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. 2025 Nov 26;25:4161. doi: 10.1186/s12889-025-25174-x

Looking at the big picture: demonstrating benefits of Bayesian latent cluster spatio-temporal analysis for understanding maternal prescription opioids misuse

Xueyi Xing 1,✉, D Max Crowley 1,2,3, Christian M Connell 2,4
PMCID: PMC12659324  PMID: 41299527

Abstract

Background

As the opioid crisis rages, maternal prescription opioid misuse (MPOM) is particularly concerning because it influences both the mother and child’s wellbeing. However, little was known about the trend of MPOM and its county-level risk factors. Potentially varying relationships between MPOM and local environmental factors across time and geospatial context constitute analytic challenges.

Objectives

(1) Employ Bayesian latent cluster modeling to detect spatial clusters in each of which the temporal association between MPOM rates and local structural risk factors is varying and unique. (2) Illustrate the spatio-temporal trend and hotspots of MPOM in Pennsylvania (PA) 2010–2013, and characterize their associations with key county-level environmental determinants.

Methods

Using Medicaid Analytic eXtract (MAX) data, 5,653 Medicaid-enrolled women who recently gave birth were identified with MPOM among 61,227 deliveries in PA during 2010–2013. County-level unemployment rate, poverty rate, race heterogeneity, population density, and total number of opioid prescribed were used as environmental risk factors. Spatial and temporal autocorrelation effects were integrated into a Bayesian latent clustering process.

Results

MPOM rates in Medicaid enrolled women increased from 7.9% to 10.6% during 2010–2013 in PA. Cluster models showed that there were three distinct spatial clusters: north and central rural counties, southwestern and southeastern metropolitan or suburban counties, and buffering counties located between the first two clusters. Hotspot counties for MPOM mainly belonged to the cluster including north and central rural counties. Spatio-temporal heterogeneity existed in the association between MPOM and environmental factors across clusters.

Conclusion

This study demonstrates the utility of the Bayesian spatio-temporal clustering approach in investigating MPOM trend. With this latent clustering analytic method, it is possible to detect space specific patterns of MPOM incident risk and its relationship with key local areal risk factors. The varying relationships between MPOM and areal structural factors have important implications for state and county MPOM prevention measures.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12889-025-25174-x.

Keywords: Bayesian, Spatio-temporal analysis, Maternal prescription opioid misuse(MPOM), Markov chain monte carlo (MCMC), Latent cluster

Background

Prescription opioid misuse (taking opioid in a manner other than prescribed, including non-medical use or abuse) [1] brings significant health and economic costs to the United States [2]. Maternal prescription opioid misuse (MPOM) is particularly concerning because it influences both the new mother and fetus’ health, safety, and wellbeing. Mothers with MPOM have elevated risks of overdoses, injuries, and multiple complications [3]. About 45–95% of newborns whose mothers exposed them to opioids during pregnancy develop neonatal abstinence syndrome (NAS), which may be associated with infants’ immediate neurologic and gastrointestinal complications, and long term adverse physical, cognitive, and behavioral outcomes [4–6]. MPOM incidents increased dramatically in recent years. From 1999 to 2014, the national rate of maternal opioid disorder at delivery more than quadrupled (increasing from 0.15 to 0.65%, with the highest increase—4.86%—documented for Vermont in 2014) [7]. Recent reports show that 0.8 to 1.4% of pregnant women self-reported nonmedical opioid use [8, 9].

Given these significant increases in recent years, it is critical to evaluate the epidemic of MPOM and its key structural and socio-economic determinants. Previous studies on prescription opioid misuse have identified certain individual-level risk factors: young aged, female, white, Medicaid enrolled, accompanying mental/substance disorders, and concurrent use of other prescription medications [10–18]. With the growing interest in examining the distribution pattern of opioid misuse, a few studies have also focused on the disparities in opioid misuse incidents across different geographic areas and subpopulations, revealing greater misuse risks in rural/suburban locality and socio-economic disadvantaged population [19, 20]. Research indicated that population density, especially in areas of low population, impacts the availability of health care facilities, may be responsible for the rural/urban difference in qualified health care services [21]. It was also reported that opioid epidemic is prompted by socioeconomic distressful environment, which is characterized with poverty, unemployment, and racial heterogeneity [22, 23]. Additionally, studies have shown that consumption level of opioid medication is closely correlated with opioid misuse and related adverse outcomes [24, 25].

