Risk exposure

What is a risk exposure?

A risk exposure is a quantification of the amount of risk present in a population or individual.

We will first consider a risk exposure in the context of an individual. An exposure will have different possible measures which fall along a distribution, and an individual will possess a specific measure within this distribution.

For example, consider the exposure systolic blood pressure. SBP ranges from about 60 to 200, and any given individual will have a specific SBP measurement.

One can also define categorical distributions. Consider, for example, the exposure has worked in mining. Here, we assign each individual either “yes” or “no”.

Risk exposure distributions can be:

  • Categorical

  • Dichotomous

  • Unordered polytomous

  • Ordered polytomous

  • Continuous

Generally, risk exposure distributions should be mutually exclusive and collectively exhaustive. In other words, the prevalence of all risk exposure categories for a categorical distribution and the risk exposure distribution’s probability density function across all possible exposure values for a continuous distribution should sum to one.

See the table for examples of each of these risk exposure distributions.

Risk exposure distributions

Distribution

Example

Possible exposure values

Dichotomous

Zinc deficiency

  • Not deficient

  • Deficient

Unordered polytomous

Tobacco use

  • None

  • Chewing tobacco

  • Cigarettes

  • Cigars

  • Other

  • Chewing tobacco AND cigarettes

  • Etc.

Ordered polytomous

Child stunting

  • No child stunting

  • Mild child stunting

  • Moderate child stunting

  • Severe child stunting

Continuous

Systolic blood pressure

Any point value within possible systolic blood pressure range

After identifying an attribute of interest, the manner in which the risk exposure is defined will be subject to the data access and the particular research question the model is meant to answer. Major considerations include the unit of analysis, the time frame of interest, data available, and sources of bias within the data.

For example, if the exposure is a one-time event with persistant effects, it can be defined as a dichotomous exposure. However, if the exposure is smoking as a risk for lung cancer, a continuous exposure defined with units of person-time such as pack years per individual will likely be more suitable.

As our models will typically use GBD estimates, some of the other typically important considerations around data will have less broad applicability to our models. However, we include these as notes. The exposure definition must account for any gaps within the attribute of interest and the data available.

For example, if one is interested in soda consumption, and is building a model based on data from soda sales in a certain region, this uncertainty needs to be incorporated into the model. Similarly, researchers generally must be concerned with biases from factors such as underreporting in the data. [Exposure_definition_and_measurement]

Risk exposures in GBD

GBD estimates pertain to the mid-year or yearly average measurements of a population with a specific location, year, sex, and age, or an aggregation of some such populations. Thus, in the context of GBD, a risk exposure is a distribution of individual exposure values within a location-year-sex-age- population.

If the exposure is dichotomous, for each location, sex, and year, GBD will estimate a continuous age trend of the proportion of, say, individuals with BMI over 30. If the exposure is continuous, then GBD estimates the distribution of the exposure variable over the population in each age, sex, year, and location.

GBD’s risk exposures will generally be less reliable than GBD cause-of-death models, and when designing a risk exposure, it is important to both learn from the GBD modeler what the entity captured by their exposure model is.

Take, for example, the GBD exposure has ever experienced intimate partner violence. Barring incredibly high mortality rates among IPV victims, we would expect the proportion of the population that has ever experienced IPV to increase monotonically with age. However, survey data consistenly reports this proportion to peak among 30-40 year olds, which is refleced in the GBD model. We believe this phenomenon to be the result of recall bias. When implementing this in a model, however, if we were to initialize a population with dichotomous and persistent IPV exposure values from GBD estimates and then allow the simulants to age for 10 years, our exposure distribution would no longer match our reference data. Thus it becomes clear that the entity we’re describing needs to be “recollection of IPV”, “recent experience of IPV”, or some other attribute that incorporates a time component.

While GBD estimates risk exposure during the modeling process, it does not publish risk exposure estimates as part of its final results. Rather, GBD publishes estimates of risk factor summary exposure values (SEVs), which can be explored in the advanced options of GBD compare. The SEV is a measure of risk-weighted prevalence and is equal to zero when no excess risk exists for a population and equal to one when the entire population is at the highest level of risk.

