Motivated by population-based geocoded data for Iowa stillbirths and live births delivered during 2005–2011, we sought to identify spatio-temporal variation of stillbirth risk. Our high-quality data consisting of point locations of these delivery events allows use of a Bayesian Poisson point process approach to evaluate the spatial pattern of events. With this large epidemiologic dataset, we implemented the integrated nested Laplace approximation (INLA) to fit the conditional formulation of the point process via a Bayesian hierarchical model and empirically showed that INLA, compared to Markov chain Monte Carlo (MCMC) sampling, is an attractive approach. Furthermore, we modeled the temporal variability in stillbirth to better understand how stillbirths are geographically linked over the seven-year study period and demonstrate the similarity between the conditional formulation of the spatio-temporal model and a log Gaussian Cox process governed by discrete space-time random fields. After controlling for important features of the data, the Bayesian temporal relative risk maps identified areas of increasing and decreasing stillbirth risk over the birth period, which may warrant further public health investigation in the regions identified.

In Iowa, a stillbirth is defined as a fetal death with a gestational weight ≥ 350 grams or a gestation age of ≥ 20 weeks. The estimated prevalence for stillbirth in Iowa is about one in 180 pregnancies compared to the U.S. estimate of one in 160 pregnancies (

During the seven-year study period, the ratio of the number of stillbirth to live birth events was 0.0044, or 0.44%; pregnancies with multiple fetuses were excluded. Because little is known about the underlying mechanism driving the spatial distribution of stillbirth events and with the relatively precise geocoded data available, a point process modeling approach was initially applied to these population-based surveillance data to quantify excess stillbirth risk (

To our knowledge, risk factor studies for stillbirth have predominantly been from population-based case-control studies (

In this paper, we use a conditional formulation of the point process via a Bayesian hierarchical model to view the joint realization of stillbirths and live births and, conditional on this realization, examine the probability that the binary label on a point is either a stillbirth or live birth. This spatial dependence addresses the labeling (delivery event), rather than the event locations themselves and simplifies analysis and interpretation compared with modeling maternal residence directly via a point process model. Importantly, with the conditional formulation of the point process we can now incorporate covariate information attached to both stillbirth and live birth. Our approach extends the conditional formulation of a Bayesian point process model to include both spatial and temporal effects and to study empirically the recovery of spatial and temporal model components in this framework. We note that adding time (i.e. delivery date) to the investigation may be critical with respect to adequate understanding of how maternal residences are geographically linked. Furthermore, for most epidemiologic applications, the relations of individual level outcomes to individual level predictors are examined, and a compelling argument can be made to consider spatial and temporal effects as contextual effects (

In developing our analytic approach, we acknowledge that a Markov Chain Monte Carlo (MCMC) approach conventionally is used to estimate posterior quantities for Bayesian models. Approximation to posterior distributions is also available through other techniques; therefore, we chose to use integrated nested Laplace approximation (INLA) in the R INLA package (

Detailed description of our proposed analytic approach begins in

Stillbirths for the years 2005 through 2011 are in the form of a set of

The scaling parameter _{0}(_{1}(

In this paper, we assumed that the stillbirth event locations _{i} : _{i} : _{0}(^{th} event in the superposition was an event of the first or the second element of the process. Conditioning on the joint realization of these processes, it is straightforward to algebraically show that the conditional probability of a stillbirth event at any location is _{0}(_{i}), is assumed within _{1}(_{i}|_{1}(_{i}|_{i}, i.e. _{0} = log(

Because a stillbirth event was observed with a delivery date, it is possible to extend the conditional formulation by considering spatio-temporal effects. Specifically, we observed within study region _{i}}, _{i}},

Using a similar argument as with the spatial model, if the _{0}(_{0}(_{1}(_{i}, where now we can define _{i}), _{i}), and _{i}, _{i}) represent a spatially correlated term, temporally correlated term, and uncorrelated spatio-temporal interaction term, respectively. This spatio-temporal interaction term allows for overdispersion.

