A novel approach to joint prediction of preeclampsia and delivery timing using semi-competing risks

Abstract

Background

Preeclampsia is a pregnancy complication that contributes substantially to perinatal morbidity and mortality worldwide. Existing approaches to modeling and prediction of preeclampsia typically focus either on predicting preeclampsia risk alone, or on the timing of delivery following a diagnosis of preeclampsia. As such, they are misaligned with typical health care interactions during which the two events are generally considered simultaneously.

Objectives

We describe the “semi-competing risks” framework as a novel approach for jointly modeling the risk and timing of preeclampsia and the timing of delivery simultaneously. Through this approach, one can obtain, at any point during the pregnancy, clinically relevant summaries of an individuals’ predicted outcome trajectories in four risk categories: not developing preeclampsia and not having delivered, not developing preeclampsia but delivered due to other causes, developing preeclampsia but not having delivered and developing preeclampsia and having delivered.

Study Design

To illustrate the semi-competing risks methodology, we present an example analysis of a pregnancy cohort from the electronic health record of an urban, academic medical center in Boston, Massachusetts (n=9,161 pregnancies). We fit an illness-death model with proportional hazards regression specifications describing three hazards for timings of preeclampsia, delivery in the absence of preeclampsia, and delivery following preeclampsia diagnosis.

Results

The results indicate nuanced relationships between a variety of risk factors and the timings of preeclampsia diagnosis and delivery, including maternal age, race/ethnicity, parity, BMI, diabetes, chronic hypertension, cigarette use, and proteinuria at 20 weeks’ gestation. Sample predictions for a diverse set of individuals highlight differences in projected outcome trajectories with regards to preeclampsia risk and timing, as well as timing of delivery either before or after preeclampsia diagnosis.

Conclusions

The semi-competing risks framework enables characterization of the joint risk and timing of preeclampsia and delivery, providing enhanced, meaningful information regarding clinical decision making throughout the pregnancy.

Background

Preeclampsia is a major perinatal condition, affecting 3–5% of pregnancies worldwide¹ with a rising incidence in the United States (US).² Despite advances in obstetric and perinatal care, preeclampsia remains a significant contributor to perinatal morbidity and mortality,³ especially in non-Hispanic Black women in the US for whom preeclampsia/eclampsia is the leading cause of maternal death.⁴

The majority of preeclampsia is diagnosed prepartum, with pathophysiological origin considered to be poor placentation.¹ While the disease begins to resolve with removal of the placenta through delivery, any clinical discussion during pregnancy surrounding the risk and management of preeclampsia should also consider the potential implications for delivery. While some individuals may give birth for other reasons before developing preeclampsia, following a preeclampsia diagnosis the timing of delivery is of vital clinical importance, specifically towards balancing risks to the infant of early delivery against the risks of prolonging a preeclamptic pregnancy. These dynamics imply that as discussions regarding preeclampsia arise in clinical encounters, there are four clinically-relevant outcome categories at any point in time: (i) still pregnant without preeclampsia; (ii) already delivered without preeclampsia; (iii) still pregnant with preeclampsia; and, (iv) already delivered with preeclampsia.

To aid clinical decision making, screening for preeclampsia is typically based on demographic characteristics, medical history, biomarkers and imaging data^5–7; to-date, more than 90 risk factors of preeclampsia have been identified,^8–10 and numerous individualized risk prediction models for preeclampsia have been developed, validated and deployed.^11–17 However, despite the clinical relevance of stratifying individuals based on the above four outcome categories across time, existing models have tended to focus solely on predicting a pregnant individuals’ risk of developing preeclampsia without consideration of the clinical importance of the timing of delivery,¹² or on predicting the timing of delivery with preeclampsia assuming no other cause of delivery before that time.¹⁸

To more directly align with the clinical considerations outlined above, we propose framing preeclampsia and delivery as so-called “semi-competing risks.”^19–21 Central to the framework is that delivery acts as a “competing risk” for preeclampsia, while the reverse is not the case. As we explain, modeling semi-competing risks builds on basic concepts in survival analysis such as the Cox model, combined to simultaneously structure the relationships between risk factors and the timings of preeclampsia and delivery. This, in turn, permits a shift away from sole consideration of the binary outcome status of preeclampsia, towards providing time-varying, multi-outcome insight with which patients and clinicians can make decisions regarding prevention strategies and monitoring, follow-up, and timing of delivery.

