Neonatal all-cause mortality: GBD 2021, MNCNH

Note

This page is adapted from the Maternal disorders: GBD 2021, MNCNH page and is also part of the MNCNH Portfolio project. In this work we are modeling several neonatal subcauses (see Modeled Subcauses) which is complicated because the Low Birth Weight and Short Gestation (LBWSG) risk factor in GBD acts on all-cause mortality during the neonatal period.

This document describes neonatal disorders overall and the strategy for capturing the burden of the neonatal subcauses in a manner that also is calibrated to match all-cause mortality and our continuous (interpolated) LBWSG risk effect on all-cause mortality.

Disease Overview

This model captures deaths due to any cause that occur during the first 28 days of life. The Low Birth Weight and Short Gestation (LBWSG) risk factor provides a single relative risk for all neonatal deaths, and this all-cause neonatal mortality model describes how we can include it in our simulations.

GBD 2021 Modeling Strategy

The all-cause neonatal mortality estimates are produced by the demographics research team. The cause-specific mortality for neonatal subcauses are estimated using the Cause of Death Ensemble model (CODEm) process. The low-birth weight and short gestation risk factor exposure and effect size was estimated by yet another GBD team.

Cause Hierarchy

  • All causes (c_294) [level 0]

    • Communicable, maternal, neonatal, and nutritional diseases (c_295)

      • Maternal and neonatal disorders (c_962)

        • Neonatal disorders (c_380) [level 3]

          • Neonatal preterm birth (c_381) [level 4]

          • Neonatal encephalopathy due to birth asphyxia and trauma (c_382) [level 4]

          • Neonatal sepsis and other neonatal infections (c_383) [level 4]

          • Hemolytic disease and other neonatal jaundice (c_384) [level 4]

          • Other neonatal disorders (c_385) [level 4]

Modeled Subcauses

Restrictions

The following table describes the restrictions from GBD 2021 and our intended use in our MNCNH model.

GBD 2017 Cause Restrictions

Restriction Type

Value

Notes

Male only

False

Female only

False

YLL only

True

Note: GBD estimates both YLLs and YLDs for neonatal disorders, but we are ignoring YLDs for this model.

YLD only

False

See above.

YLL age group start

Early Neonatal

[0, 7 days), age_group_id=2

YLL age group end

Late Neonatal

[7 days, 28 days), age_group_id=3

YLD age group start

Not applicable

YLD age group end

Not applicable

Vivarium Modeling Strategy

This model is designed to estimate deaths and YLLs during the neonatal period that could be averted by interventions targeting sepsis, respiratory distress syndrome (RDS), and possibly encephalopathy, as well as Low Birth Weight and Short Gestation (LBWSG). The model accounts for key neonatal sub-causes explicitly and groups all other causes of mortality during the neonatal period together. It focuses only on fatal outcomes (no disability). The rationale for this design is as follows:

  1. The LBWSG risk factor in GBD affects all-cause mortality during the neonatal period, so we need to model all-cause mortality and the LBWSG risk.

  2. The nonfatal burden of neonatal causes is around 10% of the total burden. Excluding YLDs simplifies the model significantly without losing much accuracy. Most of this nonfatal burden is accrued throughout life, which complicates combining it with the prevalence DALYs construct.

Scope

  1. Capture deaths by any cause during the neonatal, and the relationship between all-cause mortality and LBWSG.

  2. Capture the deaths averted by interventions that reduce the cause-specific mortality of preterm with respiratory distress and sepsis (and perhaps encephalopathy).

  3. Do not capture nonfatal burden.

Assumptions and Limitations

  • The excluded nonfatal portion of the burden is small (around 10% of the total burden).

  • The evidence base for identifying the level 4 subcauses is not as solid as I would like.

  • Preterm must be split into with and without respiratory distress syndrome (RDS) outside of GBD, since GBD does not distinguish preterms deaths with and without RDS.

