Obstructed labor and uterine rupture

Note

There were no updates to this modeling strategy between GBD 2021 and GBD 2023, so this document can be used for both rounds

Disease Overview

GBD 2021 Modeling Strategy

Cause Hierarchy

All causes (c_294) [level 0]
- Communicable, maternal, neonatal, and nutritional diseases (c_295)
  - Maternal disorders and neonatal disorders (c_962)
    - Maternal disorders (c_366)
      - Obstructed labor and uterine rupture (c_370)
        
        Obstructed labor, acute event (s_188)
        
        Rectovaginal fistula (s_189)
        
        Vesicovaginal fistula (s_190)

Obstructed labor and uterine rupture (c_370) ia a most detailed cause, at level 4 of the GBD hierarchy. It has three sequelae, detailed in the following table:

Sequelae of obstructed labor and uterine rupture
Sequela	GBD ID	Health state and disability weight	Notes
Obstructed labor, acute event	s_188	abdominopelvic problem, severe DW: 0.324 (0.22–0.442)
Rectovaginal fistula	s_189	rectovaginal fistula DW: 0.501 (0.339–0.657)	Rectovaginal fistula is defined as an abnormal opening between the vagina and the rectum with involuntary escape of flatus and/or faeces following childbirth. The non-fatal burden of fistulas is included in the non-fatal burden of obstructed labour in reporting, but estimation is described in a separate appendix section on “Fistula – impairment.”
Vesicovaginal fistula	s_190	vesicovaginal fistula DW: 0.342 (0.227–0.478)	Vesicovaginal fistula is defined as an abnormal opening between the vagina and the bladder with involuntary escape of urine following childbirth. The non-fatal burden of fistulas is included in the non-fatal burden of obstructed labour in reporting, but estimation is described in a separate appendix section on “Fistula – impairment.”

Restrictions

The following table describes any restrictions in GBD 2021 on the effects of this cause (such as being only fatal or only nonfatal), as well as restrictions on the ages and sexes to which the cause applies.

GBD 2021 Cause Restrictions
Restriction Type	Value	Notes
Male only	False
Female only	True
YLL only	False
YLD only	False
YLL age group start	10 to 14 (ID=7)
YLL age group end	50 to 54 (ID=15)
YLD age group start	10 to 14 (ID=7)
YLD age group end	95 plus (ID=235)

Vivarium Modeling Strategy

Scope

The goal of the obstructed labor (OL) model is to capture YLLs and YLDs due to obstructed labor and uterine rupture among women of reproductive age. We only model obstructed labor and uterine rupture among simulants who give (live or still) birth. This page documents how to model the baseline burden of obstructed labor and uterine rupture. Other simulation components such as c-sections will affect the rates of obstructed labor; such effects will be described on the pages for the corresponding intervention or risk effects model.

Summary of modeling strategy

Because we can assume incident cases of obstructed labor all occur at the end of pregnancy, we will not model obstructed labor and uterine rupture as a state machine with dynamic state transitions like our typical cause models. Rather, all “transitions” in the model will be modeled as decisions made during a single timestep. To obtain the decision probabilities of each incident case or obstructed labor and uterine rupture death, we will convert GBD’s annual incidence and mortality rates among women of reproductive age into event rates per birth (including stillbirths). We will track obstructed labor and uterine rupture deaths to calculate YLLs, and we will track incident cases to calculate YLDs.

Assumptions and Limitations

Cause Model Decision Graph

Although we’re not modeling obstructed labor and uterine rupture dynamically as a finite state machine, we can draw an analogous directed graph that can be interpreted as a (collapsed) decision tree rather than a state transition diagram. The main difference is that the values on the transition arrows represent decision probabilities rather than rates per unit time.

State Definitions
State	Definition
start	Parent simulant must have a live or stillbirth pregnancy as determined by the pregnancy model (due to condition on the overall intrapartum component)
OL	Parent simulant has maternal OL
parent not dead of maternal OL	Parent simulant did not die of maternal heOLmorrhage
parent died of maternal OL	Parent simulant died of maternal OL
end

Transition Probability Definitions
Symbol	Name	Definition
ir	incidence risk	The probability that a pregnant simulant experiences obstructed labor or uterine rupture
cfr	case fatality rate	The probability that a simulant who experiences obstructed labor or uterine rupture dies of that event

