Pregnancy: GBD 2021, Closed Cohort

Abbreviations

Abbreviation	Definition	Note
ASFR	Age-specific fertility rate
SBR	Stillbirth to live birth ratio
LBWSG	Low birthweight and short gestation

Overview

This model document is an adaptation of the pregnancy model document found here, which was developed for the IV iron simulation. This version differs in that it is designed for a closed rather than open cohort for the nutrition optimization simulation and therefore models pregnancies only rather than all women of reproductive age.

GBD Modeling Strategy

Pregnancy and births are not explicit outcomes in the GBD study. However, there are location- and year-specfic GBD covariates related to fertility and births, including:

Covariates

Covariate name	Covariate ID	Note
Live births (thousands)	60
Live births by sex	1106
Live births by sex and maternal age	2298
Stillbirth to live birth ratio	2267	Not specific to maternal age. Upper and lower bound estimates are equal to mean estimate (no uncertainty interval)
Age-specific fertility rate	13
Total fertility rate	2363

GBD has estimated the prevalence of pregnancy (as an intermediate variable for the estimation of various outcomes) as:

\[(ASFR + (SBR * ASFR)) * 46/52\]

Where \(ASFR\) is the age-specific fertility rate, \(SBR\) is the stillbirth to live birth ratio, and \(46/52\) is the proportion of the year spent pregnant (40 weeks) and postpartum (6 weeks).

Todo

Determine the threshold of gestational age at which a loss of pregnancy is classified as a stillbirth rather than miscarriage for the GBD covariate. Standard thresholds are 20 or 24 weeks.

Vivarium Modeling Strategy

We will model pregnancy as a characteristic of women of reproductive age in our simulations. We will inform the incidence of pregnancy using the age-specific fertility and stillbirth to live birth ratio covariates from GBD. We will inform the duration of pregnancy using the GBD 2019 exposure distribution of gestational age.

Note

For an explanation of the rationale behind the maternal disorders state in this model, see the note on maternal disorders, pregnancies, and YLDs on the nutrition optimization pregnancy concept model document.

Note

In the implementation for this model in the nutrition optimization simulation, the maternal disorders state in this diagram is referred to as the “parturition” state. Additionally, note that maternal disorders deaths occur in the first timestep of the postpartum state.

State definitions

State	Description	Note
np	Not pregnant or postpartum
p	Pregnant
md	Maternal disorders	Simulated state that lasts for single timestep in order to accrue maternal disorders YLDs - not representative of biological state. Can be with (md_w) or without (md_wo) maternal disorders while within this state according to the maternal disorders cause model document. Referred to as “prepostpartum” state in software implementation.
pp	Postpartum

Note

The duration of the maternal disorders state for the IV iron simulation was set to one week. This parameter is currently a barrier to extending the maternal IV iron simulation timestep from 1 to 2 weeks.

State prevalence table for initialization

State	Value	Note
np	0
p	1
pp	0
md_w	0
md_wo	0

State transition data

Source state	Sink state	Transition name	Transition rate	Note
np	p	incidence_p	0	Assumed zero for convenience. Note that this is typically \(\frac{ASFR + ASFR * SBR + incidence_\text{c995} + incidence_\text{c374}}{prevalence_\text{np}}\)
p	md	duration_p	Duration informed by gestational age (see below section)	Duration-based transition
md	pp	duration_md	1 timestep	Duration-based transition
pp	np	duration_pp	6 weeks (42 days) - duration_md	Duration-based transition

Data values

Parameter	Data type	Data ID	Source	Note
ASFR	Covariate	13	get_covariate_estimates: decomp_step=’iterative’ for GBD 2021	Assume lognormal distribution of uncertainty.
SBR	Covariate	2267	get_covariate_estimates: decomp_step=’iterative’ for GBD 2021	Parameter is not age specific and has no draw-level uncertainty. Use mean_value as location-specific point parameter.
incidence_c995	Incidence rate of abortion and miscarriage cause	c995	como; decomp_step=’iterative’	Use the total population incidence rate directly from GBD and do not rescale this parameter to susceptible-population incidence rate using condition prevalence.
incidence_c374	Incidence rate of ectopic pregnancy	c374	como; decomp_step=’iterative’	Use the total population incidence rate directly from GBD and do not rescale this parameter to susceptible-population incidence rate using condition prevalence.