We “cap” LBWSG RR values at a certain value in an attempt to eliminate the occurance of individual all-cause mortality risk values greater than 1 on in our simulation (and therefore avoiding an associated underestimation of neonatal mortality) while also maintaining:

  • The relative difference in mortality risk values between LBWSG exposures that are not capped, and

  • Mortality risk values very close to 1 for the individuals with the highest risk LBWSG exposures

However, in this implementation, we do not consider how modeled interventions may further increase individual-level mortality risk beyond the modifications from the LBWSG risk factor, so it is possible that we continue to have some mortality risk values greater that 1 in our simulation.

Cause Model Decision Graph

We are not modeling neonatal disorders dynamically as a finite state machine, but we can draw an directed graph to represent the collapsed decision tree representing this cause. Unlike a state machine representation, the values on the transition arrows represent decision probabilities rather than rates per unit time.

digraph NN_decisions { rankdir = TB; lb [label="live birth", style=dashed] enn_alive [label="neonate survived\nfirst 7 days"] lnn_alive [label="neonate survived\nfirst 28 days"] dead [label="neonate died"] died_of_subcause_0 [label="neonate died\nof subcause 0"] died_of_subcause_1 [label="neonate died\nof subcause 1"] died_of_subcause_K [label="neonate died\nof subcause K"] {rank=same; died_of_subcause_0 died_of_subcause_1 died_of_subcause_K } lb -> enn_alive [label = "1 - acmrisk_enn"] lb -> dead [label = "acmrisk_enn"] enn_alive -> lnn_alive [label = "1 - acmrisk_lnn"] enn_alive -> dead [label = "acmrisk_lnn"] dead -> died_of_subcause_0 [label="p_0"] dead -> died_of_subcause_1 [label="p_1"] dead -> died_of_subcause_K [label="p_K"] died_of_subcause_1 -> died_of_subcause_K [color="none", label="..."] }

Decision Point Definitions

Decision

Definition

live birth

The parent simulant has given birth to a live child simulant (which is determined in the intrapartum step of the pregnancy model)

neonate survived first 7 days

The simulant survived for the first 7 days of life

neonate survived first 28 days

The simulant survived for the first 28 days of life

neonate died

The simulant died during the first 28 days of life

neonate died of subcause k

The simulant died due to cause \(k\) for \(k = 0, 1, \ldots, K\). (Here \(k = 0\) denotes a residual “all other causes” category.)
Transition Probability Definitions

Symbol

Name

Definition

acmrisk_enn

mortality risk due to all causes during the early neonatal period

The probability that a simulant who was born alive dies during the first 7 days

acmrisk_lnn

mortality risk due to all causes during the late neonatal period

The probability that a simulant who survived the first 7 days dies between day 8 to 28 of life

p_k

cause-specific mortality fraction

The probability that a simulant death was due to cause \(k\)

Modeling Strategy

The neonatal death model requires only the probability of death (aka “mortality risk”) for the early and late neonatal time periods. These mortality risks are age-group-, sex-, and location-specific. For brevity, sex and location subscripts are omitted in all equations.

Rather than using GBD mortality rates and converting them into probability of deaths, we will use mortality risk as direct input data into our model. We will calculate mortality risk input data as age-specific death counts divided by live birth counts from GBD.

Note that this strategy does not require any conversion between rates to probabilities NOR does it require any scaling to the duration of the age group. The mortality risk calculated as described below already represents the probability of dying within a neonatal age group and can be used directly as such in the simulation.