However, few existing studies have focused on MPOM, specifically. To examine the risk and identify community structural risk factors of MPOM, a spatio-temporal analysis is warranted. The advantage of such an approach over conventional methods is that it can illustrate temporal trends and spatial variations in health outcome simultaneously [26]. Beyond providing more accurate estimates of event risk and its association with relevant risk factors, it can also assist in identifying certain patterns of temporal association with geographic characteristics in MPOM rates. These results may offer important insight for preventive measures. Yet the spatio-temporal analysis of opioid misuse is challenging. Rapid changes in opioid prescription patterns (e.g., the rises and drops in OxyContin and fentanyl), nuanced and varying local response strategies (e.g., uneven penetration of medication-assisted treatment, MAT), and differentiated access to health service facilities (e.g., expansion of rural hospital model, RHM) raise concerns about the standard assumption of a fixed association between outcome and related risk factors. Furthermore, spatial spillover and temporal lagging effects must be considered appropriately [27]. A more practical assumption is that the MPOM incidents may respond varyingly to related risk factors across space and time units.

Geographically Weighted Regression (GWR) has been increasingly used to capture spatial heterogeneity by allowing model coefficients to vary across geographic locations, providing localized estimates rather than assuming a single global relationship [28]. Building on GWR, Geographically and Temporally Weighted Regression (GTWR) extends this framework to incorporate temporal variation, thereby enabling coefficients to vary simultaneously across both space and time [29]. More recently, Multiscale Geographically Weighted Regression (MGWR) has been introduced to allow different predictors to operate at different spatial scales, improving model flexibility and interpretability [30]. These approaches have clear advantages: they are intuitive, visually interpretable, and effective in identifying local variations in associations between predictors and outcomes.

However, they also face some application restrictions. First, they are highly sensitive to sample size and data density, with performance deteriorating when observations are sparse or unevenly distributed. Second, they require careful bandwidth selection, and results can be unstable if bandwidth parameters are misspecified. For relatively rare outcomes or datasets of moderate size—such as maternal prescription opioid misuse (MPOM) measured at the county-year level, these challenges constrain the applicability of such models. In contrast, Bayesian spatiotemporal clustering methods address some of these challenges by stabilizing estimates in data-sparse areas through partial pooling, explicitly modeling uncertainty, and providing flexible hierarchical structures that can capture both global and local variations. Therefore, a spatio-temporal study which accommodates the variations in the associations between MPOM and local environmental factors is necessary.

In this study, the research team utilized a Bayesian latent-cluster analytic strategy to incorporate spatial and temporal components to analyze county-level pooled cross-sectional data of delivered mothers enrolled in Medicaid in Pennsylvania 2010–2013. Pennsylvania is a geographically and socioeconomically diverse state located in the Northeastern and Mid-Atlantic regions of the United States. It consists of 67 counties that span a wide spectrum, from densely populated metropolitan areas such as Philadelphia in the east and Pittsburgh in the west, to sparsely populated rural regions across the central and northern parts of the state. Pennsylvania is also culturally heterogeneous, with influences from Quaker, Pilgrim, and Amish traditions—historical patterns that continue to shape community values, family support systems, health behaviors, and patterns of healthcare utilization. Economically, the state reflects a mixed profile: long-standing industrial and coal-mining communities exist alongside knowledge-based and service economies concentrated in urban hubs. While inner-city neighborhoods in metropolitan areas often face challenges related to poverty, crime, and social instability, rural counties experience different but equally persistent barriers, including economic decline, limited healthcare access, and higher poverty rates. These combined contrasts—urban versus rural, industrial versus post-industrial, traditional versus modern—create a unique context that heightens the relevance of Pennsylvania as a case study for investigating the spatiotemporal patterns of maternal prescription opioid misuse. The aims are: (1) utilize a Bayesian latent cluster modeling method to identify potential spatial clusters allowing varied and unique associations between MPOM outcomes and local structural determinants; (2) illustrate the spatio-temporal trend and hotspots of MPOM in Pennsylvania 2010–2013, and characterize its relationship with key county-level environmental risk factors.

