Non-standard Risk Exposure and Effect Models

vivarium_public_health provides two components for modeling the impact of some health attributes on others:

Risk: Model of the underlying exposure based on a continuous or categorical distribution.
RiskEffect: Model of the impact of different exposure levels on another health attribute.

The standard model is to think of exposure to environmental, metabolic, and behavioral risk factors and their impact on disease incidence rates. However, we’ve found many situations to extend this model to other attributes, such as interventions and their impacts on other risks, diseases, or mortality itself.

In order to support these extended models, we’ve made the Risk and RiskEffect components configurable. This tutorial explains the various configuration options you can use with these two components.

Exposure Models

We model exposure using the Risk component. Consider its configuration options:

"exposure": This option represents the exposure data source. It defaults to the value "data".
"rebinned_exposure": This option tells the component if a categorical exposure with more than two categories should be rebinned into two categories. It defaults to an empty list, indicating that the underlying exposure model should be used.
"category_thresholds": This option tells the component how to split continuous exposure models into a categorical model. It defaults to an empty list, indicating that the underlying exposure model should be used.

The name input when the Risk is created also has an impact on the behavior. Names are provided as <type>.<name> where type refers to the type of entity being modeled and name is the name of the entity. Available types are "risk_factor", "coverage_gap", and "alternative_risk_factor". Some configuration options are only available for certain entity types, as summarized in the table below.

Configuration Options
	exposure	rebinned_exposure	category_thresholds
risk_factor	✓	✓	X
coverage_gap	✓	X	X
alternative_risk_factor	X	X	✓

We’ll take each of these entity types one-by-one to see how we can configure them.

`risk_factor`

For the risk_factor entity type, both the "exposure" and "rebinned_exposure" configuration options are available to us. In the model specification, we can specify the component to use its defaults with

components:
    vivarium_public_health:
        risks:
            - Risk("risk_factor.my_risk_factor")

We declare the component but don’t declare any configuration options for it. This will cause the risk component to look up any available exposure information in the Artifact and use the data as presented.

If we change the "exposure" option to the name of a covariate as

components:
    vivarium_public_health:
        risks:
            - Risk("risk_factor.my_risk_factor")

configuration:
    my_risk_factor:
        exposure: covariate.my_covariate

the component will look for the covariate estimate in the Artifact rather than for the risk factor exposure. Only covariates with a proportion estimate can be substituted for risk exposure. The covariate proportion will be used as the proportion of people exposed to the risk factor.

Finally, we can specify an integer or float value to the "exposure" option to directly set the proportion of people exposed.

components:
    vivarium_public_health:
        risks:
            - Risk("risk_factor.my_risk_factor")

configuration:
    my_risk_factor:
        exposure: 0.6

If the underlying exposure distribution is polytomous (that is, it has multiple categories of exposure), we can use the "rebinned_exposure" option to separate those categories into an “exposed” and “unexposed” category. The set of categories to rebin into the “exposed” group should be specified as a list of strings to the "rebinned_exposure" option.

components:
    vivarium_public_health:
        risks:
            - Risk("risk_factor.my_polytomous_risk_factor")

configuration:
    my_polytomous_risk_factor:
        rebinned_exposure: ["cat1", "cat2", "cat3"]

This will reformat the exposure data to consider anyone in “cat1”, “cat2”, or “cat3” as exposed, and all other exposure categories as unexposed.

Using the "rebinned_exposure" option will cause the relative risk for all RiskEffect components to also be rebinned.

Note

Exposure data is formatted with the typical demographic columns for age, sex, location, and year and a value column. If the exposure data is categorical, it also has a “parameter” column with string values of “cat1”, “cat2”, etc. The categories are presumed to be sorted by severity with “cat1” being the worst.

`coverage_gap`

A coverage_gap entity type is a way of phrasing the lack of coverage of an intervention as a risk factor. The only think to keep in mind when using a coverage gap is what exposure means (1 - intervention coverage). Otherwise, the configuration options and caveats are the same as the risk_factor entity type.

In practice, coverage gaps have a dichotomous distribution, so the "rebinned_exposure" option does not come into play.

`alternative_risk_factor`

The alternative_risk_factor is an entity type that indicates we have both continuous and categorical representations of the exposure. They are used when an intervention acts on a continuous exposure representation, but the effects of the exposure are specified in terms of the categorical exposure representation.

The only relevant configuration option is the "category_thresholds" option, which must be specified. All other keys must be left at their default values.

components:
    vivarium_public_health:
        risks:
            - Risk("alternative_risk_factor.my_risk_factor")

configuration:
    my_risk_factor:
        category_thresholds: [7, 8, 9]

The above configuration would correspond to a risk with a continuous exposure. Individuals in the simulation would be assigned some actual value in this distribution (e.g. 7.32 or 9.85). When calculating effects, individuals would be assigned a category based on which group they sit in, as defined by the thresholds in the configuration. The thresholds here correspond to the groups less than 7, between 7 and 8, between 8 and 9, and more than 9. For use in determining effect sizes, these groups will be labelled cat1, cat2, cat3, and cat4 respectively.

Effect Models

Non-standard effect models can only be used with dichotomous exposure models (models where someone is either exposed or not exposed. The available configuration options all correspond to generating a relative risk for the exposed population from a set of parameters.

