Postpartum hemorrhage

Disease Overview

GBD 2023 Modeling Strategy

Cause Hierarchy

Postpartum hemorrhage does not appear in the GBD cause hierarchy. It is a subset of maternal hemorrhage (c_367), which is a most detailed cause in GBD 2023. The relevant portion of the GBD hierarchy is as follows:

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) is 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
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 2023 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 2023 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 postpartum hemorrhage model is to capture YLLs and YLDs due to postpartum hemorrhage among people giving birth. We only model postpartum hemorrhage among simulants who give (live or still) birth. This page documents how to model the baseline burden of postpartum hemorrhage. Other simulation components such as c-sections will affect the rates of postpartum 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 postpartum hemorrhage all occur at the end of pregnancy, we will not model postpartum 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 postpartum 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 postpartum 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 postpartum hemorrhage
moderate	Parent simulant has moderate postpartum hemorrhage (i.e., blood loss greater than 500 mL but less than 1 liter)
severe	Parent simulant has severe postpartum hemorrhage (i.e., blood loss 1 liter or more)
parent did not die of postpartum hemorrhage	Parent simulant did not die of postpartum hemorrhage
parent died of postpartum hemorrhage	Parent simulant died of postpartum hemorrhage
end

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

Probabilities

The postpartum 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 (CFR) will be computed as

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

If this calculation results in a CFR exceeding 1, it should be clipped to 1. However, we should record this somehow and revisit this strategy if it happens often.

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 postpartum 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
postpartum_fraction	fraction of maternal hemorrhage cases that are postpartum	The exponentiated prediction of the GBD 2023 crosswalk model, age group specific using the age midpoint of the age group	Sample uncertainty from the normal distribution of uncertainty around the prediction. See https://github.com/ihmeuw/vivarium_gates_mncnh/pull/308 for data and details about how to extract this value. Note that there is a separate crosswalk for antepartum hemorrhage specifically, but there is no guarantee of the antepartum and postpartum fractions summing to 1 in the GBD data, so we will use the postpartum fraction from the overall maternal hemorrhage crosswalk to calculate the antepartum fraction as (1 - postpartum_fraction).
ir	postpartum hemorrhage incidence risk per birth	postpartum_fraction * incidence_c367 / birth_rate	The value of ir is a probabiity in [0,1]. Denominator includes live births and stillbirths.
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

Limitations

Because we use the YLD rate and mortality rate of maternal hemorrhage overall, we are assuming that these are the same for postpartum hemorrhage as for antepartum hemorrhage.
We assume that all postpartum hemorrhage fatalities occur among those with severe postpartum hemorrhage, which may not be the case in reality.
We assume that postpartum hemorrhage is uncorrelated with antepartum hemorrhage, except for the causal effect through hemoglobin. In reality, there may be both confounding and a direct causal effect.
Splitting out maternal hemorrhage (modeled as one cause in the GBD) into antepartum and postpartum hemorrhage (modeled as two separate causes in our model, with a vicious cycle between them through hemoglobin) will lead us to overestimate the total burden of maternal hemorrhage relative to GBD due to cases that have both antepartum and postpartum hemorrhage and have double-shifted hemoglobin.