Materials and Methods

Study Population

This study uses electronic health record (EHR) data from 9,161 pregnancies at Beth Israel Deaconess Medical Center (BIDMC), Boston, MA, from 2016–2019. We included all singleton live births of anyone who received any prenatal care and delivered at BIDMC during this period.

Outcome Ascertainment

Diagnoses of preeclampsia were identified using ICD-10 codes O11 and O14. To ascertain timing of preeclampsia diagnosis, we used time of hospital admission preceding delivery as a proxy, following other studies of preeclampsia timing.²²

Factors Considered as Inputs in Prediction Models

We considered a broad range of clinically-relevant factors as potential inputs into the prediction models including demographic characteristics, pre-existing health conditions, and laboratory results. Detailed definitions of all covariates are provided in the Supplementary Materials. Throughout, the absence of an abnormal laboratory value or ICD-10 diagnostic code was considered to represent a normal lab value or absence of that condition.

The Clinical Scenario

The clinical scenario we seek to inform is a (hypothetical) interaction between a pregnant individual and their health care provider, specifically as they approach the 20-week mark from which preeclampsia might be diagnosed. While we focus on this mark as a critical opportunity to inform decision-making, the approach can be used to generate joint risk profiles at any point during the pregnancy.

Semi-Competing Risks

Within the semi-competing risks framework, delivery is viewed as a competing risk for preeclampsia but not vice versa. Figure 1A presents this dynamic graphically, with each box representing a possible state of the pregnancy, and arrows showing potential “transitions” from one state to the next; after preeclampsia diagnosis, there is an arrow leading to subsequent delivery, but after delivery there is no arrow to preeclampsia diagnosis.

Figure 1:

Graphical representations of analytical prediction frameworks for preeclampsia.

A: semi-competing risks framing of the timing of preeclampsia and delivery, acknowledging that individuals can give birth after preeclampsia diagnosis, but not vice versa. B: competing risks framing of the timing of preeclampsia and delivery, reflecting the assumption that individuals can experience one or the other, but not both. C: binary risk prediction methods frame preeclampsia as a binary outcome, omitting consideration of timing, or the role of delivery.

By contrast, Figure 1B illustrates framing preeclampsia and delivery as competing risks of each other, rather than semi-competing risks^23,24; note the omission of the arrow from preeclampsia to delivery. A major conceptual drawback of this framing, however, is that it fails to align with the actual potential clinical course of a pregnancy; preeclampsia clearly does not preclude delivery and, therefore, cannot be a competing risk for it. Practically, applying standard methods for the competing risks framing of preeclampsia and delivery to the present context will generally involve censoring person-time following preeclampsia.²² Thus, even though the timing of delivery is typically known, this information is effectively thrown away. We point out, however, that framing preeclampsia and delivery as competing risks differs from another popular “competing risk” model for this setting, which focuses on “delivery without preeclampsia diagnosis” and “delivery after preeclampsia diagnosis” as a pair of competing risks rather than directly modeling the timing of preeclampsia diagnosis.^17,18

Finally, Figure 1C provides a graphical representation of the standard univariate framing of preeclampsia (i.e., a yes/no binary outcome modeled, say, via logistic regression). Here the conceptual drawback is that delivery is completely ignored, so that joint risk prediction is precluded altogether.

The Illness-Death Model

To leverage available information on the timing of preeclampsia and delivery, and align the analysis with the graphical representation in Figure 1A, we fit an “illness-death” multi-state model.²⁰ Under this model, each of the three transitions of Figure 1A is “sped up” or “slowed down” by individual risk factors, and the interplay between these possible transitions determines the observed preeclampsia and delivery outcomes. Intuitively, a factor that “speeds up” the occurrence of preeclampsia and “slows down” the occurrence of delivery makes it more likely that preeclampsia will arise before delivery, and corresponds with increased absolute risk of preeclampsia. By contrast, a factor that “slows down” the occurrence of preeclampsia and “speeds up” the occurrence of delivery makes it more likely that the person will give birth before preeclampsia arises, and corresponds with decreased absolute risk of preeclampsia.