A Bayesian hierarchical model was used for fitting models (1) and (2) to our stillbirth surveillance data. The focus in our analysis was to make inference about the coefficients _{i}), _{i}), _{i}, _{i}), and

We adopted an intrinsic conditional autoregressive (CAR) prior distribution for the spatially correlated heterogeneity ^{th} area (i.e. the regions which share common geographical boundaries with the ^{th} region) and _{i} was the first-order neighborhood of the ^{th} region. Following

With INLA, modestly informed priors on the hyperparameters for random effects were shown to be needed in a suite of simulation studies comparing INLA with MCMC sampling results using OpenBUGS in Bayesian disease mapping (

To support the use of INLA, as opposed to MCMC sampling, as a reliable algorithm to estimate posterior quantities for the spatial and spatio-temporal models we are proposing, simulation studies, defined by three general parameterizations of the intensity function

The ^{th} area. The first-order neighborhood was found from a Dirichlet tessellation for a point process. We set

The intensity function _{1}, i.e. the coefficient ascribed to a spatially-referenced covariate driving the point pattern in the spatial model

In our simulation studies, we used the bounded state of Iowa for region _{0} = 0), _{0}(_{0}, a constant, and

Intensity parameterizations I and II, respectively, allow us to assess the reasonableness of an intrinsic CAR prior specificiation as an approximation to a latent GMRF and to assess the recovery of the true parameter _{1} in the presence of unobserved spatial variation for both Bayesian estimation methods in the spatial-only setting. For both Bayesian estimation methods, to evaluate the recovery of all true parameters used in generating the spatio-temporal point process, separable in space and time, we used intensity parameterization III.

The standardized spatially-referenced covariate _{i}, _{i})} had a separable correlation structure. Within this assumption, the likelihood remained that of a conditionally modulated Poisson process. The temporal component

In each simulated experiment, we generated 100 realizations. For each realization, posterior quantiles were estimated from the Bayesian spatial and spatio-temporal models using INLA (version 0.0–1468872408) and MCMC sampling. The total number of iterations used in MCMC sampling was 750,000 with the first 250,000 treated as burn-in. To decrease autocorrelation, samples were thinned, using only every 50^{th} step in the sampler. The simulation studies were implemented in R using the INLA package and R2OpenBUGS. Tabular summaries were used to display the average measure of error (i.e. the bias) and the corresponding standard deviation.

As part of our goal for conducting simulation studies, we assessed the reasonableness of an intrinsic CAR prior specification as an approximation to a latent GMRF assuming the conditional formulation of the spatial model. We considered modest (_{w} = 0.708), large (_{w} = 1.225), and very large (_{w} = 2.5) unobserved variation for the latent GMRF. Because we assumed the ratio of case to control events was one (i.e. _{0} (i.e. log(_{0} was well estimated and the average measure of error associated with _{0} was consistently negligible (data not shown). The top portion of _{w} used in simulating the point patterns. Compared to INLA, however, the average measure of error was consistently smaller with MCMC sampling. Although the average measure of error increased for both estimation methods in the presence of incrementally larger unobserved spatial variation, both estimation methods arguably performed reasonably well in the presence of modest unobserved spatial variation. With a point pattern of size

As part of our goal for conducting simulation studies, we also assessed the recovery of the true parameter _{1} in the presence of modest unobserved spatial variation. The average measure of error for three effect sizes are shown in the bottom portion of

We assessed the recovery of all true parameters used in generating the point process, separable in space and time, using INLA and MCMC sampling to fit the spatio-temporal model. _{1} and for the standard deviation _{g} associated with the white noise of the first-order autoregressive time series. On average, the time dependent parameter _{w}) was underestimated by a similar magnitude as seen with Intensity Parameterization I. The average runtimes for INLA and MCMC sampling with a point pattern of size

In the conditional formulation of the spatial and spatio-temporal models, applicable to a more general setting than with the nuanced parameterization applied to our stillbirth data, INLA gave reasonable results compared to MCMC, particularly for the epidemiologically interesting parameter _{1}. Furthermore, results from the simulation study using INLA to estimate the spatio-temporal model suggested that the time dependent parameter _{w} was negatively biased for both methods which we believe was likely due to the inability of the conditional formulation of the models to capture the additional randomness associated with the intensity surface. With the focus of our epidemiologic application being on the vector of

