Maternal hemorrhage

Note

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

        • Maternal hemorrhage (c_367)

          • Maternal hemorrhage with less than 1 liter blood loss (s_180)

          • Maternal hemorrhage with greater than 1 liter blood loss (s_181)

          • Mild anemia due to maternal hemorrhage (s_182)

          • Moderate anemia due to maternal hemorrhage (s_183)

          • Severe anemia due to maternal hemorrhage (s_184)

Maternal hemorrhage (c_367) ia a most detailed cause, at level 4 of the GBD hierarchy. It has five sequelae, detailed in the following table:

Sequelae of maternal hemorrhage

Sequela	GBD ID	Health state and disability weight	Notes
Maternal hemorrhage with less than 1 liter blood loss	s_180	abdominopelvic problem, moderate DW: 0.114 (0.078–0.159)
Maternal hemorrhage with greater than 1 liter blood loss	s_181	abdominopelvic problem, severe DW: 0.324 (0.22–0.442)
Mild anaemia due to maternal haemorrhage	s_182	anaemia, mild DW: 0.004 (0.001–0.008)
Moderate anaemia due to maternal haemorrhage	s_183	anaemia, moderate DW: 0.052 (0.034–0.076)
Severe anaemia due to maternal haemorrhage	s_184	anaemia, severe DW: 0.149 (0.101–0.209)

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	50 to 54 (ID=15)

Vivarium Modeling Strategy

Scope

The goal of the maternal hemorrhage model is to capture YLLs and YLDs due to maternal hemorrhage among women of reproductive age. We only model maternal hemorrhage among simulants who give (live or still) birth. This page documents how to model the baseline burden of maternal hemorrhage. Other simulation components such as c-sections will affect the rates of maternal hemorrhage; 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 maternal hemorrhage all occur at the end of pregnancy, we will not model maternal hemorrhage 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, we will convert GBD’s annual rates among females of reproductive age into conditional event rates. We will track maternal hemorrhage deaths to calculate YLLs, and we will track incident cases by severity to calculate YLDs.

Assumptions and Limitations

Cause Model Diagram

Although we’re not modeling hemorrhage 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)
hemorrhage	Parent simulant has maternal hemorrhage
moderate	Parent simulant has moderate maternal hemorrhage (i.e., blood loss greater than 500 mL but less than 1 liter)
severe	Parent simulant has severe maternal hemorrhage (i.e., blood loss 1 liter or more)
parent did not die of maternal hemorrhage	Parent simulant did not die of maternal hemorrhage
parent died of maternal hemorrhage	Parent simulant died of maternal hemorrhage
end

Transition Probability Definitions

Symbol	Name	Definition
ir	incidence risk	The probability that a pregnant simulant gets maternal hemorrhage
severe_fraction	severe fraction	The probability that a simulant with maternal hemorrhage has severe hemorrhage (i.e., blood loss of 1 liter or more)
cfr	case fatality rate	The probability that a simulant with severe hemorrhage dies of that hemorrhage

Probabilities

The maternal hemorrhage cause model requires three probabilities, the incidence risk (ir) per birth, the severe fraction (severe_fraction), and the case fatality rate (cfr), for use in the decision graph. The incidence risk per birth will be computed as

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

The severe fraction will be computed as

\[\text{severe\_fraction} = \frac{\text{incidence\_s181}}{\text{incidence\_s181} + \text{incidence\_s180}}.\]

The case fatality rate will be computed as

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

Calculating years lived with disability

We apply the YLDs per case for the corresponding severity level to each incident case to calculate YLDs.

\[\text{ylds\_per\_case\_severe} = \frac{\text{yld\_rate\_s181}}{\text{incidence\_s181}}\]

\[\text{ylds\_per\_case\_moderate} = \frac{\text{yld\_rate\_s180}}{\text{incidence\_s180}}\]

Note that we do not include YLDs for mild, moderate, or severe anemia due to maternal hemorrhage (s_182, s_183, s_184) in our calculations because these sequelae are already counted under the anemia cause model, and we want to avoid double counting.

Data table

The following table shows the data needed from GBD for these calculations.

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	maternal hemorrhage incidence risk per birth	incidence_c367 / birth_rate	The value of ir is a probabiity in [0,1]. Denominator includes live births and stillbirths.
cfr	case fatality rate of maternal hemorrhage	csmr_c367 / incidence_c367	The value of cfr is a probabiity in [0,1]
incidence_c367	incidence rate of maternal hemorrhage	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_c367.
incidence_s181	incidence rate of severe maternal hemorrhage	como
incidence_s180	incidence rate of moderate maternal hemorrhage	como
csmr_c367	maternal hemorrhage cause-specific mortality rate	deaths_c367 / population	Note that deaths / (average population for year) = deaths / person-time
deaths_c367	count of deaths due to maternal hemorrhage	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_s180	YLD rate per person-year due to moderate maternal hemorrhage	como
yld_rate_s181	YLD rate per person-year due to severe maternal hemorrhage	como

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 maternal hemorrhage model is run

• Number of maternal hemorrhage cases and maternal hemorrhage deaths in each age group

• Number of maternal hemorrhage YLDs and YLLs in each age group

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

• Validate the maternal hemorrhage incidence risk and case fatality rate in each age group against the corresponding quantities calculated from GBD data

• Validate the number of maternal hemorrhage deaths per population against the maternal hemorrhage CSMR from GBD

• Validate the total maternal hemorrhage YLDs and YLLs per population

References