For the analyses presented here, we fit an illness-death model as a trio of related Cox models (each called a “submodel”), one for each of the three possible transitions in Figure 1A. Conceptually, each transition submodel shares key features with the standard Cox model, while collectively there are important differences that are adopted to align with the clinical context at-hand. The model permits different sets of covariates to influence the timing of preeclampsia and the timing of delivery either pre- or post-diagnosis of preeclampsia, and it also provides the flexibility for a given risk factor to either “speed up” or “slow down” each transition differently (e.g., a risk factor may be positively associated with the timing of preeclampsia but negatively associated with the timing of delivery). See the Supplementary Materials for additional mathematical detail, the specifications we adopted, and the fitting process using the SemiCompRisks package in R.²⁵ We selected covariates from Table 1 for inclusion in each transition submodel using a forward selection algorithm based on the Akaike Information Criterion (AIC), a measure of model fit.

Table 1:

Characteristics of study population overall and according to observed preeclampsia diagnosis and delivery outcome

	Total Births (n=9161)	Births with Preeclampsia (n=930)	Births without Preeclampsia (n=8231)
Maternal Age ≥ 35	2783 (30.4%)	314 (33.8%)	2469 (30%)
Parity ≥ 1	4642 (50.7%)	361 (38.8%)	4281 (52%)
Previous Preeclampsia	270 (2.9%)	73 (7.8%)	197 (2.4%)
Current or Prior Cigarette Use	1008 (11%)	120 (12.9%)	888 (10.8%)
Pre-existing Hypertension	542 (5.9%)	214 (23%)	328 (4%)
BMI ≥ 30	2187 (23.9%)	385 (41.4%)	1802 (21.9%)
Pre-existing Diabetes	253 (2.8%)	79 (8.5%)	174 (2.1%)
Proteinuria	59 (0.6%)	17 (1.8%)	42 (0.5%)
Self-reported Race/Ethnicity
White Race/Ethnicity	4420 (48.2%)	436 (46.9%)	3984 (48.4%)
Black Race/Ethnicity	1459 (15.9%)	172 (18.5%)	1287 (15.6%)
Hispanic Race/Ethnicity	789 (8.6%)	72 (7.7%)	717 (8.7%)
Asian Race/Ethnicity	896 (9.8%)	40 (4.3%)	856 (10.4%)
Other/Unknown Race/Ethnicity	1597 (17.4%)	210 (22.6%)	1387 (16.9%)

Individualized Risk Prediction

After fitting the illness-death model, mathematical formulae provided in the Supplementary Materials enable calculating probabilities that an individual will be in each of the four clinically-relevant outcome categories, at any time after 20 weeks’ gestation.^24,26 Additionally, these predictions can be updated with follow-up outcome information, such as predicting subsequent timing of delivery under a hypothetical preeclampsia diagnosis at 28 weeks (or any other time).

Results

Study Population

Table 1 summarizes baseline characteristics of the cohort, stratified by eventual preeclampsia diagnosis. The overall preeclampsia rate was 10%, with a median time of diagnosis of 37.0 weeks (Inter-Quartile Range [IQR] 34.4–38.9). Figure 2 shows the relative (unadjusted) timings of diagnosis and delivery among those with preeclampsia. For these individuals, the median time of delivery was 37.3 weeks (IQR 35.3–39), versus 39.3 weeks (IQR 38.3–40.3) among those without preeclampsia. Figure 3 shows Kaplan-Meier plots, with panel A the time of preeclampsia diagnosis (treating delivery as censoring), and panel B the time to delivery stratified by final preeclampsia status.

Figure 2:

Scatterplot of gestational age at delivery versus at preeclampsia diagnosis, among individuals diagnosed with preeclampsia.

None.

Figure 3:

Kaplan-Meier plots of preeclampsia diagnosis and delivery timing

A: Kaplan-Meier plot for time to preeclampsia diagnosis, treating deliveries that occur without preeclampsia as censored observations. B: Kaplan-Meier plot for time to delivery, stratified by observed preeclampsia diagnosis status at delivery.

