Antepartum hemorrhage

Disease Overview

GBD 2023 Modeling Strategy

Cause Hierarchy

Antepartum 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 antepartum hemorrhage model is to capture YLLs and YLDs due to antepartum hemorrhage among pregnant people. This page documents how to model the baseline burden of antepartum hemorrhage. Hemoglobin after the later ANC visit will affect the rates of antepartum hemorrhage; such effects are described on the relevant risk effects model page.

Summary of modeling strategy

We will not model antepartum hemorrhage as a state machine, but as a one-time decision. We will choose whether the pregnant person has antepartum hemorrhage at some time during pregnancy. To obtain the decision probabilities, we will convert GBD’s annual rates among females of reproductive age into conditional event rates. We will track antepartum hemorrhage deaths to calculate YLLs, and we will track incident cases by severity to calculate YLDs.

Cause Model Diagram

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

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

Probabilities

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

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

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

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

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 antepartum 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	antepartum hemorrhage incidence risk per pregnancy	(1 - postpartum_fraction) * incidence_c367 / pregnancy_rate	The value of ir is a probabiity in [0,1]. Denominator includes all pregnancies.
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.
pregnancy_rate	pregnancy rate	(1 + SBR) * ASFR + incidence_c995 + incidence_c374	Units are total pregnancies 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.
incidence_c995	Incidence rate per person-year of abortion and miscarriage	como
incidence_c374	Incidence rate per person-year of ectopic pregnancy	como
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

Limitations

Because we use the severity split and mortality rate of maternal hemorrhage overall, we are assuming that these are the same for postpartum hemorrhage as for antepartum hemorrhage. In reality, postpartum hemorrhage is likely to be more severe.
We assume that the impact of antepartum hemorrhage on hemoglobin is the same as the impact of postpartum hemorrhage on hemoglobin, which is likely not true. We suspect that APH would have a smaller impact on average; however, the MarketScan data the GBD effect is calculated from are from PPH in the US, so may already be capturing a smaller average impact than we would expect from PPH in a lower-resource setting.
We assume that all antepartum hemorrhage fatalities occur among those with severe antepartum 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.
We assume that when a simulant has both antepartum hemorrhage and a later ANC visit, the ANC visit occurs before the onset of antepartum hemorrhage. Antepartum hemorrhage typically occurs late in pregnancy, so this would often be the case. Also, in real life, antepartum hemorrhage may lead directly to delivery, even if the fetus is premature, so we don’t think there are likely to be many cases of ANC visits occurring after the onset of antepartum hemorrhage.
We assume that antepartum hemorrhage is uncorrelated with the length of pregnancy and the probability of stillbirth (except through hemoglobin), which is likely not true.
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.