While the SEV can be useful for assessing trends in risk exposure over time or comparing risk exposures across demographic groups, it is less useful for our purposes. To obtain GBD estimated risk exposures, we must instead use get_draws().

Categorical risk exposures can typically be obtained using source='exposure' with a specified risk factor rei_id.

Continuous risk exposures can be more complicated to obtain. Continous exposures in GBD are typically estimated according to an ensemble distribution and require data the specifies the 1) mean, 2) variance, and 3) ensemble weights of the distribution. Distribution mean and variance are typically estimated as modelable entities and can be obtained using get_draws() using source='epi' with the specified modelable entity IDs (ask the GBD modeler when in doubt for which one to use!). Ensemble distribution weights for continuous risk exposures in GBD 2019 can be found here: /ihme/epi/risk/ensemble/_weights/gbd_2019/.

Todo

Update file path to future GBD rounds when available.

Note

Sometimes GBD estimates the underlying continuous distribution of a risk exposure and then converts the risk exposure into a categorical distribution for use in downstream modeling steps (this is done for child growth failure risk exposures, for example). Keep this in mind in case the standard GBD risk exposure is categorical but you would prefer continuous for your modeling purposes and ask the GBD modeler if this is the case.

Risk exposures in Vivarium

In Vivarium, each simulant will be assigned an exposure value. We will typically derive these values from a population-level distribution provided by a GBD risk exposure.

Any given attribute that we are interested in may be codified in a variety of ways. The choices to make include which distribution to use, how to measure the risk, and what time frame within which to consider the risk. We include some examples below.

Say we are modeling BMI as a risk exposure. BMI could be included as a continuous variable, or binned into {<20, 20-25,>25}. This decision will be based on the outcomes of interest and data availability.

If we are interested in BMI as a risk for IHD, we might only be interested in current BMI. However, if we are modeling BMI as a risk for osteoporosis, it is possible that we will be interested in the cumulative history of BMI.

Assume we are intersted in capturing smoking as a risk exposure. If the outcome of interest is lung cancer, we will be interested in a subject’s full history of smoking. This might include:

  1. if the subject has ever been a regular smoker

  2. if so, with what frequency per week the subject smoked cigarettes

  3. the type of cigarettes smoked

We could decide to encode these as a dichotomous variable (a), a categorical variable (b), and a second categorical variable (c), and include these as three different risk exposures in our model. This will necessitate some set of interactions that occur amongst the different exposures. Alternatively, we might define the risk exposure smoking score, which is a function of (a) (b) and (c), and which has some continuous or ordered categorical distribution.

Note that in each case our smoking model captures the same information, but in the former we push the complexity of quantifying different types of smoking histories to another part of the model, and in the former we wrap this complexity into the exposure component.

Useful resources related to risk exposure models in Vivarium include:

Theoretical Minimum Risk Exposure Level/Distribution (TMREL/D)

The theoretical minimum risk exposure level (TMREL) is the level of risk exposure that would minimize the risk of an adverse outcome for an individual.

For example, the TMREL for smoking would be “has never smoked.” The corresponding concept on the population level is the theoretical minimum risk exposure distribution (TMRED), which is the distribution of risk exposure that would yield the lowest possible population risk. For smoking, the TMRED would be the degenerate probability distribution assigning everyone in the population to the TMREL category “has never smoked.” [WHO-Global-Health-Risks-Annex], [GBD-2017-Risk-Appendix-Modeling-Risk-Factors]

Todo

Add formal mathematical definitions of TMREL and TMRED.

As discussed in the causality section of the causal diagrams page, counterfactual analysis is used to describe the causal relationship between a risk factor and an outcome. The TMRED is a particular choice of counterfactual exposure distribution used for the causal attribution of disease burden to a given risk factor in a population (see Population Attributable Fraction). Other choices of counterfactual include the plausible minimum risk, feasible minimum risk, and cost-effective minimum risk, each of which can obviously depend on specific attributes of the population under consideration. On the other hand, Murray et al. state in [Comparative-quantification-health-risks-2003]:

“Biological principles as well as considerations of equity would necessitate that, although the exposure distribution for theoretical minimum risk may depend on age and sex, it should in general be independent of geographical region or population.”