Joint Risk Profiles

To demonstrate the clinical utility of the proposed approach, consider four example individuals labeled A-D, with covariates as shown in Table 3. For each individual, we used the fit of an illness-death model to the EHR data from BIDMC to generate a “risk profile” of four probabilities corresponding to the events of: (1) having yet to be diagnosed with preeclampsia or given birth; (2) having given birth without first being diagnosed with preeclampsia; (3) having given birth after being diagnosed with preeclampsia; or (4) having been diagnosed with preeclampsia and not yet given birth. These probabilities were predicted at numerous time points, stacked and plotted as a panel presented in Figure 4; the height of each colored area represents the predicted probability that the individual will be in that category at that time, with probabilities summing to 1.00 (i.e., 100%) at each time point.

Table 3:

Characteristics of sample individuals presented in Figures 4 and 5

	Individual
	A	B	C	D
Maternal Age ≥ 35	Yes	No	No	Yes
Parity ≥ 1	Yes	No	No	No
Previous Preeclampsia	No	No	No	No
Current or Prior Cigarette Use	No	Yes	No	Yes
Pre-existing Hypertension	No	No	Yes	Yes
BMI ≥ 30	Yes	Yes	No	Yes
Pre-existing Diabetes	No	Yes	No	Yes
Proteinuria	No	No	Yes	No
Race/Ethnicity	White	Black	Other/Unknown	White

Figure 4:

Sample predicted risk profiles for four sample individuals

For each time point on the x-axis, the height of each area represents the individual’s predicted probabilities of being in each respective outcome category at that time. The combined height of the blue and purple bars at the right end gives the individual’s predicted overall risk of developing preeclampsia. Each individual’s risk factors are as defined in Table 3.

To illustrate the interpretation of these results, suppose interest lies in predicting what state individual D will be in at week 34. Reading Figure 4D vertically at 34 weeks, the model predicts that by that time, individual D has a 65% chance of being pregnant without preeclampsia (grey), a 2% chance of having given birth without preeclampsia (red), a 15% chance of having developed preeclampsia and already given birth (purple), and an 18% chance of having developed preeclampsia and still being pregnant (blue). Because the plots illustrate these profiles over time, we can read off probabilities at any time point; at 37 weeks, for example, individual D has a 23% chance of being pregnant without preeclampsia, an 18% chance of having given birth without preeclampsia, a 45% chance of having developed preeclampsia and already given birth, and a 13% of having developed preeclampsia and still being pregnant. Thus, the figure characterizes the evolution of an individual’s risk over time.

Though each risk profile stratifies the joint risks of both preeclampsia and delivery, we can also collapse these four categories into simple overall probabilities of developing preeclampsia, or of delivery, by a certain time. The absolute risk of developing preeclampsia by week 40, for example, comprises the combined height of the blue and purple bars at the right end of the plot. For individuals A-D, this is predicted to be 8%, 22%, 52% and 67%, respectively. Similarly, the overall probability of giving birth by week 37 is given by the combined height of the purple and red bars at that time, and for these individuals is 18%, 31%, 43%, and 63% respectively.

Prediction of Delivery Post-Diagnosis of Preeclampsia

Figure 5 illustrates the ability to dynamically update predictions based on preeclampsia diagnosis at future time points, using the scenario that individuals A-D were each diagnosed with preeclampsia at week 28. In this scenario their probabilities of delivery by week 37 are predicted to be 99%, 93%, 98%, and 84% respectively. The overall trajectories are more varied, with the 75^th percentile predicted delivery times for individuals with the same covariate patterns as A-D being 30.8, 33.4, 32.0, and 35.3 weeks respectively. Note, while these predictions depend solely on baseline risk factors (through the model specification), they reflect differing patterns in the gestational age at delivery for different patients, and could be used to guide clinical decisions about hospitalization and level of care.

Figure 5:

Sample predicted probabilities of delivery after preeclampsia diagnosis at 28 weeks for four sample individuals

For each time point on the x-axis, the height of each line represents the probability of giving birth by that time given preeclampsia diagnosis at 28 weeks of gestation. Each individual’s risk factors are as defined in Table 3.

