the health and social care that some elderly people rely on, often referred to as the Potential Support Ratio (PSR) (Lomax et al., 2020). These issues are not confined to just the UK (Balachandran et al., 2017).

To adapt to these challenges, policy makers require robust evidence about current and future trends across a broad range of health and socio-economic outcomes. Having suitable modelling tools which are capable of assessing the multi-domain and inter-related outcomes for an ageing population and the ability to assess scenarios and trade-off in terms of policy development has the potential to inform this evidence base substantially. In this paper we discuss the development of one such model and its application to an ageing English population.

A combination of factors contribute to the future heath and economic outcomes for individuals within the population. These can be demographic (age, sex, ethnicity), relate to educational attainment or past employment, and/or dependent on current health status or individual risk factors (for example smoking, drinking and exercise). This combination of unique attributes soon adds up to a complex picture and so is best handled by considering each individual rather than aggregating over groups or attributes. Interventions or policy experiments can then be applied to individuals to test how outcomes might differ in the future.

We present a microsimulation model for the English population aged 50 and over. The English Future Elderly Model (E-FEM) accounts for demographic change, ageing, disability, and mortality, and has been adapted from the US FEM, initially created by a team at RAND and now developed at the Leonard P. Schaeffer Center for Health Policy and Economics at the University of Southern California (Goldman et al., 2004). We utilise longitudinal survey data from the English Longitudinal Study of Ageing (ELSA) which enables detailed assessment of individual characteristics across a broad range of domains. The aim of this paper is to describe the development of this model and demonstrate its utility as a tool for understanding the potential future trajectories of the ageing English population. We are motivated by the following research questions: (i) How can we build and validate a model that reflects the complex and multi-faceted health and economic status of the English population aged over 50? (ii) How do policy intervention experiments impact on the outcomes for this population?

It is our intention to describe how the model works, provide validation of both inputs and outputs in an English context and demonstrate the model’s utility with some example scenarios. We intend for this paper to act as a reference for further work which will be focused on specific policy questions and health outcomes.

The remainder of the paper is structured as follows: Section 2 provides context for the model and discusses previous FEM applications; Section 3 sets out the model design for the E-FEM; Section 4 deals with validation of outputs; Results are presented and discussed in Section 5; finally Section 6 offers some conclusions and avenues for further work.

In this section we discuss two substantive themes: (i) a brief summary of a number of models which are designed for either assessing the elderly population or are focused on health; and (ii) discussion of the background to the FEM, including existing applications of the model.

One of the earliest examples of a dynamic microsimulation model designed specifically for health policy analysis was POPREP, applied to the United States and later adapted to simulate the Egyptian population (Khalifa, 1972). POPREP was used to assess the impact of different methods of family planning on the rate of conception (Mustafa, 1973). Aside from POPREP, until the 1990s, health microsimulation models were typically static rather than dynamic owing to the computational cost of individual-level modelling compared with macromodels (Schofield et al., 2018). These static microsimulation models rely on static ageing methods, where input microdata is transformed to fit expected demographic and health constraints at the next time step. Examples of these early static models include the evaluation of disease screening (Habbema et al., 1985; Van Oortmarssen et al., 1981), and assessing fertility (Santow, 1976).

As the development of more complex dynamic microsimulation models to examine health policy questions became more prevalent, many of these were written for specific disease processes rather than to take in to account a wide range of outcomes (Rutter et al., 2011). This is largely owing to the difficulty in creating microsimulation models in the first place - building a model from scratch requires a skilled programmer and a significant time investment. Examples include Meester et al. (2015) for the screening of colorectal cancer, Mytton et al. (2018) for evaluating cardiovascular disease prevention in the UK, and Su et al. (2015) for assessing the clinical and economic impact of obesity.

More recently, some research groups have moved to creating microsimulation frameworks to speed up the process of development, enabling much quicker development of models. Examples of large frameworks are LIAM2, () and Modgen developed by Statistics Canada (de Menten et al., 2014; Canada, 2009. These frameworks provide a generic toolkit to handle basic functions of microsimulation such as input/output, cross-sectional ageing, event management, and custom scenario generation, leaving researchers who use them to focus on developing models rather than software. Providing these functions in a user-friendly manner reduces the expertise and time needed to create new models from scratch and potentially opens up a range of new possibilities for using microsimulation to answer pertinent policy-relevant questions.

In this section we discuss the development of the E-FEM, outlining the data used, model design, imputation of missing variables and the transition models estimated on the data.

