YLDs due to other causes¶
Years lived with disability (YLDs) are an important measure of health loss and contribute to estimates of disability adjusted life years (DALYs) in our model. This document discusses how YLDs are tracked in vivarium by default, how that compares to GBD methodology, and discusses potential improvements to this default behavior.
Background and Motivation¶
GBD methodology¶
Disability weight estimation¶
The GBD study relies on disability weights (DWs) to estimate years lived with disability (YLDs). DWs represent the magnitude of health loss associated with a specific health outcome and are measured on a scale from 0 to 1; 0 implies a state equivalent to full health and 1 equivalent to death.
Disability weights have been estimated through a series of surveys, described in detail in the GBD methods appendix along with a complete listing of disability weight values for all health states included in the GBD study.
Comorbidity correction¶
The disability weights estimated through the process described above consider each health state individually and must be corrected for the simultaneous presence of multiple disability-causing health states within a given individual. This correction accounts for the assumption that disability weights from comorbid conditions scale multiplicatively rather than additively. So in effect, the reduction in health due to a newly acquired cause of disability is quantified as greater for an individual who was previously in perfect health than for an individual who was already subject to some non-zero baseline level of morbidity.
The COMO process in GBD assumes total independence between health states and does not account for any correlation that may exist between related health states (beyond correlation induced by location, age, and sex, which is accounted for through its stratified adjustments). As reported in the GBD 2019 methods appendix, “[GBD] tested the contribution of dependent and independent comorbidity in the US MEPS data and found that independent comorbidity was the dominant factor even though well-known examples of dependent comorbidity exist, such as clustering of conditions like diabetes and stroke or anxiety and alcohol use disorders” (p. 475).
The GBD study performs this comorbidity correction (termed “COMO”) using a microsimulation, described below. The microsimulation is performed at the age-, sex-, location-, and year-specific level. For GBD 2019, the population size of each microsimulation was 40,000. In this microsimulation, each simulant is exposed to an independent probability of having any of the sequelae including in GBD using the estimated sequela prevalence.
Note
The COMO adjustment is run and maintained by IHME central computation. The repository can be found here (as of May, 2023).
According to correspondence with a central computation representative: the COMO adjustment ensures that no simulant may simultaneously possess mutually exclusive sequelae (mild AND moderate diarrhea, for instance), nor may they simultaneously possess mutually exclusive impairments (such as mild AND moderate anemia). A simulant may, however, simultaneously possess more than one sequelae that correspond to the same healthstate (for example: the sequelae ectopic pregnancy and intestinal perforation due to paratyphoid, which are both included in the abdominopelvic problem healthstate. In this case, an individual who simultaneously possesses both of these sequelae that share the same health state, the individual will in effect experience the abdominopelvic problem healthstate as approximately twice as severe than if they only possessed a one of these sequelae).
Note, a list of GBD sequelae and healthstate pairs can be obtained with the
db_queries.get_sequela_metadata()shared function.
Additionally, the COMO adjustment handles exceptions for impairments as well as certain GBD causes (including injuries, sexual violence, and “residual” causes, epilepsy, and intellectual disability) for which DWs are estimated through separate, custom processes.
The COMO adjustment also handles aggregation of cause prevalence and incidence up the GBD cause hierarchy. In this process, some sub-causes of a parent cause assumed to be independent (and scale multiplicatively) and others assumed to be mutually exclusive (and scale additively).
Once this population has been initialized, the comorbidity correction is performed as follows:
For each simulant, the overall disability weight is calculated as the multiplicative combination of each of the sequela that the simulant possesses according to the following equation:
Where: \(DW_k\) is the disability weight for the \(k\)-th disease sequelae that the simulant possesses.
Once this overall disability weight is computed for each individual simulant, it is then disaggregated into its component parts once more to obtain cause-specific disability weights adjusted for comorbidity according to the following formula:
Where: \(ADW_k\) is the comorbidity-adjusted disability weight for sequela \(k\) among a given simulant.
Then, cause-specific YLDs per capita in an age-sex-location-year are computed as the sum of the adjusted DWs for each sequela across all n simulants in the microsimulation as:
The implication of the COMO adjustment for GBD YLDs attributable to a parent cause should be exactly equal to the sum of YLDs attributed to each of its sub-causes. Additionally, the YLDs attributable to a given sequela after the COMO adjustment will be less than the product of the disability weight and the prevalence for that sequela.