To avoid confusion with mortality rates (typically referred to as the all-cause mortality rate, ACMR, or cause-specific mortality rates, CSMRs), we will refer to mortality risk as ACMRisk (all-cause mortality risk) and CSMRisk (cause-specific mortality risk), where:

\[ \begin{align}\begin{aligned}\text{ACMRisk}_\text{ENN} = \frac{\text{deaths due to all causes in the ENN age group}}{\text{live births}}\\\text{ACMRisk}_\text{LNN} = \frac{\text{deaths due to all causes in the LNN age group}}{\text{live births} - \text{deaths due to all causes in the ENN age group}}\end{aligned}\end{align} \]

and for a given cause of death:

\[ \begin{align}\begin{aligned}\text{CSMRisk}_\text{ENN} = \frac{\text{cause-specific deaths in the ENN age group}}{\text{live births}}\\\text{CSMRisk}_\text{LNN} = \frac{\text{cause-specific deaths in the LNN age group}}{\text{live births} - \text{deaths due to all causes in the ENN age group}}\end{aligned}\end{align} \]

Note that this strategy was updated in May of 2025 from a prior strategy of converting GBD mortality rates to probabilities. The pull request that updated this strategy can be found here for reference. This strategy update was pursued following verification and validation issues in neonatal mortality and an exploration of potential solutions in model runs 6.1 through 6.4. Ultimately, a change from mortality rates to mortality risk was preferred given that it is the more policy relevant measure in the context of neonates, and accurately apportioning person time alive within the neonatal age group given the input data available to us was a challenge we judged to be unnecessary.

The calculation of \(\text{ACMRisk}_i\) (the all-cause mortality risk for a single simulant, \(i\)) is a bit complicated, however. We begin with a population ACMRisk and use the LBWSG PAF to derive a risk-deleted ACMRisk to which we can then apply the relative risk of LBWSG matching any risk exposure level. Mathematically this is achieved by the following formula. Starting with this equation, we omit age group subscripts for brevity; all quantities are still age-, sex-, and location-specific.

\[\begin{aligned} \text{ACMRisk}_{\text{BW},\text{GA}} &= \text{ACMRisk} \times (1 - \text{PAF}_{\text{LBWSG}}) \times \text{RR}_{\text{BW},\text{GA}}, \end{aligned}\]

where \(\text{ACMRisk}_{\text{BW},\text{GA}}\) is the all-cause mortality risk for a population with birth weight \(\text{BW}\) and gestational age \(\text{GA}\), \(\text{ACMRisk}\) is the all-cause mortality risk for the total population in one of the neonatal age groups (i.e., \(\text{ACMRisk}\) equals \(\text{ACMRisk}_\text{ENN}\) or \(\text{ACMRisk}_\text{LNN}\) as defined above), \(\text{PAF}_{\text{LBWSG}}\) is the population attributable fraction for LBWSG, and \(\text{RR}_{\text{BW},\text{GA}}\) is the relative mortality risk for a specific birth weight \(\text{BW}\) and gestational age \(\text{GA}\).

To obtain the ACMRisk for a specific simulant (\(\text{ACMRisk}_i\)), we subtract off the population CSMRisks for each modeled subcause for the birth weight and gestational age of the simulant, and then add back in the (potentially pipeline-modified) individual CSMRisks for the specific simulant, which might differ from baseline due to intervention coverage:

\[\begin{aligned} \text{ACMRisk}_i &= \text{ACMRisk}_{\text{BW}_i,\text{GA}_i} - \sum_k \text{CSMRisk}_{\text{BW}_i,\text{GA}_i}^{k} + \sum_k \text{CSMRisk}_{i}^{k}, \end{aligned}\]

where \(\text{BW}_i\) and \(\text{GA}_i\) are the birth weight and gestational age for simulant \(i\), \(\text{CSMRisk}_{\text{BW}_i,\text{GA}_i}^{k}\) is the cause-specific mortality risk for subcause \(k\) for a population with the same gestational age and birth weight as this simulant, and \(\text{CSMRisk}_{i}^{k}\) is the cause-specific mortality risk for subcause \(k\) for simulant \(i\) (both detailed in the Modeled Subcauses linked from this page).