3.2. Model design

The E-FEM is a first-order Markov chain model competing risks model. The Markovian nature of the model means that characteristics that get assigned at time T (the present) only depend on characteristics at time T-1 (the previous timestep). As a result of this, the order that these changes are made in the simulation is inconsequential, as each characteristic is simply a function of several factors at time T-1. The order that is important in the E-FEM however is what we describe as the ’causal pathway’. That is, risk behaviours lead to chronic disease and functional limitations, which in turn have an impact on economic outcomes. For example, BMI is a predictor of the incidence of stroke, which can lead to functional limitations, which in part predict a respondents working status. These pathways are determined individually in the transition models of each characteristic.

Running the E-FEM happens in two phases - preparation and simulation. In the preparation phase raw ELSA survey data are harmonised, cleaned, and variables of interest are extracted in order to create starting populations. Transition models are estimated from one of the starting populations, and all this information is written into configuration files for use in the simulation. Preparation is handled in Stata (StataCorp, 2021). The simulation phase then takes the starting population and ages individuals, dynamically applying the transition probabilities between each wave to transform the state of simulants and project them into the future. We can think of these as projections of the future of the ELSA survey respondents, which we use to represent the future of the English population due to the representative nature of the survey and the re-weighting to 2011 Census and mid-year population estimates and projections.

The E-FEM can run both whole population and cohort simulations. The structure of both of these simulation types is shown in Figure 1. Population level simulations begin with the stock population, which includes all ELSA core respondents aged 51 or over in wave 6 (2012). At each wave of the population simulation, the replenishing cohort is included, refreshing the stock population with people aged 51 and 52. This is to ensure the age distribution of the sample remains representative. The cohort simulation does not refresh the sample over time, and instead follows only people aged 51 and 52 from the replenishing cohort.

Figure 1

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In this section we validate a number of model outcomes. We focus on both internal validation (comparing predicted model outcomes with observed model inputs) and external validation by comparing model outputs with distributions seen in other datasets.

4.1. Internal validation

Internal validation of a microsimulation amounts to comparing the distribution of attributes between simulated outputs and the original data. In this work we employ three methods of internal validation; cross-validation, handover plots and Receiver Operating Characteristic (ROC) curves.

For cross-validation the original population was split in two, using only half of the population to estimate transition models. The remaining half was then simulated over the same time period as ELSA (2002 - 2016) using these models. We compared simulated outputs with ELSA data by performing t-tests, the results of which are provided in Tables A3. The handover plots and ROC curves will be presented in more detail below.

4.1.1. Handover plots

Handover plots are not a form of statistical validation, but rather a form of face validity. They give a quick visual indication that simulated outputs follow the same trend as the input data, and confirm that the model is behaving as expected. To generate these plots we estimated transitions using only data from waves 1-4 of ELSA, and produced a starting population based on respondents in wave 5 which was then simulated from wave 5 to 8. Combining these data, the plots in Figure 2 show the ’handover’ of chronic disease prevalence from ELSA to the simulation. For each chronic disease, the simulation continues a reasonable pattern from the original data, the predicted values are not noisy and the direction and magnitude of the trend appears sensible and in-line with expectations. Additional handover plots are provided in Figure A1.

Figure 2

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4.1.2. Receiver operating characteristic

In order to investigate the efficacy of binary transitions in the model, we used Receiver Operating Characteristic (ROC) curves. First proposed by (Pandya et al., 2017) in a cardiovascular disease policy microsimulation, ROC curves are used to validate a binary classification, comparing the true-positive rate against the false-positive rate. The Area Under the Curve (AUC) relates to the accuracy of the prediction, with 1 being perfect classification when comparing simulated data to real, and 0.5 meaning the classification is no better than random.

For this analysis, we used the cross-validation population described above, where one half was used to estimate transition models and the remaining half used in the simulation. We simulated this population 500 times from 2002 - 2012 before pooling the results of each run to create a summary output file, which was then compared with ELSA data. The results of this analysis for key binary response variables are shown in Figure 3. In all cases the classification is better than random, and in some cases much better. For example, the AUC for predicting obesity (BMI > 30) and mortality is 0.85 and 0.83 respectively. Predicting chronic disease incidence is not as effective however, with AUCs ranging from 0.55 to 0.70. Additional ROC curves are provided in Figure A2.

Figure 3

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4.2. External validation

External validation involves comparing simulated outputs against independent external datasets. This is often more challenging than internal validation, as finding comparable datasets off the shelf is difficult since question wording and sample selection in surveys often differ. In the case of the E-FEM, chronic disease prevalence and incidence levels are projected into the future, starting in 2012. We can therefore use data published between 2012 and the present to validate the model over short time periods.