Methods

Study participants, data sources, and measures

A secondary data analysis was conducted for Medicaid enrolled pregnant and delivered women, which is a high-risk population for opioid prescription and misuse [9, 10]. Participants inclusion criteria are: (1) indication of a live child birth during 2010–2013, (2) maternal age between 15 and 55 at the time of birth, (3) enrollment in Medicaid for all the months during the pregnancy and the postnatal (0-to-1 years old) period, and (4) identification of the mother-child pair in Medicaid records. Note that following the Medicaid pregnancy identification algorithm [31], we defined the reproductive age range as 15–55 years, increasing the lower bound from 12 to 15 to exclude very early adolescents. These inclusion criteria follow prior research utilizing Medicaid files to identify medication use during pregnancy in a birth cohort [31].

Delivered mothers cohort was derived from Medicaid Analytic eXtract (MAX) data which contain national deidentified Medicaid enrollment and utilization records from 1999 to 2015. Opioid misuse status was calculated based on prescriptions from 10-month before to 1-year after the delivery by using Katz et al. algorithm, which defined misuse as having no less than two prescribers and no less than two pharmacies for the same opioid during a 12-month period [32]. The outcome is the relative risk of MPOM incidents (pre or post-delivery MPOM), measured by the standardized incident ratios (SIR) of MPOM for each county at each time period [33]. Standardized incidence ratio (SIR) was calculated as the ratio of observed number of MPOM cases and expected number of MPOM cases1, which is an indicator of MPOM risks.

Total amount of opioid prescriptions, unemployment rate, poverty rate, racial heterogeneity (measured by the percentage of African Americans in the population), and population density were selected as key environmental risk factors in the analytic model. We selected poverty, unemployment, racial heterogeneity, population density, and opioid prescribing rates as covariates because each has been shown to influence substance use patterns and maternal opioid misuse. Poverty, unemployment, and over prescription are strongly linked to higher risk of opioid misuse due to economic stress and reduced healthcare access [34–36]. Racial and ethnic composition captures disparities in opioid exposure and treatment access, as prior studies have documented systematic differences in outcomes across groups [37, 38]. Population density reflects urban–rural contrasts; rural counties often have higher prescribing rates and fewer treatment resources, while urban areas may face different structural risks [34]. Including these variables allows us to account for socioeconomic, demographic, and structural factors known to shape maternal prescription opioid misuse.

Annual numbers of dispensed opioids were calculated based on IQVIA Xponent data, which include opioid-related (for pain-management or opioid addiction treatment) prescriptions filled at pharmacy stores or delivered by mail in PA. Unemployment rates were collected from employment data from PA Department of Labor. Poverty rates, racial heterogeneity, and population density were extracted from American Community Survey (ACS) one year estimation data from Census Bureau. All data were aggregated to county-level annual data. County-level analyses were chosen for several reasons. First, counties in Pennsylvania represent meaningful administrative and community units, with relatively consistent environments in terms of community characteristics, population composition, access to healthcare services, and public health regulation. This makes counties an appropriate level for examining community-level risk factors and interventions. Second, while smaller spatial units (e.g., ZIP codes, census tracts) could in principle provide finer detail, such subdivisions often yield very sparse case counts for maternal prescription opioid misuse (MPOM), which would result in unstable estimates and reduce statistical power. Moreover, Medicaid data use regulations impose strict privacy and confidentiality constraints, making analysis below the county level infeasible. Finally, county-level analysis offers a practical balance: it preserves sufficient case counts for robust statistical modeling while still capturing meaningful geographic variation across urban, suburban, and rural communities. For these reasons, counties were determined to be the most appropriate geographic unit for this study. Study approval was obtained from the Penn State Institutional Review Board.