Data Tables

The obstructed labor and uterine rupture cause model requires two probabilities, the incidence risk (ir) per birth and the case fatality rate (cfr), for use in the decision graph. The incidence risk per birth will be computed as

\[\text{ir} = \frac{\text{OL cases}}{\text{births}} = \frac{\text{(OL cases) / person-time}} {\text{births / person-time}} = \frac{\text{OL incidence rate}}{\text{birth rate}}.\]

The case fatality rate will be computed as

\[\begin{split}\begin{aligned} \text{cfr} &= \frac{\text{OL deaths}}{\text{OL cases}} \\ &= \frac{\text{(OL deaths) / person-time}} {\text{(OL cases) / person-time}} = \frac{\text{OL cause specific mortality rate}} {\text{OL incidence rate}}. \end{aligned}\end{split}\]

The following table shows the data needed from GBD for these calculations as well as for the calculation of YLDs in the next section.

Note

All quantities pulled from GBD in the following table are for a specific year, sex, age group, and location unless otherwise noted (e.g., SBR). Our simulation only includes pregnant women of reproductive age, so the sex will always be female. However, even though all of our simulants will be pregnant, we still pull each quantity for all females in a given year, age group, and location, because this is the default behavior of GBD. Since we are using the same total population in all the denominators, the person-time will cancel out in the above calculations to give us the probabilities we want.

Data values and sources
Variable	Definition	Value or source	Note
ir	obstructed labor and uterine rupture incidence risk per birth	incidence_c370 / birth_rate	The value of ir is a probabiity in [0,1]. Denominator includes live births and stillbirths.
cfr	case fatality rate of obstructed labor and uterine rupture	csmr_c370 / incidence_368	The value of cfr is a probabiity in [0,1]
incidence_c370	incidence rate of obstructed labor and uterine rupture	como	Use the total population incidence rate directly from GBD and do not rescale this parameter to susceptible-population incidence rate using condition prevalence. Total population person-time is used in the denominator in order to cancel out with the person-time in the denominators of birth_rate and csmr_c370.
csmr_c370	obstructed labor and uterine rupture cause-specific mortality rate	deaths_c370 / population	Note that deaths / (average population for year) = deaths / person-time
deaths_c370	count of deaths due to obstructed labor and uterine rupture	codcorrect
population	average population in a given year	get_population	Specific to age/sex/location/year demographic group. Numerically equal to person-time for the year.
birth_rate	birth rate (live or still)	(1 + SBR) ASFR	Units are total births (live or still) per person-year
ASFR	Age-specific fertility rate	get_covariate_estimates: coviarate_id=13	Assume lognormal distribution of uncertainty. Units in GBD are live births per person, or equivalently, per person-year.
SBR	Stillbirth to live birth ratio	get_covariate_estimates: covariate_id=2267	Parameter is not age specific and has no draw-level uncertainty. Use mean_value as location-specific point parameter.
yld_rate_c370	rate of obstructed labor and uterine rupture YLDs per person-year	como	Use this standard value for all locations except Pakistan. For Pakistan, rather than loading GBD data, use the values in the csv file here `/mnt/team/simulation_science/pub/models/vivarium_gates_mncnh/data/pakistan_obstructed_labor_yld_rate.csv`. See note below this table for a detailed explanation.
ylds_per_case_c370	YLDs per case of obstructed labor and uterine rupture	yld_rate_c370 / incidence_c370

The GBD model of the maternal obstructed labor and uterine rupture cause involves estimation of fistula impairment burden (inclusive of both rectovaginal and vesicovaginal fistulas). The burden of fistula is estimated for all GBD locations in DISMOD and prior to being run through GBD processes such as COMO, the burden values are overwritten with zeros for a select set of locations that are expected to have zero/negligible burden of fistula (due to prompt surgical correction). In GBD 2021 and GBD 2023, according to a correspondence with the GBD modelers (including Mae Dirac), Pakistan was erroneously included in the list of locations assigned zero burden. This error arose as a result of adding Pakistan subnational locations to the GBD location hierarchy and neglecting to add these new subnational location IDs to the list of locations with non-zero burden (the national Pakistan location ID was on the list, but it was no longer the most detailed location for which burden is directly estimated). Therefore, the GBD estimates of YLDs due to the maternal obstructed labor and uterine rupture cause is underestimated.

To address this, we have examined the typical age-specific ratio of YLDs due to maternal obstructed labor and uterine rupture cause relative to the fistula prevalence from DISMOD prior to overwriting certain locations with zeros (representing the prevalence-weighted average COMO-adjusted disability weight of rectovaginal and vesicovaginal fistulas). We then multiply these values by the DISMOD prevalence of fistula in Pakistan to achieve an estimate of YLDs due to fistula (s189 and s190) per person-year. We then add this to the YLD rate for the remaining sequela of maternal obstructed labor and uterine rupture (obstructed labor, acute event, s188) to obtain the yld_rate_c370 parameter value.