4.2.1. Comparison with age UK almanac reported disease prevalence

The Age UK almanac of disease profiles in later life (Melzer et al., 2015) is a collection of statistics on the prevalence of chronic diseases in elderly people, reported by sex and 5 year age group (over 60).

We ran a cohort simulation of the E-FEM for a 12-year period between 2004 to 2016 and compared the prevalence of a number of chronic diseases at the end of the simulation with those reported in the Age UK data. The results of the comparison can be seen in Figure 4 where the comparison is broken down by age group and sex. The graphs provide a good indication that the E-FEM is, on the whole, predicting chronic disease prevalence well (at least over a 12-year projection period) when compared to the results reported in the Age UK data. Unusual results in the 100 plus population from the E-FEM are most likely caused by a small sample size, as not many simulants survive to that age in the model. We were not able to compare the prevalence of cancer or heart disease in this validation as the Age UK definitions did not match those from ELSA. In the Age UK data cancer diagnosis relates to the previous 5 years only, whereas ELSA asks if the respondent has ever been diagnosed. Heart disease in the Age UK data was defined as one or more of a limited number of conditions, compared with ELSA which reports any heart condition as heart disease.

Figure 4

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4.2.2. Smoking

We ran the E-FEM model to 2018 and compared our estimates of smoking prevalence with data for the same year reported in a fact sheet published by Action on Smoking and Health (ASH) (ASH, 2020), a public health charity in the UK that works to eliminate the harm caused by tobacco, and produces statistical reports on smoking habits broken down by sex and age group. Figure 5 shows the comparison between simulated (E-FEM) and observed (ASH) data in 2018. In both age groups, the E-FEM is under-predicting the prevalence of current smokers by approximately 1-2 percentage points.

Figure 5

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The E-FEM provides a model capable of undertaking policy experimentation across a wide range of health outcomes. To illustrate the utility of the model, we present results from the baseline projections alongside two counterfactual scenarios, focused on heart disease and smoking. Heart disease provides an opportunity to demonstrate a change in outcomes where a chronic disease is directly impacted by model scenarios. Smoking provides an example where an intervention on a behaviour has an impact on health outcomes and survival.

5.2. Heart disease

Heart disease in ELSA is a catch-all term which encapsulates a range of conditions that affect the heart’s structure and function and is part of a broader set of conditions which are known as Cardiovascular Disease (CVD). CVD is the leading cause of death worldwide, accounting for approximately 31% of all mortality (WHO, 5AD). In England, it is also one of the largest causes of premature mortality, with 33,812 people under the age of 75 dying from CVD in 2016 alone (Public Health England, 2AD). Mortality data from 2001 to 2016 in England has shown a long-term decline in the death rate from CVD, which is reported as one of the main reasons for the increase in life expectancy over this time period. Whilst mortality from CVD has decreased, morbidity has increased as people live longer with these conditions, which has increased the burden on health and social care. Public Health England (PHE) estimates that annual healthcare costs alone for CVD amount to an estimated £7.4 billion, whilst non-healthcare costs are much higher, estimated at £15.8 billion. CVD is one of the most significant targets for PHE, with numerous ongoing strategies for disease prevention. Table 5 shows the regression model used to estimate Heart Disease transitions in the E-FEM.

Table 5

	Heart Disease
Male	0.108***
White	-0.0729
Less than Secondary Education	-0.0642
Higher or further education	0.0194
Lag of age spline, less than 65	0.0103
Lag of age spline, 65 to 74	0.0262***
Lag of age spline, more than 75	0.0182***
Lag of BMI spline, less than 30	0.163
Lag of BMI spline, more than 30	0.218
Lag of ever smoker	0.0259
Lag of current smoker	0.0264
Lag of heavy smoker (>20 cigs/day)	0.0836
Lag of problem drinker (>12 drinks/week)	-0.0318
Lag of doctor ever - Diabetes	0.0520
Lag of doctor ever - Hypertension	0.163***
Lag of doctor ever - High Cholesterol	0.0659*
Lag of activity level - Low	0.174**
Lag of activity level - Moderate	0.0979*
Constant	-3.172***
N	22,333
Pseudo R2	0.0335

We used the E-FEM to investigate the total burden of disease in the elderly population by comparing the baseline projection to the counterfactual scenario in which nobody developed heart disease whilst in the model. The input populations were not modified in any way for this scenario, so any simulants in the stock or replenishing populations with heart disease were kept in the model. Figure 6 compares the average age at death between the baseline and intervention scenarios. There are improvements to overall survival in the intervention, with a significant difference emerging in 2028 of 0.5 years that increases to 1.2 years in 2050.