Historical behavior in vivarium¶
For a given vivarium simulation, we have typically developed individual cause models for specific conditions. Conditions to include in a simulation are selected based on relevance to the research question and are not exhaustive of all conditions modeled in GBD. This poses a question of how to handle morbidity and mortality due to causes not explicitly modeled within our simulation (“background” causes). Historically, vivarium has handled background morbidity differently from background mortality, as described below.
Background mortality¶
Vivarium automatically models background mortality in addition to mortality due
to modeled causes as mortality due to other_causes. The cause-specific
mortality rate of other_causes is equal to:
Where: \(ACMR\) is the all-cause mortality rate and \(CSMR_c\) is the cause-specific mortality rate of a modeled cause \(c\).
Background morbidity¶
Historically, vivarium has not modeled background morbidity. Rather, by default, vivarium models morbidity due to modeled causes only. Among the modeled causes, a partial comorbidity adjustment is performed.
Specifically, for a simulant that possesses multiple causes of disability simultaneously, the YLDs accrued for that simulant in a given timestep are equal to:
Vivarium can then observe YLDs due to all modeled causes AND/OR cause-specific YLDs accrued in the simulation. Notably, the sum across cause-specific YLDs will be greater than the “all-cause” YLDs in vivarium simulation outputs using this methodology.
Problem space¶
There are multiple problems with the default vivarium behavior not to model background morbidity, including:
Comorbidity adjustment issues
Cannot calculate cause-specific YLDs adjusted for comorbidity even just among modeled causes, resulting in overestimation of cause-specific YLDs relative to “all cause” YLDs among modeled causes
Does not adjust for comorbidity due to unmodeled causes, resulting in overestimation of YLDs due to modeled causes relative to GBD estimates
Underestimation of total YLDs
Only observe a subset of total YLDs within our simulation. While we can calculate YLDs averted between scenarios, we cannot accurately calculate percent reduction in all-cause YLDs or DALYs relative to baseline because we do not model YLDs due to all causes at baseline.
Causes us to overestimate impact of a death averted in our simulation. An averted death in the alternative relative to baseline scenario result in some number of YLLs averted, but really this person should then start accruing YLDs overtime, which will decrease the number of DALYs averted relative to baseline.
Proposal¶
To address these issues, we propose to update the default vivarium behavior to model background morbidity in a similar manner to the default behavior to model background mortality. Additionally, we propose the incorporation of cause-specific COMO-adjusted YLDs into vivarium observers.
1. Background morbidity¶
In order to model YLDs due to non-modeled background causes, we must estimate a “cause-deleted” disability weight that represents the disability weight for all GBD causes except for those explicitly modeled in a given vivarium simulation. This “cause-deleted” disability weight should be adjusted for comorbidity of all individual causes of disability included in background morbidity, but NOT adjusted for comorbidity with modeled causes (which instead will be performed within the simulation).
The ideal approach to estimating this cause-deleted COMO adjusted disability weight due to unmodeled causes would be to perform the COMO adjustment as is done in the central computation process while excluding modeled sequelae. This should be done at the location/age/sex/year-specific level. Integrating the central computation code into vivarium processes would be ideal so that we will replicate all of the exceptions and maintain any regular updates to their process.
However, until this is able to be achieved, an interim solution will be to estimate the DW due to background morbidity as the difference between the all-cause YLD rate and the sum of the YLD rate due to all modeled causes of disability at the location/age/sex/year-specific level:
Note
This interim solution will systematically underestimate the DW due to background morbidity. This underestimation will be larger when the relative share of YLDs due to modeled causes of YLDs due to all causes is large.
Todo
Update this section to alternate equation with notebook proof, but first generalize to multiple causes.
2. Adjusted YLD observer¶
To align with this proposal, the default YLD observer in vivarium should function so that the amount of YLDs due to cause \(YLDs_c\) accrued on a given timestep is equal to:
Where:
Parameter |
Definition |
|---|---|
\(YLDs_c\) |
YLDs accrued due to cause c on a given timestep for a given simulant |
\(DW_c\) |
Disability weight for cause c (prevalence-weighted average of sequelae DWs) |
\(\sum_{mc=1}^n DW_\text{mc}\) |
Sum of disability weights for all n modeled causes the simulant possesses, INCLUDING background other causes |
\(DW_\text{overall}\) |
\(1 - \prod_{mc=1}^n (1 - DW_\text{mc})\) |
\(\text{timestep scalar}\) |
Duration of simulation timestep, in years |
Challenges to consider¶
Consider updating current behavior of cause DW equal to prevalence-weighted average of sequela DWs
Alternative would be to assign sequela-specific DW based on prevalence-weighted probability (assuming mutually exclusive sequelae)