The IRCID began actively monitoring stillbirth deliveries statewide in 2005 (

The event locations of all live births in Iowa, during the study period from families who experienced at least one stillbirth during the study period, were included in the set of control event locations. This corresponded to 1,150 control event locations for which all had covariate information. A complete set of covariate information was available for 270,323 control event locations from families who did not experience a stillbirth during the study period. These 270,323 control event locations corresponded to 195,502 unique families. Because of the considerable memory requirements needed to process the neighborhood relation between event locations, defined based on the Dirichlet tesselation, and to fit the spatial-temporal models, 50,000 (25%) control families were randomly selected from the 195,502 unique families. Our analysis included 71,316 events (1,195 stillbirth events, including 1,150 sibling controls; 68,971 remaining controls), which corresponded to 51,181 families. We repeated our analyses on three randomly sampled data sets of similar size, and the results remained robust for each data set (data not shown). The spatial distribution of stillbirth event locations did not differ appreciably from the distribution of the event locations for the at-risk population, namely, maternal residence at delivery for each live birth (

Our surveillance data were observed with a time label, defined as the number of days from January 1, 2005, and a spatial location, namely, the maternal residence at the time of a stillbirth or live birth event.

We fit several Bayesian spatial and spatio-temporal logistic regression models for the binary outcome (stillbirth, live birth), where the probability was a function of space-only or space and time (

From our final model that included the point-level covariates maternal age at delivery and maternal race/ethnicity, as well as the regional-level (ZCTA) covariates percent of childbearing women with less than a bachelor’s degree and median income, and controlled for the live birth events, the posterior expected estimates for the spatial correlation component, temporal correlation component, the spatio-temporal residual component, and the time series plot indexed by the number of days from January 1, 2005 are displayed in

Identifying where stillbirth prevalence exceeds a certain relative risk threshold over time can be more useful than reporting posterior quantities from fitting the model. Therefore, to assess localized spatio-temporal behavior of the model and the assessment of unusual aggregation of stillbirth events over time, heat-contour maps of relative risk within the time intervals 2005–2006, 2007–2008, and 2009–2011 were investigated. For the 1,195 stillbirth events,

In our epidemiologic setting where it can reasonably be assumed that the stillbirth and live birth event locations arise from independent Poisson point processes, the conditional formulation of the point process model still allowed us to capture the salient features of our stillbirth surveillance data while quantifying localized geographic regions of high relative risk. Moreover, the conditional approach greatly simplified the analysis and interpretation compared with modeling the maternal residence via a point process model. As opposed to the point process modeling approach applied initially, the conditional formulation was easily extended to include temporal effects and allowed for the inclusion of covariate information attached to both stillbirth and live birth; therefore, we were now able to quantify geographic regions of excess stillbirth risk after adjusting for our set of covariates, and both spatial and temporal effects. Although we were no longer modeling the spatial distribution of event locations, we can still, to some extent, assume that the data arose from a LGCP where the intensity of the process is governed by a GMRF. That is, conditional on the intensity, the data are a Poisson point process and then conditional on the locations we showed that we can reasonably account for unobserved spatially correlated heterogeneity assuming an intrinsic CAR specification within a relatively simple Bayesian spatial logistic regression model estimated with INLA.

In our data application, we added the time of a stillbirth event to the event location to facilitate our understanding of how stillbirth events were geographically linked within Iowa during the study period. Although we did not model the spatio-temporal distributions of the event locations directly, we can pragmatically assume that the data arose from a spatio-temporal LGCP where the intensity of the process was governed by discretized space-time random fields. Our general simulation study demonstrated the similarity between the conditional formulation of the spatio-temporal model and a spatio-temporal LGCP. In particular, in the presence of modest spatial variation associated with the GMRF, the conditional formulation of the spatio-temporal model estimated with INLA was sensitive to modest and strong temporal dependence assuming a first-order autoregressive model.

The argument for using the INLA R package to estimate the Bayesian spatial and spatio-temporal models was twofold. First, INLA provided a faster and reasonably accurate alternative to MCMC sampling for posterior parameter estimation. Ideally, results using INLA should be close to the MCMC approach to estimation, which we observed in our simulation studies applicable to a more general setting for the recovery of the parameter _{1}, the time dependent parameter _{g} associated with the white noise, but less so for the recovery of the variance

The parameterization of the modeled excess risk component in the multiplicative formulation of the intensity function flexibly permitted inclusion of model components that captured important and nuanced features of the application, such as a maternal contextual effect. Additionally, the spatio-temporal model allowed us to obtain a quantitative description of variation in local intensity of stillbirth events in space and time. Although our focus was on relative risk estimation rather than cluster detection, localized areas of excess aggregation of stillbirth events over time were quantified based on a host of important features captured by our model parameterization and identified for further investigation. There was some agreement as well as some differences between the results obtained from the conditional approach and the findings previously obtained from the point process approach. The mapped regions of high levels of spatially correlated heterogeneity were qualitatively similar to the mapped regions obtained from the point process model applied to these data, and, notably, neither map indicated a random scatter of areas of high levels. Although maternal age at the time of a stillbirth delivery was not shown to be associated with the spatial distribution of stillbirth after applying the point process model, it was predictive in the conditional approach that modeled the conditional probability of stillbirth; the latter finding was consistent with a recent systematic review and meta-analysis from 14 case-control studies that showed advanced maternal age increases the odds of stillbirth (