The calculations to obtain these values are performed in the notebook linked here. Note that this notebook is housed in the research repository rather than simulation repository because this calculation is not expected to be generalized or repeated for other locations or GBD rounds, etc.

Calculating Burden

Years of life lost

The years of life lost (YLLs) due to obstructed labor or uterine rupture for a simulant who dies of obstructed labor or uterine rupture at age \(a\) should equal \(\operatorname{TMRLE}(a) - a\), where \(\operatorname{TMRLE}(a)\) is the theoretical minimum risk life expectancy for a person of age \(a\).

Years lived with disability

For simplicity, each simulant with an incident case of obstructed labor or uterine rupture in a given age group will accrue the same number of years lived with disability (YLDs). Specifically, the total number of obstructed labor YLDs accrued by each affected simulant should be the average number of YLDs per case of obstructed labor or uterine rupture in the simulant’s age group, which is defined in the above data table as

\[\begin{split}\begin{aligned} \text{ylds\_per\_case\_c368} &= \frac{\text{OL YLDs}}{\text{OL cases}}\\ &= \frac{\text{(OL YLDs) / person-time}} {\text{(OL cases) / person-time}} = \frac{\text{OL YLD rate}}{\text{OL incidence rate}}. \end{aligned}\end{split}\]

We are using the fact that each simulant can get at most one case of obstructed labor or uterine rupture during the simulation, so the average number of YLDs per affected simulant is the same as the average number of YLDs per case. Simulants with a case of obstructed labor or uterine rupture should accrue YLDs whether or not they die.

Limitation

The above strategy of computing average OL YLDs per case should correctly capture total YLDs for the acute sequela “obstructed labor, acute event”. However, when we compute averted YLDs, the above calculation will not correctly count uncured or untreated fistula YLDs from the long-term sequelae “rectovaginal_fistula” or “vesicovaginal_fistula”, for two reasons:

Fistula YLDs for a given age group will include not only OL or uterine ruptures caused by current births, but by OL or uterine ruptures caused by prior births. This means that we are assigning extra YLDs to each current OL or uterine rupture case that are actually being accrued by other, nonpregnant people in the population who have lasting impacts of a previous birth and have nothing to do with the OL or uterine rupture case we are modeling.
If the modeled birth and uterine rupture case does lead to an uncured or untreated fistula, the total fistula YLDs will be spread out over the simulant’s remaining lifetime, occurring in later age groups, not entirely in the simulant’s current age group (when using the “prevalence YLD” approach currently employed by GBD). Thus we will be missing a portion of the YLDs caused by the current birth events when we tally up YLDs for births in the simulant’s current age group.

Thus, if we avert a case of OL or uterine rupture, we will be simultaneously averting extra YLDs that we shouldn’t be, because we are counting YLDs that don’t actually belong to the simulant whose case was averted, as well as missing YLDs that should have been averted because we are only counting YLDs in the simulant’s current age group, and not the YLDs that they would accrue in later years. Since births and hence incident cases of OL or uterine rupture generally decrease with age, while cases of uncured or untreated fistulas increase with age until age group 11 (and fistula YLDs can continue accruing all the way through the 95+ age group, unlike YLDs caused by sepsis or hemorrhage), we might be systematically undercounting the YLDs that would be averted by each averted case of OL, because for a OL case, the missed YLDs for the simulant in question will on average be greater than the extraneous YLDs from other simulants in the same age group.

It may be possible to develop a different strategy of counting YLDs (such as switching to “incidence YLDs”) that would help correct this bias, but the discrepancy will likely be a relatively small proportion of total DALYs, so we are willing to accept this limitation for now.

Validation Criteria

In order to verify and validate the model, we should record at least the following information:

Number of simulants with live/stillbirth pregnancies in each age group before the OL and uterine rupture model is run
Number of OL and uterine rupture cases and OL and uterine rupture deaths in each age group
Number of OL and uterine rupture YLDs and YLLs in each age group

Using the above data, we should be able to verify/validate the following:

Validate the OL and uterine rupture incidence risk and case fatality rate in each age group against the corresponding quantities calculated from GBD data
Validate the number of OL and uterine rupture deaths per population against the OL and uterine rupture CSMR from GBD
Validate the total OL and uterine rupture YLDs and YLLs per population against the rates from GBD