Statistics analysis

A Bayesian hierarchical latent class modeling strategy was utilized. We assume that the MPOM follows a count outcome distribution (e.g., Poisson) as.

graphic file with name d33e433.gif 1

whereInline graphic is the expected count of the MPOM and Inline graphic is the relative risk in the ith county and tth year. Then Inline graphicis modeled by

graphic file with name d33e466.gif 2

where Inline graphic represents the vector of covariates (including intercept, total amount of opioid prescriptions, unemployment rates, poverty rate, racial heterogeneity, and population density in this case) of county i at year t, and Inline graphic denotes the vector of the corresponding coefficients. Following Choi, et al., we presume that there are m latent clusters among PA counties, in which the temporal trends of the associations between outcomes and covariates are different across spatial domains, but are alike within the same spatial cluster [39]. Thus, we specify the vector of covariates’ coefficients, Inline graphic, as

graphic file with name d33e498.gif 3

where m is the indicators of spatial clusters and Inline graphic shows which spatial cluster the observed state belong to. We consider Inline graphic follows a categorical distribution.

graphic file with name d33e515.gif 4

where Inline graphic is the probability of county i belongs to cluster m (Inline graphic>0 and Inline graphic).

Next, we model the Inline graphic as

graphic file with name d33e542.gif 5

where Inline graphic is un-normalized weights. Given its non-negative attribute, we assign a lognormal distribution to Inline graphic.

graphic file with name d33e556.gif 6

where Inline graphic is spatially dependent mean, and Inline graphic is the variance of Inline graphic.

To add a spatial dependency structure, we assign a conditional autoregressive (CAR) distribution to Inline graphic

graphic file with name d33e579.gif 7

where Inline graphic is the number of the neighboring counties which are also in the same cluster of county i, Inline graphic=1 if i and j are adjacent counties and Inline graphic=0 otherwise. Hence, assuming an CAR, the mean of county i is smoothed as the average of the means of its neighbour counties of a same cluster, and the variance is the variance of Inline graphicdivided by Inline graphic. A random walk distribution showing temporal autocorrelation components were also imbedded to the weight calculation process (details of the model are documented in the supplementary file). In Brief, we employed a conditional autoregressive (CAR) Bayesian latent-cluster spatiotemporal model to analyze data collected across time and different geographical areas. Specifically, we modeled cluster membership using a categorical distribution, with cluster weights standardized through a lognormal distribution to ensure that the probabilities of belonging to mutually exclusive clusters sum to one. The CAR prior was then incorporated into the estimation of the lognormal parameters (Inline graphic), introducing spatial dependence into the hierarchy framework. In this setup, the mean of the feature of a given county is smoothed toward the average of its neighboring counties within the same cluster, while the variance is defined as the variance of Inline graphicdivided by Inline graphic, the number of neighboring counties belonging to the same group.

Standardized variables were used in the model. Posterior computation was processed by WinBUGS, JAGS and R software via the Markov Chain Monte Carlo (MCMC) algorithm. MCMC convergence was diagnosed by trace plots, autocorrelations plots, and Geweke’s z-test. In order to decide the best number of the spatial clusters in the models, the models with a range of the number of clusters were estimated. Because the total number of spatial units (67 counties) is not large, a reasonable estimation of the number of clusters is between two to six. The final model was determined by the model with the best comparison measures (Deviance information criterion, DIC [27] and negative cross-validatory predictive log-likelihood, NLLK [40]) by estimating Poisson and negative binomial models with different numbers of clusters. Hotspots were identified by exceedance probability method, which measures the probability of MPOM incident rates exceeding the average risk in PA for each area [41].

