20 January 2010

Published in: Longevity - mortality, Catastrophe - weather

Modelling infectious disease risk

The entire realm of possible pandemic characteristics can be quantified using historical data, as well as established principles of epidemiology, virology and mathematical analysis and modelling, explains Dr Maura Sullivan

Over the last few decades, at least 30 unknown disease agents have been identified in humans for which no cures are currently available -- including human immunodeficiency virus (HIV), severe acute respiratory syndrome (SARS), Ebola and bovine spongiform encephalopathy ("mad cow disease").

The discovery of influenza A/H5N1 ("avian flu") redefined the virulence scale for influenza and caused the global community to re-evaluate the threat posed by influenza viruses. The subsequent emergence of 2009 pandemic H1N1 ("swine flu") again called into question what was known about flu viruses. While they typically have strong seasonality and a preference for temperate regions, the H1N1 virus emerged in spring 2009 in Mexico and, despite being a mild virus, it has caused a significantly higher-than-average death toll in the young and healthy. Because of the constant adaptation of microbes, particularly viruses, the past alone cannot be used to predict the future of influenza and other infectious disease outbreaks.

Analytical and statistical models are critical in understanding and managing infectious-disease risk. Using historical data as well as established principles of epidemiology, virology and mathematical analysis and modelling, the entire realm of possible pandemic characteristics can be quantified without being limited by historical precedent. Models can give a quantitative framework through which to evaluate risk, explore sensitivity and make informed decisions.

Models are only as good as their ability to capture underlying trends, reflect data, and explore uncertainty. Modelling requires a balance between capturing enough data to adequately explain the observed trends and over-parameterization where nothing substantive can be construed from the model output. Good modelling involves using mathematics to understand which variables are the key drivers and the uncertainty and interaction between those variables as well as separating correlation from causation. Every variable that impacts infectious disease should not be included, so, when developing a model framework, keeping the objective of the model and available data in the forefront will result in the best framework to answer the question at hand.

Life insurance companies use these analytical approaches to assess the levels of sudden payouts of death benefits that they could incur, above their expected payouts for a year -- the "excess mortality" loads -- for their portfolios of insureds. Excess mortality loads from unprecedented events like new disease outbreaks, or terrorist attacks, are difficult to estimate from traditional analysis of past mortality trends. Event-based modelling of excess mortality enables them to assess their capital needs for life catastrophe and to manage their risk, through reinsurance, portfolio diversification and through mortality bonds for the capital markets, such as the VITA IV bond launched by Swiss Re in November 2009, using RMS modelling.

The RMS model contains thousands of different potential pandemic scenarios. The impact of each pandemic, in terms of its mortality and morbidity rates on different age groups in all the countries affected resulting from the combination of pandemic characteristics, is modelled using a variation on a commonly-used epidemiological approach called a susceptible, infected and recovered ("SIR") model.

A visual representation of the SIR modelling framework is shown below. The model computes the theoretical number of people infected with an infectious disease in a closed population over time. Each individual model run is deterministic, and by simulating thousands of pandemics the effects of variables such as vaccines, countermeasures, changes in virulence and transmissibility and antiviral effectiveness can be quantified.

The susceptible population in the model decreases through vaccination and exposure to the virus; conversely, it increases by the loss of vaccine-acquired immunity. Vaccinated individuals are not considered to be completely protected; they become exposed at a much lower rate than the susceptible population.

After exposure, individuals progress to one of the infected states including asymptomatic, sub-clinical, clinical and hospitalized. The proportion of individuals progressing into each category depends on the viral characteristics. As the virulence of the virus increases, so does the proportion of the infected receiving treatment. The duration of infectiousness and transmission probabilities decrease for those receiving treatment. Through this mechanism, the model parameters allow behavioural and medical quarantine to be simulated.

An increase in viral virulence results in lower average transmissibility within the model. This is because individuals with a severe virus tend to be too ill to be out in the community transmitting the virus, and those receiving treatment or who are hospitalized will have reduced contacts and transmissibility because of precautionary measures such as masks, gloves and isolation. Individuals remain infectious during the entire course of their clinical infection. Once they have progressed out of the infectious state they can no longer transmit the virus to others.