In addition to determining which simulants die due to any cause, we also need to determine which subcause is underlying the death. This is done by sampling from a categorical distribution obtained by renormalizing the CSMRisks:

\[\begin{aligned} \text{Pr}[\text{subcause} = k\;|\;\text{neonate died}] &= \frac{\text{CSMRisk}_{i}^{k}} {\text{ACMRisk}_i}, \end{aligned}\]

including a special \(k=0\) for the residual “all other causes” category defined by \(\text{CSMRisk}_{i}^{0} = \text{ACMRisk}_i - \sum_{k=1}^K \text{CSMRisk}_{i}^{k}.\)

Data Tables

Note

All quantities pulled from GBD in the following table are for a specific year, sex, age group, and location.

Data values and sources

Variable

Definition

Value or source

Note

enn_all_cause_death_count

Death count in the early neonatal age group

GBD: source=’codcorrect’, metric_id=1, cause_id=294

lnn_all_cause_death_count

Death count in the early neonatal age group due to all causes

GBD: source=’codcorrect’, metric_id=1, cause_id=294

enn_cause_specific_death_count

Count of deaths due to cause C in the early neonatal age group

GBD: source=’codcorrect’, metric_id=1

lnn_cause_specific_death_count

Count of deaths due to cause C in the late neonatal age group

GBD: source=’codcorrect’, metric_id=1

live_birth_count

Count of live births

GBD: covariate_id = 1106

acmrisk_enn

all-cause mortality risk in the early neonatal age group

enn_all_cause_death_count / live_birth_count

acmrisk_lnn

all-cause mortality risk in the late neonatal age group

lnn_all_cause_death_count / (live_birth_count - enn_all_cause_death_count)

csmrisk_enn

Cause-specific mortality risk in the early neonatal age group

enn_cause_specific_death_count / live_birth_count

csmrisk_lnn

Cause-specific mortality risk in the late neonatal age group

lnn_cause_specific_death_count / (live_birth_count - enn_all_cause_death_count)

\(\text{ACMRisk}\)

All-cause mortality risk

either acmrisk_enn or acmrisk_lnn depending on the simulant’s age group

\(\text{CSMRisk}\)

Cause-specific mortality risk

either csmrisk_enn or csmrisk_lnn depending on the simulant’s age group

\(\text{PAF}_\text{LBWSG}\)

population attributable fraction of all-cause mortality for low birth weight and short gestation

See note below for how to calculate

Note that the relative risks used to calculate the PAFs are capped below the \(\text{RR}_\text{max}\) value

\(\text{RR}_{\text{BW},\text{GA}}\)

relative risk of all-cause mortality for low birth weight and short gestation, capped at the specified maximum value

\(\min(\text{RR}_\text{max}, \text{RR}_\text{LBWSG})\)

\(\text{RR}_\text{LBWSG}\)

relative risk of all-cause mortality for low birth weight and short gestation, as interpolated from GBD

interpolated from GBD values, as described in Low Birth Weight and Short Gestation (LBWSG) docs

\(\text{RR}_\text{max}\)

Enforced maximum value for LBWSG relative risk

Location/draw/age group/sex-specific value calculated according to process in this notebook

Note that the calculation of these values depends on the following artifact keys, which will need to be generated for the GBD 2023 update prior to calculating the RR cap values for GBD 2023 (which are themselves an input to the LBWSG PAF calculation simulation)

  • 'cause.all_causes.all_cause_mortality_risk'

  • 'risk_factor.low_birth_weight_and_short_gestation.birth_exposure'

  • 'risk_factor.low_birth_weight_and_short_gestation.relative_risk'

Capping of LBWSG RRs is intended to guarentee that there will be no individual mortality risk value is greater than 1 in our simulation

\(\text{CSMRisk}^k_{\text{BW},\text{GA}}\)

cause-specific mortality risk for subcause k, for population with birth weight BW and gestational age GA

GBD + assumption about relative risks

see subcause models for details

\(\text{CSMRisk}^k_i\)

cause-specific mortality risk for subcause k, for individual i

GBD + assumption about relative risks + intervention model effects

see subcause models for details

Details of the LBWSG PAF calculation

As stated in the table above, \(\text{PAF}_\text{LBWSG}\) is the population attributable fraction of all-cause mortality for low birth weight and short gestation. It is computed so that PAF = 1 - 1 / E(\(\text{RR}_{\text{BW},\text{GA}}\)) from the capped interpolated relative risk function (with expectation taken over the distribution of LBWSG exposure).