Note

NOTE: this was NOT implemented for IV iron (deprioritized as it was thought to have little influence on results). To be implemented for the nutrition optimization project average duration of pregnancy will need to be calculated as described below.

AGE SHIFTING: The incidence rates in the table above are measured at the end of pregnancy. However, we will use them to inform the rates of the beginning of pregnancy. In order to avoid causing pregnancies to end at older ages than they should in our simulation, we will implement a custom “pregnancy age” in our vivarium simulation that is equal to a simulant’s actual age minus the average duration of pregnancy. This “pregnancy age” should be used to index which pregnancy incidence rate (incidence_p) value the simulant is subject to at any given time.

The average duration of pregnancy (pregnancy age shift) was calculated assuming that live and still births have a duration of 40 weeks and that ectopic pregnancies and miscarriages/abortions have an average duration of 15 weeks (the midpoint between 6 weeks (assumed minimum duration of an identified pregnancy) and 24 weeks (cutoff between miscarriage and stillbirth)) and according to the location-specific distribution of birth outcomes. These values were calculated for the IV iron simulation in this notebook.

Restrictions

Restriction Type	Value	Notes
Male only	False
Female only	True
Age group start	10 to 14 years	ID=7
Age group end	50 to 54 years	ID=15

Note

Pregnancy modeling steps:

At initialization:

1. Assign pregnancy state according to state prevalence values

2. Assign partial or full term duration according to table in Pregnancy term lengths section

3. Assign sex of infant if pregnancy is full term (stillbirth or live birth)

4. Assign duration of pregnancy depending on term length and, if applicable, sex of the infant

5. Determine the amount of time remaining in pregnancy from the duration of pregnancy: for closed cohort, assume simulation starts at day 0 of all pregnancies

6. Begin simulation

During simulation:

• Determine pregnancy model state according to state at initialization and state transition rates.

• Upon transition from the np to p state, follow steps 2-4 described above. (should not occur for closed cohort)

• Upon birth (transition out of p state), assign pregnancy outcome

  • other for partial duration pregnancies

  • live_birth or stillbirth for full duration pregnancies, according to table in Pregnancy outcomes section

(Specific instructions for each of these steps described in the following sections.)

Pregnancy term lengths

At the beginning of pregnancy, it should be determined whether the pregnancy will be partial term or full term according to the probabilities in the table below.

Pregnancy term lengths probabilities

Term length	Probability	Note
Partial term	(incidence_c995 + incidence_c374) / (ASFR + ASFR * SBR + incidence_c995 + incidence_c374)
Full term	1 - probability_partial_term

Sex of infant

Note

The IV iron simulation assumed 50/50 probability

For pregnancies that result in live birth or stillbirth outcomes, infant sex should be determined and recorded acording to the probability of male sex shown in the table below (probability of female birth is equal to 1 minus the probability of male birth). This should be performed at the start of pregnancy (transition from np to p states) or upon initialization into the p state. These sex ratios were calculated using the live births by sex 2020 GBD covariate (ID 1106), shown here. Note that there is no variation by draw in this parameter.

Probability of male birth

Location	Location ID	Value
Pakistan	165	0.514583
Nigeria	214	0.511785
Ethiopia	179	0.514271

Duration of pregnancy

A duration of pregnancy value will need to be assigned to all pregnancies regardless of the pregnancy outcome. This value will inform the duration that the simulant remains in the pregnancy state prior to transitioning to the postpartum state.

For partial term pregnancies (that result in abortion/miscarriage/ectopic pregnancy), assign a duration of pregnancy sampled from a uniform distribution beween 6 and 24 weeks (individual heterogeneity with no parameter uncertainty).