Many academic models use an SIR-based approach, but the RMS model is the only one in the market that looks at infectious disease probabilistically. The model, first released in 2006, has been employed by primary life and health insurers, reinsurers and corporations to understand better their potential loss, develop continuity plans using scenarios and transfer risk.

In light of the 2009 H1N1 pandemic, RMS expanded the infectious disease model to include 2,016 scenarios specifically parameterized to represent the spectrum of potential losses from the pandemic H1N1 virus. The figure below represents the variables model probabilistically in the H1N1 and standard infectious disease models and includes a selection of key variables including transmissibility and virulence, demographic impact, vaccine production, non-pharmaceutical interventions and antiviral efficacy.

The H1N1 parameterization differs from the RMS standard infectious disease model in part because certain variables, such as region of outbreak, were already fixed. In addition, the solution space for an existing virus is much smaller than the solution space for the entire range of infectious disease. In building the H1N1 model, early reports on viral genetics were interpreted to develop a realistic range for the potential progression of the virus. A model for a virus like H5N1 avian flu would contain a much more severe virulence distribution and lower expected value for transmissibility based on the genetics of the virus.

Statistical distributions are used to represent the variability associated with virulence and transmissibility. The distributions are parameterized with median values of observed flu viruses with similar characteristics and published estimates of values from historical pandemics and seasonal flu outbreaks. Although, the mean values can be developed using observed data, the parameterization should capture the full range of viral characteristics and the potential for a long-tail.

Since very severe events occur rarely or, in some cases have never occurred, expert judgment is key in the parameterization of the tail. One of the principal advantages of modelling versus a purely statistical or historical approach is that modelling allows for the possibility of occurrence of events unlike those that have ever been seen in the past. The tail of the distribution has significantly more uncertainty, but the full spectrum of possibilities can be reflected in the assessment of risk.

Model efficacy depends not only on framework and methodology, but also largely on the model's objective and the corresponding data. Country-level modelling is sufficient for understanding potential risk to a geographically diverse life insurance book or modelling population risk, but would be inadequate for a group life insurer specializing in high-risk populations, like healthcare workers.

One model is not sufficient to reflect all needs and tailored models have used baseline mortality differences between insured and uninsured populations, the effect of co-infection on mortality rates, occupational exposures and geographic and demographic inputs to further refine risk. Often, there is a need for a model to explore the risk differential where concrete data is not available.

Expert judgment plays a key role in determining if there are correlated measures that can be used. For example there may be no data on risk between individuals of two occupations. However, models can explore the difference in contact rates, baseline mortality rates, and correlates for underlying health status like smoking rates or socioeconomic status to develop the mean and deviation around the mortality differences in the two groups. A crucial aspect of modelling is the ability to do sensitivity analyses around key parameters. Even when data is lacking the ability to understand the range of outcomes, the interactions between variables and the relative importance of variables can assist in decision-making.

Despite remarkable advances in medical science and technology, infectious diseases remain among the leading causes of death worldwide and directly account for a quarter to a third of all mortality. The discovery of antibiotics, improved sanitation and hygiene, and effective disease surveillance and childhood vaccination programmes have reduced the impact of infectious diseases, especially in the developed world, resulting in a false sense of security about the threat of infectious disease outbreaks.

In general, viruses are exceptionally adaptable organisms. They are constantly undergoing genetic change resulting in new strains of disease that are immune to standard treatments or that have more effective transmission. Emerging (newly identified) infectious diseases and re-emerging diseases (known diseases that experience resurgence because of changed host-agent-environment conditions) are continuing to appear and spread geographically in both developed and developing countries, creating challenges for the medical community.

The dynamics of infectious disease and the potential risks posed by new and emerging strains can be quantified and better understood with the use of mathematical models. Models are only as good as the input data and calibration, but, by using information about transmission dynamics, genetics and interventions, the spectrum of risk can be better understood.

Dr. Maura Sullivan is director, excess mortality solutions, Risk Management Solutions Maura.sullivan@rms.com

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