We model exposure effects using the RiskEffect component. Let’s look at its configuration options:

"relative_risk": Option for specifying a relative risk value directly. If provided, no other configuration options may be specified.
"mean": Option for specifying that the relative risk should be drawn from a normal distribution with this mean. Must also provide a value for "se". No other options may be specified.
"se": Option for specifying that the relative risk should be drawn from a normal distribution with this standard error. Must also provide a value for "mean". No other options may be specified.
"log_mean": Option for specifying that the relative risk should be drawn from a lognormal distribution with this mean. Must also provide a value for "log_se" and may provide a value for "tau_squared". No other options may be specified.
"log_se": Option for specifying that the relative risk should be drawn from a lognormal distribution with this standard error. Must also provide a value for "log_mean" and may provide a value for "tau_squared". No other options may be specified.
"tau_squared": Option for specifying a parameter representing inter-study heterogeneity in a lognormal distribution. Can optionally be supplied when specifying a relative risk to be drawn with a lognormal distribution with "log_mean" and "log_se".

When a RiskEffect is created, it takes two arguments: the name of the exposure model and the name of the target attribute that should be altered. The exposure model should be named the same as the argument to Risk and the target attribute should be in the form <type>.<name>.<measure>. type and name specify the entity the effect targets and measure tells the RiskEffect which specific attribute of the entity to alter. Common targets are exposure for other Risk entities and incidence rates for diseases.

The Default Case

If we specify no configuration options in the model specification, we end up with something like:

components:
    vivarium_public_health:
        disease:
            - SIS('my_infectious_disease')
        risks:
            - Risk('risk_factor.my_risk_factor')
            - RiskEffect('risk_factor.my_risk_factor', 'cause.my_infectious_disease.incidence_rate')

In this situation, the vivarium_public_health components will assume all parameters will come from data. The SIS component will load measures like prevalence, incidence rate, excess mortality rate, and others to inform the initialization and dynamics of the model. The Risk will load exposure information. The RiskEffect will load the population attributable fraction and the relative risk associated with the risk-cause pair, and link the disease and risk model with this data.

The configuration block for RiskEffect is specified as

configuration:
    effect_of_<exposure_entity_name>_on_<target_entity_name>:
        <target_entity_measure>:
            ...options...

where <exposure_entity_name> is the <name> provided to the associated Risk component and the <target_entity_name> is the name provided to the component used in the target, usually another Risk or a disease model.

Specifying a Relative Risk Value

If you’re in a situation where the size of the effect (the relative risk) between an exposure model and its target outcome are unknown, one option is to specify a single value for the relative risk.

components:
    vivarium_public_health:
        disease:
            - SIS('my_infectious_disease')
        risks:
            - Risk('risk_factor.my_risk_factor')
            - RiskEffect('risk_factor.my_risk_factor', 'cause.my_infectious_disease.incidence_rate')

configuration:
    effect_of_my_risk_factor_on_my_infectious_disease:
        incidence_rate:
            relative_risk: 20

For this to work, the exposure modeled by the Risk must be a dichotomous exposure (only exposed or not exposed). The "relative_risk" option provided will be assigned and used for the exposed group. Specifying a relative risk this way will cause the population attributable fraction to be calculated using the provided exposure model, and so it does not need to be provided.

Specifying a Relative Risk Distribution

If you have some idea of the uncertainty in the relative risk, you can specify distribution parameters and have the relative risk value drawn from that distribution for each simulation. There are two options for distributions to use.

The first is to sample from a normal distribution. You can do so by providing the following configuration options:

components:
    vivarium_public_health:
        disease:
            - SIS('my_infectious_disease')
        risks:
            - Risk('risk_factor.my_risk_factor')
            - RiskEffect('risk_factor.my_risk_factor', 'cause.my_infectious_disease.incidence_rate')

configuration:
    effect_of_my_risk_factor_on_my_infectious_disease:
        incidence_rate:
            mean: 10
            se: 3

This will sample a new relative risk from a normal distribution with mean ten and standard error three in each simulation. The distribution is clipped so that values below one are set at one. Both the "mean" and "se" options must be provided. The "mean" should be greater than one and the "se" greater than zero.

A second option is to sample the relative risk from a lognormal distribution. This can be done with the following configuration options:

components:
    vivarium_public_health:
        disease:
            - SIS('my_infectious_disease')
        risks:
            - Risk('risk_factor.my_risk_factor')
            - RiskEffect('risk_factor.my_risk_factor', 'cause.my_infectious_disease.incidence_rate')

configuration:
    effect_of_my_risk_factor_on_my_infectious_disease:
        incidence_rate:
            log_mean: 10
            log_se: 3
            tau_squared: 0.5

This will produce a relative risk value:

\[\begin{split}\textrm{RR} &= \exp(\mu + \sigma X + Y) \\ X &\sim N(0, 1)\\ Y &\sim N(0, \tau^2)\end{split}\]

The "tau_squared" parameter is an adjustment for inter-study heterogeneity and is not required to use the lognormal distribution.

Like the normal distribution, values below one will be clipped and set to one. All three parameters, the "log_mean", the "log_sd" and the "tau_squared", should be greater than zero if provided.

Note

The parameterized RiskEffect can be used with a parameterized version of the vivarium_public_health.risks.base_risk.Risk. The only requirement for use is that exposure model be dichotomous.