There were several limitations of our methodologic approach. We adopted a CAR prior for the spatially correlated heterogeneity where the neighborhood relation between event locations was based on a Dirichlet tessellation for a point process. This defensible approach for defining neighbors resulted in a connected graph (or collection of nodes and contiguous edges) that required high memory requirements to process; coupled with the rather high memory requirements needed to fit the spatio-temporal model we, therefore, based our inference on a random sample of 50,000 control families or 25% of the 195,502 unique families. However, the analysis was repeated on 3 randomly sampled data sets of similar size and the conclusions were unchanged. As this was a descriptive analysis, edge effects were ignored. Also, for environmental risk assessment where continuous risk fields may be affecting the at-risk population, a range of appropriate and suspected spatio-temporal covariates are needed to quantitatively describe excess risk. An autoregressive prior distribution was used, assuming a first-order autoregressive model. Although this choice for a prior distribution allowed for a linear (i.e. with respect to the previous value) non-parametric temporal effect, alternative formulations could be considered for the temporal component. Lastly, further work is needed to validate the final model applied to our stillbirth data.

There were also some notable study design limitations. Although the maternal residence at delivery was used to represent exposure to environmental risk, albeit treated as a contextual effect in our model formulation, it ignored the possibility that exposure to environmental risks may occur elsewhere. Also, the residence at delivery may not represent the residence at conception or during early pregnancy. In addition, unavailable fetal and maternal risk factors not included in our model limits the interpretation of our results. Future follow-up of mothers within the spatial and temporal geographic regions of excess risk compared to non-risk may provide insights into these unmeasured environmental and social factors. Lastly, a longer study time period is needed to better characterize spatio-temporal changes in relative risk.

Using a conditional approach to modeling the geocoded stillbirth and live birth data, we quantified and mapped the excess stillbirth risk in the presence of spatial and temporal heterogeneity and after adjusting for covariates attached to both stillbirth and live birth. Our model was fitted with INLA, as opposed to MCMC sampling, with reasonable accuracy, and INLA accommodated our large data set. Furthermore, our use of the conditional formulation was readily extended to include temporal effects. To our knowledge, our study is the first to conduct a formal spatio-temporal analysis of stillbirth surveillance data. Although the temporal correlation component indicated temporal variations with marked changes in several areas across the state, the residual space-time component indicated that there was extra variation remaining not captured by the separable space-time components and covariates available for analysis. Nonetheless, our Bayesian relative risk maps indicated increasing and decreasing risk over the birth period, which may warrant further public health investigation in the geographic regions identified.

This research was supported in part through computational resources provided by The Department of Biostatistics at The University of Iowa. This research was also supported by funding from the Iowa Stillbirth Surveillance Project (5U50DD000730), Iowa CBDRP: Birth Defects Study To Evaluate Pregnancy Exposures (5U01DD001035), and The University of Iowa Environmental Health Sciences Research Center (P30 ES005605). The authors gratefully thank Dong Liang, Anthony Rhoads, and Derek Shen for their assistance with data cleaning, data preparation, and data management.

First, we simulated

For large _{1}, _{2}, …, _{N}} assuming complete spatial random ness within

Generate

Calculate

Define

Thin the simulated process as follows

Randomly draw a point

Generate a random number

If

Repeat (a)-(c) until the desired number of points (

The

The case event locations were a realization of a Poisson point process on _{0}(_{0}. Conditional on the _{i}, which we call _{i}) which labels the event either as a case (_{i} = 1) or a control (_{i} = 0). Conditioning on the joint realization of these point processes, the conditional probability of a case at any location is

We assumed a separable covariance function in space and time (i.e. an additive form in spatial and temporal effects) without a space-time residual. First, we simulated

For the given conditional specification of the Gaussian Markov random field (GMRF) and nonstationary mean