Figure 6

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5.3. Smoking

The impact of smoking on public health has been studied extensively, and the link between tobacco smoke and chronic health conditions is well understood (Newcomb and Carbone, 1992; Prasad et al., 2009; Al-Bashaireh et al., 2018). Various forms of tobacco control interventions have been attempted around the world, including mass media campaigns (Kuipers et al., 2018), advertising bans (Harris et al., 2006), price increases (Chaloupka et al., 2012), workplace and school smoking bans (Brown et al., 2009), and the addition of warning labels to packaging (Hammond et al., 2006). The outcomes of interest are usually health-related, however some studies have focused on Socio-Economic Status (SES), which has strong links to health. Table 6 shows the transition model for both starting and stopping smoking.

Table 6

	Smoking
	Started	Stopped
Male	0.112**	0.0263
White	0.0228	0.257
Less than Secondary education	0.188***	-0.106*
Higher or Further education	-0.154**	0.215**
Lag of age spline, less than 65	-0.00572	0.0188***
Lag of age spline, 65 to 74	-0.0186**	-0.00979
Lag of age spline, more than 75	-0.0289**	0.0171
Lag of BMI spline, less than 30	-0.414*	0.839***
Lag of BMI spline, more than 30	0.25	0.0703
Constant	-0.649	-5.060***
N	41951	6157
Pseudo R2	0.019	0.0129

Figure 7 compares the average age at death in both the baseline and intervention case (where smokers in the cohort stop smoking and nobody starts smoking). This figure includes the whole population, including both smokers and non-smokers. Results show that average death age is only slightly higher in the no smoking scenario.

Figure 7

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However, smoking does not just impact on mortality, but also has strong links to increased morbidity. This relationship is most obvious when looking at lung disease. Figure 8 plots the prevalence of lung disease in both the baseline and no smoking scenarios, once again including both smokers and non-smokers. There is a clear and significant difference between the scenarios, with prevalence of lung disease being approximately 1.5 percentage points lower after simulating both cohorts for 30 years. This difference is across the whole population, and not just smokers.

Figure 8

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5.3.1. Treatment on the treated

To further illustrate this link, we looked at the difference in life years and disability-free life years for smokers between the two scenarios, this time in a ’treatment on the treated’ analysis where only smokers are included. The results of this analysis are shown in Table 7. When looking at smokers only as opposed to the whole cohort, the improvement in life expectancy and healthy life expectancy is much more obvious. Smokers who quit at age 50 in this model live on average 7 years longer than if they did not. However, the improvement in disability-free life-expectancy is only approximately 4.5 years, suggesting that while those who quit live longer, only a proportion of this time equates to disability-free years.

Table 7

Scenario	Life Years	Disability-free Life Years
Baseline	24.4	16.9
Intervention	31.4	21.4

We can run analyses by sub-population using the E-FEM. In the case of smoking we investigate how the intervention affects smokers by different levels of education. Table 8 shows the average increase in life years and disability-free life years by level of education. The largest overall improvement in life expectancy can be seen for the median educational level (level 2), with over eight years improvement. Those in the lowest education group (level 1) show the smallest average improvement in life years (5.5), as well as the lowest improvement in disability-free life years (3.4). These results suggest that other comorbidities disproportionately affect those with the lowest educational attainment, so even though intervention on a single attribute (smoking) delivers the substantial improvements in life expectancy, only a proportion of these extra years are disability free.

Table 8

Education Level	Life Years Improvement	Disability-free Life Years Improvement
1	5.5	3.4
2	8.4	5.3
3	7.7	5.4

We set out with the aim of discussing the development of a dynamic microsimulation model for an ageing English population, the E-FEM. In this paper we have demonstrated how data from ELSA has been harmonised, cleaned and variables imputed to make it suitable for our model. Validation, both internal and external, demonstrates that the E-FEM is capable of accurately predicting health outcomes and disease states in to the future while results demonstrate that on a whole population and on a cohort the model can inform disease and mortality outcomes under counterfactual scenarios. We show results for a heart disease and a smoking intervention to demonstrate the type of experiments that can be run using the E-FEM but the model can be used to estimate a wide range of potential outcomes.

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Author details

1. Luke Archer

   The University of Leeds, Leeds, UK

   For correspondence

   l.archer@leeds.ac.uk

   Competing interests

   No competing interests reported.

2. Nik Lomax

   The University of Leeds, Leeds, UK

   Competing interests

   No competing interests reported.

   "This ORCID iD identifies the author of this article:" 0000-0001-9504-7570

3. Bryan Tysinger

   University of Southern California, Los Angeles, USA

   Competing interests

   No competing interests reported.

   "This ORCID iD identifies the author of this article:" 0000-0002-8497-3664