Hazard Ratio Estimates

Finally, the underlying illness-death model estimates used to generate the above predictions can also be examined themselves. Table 2 presents these estimated hazard ratios for each transition-specific submodel. Recalling that the predicted probabilities depend on the complex interplay by which factors “speed up” and “slow down” preeclampsia and delivery, these estimates reflect how each covariate affects the resulting risk profiles. For example, pre-existing diabetes is associated both with earlier preeclampsia (HR 2.35; 95% CI: 1.84, 3.01) and longer time from preeclampsia to delivery (HR 0.63; 95% CI: 0.49, 0.80), and thus may represent a risk factor for a clinical course that involves earlier diagnosis of preeclampsia that, in turn, requires longer hospitalization before delivery. By contrast, being parous is associated with later preeclampsia (HR 0.56; 95% CI: 0.49, 0.64) and shorter time from preeclampsia diagnosis to delivery (HR 1.35; 95% CI: 1.17, 1.56), which may correspond clinically with at-term diagnosis of preeclampsia where delivery is not delayed. Importantly, not all risk factors are included in all transitions. For example, previous preeclampsia is associated with earlier preeclampsia but not with earlier delivery; that is, it was not included by the forward selection algorithm in the models for timing of delivery. Finally, we included coefficients comparing the time from preeclampsia diagnosis to delivery when diagnosed in the intervals of <28 weeks, 28–32 weeks, 32–34 weeks, 34–37 weeks, and ≥37 weeks. The results show strong association between later diagnosis and shorter time to subsequent delivery, reflecting the pattern seen in Figure 2.

Table 2:

Illness-death model results

	Hazard Ratio (95% CI)
	Time to Preeclampsia Diagnosis	Time to Delivery Without Preeclampsia	Time to Delivery After Preeclampsia
Maternal Age ≥ 35	1.22 (1.06, 1.4)	1.06 (1.01, 1.11)	0.87 (0.76, 1.01)
Parity ≥ 1	0.56 (0.49, 0.64)	1.33 (1.27, 1.39)	1.35 (1.17, 1.56)
Previous Preeclampsia	2.78 (2.16, 3.58)	…	…
Current or Prior Cigarette Use	…	1.07 (1, 1.15)	0.75 (0.61, 0.92)
Pre-existing Hypertension	4.86 (4.10, 5.77)	1.62 (1.45, 1.82)	0.77 (0.65, 0.90)
BMI ≥ 30	1.65 (1.44, 1.9)	…	0.9 (0.78, 1.03)
Pre-existing Diabetes	2.35 (1.84, 3.01)	2.27 (1.95, 2.64)	0.63 (0.49, 0.80)
Proteinuria	1.45 (0.89, 2.37)	…	…
Black Race/Ethnicity	…	0.94 (0.88, 1)	…
Asian Race/Ethnicity	0.52 (0.38, 0.72)	1.1 (1.02, 1.18)	…
Other/Unknown Race/Ethnicity	1.5 (1.28, 1.75)	…	0.85 (0.73, 1.00)
Preeclampsia Diagnosis 28–32 Weeks	…	…	2.13 (1.43, 3.18)
Preeclampsia Diagnosis 32–34 Weeks	…	…	2.69 (1.83, 3.96)
Preeclampsia Diagnosis 34–37 Weeks	…	…	8.94 (6.18, 12.9)
Preeclampsia Diagnosis ≥37 Weeks			33.04 (22.0, 49.6)

Cause-specific hazard ratios for every selected covariate within each of the three transition submodels of the multivariable illness-death model, estimated simultaneously. Missing estimates denoted “...” indicate that the covariate was not included in the corresponding transition submodel by the forward selection algorithm.

Comments

Principal Findings

In this paper, we apply the semi-competing risks framework to joint risk prediction of preeclampsia and delivery, using data on a cohort of 9,161 pregnancies from BIDMC. As highlighted in Table 2 and Figures 4 and 5, performing statistical analyses within this framing enables a comprehensive understanding of the joint risks of preeclampsia and delivery, and the interplay by which factors affect these outcomes. In this sense, semi-competing risks provides an opportunity to better inform discussions between pregnant individuals and their health care providers, an opportunity that is not exploited by existing approaches.

Results in the Context of What is Known

To-date, prediction models have primarily focused either on the risk of preeclampsia¹¹ or the time to delivery after preeclampsia development.¹⁸ The approach represented here is fundamentally different in that it facilitates individualized prediction of four risk categories representing the joint outcomes of preeclampsia and delivery across time, directly aligning with clinical care considerations.