For large _{1}, _{2}, …, _{N}} assuming complete spatial randomness within

For each of the

Generate a first order autoregressive time series

Generate

Calculate

Define

Thin the simulated process as follows

Randomly draw a point

Generate a random number

If

Repeat (a)-(c) until the desired number of points (

The case event locations were a realization of a spatio-temporal Poisson point process on _{0}(_{0}. Conditional on the _{i}, _{i}), which we call _{i}) which labeled the event either as a case (_{i} = 1) or a control (_{i} = 0). Conditioning on the joint realization of these point processes, the conditional probability of a case at any event location was

Ratio of stillbirth deliveries to 1000 live births: Months since January 1, 2005 of successive stillbirth deliveries per 1000 live births between January 1, 2005 and December 31, 2011.

Bayesian disease maps from the final model: For the 1,195 stillbirth deliveries, the posterior expected estimates from the Bayesian spatio-temporal logistic model fit to the stillbirth surveillance data: four displays correponding to the spatial component (a), a temporal correlation component (b), a space-time residual component (c), and a time component time series plot indexed by the number of days from January 1, 2005 (d). The red dotted lines in (d) indicate one-year intervals. Estimated posterior quantities were obtained from the integrated nested Laplace approximation.

Bayesian disease maps of relative risk from the final model: Bayesian relative risk maps, presented as heat-contour plots, based on the estimated posterior expectations of all model components from the spatio-temporal Bayesian hierarchical model that controlled for the live births, mapped at the maternal residence for the 1,195 stillbirth deliveries. Estimated posterior quantities were obtained from the integrated nested Laplace approximation.

Average estimated mean of the posterior distribution (standard deviation) and average measure of error associated with the conditional approach to estimation via INLA and MCMC for intensity parameterizations I and II based on 100 realizations of point patterns of size

Intensity Parameterization I: log λ_{1}(s|_{0} + | |||||
---|---|---|---|---|---|

True Value (_{w}) | |||||

0.708 | 1.225 | 2.5 | Runtime | ||

0.5495 (0.0541) | 0.6620 (0.0827) | 1.1702 (0.1612) | 2.8 sec | ||

−0.1585 | −0.5630 | −1.3300 | |||

0.6290 (0.0809) | 0.7707 (0.1400) | 1.708 (0.2948) | 3290 sec | ||

−0.0790 | −0.4543 | −0.7920 | |||

Intensity Parameterization II: log λ_{1}(s|_{0} + _{1} | |||||

True Value (_{1}) | |||||

−0.50 | −0.25 | 0.00 | |||

−0.4896 (0.0650) | −0.2411 (0.0548) | 0.0051 (0.0520) | |||

0.0104 | 0.0089 | 0.0051 | |||

−0.4908 (0.0614) | −0.2352 (0.0622) | −0.0048 (0.0566) | |||

0.0092 | 0.0148 | −0.0048 |

Note: INLA = integrated nested Laplace approximation; MCMC = Markov chain Monte Carlo; SD = standard deviation. Modest unobserved spatial variation (i.e. _{w} = 0.708 or _{1} was set to a normal distribution with mean 0 and variance 1000.

Average measure of error (standard deviation) associated with the conditional approach to estimation via INLA and MCMC for intensity parameterization III.

Intensity Parameterization III: logλ_{1}(s|_{0} + _{1} | |||||||
---|---|---|---|---|---|---|---|

True Value | Average Measure of Error (Standard Deviation) | ||||||

_{1} | |||||||

_{w} = 0.708 | _{g} = 0.35 | 0.50 | −0.50 | 0.0094 (0.0644) | −0.1796 (0.0433) | −0.0548 (0.2421) | −0.0002 (0.0505) |

0.50 | −0.25 | 0.0075 (0.0565) | −0.1836 (0.0435) | −0.0490 (0.2161) | −0.0030 (0.0600) | ||

0.50 | 0.00 | −0.0053 (0.0549) | −0.1904 (0.0362) | −0.0607 (0.2395) | −0.0010 (0.0596) | ||

_{w} = 0.708 | _{g} = 0.35 | 0.90 | −0.50 | 0.0213 (0.0640) | −0.1740 (0.0481) | −0.0717 (0.1040) | −0.0057 (0.0672) |

0.90 | −0.25 | 0.0054 (0.0576) | −0.1902 (0.0436) | −0.0683 (0.0916) | −0.0095 (0.0646) | ||

