Maternal sepsis and other maternal infections

Note

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

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 sepsis and other maternal infections (c_368)
        
        Infertility due to puerperal sepsis (s_675)
        
        Puerperal sepsis (s_937)
        
        Other maternal infections (s_938)

Maternal sepsis and other maternal infections (c_368) ia a most detailed cause, at level 4 of the GBD hierarchy. It has three sequelae, detailed in the following table:

Sequelae of maternal sepsis and other maternal infections
Sequela	GBD ID	Health state and disability weight	Notes
Infertility due to puerperal sepsis	s_675	infertility, secondary DW: 0.005 (0.002–0.011)	Modeled under the infertility impairment. Secondary infertility means inability to have a livebirth after you’ve already had at least one child.
Puerperal sepsis	s_937	infectious disease, acute episode, severe DW: 0.133 (0.088–0.19)
Other maternal infections	s_938	infectious disease, acute episode, moderate DW: 0.051 (0.032–0.074)

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 sepsis model is to capture YLLs and YLDs due to maternal sepsis (and other maternal infections) among women of reproductive age. We only model maternal sepsis among simulants who give (live or still) birth. This page documents how to model the baseline burden of maternal sepsis. Other simulation components such as azithromycin and c-sections will affect the rates of maternal sepsis; 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 sepsis all occur at the end of pregnancy, we will not model maternal sepsis 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 of each incident case or maternal sepsis death, we will convert GBD’s annual incidence and mortality rates among women of reproductive age into event rates per birth (including stillbirths). We will track maternal sepsis deaths to calculate YLLs, and we will track incident cases to calculate YLDs.

Assumptions and Limitations 

Cause Model Decision Graph 

Although we’re not modeling sepsis 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.

Todo

Put an explanation like the following (but with more precision) on some central page (rather than on each individual model page):

To convert the graph to a decision tree, recursively split nodes with more than one incoming arrow until all nodes except the root have one incoming edge. Each time a node is split, all its outgoing edges are replicated, which may lead to additional downstream splits. Equivalently, the tree structure can be implicitly recovered by remembering the path taken to get to each node.

Jira ticket: https://jira.ihme.washington.edu/browse/SSCI-2006

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)
sepsis	Parent simulant has maternal sepsis
parent not dead of maternal sepsis	Parent simulant did not die of maternal sepsis
parent died of maternal sepsis	Parent simulant died of maternal sepsis
end

Transition Probability Definitions
Symbol	Name	Definition
ir	incidence risk	The probability that a pregnant simulant gets maternal sepsis or another maternal infection
cfr	case fatality rate	The probability that a simulant with sepsis or another maternal infection dies of that infection

Data Tables 

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

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

The case fatality rate will be computed as

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

The following table shows the data needed from GBD for these calculations as well as for the calculation of YLDs in the next section.

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 sepsis incidence risk per birth	incidence_c368 / birth_rate	The value of ir is a probabiity in [0,1]. Denominator includes live births and stillbirths.
cfr	case fatality rate of maternal sepsis	csmr_c368 / incidence_368	The value of cfr is a probabiity in [0,1]
incidence_c368	incidence rate of maternal sepsis and other maternal infections	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_c368.
csmr_c368	maternal sepsis cause-specific mortality rate	deaths_c368 / population	Note that deaths / (average population for year) = deaths / person-time
deaths_c368	count of deaths due to maternal sepsis and other maternal infections	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_c368	rate of maternal sepsis YLDs per person-year	como
ylds_per_case_c368	YLDs per case of maternal sepsis	yld_rate_c368 / incidence_c368

Calculating Burden 

Years of life lost 

The years of life lost (YLLs) due to maternal sepsis for a simulant who dies of maternal sepsis or other maternal infections at age \(a\) should equal \(\operatorname{TMRLE}(a) - a\), where \(\operatorname{TMRLE}(a)\) is the theoretical minimum risk life expectancy for a person of age \(a\).

Years lived with disability 

For simplicity, each simulant with an incident case of maternal sepsis or other maternal infections in a given age group will accrue the same number of years lived with disability (YLDs). Specifically, the total number of maternal sepsis YLDs accrued by each infected simulant should be the average number of YLDs per case of maternal sepsis in the simulant’s age group, which is defined in the above data table as

\[\begin{split}\begin{aligned} \text{ylds\_per\_case\_c368} &= \frac{\text{sepsis YLDs}}{\text{sepsis cases}}\\ &= \frac{\text{(sepsis YLDs) / person-time}} {\text{(sepsis cases) / person-time}} = \frac{\text{sepsis YLD rate}}{\text{sepsis incidence rate}}. \end{aligned}\end{split}\]

We are using the fact that each simulant can get at most one case of maternal sepsis during the simulation, so the average number of YLDs per infected simulant is the same as the average number of YLDs per case. Simulants with a case of sepsis should accrue YLDs whether or not they die.

Limitation

The above strategy of computing average maternal sepsis YLDs per case should correctly capture total YLDs for the acute sequelae “puerperal_sepsis” and “other_maternal_infections”. However, when we compute averted YLDs, the above calculation will not correctly count secondary infertility YLDs from the long-term sequela “infertility_due_to_puerperal_sepsis”, for two reasons:

Infertility YLDs for a given age group will include infertility triggered not only by sepsis cases caused by current births, but by sepsis cases caused by prior births. This means that we are assigning extra YLDs to each current sepsis case that are actually being accrued by other, nonpregnant people in the population who have lasting impacts of a previous birth and have nothing to do with the sepsis case we are modeling.
If the modeled birth and puerperal sepsis case does cause infertility, the total infertility YLDs will be spread out over the simulant’s remaining reproductive years, occurring in later age groups, not entirely in the simulant’s current age group. Thus we will be “missing” a large portion of the YLDs caused by the current birth events when we tally up YLDs for births in the simulant’s current age group.

Thus, if we avert a case of sepsis, we will be simultaneously averting extra YLDs that we shouldn’t be, because we are counting YLDs that don’t actually belong to the simulant whose case was averted, as well as missing YLDs that should have been averted because we are only counting YLDs in the simulant’s current age group, and not the YLDs that they would accrue in later years. Since births and hence incident cases of maternal sepsis generally decrease with age, while cases of secondary infertility generally increase with age, we will probably be systematically undercounting the YLDs that would be averted by each averted case of sepsis, because for a sepsis case, the missed YLDs for the simulant in question will on average be greater than the extraneous YLDs from other simulants in the same age group.

It may be possible to develop a different strategy of counting YLDs that would help correct this bias, but the discrepancy will likely be a relatively small proportion of total DALYs, so we are willing to accept this limitation for now.

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 sepsis model is run
Number of maternal sepsis cases and maternal sepsis deaths in each age group
Number of maternal sepsis YLDs and YLLs in each age group

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

Validate the maternal sepsis incidence risk and case fatality rate in each age group against the corresponding quantities calculated from GBD data
Validate the number of maternal sepsis deaths per population against the maternal sepsis CSMR from GBD
Validate the total maternal sepsis YLDs and YLLs per population against the rates from GBD