However, the authors go on to add:

“Exceptions to this are however unavoidable. An example would be the case of alcohol consumption, which in limited quantities and certain patterns, has beneficial effects on cardiovascular mortality, but is always harmful for other diseases such as cancers and accidents. In this case, the composition of the causes of death as well as drinking patterns in a region would determine the theoretical minimum distribution.”

Note

The above quote from [Comparative-quantification-health-risks-2003] is included to illustrate the subtleties in conceptualizing the TMREL as described by an original source advocating its use. However, the description of the beneficial effects of alcohol is outdated, as the latest research from IHME and Oxford shows that there is no safe level of alcohol consumption.

Based on more current research, here are some examples of risk factors with TMRELs that may depend on geography or population:

  • Hemoglobin levels in the blood increase at high altitude, so the TMREL for hemoglobin concentration would be geography-dependent, with populations living at higher altitudes having a higher TMREL than those living at lower altitudes. GBD handles this situation not by explicitly defining different TMRELs, but rather by using altitude-adjusted hemoglobin data to estimate anemia prevalence.

  • High Body Mass Index (BMI) is associated with increased risk of death in the general population, but it may be protective agianst some cancers and other chronic diseases (this phenomenon is termed the “obseity paradox”). Thus, the optimal BMI (for minimizing overall risk) in a given population may depend on the leading causes of death or exposure to other risk factors in the population.

The smoking example above illustrates two features of the TMREL that are typical of many risk factors:

  1. We imagine that everyone in the population has the same TMREL

  2. The TMREL is zero or no exposure

However, neither of these conditions is necessary. In some cases, particularly for continuous risk exposure variables, the TMREL may be a nonzero exposure level. Moreover, there may be multiple TMRELs experienced by different members of the population. For example, in GBD 2017 [GBD-2017-Risk-Appendix-Modeling-Risk-Factors]:

  1. The TMREL for radon exposure is taken to be 10 Bq/m3, which is equivalent to the average outdoor concentration of radon [ICRP].

  2. The Low Birth Weight and Short Gestation risk factor has multiple TMREL categories since healthy babies have many different birth weights and gestational ages.

These examples illustrate some complexities in defining the TMREL and TMRED for a given risk factor. For continuous risk exposure variables — such as radon exposure, or hemoglobin concentration, or systolic blood pressure — it may be impossible to define a single TMREL for the population, as we expect different individuals to have different radon exposure levels or hemoglobin levels or blood pressures, even in a theoretical population where risk is minimized. In this case the TMRED will be a nontrivial probability distribution. For example, a plausible TMRED for radon exposure would be some probability distribution of positive radon exposure levels concentrated near the point 10 Bq/m3. We will further discuss this point below.

Todo

Add a more in-depth discussion of TMREDs for continuous exposure variables, based on systolic blood pressure example in [Estimating-Attributable-Burden].

Also, say something about whether there should be different TMRELs for different risk-outcome pairs, and how GBD handles this.

Add some discussion of issues brought up in PR 153:

  • More in-depth description of counterfactual scenario, where one risk is set to the TMRED, but everything else is held constant, including exposure to other risk factors. Note that causally affected risk exposures would also change, as in the case of mediation (see BMI, SBP, mortality example in PR).

  • Mention approaches other than TMREL/D, e.g. No observed adverse effect level (NAOEL) and Lowest observed adverse effect level (LOAEL), and methods from cost-analysis.

  • Operationally, GBD only defines one TMRED for each risk factor, rather than one for each risk-outcome pair.

  • GBD assumes risks are monotonic (is that still true with splines in GBD 2019+?), but this is not necessarily true (for example: BMI, sodium).

  • Clarify discussions of TMREL/D that depends on geography and/or biological features of the population, and of definitions of TMREL/D for population vs. individual (formal mathematical definitions should help with this).

Fix broken links in citations [WHO-Global-Health-Risks-Annex] and [Estimating-Attributable-Burden].

References

Exposure_definition_and_measurement

Developing a Protocol for Observational Comparative Effectiveness Research: A User’s Guide.Agency for Healthcare Research and Quality (US), Jan 2013 Retrieved 11 March 2020. https://www.ncbi.nlm.nih.gov/books/NBK126190/