0.90 | 0.00 | 0.0046 (0.0591) | −0.1823 (0.0444) | −0.0810 (0.1036) | −0.0118 (0.0692) | ||

_{w} = 0.708 | _{g} = 0.35 | 0.50 | −0.50 | 0.0107 (0.0696) | −0.0975 (0.0740) | −0.0098 (0.2428) | −0.0122 (0.0655) |

0.50 | −0.25 | −0.0013 (0.0614) | −0.1095 (0.0675) | −0.0284 (0.1845) | −0.0031 (0.0676) | ||

0.50 | 0.00 | −0.0040 (0.0633) | −0.1006 (0.0768) | −0.0160 (0.1963) | −0.0035 (0.0595) | ||

_{w} = 0.708 | _{g} = 0.35 | 0.90 | −0.50 | 0.0071 (0.0659) | −0.1068 (0.0625) | −0.0532 (0.0934) | 0.0009 (0.0667) |

0.90 | −0.25 | 0.0052 (0.0555) | −0.0959 (0.0652) | −0.0484 (0.0808) | 0.0000 (0.0616) | ||

0.90 | 0.00 | 0.0102 (0.0553) | −0.1074 (0.0828) | −0.0478 (0.0758) | 0.0015 (0.0652) |

Note: INLA = integrated nested Laplace approximation; MCMC = Markov chain Monte Carlo. Results are based on 100 realizations of point patterns of size _{1} was set to a normal distribution with mean 0 and variance 1000. The standard deviation associated with the white noise of the first-order autoregressive time series was set to _{g} = 0.35, which corresponded to a marginal standard deviation of _{m} = 0.4041 and _{m} = 0.8030 when

Model preference using the deviance information criterion (DIC).

Model | Covariates | DIC | Runtime |
---|---|---|---|

None | 12068.05 | 845 sec | |

^{T} ( | Included | 11991.31 | 722 sec |

None | 11996.36 | 80958 sec | |

^{T}( | Included + Urban vs. Rural Indicator | 11926.05 | 136289 sec |

^{T}( | Included | 11922.89 | 143282 sec |

Note: The included vector of covariates ^{T} comprised maternal age at delivery, an indicator for maternal race/ethnicity, and the ZCTA-level covariates percentage of childbearing women with less than a bachelor’s degree and median income; continuous covariates were centered and standardized. The percent of child-bearing women with less than a bachelor’s degree and median income were calculated for each ZCTA from the 2007–2011 American Community Survey data. A ZCTA was designated as urban if it intersected with the urbanized areas of Iowa, as defined by the 2010 census (US Census Bureau) or as rural if it did not intersect with urbanized areas; urbanized areas are defined by the census as having a population of >50,000 residents with a density of at least 500 people per square mile. The model parameters

Estimated posterior quantities from fitting the final model.

Description of Explanatory Variable | Mean (SD) | 95% Credible Interval | ||
---|---|---|---|---|

Intercept | _{0} | −4.5520 (0.0401) | −4.6312 | −4.4738 |

Maternal Age (Years) | _{1} | 0.0692 (0.0292) | 0.0117 | 0.1265 |

Other Races/Ethnicities versus non-Hispanic White Indicator | _{2} | 0.6733 (0.0712) | 0.5327 | 0.8122 |

Percent of Childbearing Women with Less than a Bachelor’s Degree | _{3} | 0.0973 (0.0392) | 0.0201 | 0.1739 |

Median Income | _{4} | 0.0172 (0.0384) | −0.0578 | 0.0929 |

Spatial Component | 4.4863 (1.4223) | 2.4824 | 7.9881 | |

Temporal Component | 0.8517 (0.1432) | 0.4604 | 0.9938 | |

13.9404 (6.0656) | 6.8327 | 29.7302 | ||

Space-Time Residual Component | 4.6876 (1.6492) | 2.2746 | 8.6778 | |

Maternal Contextual Effect | 5.3071 (1.7304) | 2.8016 | 9.5144 |

Note: All continuous covariates were centered and standardized. Estimates of posterior quantities were obtained from the INLA package. The percent of child-bearing women with less than a Bachelor’s degree and median income were calculated for each ZCTA from the 2007–2011 American Community Survey data. Other race/ethnicities included unknown race/ethnicity. Precisions are presented for the random effects. The corresponding mean of the estimated posterior distribution for _{w}, _{m}, _{c}, and _{γ} were 0.4721, 0.2678, 0.4619, and 0.4341, respectively.