Clinical Implications

The semi-competing risks approach represents a new framework for individualized prediction of pregnancy outcomes to inform clinician and patient decision-making. Indeed, individuals A-D described in Table 3 would likely benefit from different care decisions based on their predicted risks. Those with higher risk for preterm preeclampsia diagnosis as shown in Figure 4 might be given more frequent prenatal care, while those with higher predicted chance of preterm delivery might choose to deliver at a center with neonatal intensive care (NICU) services. In addition, those with lower predicted probabilities of preterm delivery after preeclampsia diagnosis as shown in Figure 5 might remain outpatient instead of being hospitalized, with less disruption in family life and lower use of resources.

Practically, these tools could easily be incorporated interactively in health care provider systems to facilitate discussions and communication regarding risk stratification throughout pregnancy. As a proof-of-principle, we present a sample version of a web-based app at https://harrisonreeder.shinyapps.io/SCRRiskPrediction, which demonstrates how these figures could be reported, as well as how modifying risk factors or clinical decisions (e.g., initiation of aspirin during the first trimester) may impact an individual’s joint risk profile.

Strengths and Limitations

A key strength of this study is the use of a large, good quality EHR dataset which can provide real world evidence of the effectiveness of screening and patient care that is straightforward to replicate and implement using other similar records. Though our analysis is restricted to live births,²⁷ the primary goal of this work is to illustrate the proposed methodology and highlight its potential clinical utility. Our study population also reflects the diverse demographics of the Suffolk County area that BIDMC covers, and specifically those who sought prenatal care from a teaching/research hospital, which may explain the slightly larger observed prevalence of preeclampsia relative to the overall population. Lastly, time of admission may be a biased proxy for preeclampsia diagnosis timing if some diagnoses were not immediately admitted, however we expect any effect to be small as at this institution nearly all preeclampsia diagnoses result in admission.

Additionally, we used only a limited set of predictors in our model; again, our purpose was to illustrate the methodology, rather than propose or validate a particular fitted risk prediction model. In particular, we acknowledge concerns about including race/ethnicity in prediction models for clinical use, which can encode and perpetuate health inequities based on social determinants of health such as lack of access to care, food insecurity, and racism, rather than biological difference.^28,29

Finally, the current study does not explicitly model other events that can arise during pregnancy, nor postpartum outcomes such as postpartum preeclampsia. Though symptoms of preeclampsia can persist in the postpartum period, it is a rare de novo clinical entity,^30–35 which is poorly understood. Nevertheless, more general “multi-state” model extensions can characterize additional outcome states through time (i.e., drawing additional boxes and arrows in the diagram of Figure 1A),²⁴ and could be used to model additional pre- or postpartum outcomes, such as those identified by the International Collaboration to Harmonise Outcomes for Pre-eclampsia.³⁶

Research Implications

Acknowledging the data’s limitations, future research is needed to develop and validate semi-competing risk prediction models in new cohorts and with additional predictors. Validating prediction accuracy for multi-category risk profiles is itself an active area of methodological research³⁷; the Supplementary Materials contain estimates of predictive performance for the presented model using cross-validated area under a time-dependent receiver operating characteristic curve (AUC).³⁸

The semi-competing risks framework’s four-category stratification may also be useful for the design and implementation of clinical trials evaluating preeclampsia prevention strategies such the administration of low dose aspirin.³⁹

Conclusions

The semi competing risks framework characterizes the risk of preeclampsia and timing of delivery beyond current modeling approaches. This framework offers potential to improve our ability to make clinically meaningful predictions about individuals’ risk for preterm preeclampsia and preterm birth in the setting of preeclampsia; such predictions might aid in allocating resources judiciously based on individual risk strata while optimizing maternal and fetal outcomes.

AJOG at a Glance.

A. Why was this study conducted?

Clinical decision-making for preeclampsia prevention and care depends on the interplay of preeclampsia risk and delivery timing. This study describes the “semi-competing risks” framework for clinically relevant joint prediction of preeclampsia and delivery status across time.

B. What are the key findings?

Use of the semi-competing risks framework enables identification of how risk factors are associated with the time to preeclampsia and the time to delivery simultaneously, permitting the stratification of pregnant individuals based on both outcomes jointly, over time. Pregnant individuals with differing baseline medical histories and laboratory measurements show substantial differences in predicted outcome trajectories, suggesting that individualized approaches to monitoring and care are warranted.

C. What does this study add to what is already known?

Semi-competing risks methods enable clinically meaningful, individualized risk prediction that permit novel stratification of pregnant individuals on the basis preeclampsia and delivery jointly.