For full term pregnancies (that result in live births or stillbirths), duration of pregnancy should be determined by gestational age exposure, which should be assigned according to the process for assigning LBWSG exposures described in the risk correlation document between maternal BMI, maternal hemoglobin, and infant LBWSG exposure. The LBWSG exposure distribution used to assign gestational age exposures should be specific to the sex of the infant for a given pregnancy (discussed in the above section) and may also be modified by antenatal supplementation intervention coverage. Note that the gestational age distribution is measured in weeks and will need to be converted to the equivalent simulation time measure.

Note

The impact of antenatal supplementation intervention coverage on pregnancy duration (distinguished from its effect on infant LBWSG exposure here) will have a minimal impact on total DALYs modeled in the nutrition optimization simulation (will only affect anemia YLDs by extending for the duration of the gestational age shift). Therefore, it would be an acceptable limitation to ignore the impact of this intervention coverage on pregnancy duration if it is convenient for implementation as long as the intervention continues to impact infant LBWSG exposures.

Todo

Update the above note to reflect what is actually implemented.

Pregnancy outcomes

At or before the time of birth, pregnancy outcome must be determined for each pregnancy as either a 1) live birth, 2) stillbirth, or 3) other (ectopic pregnancy, abortion/miscarriage). The probability of each pregnancy outcome dependent on the pregnancy term length and probabilities of each outcome conditional on pregnancy term are defined in the table below.

Pregnancy outcome probabilities conditional on pregnancy term length

Pregnancy term length	Outcome	Conditional probability	Note
Partial term	Live birth	0
Partial term	Stillbirth	0
Partial term	Other (abortion, miscarriage, ectopic pregnancy)	1
Full term	Live birth	ASFR / (ASFR + ASFR * SBR)	The probability of a livebirth outcome is modified by antenatal supplementation intervention coverage.
Full term	Stillbirth	(ASFR * SBR) / (ASFR + ASFR * SBR)	The probability of a stillbirth outcome is modified by antenatal supplementation intervention coverage.
Full term	Other (abortion, miscarriage, ectopic pregnancy)	0

Note

The current modeling strategy is dependent on our assumption that live births and stillbirths have the same duration. There is ongoing work at IHME to estimate gestational age at birth distributions among stillbirths.

Assumptions and limitations

• We assume that the gestational age distribution of stillbirths is equal to the gestational age distribution of live births. This is a limitation of our analysis given the lack of data on the distribution of gestational ages for which these outcomes occur. Given that the gestation for these outcomes is likely shorter than gestation for live births on average, we are likely overestimating the average duration of pregnancy for outcomes other than live births.

• We assume that all abortions, miscarriages and ectopic pregnancies occur uniformly between six and 24 weeks gestatation. Six weeks was chosen as a reasonable earliest possible time of pregnancy detection (prior to which miscarriages would be undiagnosed) and 24 weeks was chosen as the threshold between miscarriage and stillbirth.

• We assume that abortions that occur after 24 weeks are not considered stillbirths for estimation of the stillbirth to livebirth ratio. We may overestimate the incidence rate of pregnancy due to this assumption.

• We are limited in the assumption that the stillbirth to livebirth ratio does not vary by maternal age and does not incorporate an uncertainty distribution.

• We do not model any morbidity (YLDs) associated directly with pregnancy.

• We do not distiguish between intended and unintended pregnancies.

• We do not consider the impact of birth interval timing or family size in our model of pregnancy.

• We do not consider the impact of singleton versus non-singleton pregnancies.

• We are limited in that we apply the age-specific fertility rate to the beginning of pregnancy when it is actually measured at the end of pregnancy (birth). Therefore, maternal age at birth in our simulation will be overestimated due to simulants becoming pregnant in one age group and giving birth in the next.

Verification and validation criteria

The following should validate: - Average duration of pregnancy - Duration of maternal disorders and postpartum states - Rates of each birth outcomes

References