For the early neonatal age group, the LBWSG exposure at birth is used. For the late neonatal age group, we will use the LBWSG exposure at 8 days of life (start of the late neonatal age group after all early neonatal deaths have occurred). This LBWSG exposure is not directly available from GBD. Therefore, we will need to produce it ourselves according to the following steps:

Using the LBWSG PAF calculation simulation:

  • For the calculation of the early neonatal PAF:

    • Population size = use that specified on the preterm birth cause model document (see note about the calculation of the normalizing constant)

    • LBWSG exposure specific to birth age group

    • LBWSG relative risk values are interpolated and capped at the location/draw/age group/sex-specific maximum RR value (\(\text{RR}_\text{max}\))

  • For the calculation of the late neonatal PAF:

    1. Assign all-cause mortality risk values to each simulated individual using the early neonatal LBWSG RR values (interpolated and capped), early neonatal LBWSG PAF (as calculated above), and early neonatal all-cause mortality risk

    2. Take a “time step” of ~7 days that advances the population past the early neonatal mortality application, but before late neonatal mortality has been applied. Mortality should be applied (simulants should die) according to their LBWSG-affected all-cause mortality risk values (no need to consider cause-specific mortality and/or interventions in this step).

    3. Record the number of deaths that occur in each LBWSG exposure category \(\text{cat}\) as \(n^\text{deaths}_\text{cat}\)

    4. Among the surviving simulants, re-assign LBWSG RR values using the late neonatal interpolated RR values and the late neonatal-specific RR caps

    5. Use the RR values from step 4 (among surviving simulants only) for the calculation of the mean relative risk among the given LBWSG exposure category, \(E(\text{RR})_\text{cat}\)

    6. To calculate the overall population mean RR (\(E(\text{RR})_\text{population}\)), take a weighted average of the category-specific mean relative risk values weighted by the category-specific LBWSG exposure prevalence AT BIRTH (\(p^\text{birth}_\text{cat}\)) multiplied by the fraction of simulants who survived past the early neonatal age group, equal to: \(\frac{n_\text{cat} - n^\text{deaths}_\text{cat}}{n_\text{cat}}\), where \(n_\text{cat}\) is the number of simulants initialized into each category before mortality was applied (the number of grid points in each category). Note that \(n_\text{cat}\) will not vary by LBWSG exposure category.

So,

\[E(\text{RR})_\text{population} = \frac{\sum_{\text{cat}} E(\text{RR})_\text{cat} \times p^\text{birth}_\text{cat} \times \frac{n_\text{cat} - n^\text{deaths}_\text{cat}}{n_\text{cat}}}{\sum_{\text{cat}} p^\text{birth}_\text{cat} \times \frac{n_\text{cat} - n^\text{deaths}_\text{cat}}{n_\text{cat}}}\]

Calculating Burden

Years of life lost

The years of life lost (YLLs) due to neonatal disorders are calculated assuming age \(a=14 \text{ days}\), and equals \(\operatorname{TMRLE}(a) - a\), where \(\operatorname{TMRLE}(a)\) is the theoretical minimum risk life expectancy for a person of age \(a\).

Years lived with disability

For simplicity, we will not include YLDs in this model.

Validation Criteria

Neonatal mortality risk (due to all causes and at the cause-specific level) in simulation should match corresponding quantity as derived from GBD estimates.

Relative Risk of neonatal death at specific categories of LBWSG exposure should be within 10% of same ratio derived from GBD. (We don’t expect it to match exactly because of (1) our interpolation of the RRs, and (2) we use a constant mortality hazard at each BW-GA level, rather than the GBD’s more complex model.)

References