Results

Demographics of the study participants

Over the period of 2010–2013, a total of 5,653 MPOM cases were identified among 61,227 deliveries with continuous Medicaid enrollment through the prenatal and 0-to-1 year periods. The overall MPOM rates during pre-delivery or post-delivery stage was 8.59%. The annual MPOM case numbers and total deliveries numbers are presented in Table 1. Both the absolute number of MPOM cases and the corresponding rates increased steadily over time—from 1,011 cases (7.9%) in 2010 to 1,120 cases (9.4%) in 2011, and then to 2,226 cases (10.6%) in 2013—with the exception of a slight decline in 2012, when the rate dropped to 8.4% compared to 2011. The statistical summary of the outcome and major risk factors are shown in Table 2.

Table 1.

MPOM cases and total number of deliveries by year

Year MPOM cases Total deliveries MPOM rate (%)
2010 1,011 12,772 7.9
2011 1,120 11,957 9.4
2012 1,296 15,388 8.4
2013 2,226 21,110 10.6
Total 5,653 61,227 8.6
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MPOM Maternal prescription opioid misuse

Table 2.

Summary statistics for variables used in the analysis

Variables Min Max Mean SD
MPOM cases (by county and year) 0 217 21.1 22.8
Unemployment rate (%) 5.8 12 8.6 1.3
Number of opioid prescriptions 0 1,640,8 11,399.8 66,018.5
Percentage of American Africa population (%) 0.3 44.7 4.7 6.6
Poverty rate (%) 5.8 27.9 13.6 3.5
Population density (people per square mile) 12.4 11,621.5 470.2 1440.2
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MPOM Maternal prescription opioid misuse

The count histogram (Fig. 1) shows that 19 counties (28.4%) reported zero MPOM cases in 2010. However, this number kept declining over the years. In 2013, only one county (1.5%) had zero MPOM counts. Meanwhile, the peaks of the histograms shifted to the right gradually, suggesting the increasing trend of MPOM over time. Since no excessive zero counts presented in the data, zero-inflated Poisson and negative binomial models were not considered.

Fig. 1.

Fig. 1

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MPOM count histograms by year. Note: MPOM Maternal prescription opioid misuse

Mapping of crude SIRs

A map of crude SIRs of MPOM by quartiles (Fig. 2) also reflects the increasing pattern of MPOM during 2010–2013. The SIRs in almost all the counties in PA were elevated over the years. It appears that counties in the north/central region experienced the MPOM epidemic earlier and more severely than southern counties. In contrast, the southwestern and southeastern parts of PA remained as low risk regions for MPOM over time. However, to test if this geographical disparity statistically holds or is just a misrepresentation caused by extreme observations, a spatio-temporal analytic model is needed.

Fig. 2.

Fig. 2

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Maps of crude standardized incidence ratios (SIR) of MPOM by year. Notes: (a) Standardized incidence ratio (SIR) =observed number of MPOM cases/expected number of MPOM cases, which is an indicator of MPOM risks. Expected number of MPOM=the number of delivered women in county i at year t/total number of delivered women in PA total number of women with MPOM during 2010-2013 in PA. (b) SIRs are presented by quartile cuts ([0, 0.26] first quarter, (0.26, 0.94] second quarter, (0.94, 1.42], third quarter, (1.42, 2.91] fourth quarter)

Cluster analysis

A Poisson and a negative binomial model using previously mentioned clustering strategy were applied to the data. 100,000 MCMC iterations were conducted for each model, dropping the initial 40,000 samples as burn-in. Only every 20th iteration was sampled (thinning) to mitigate the influence of the autocorrelations between the parameter estimates. The final 3,000 samples were then utilized for summarizing the parameter values. Trace plots, autocorrelation plots, as well as the Geweke test, illustrated convergence of both models. We examined the equal mean–variance assumption in our data using overdispersion tests and did not find evidence supporting overdispersion (p > 0.05). Posterior predictive checks further confirmed that observed within-cluster variances and cluster means were consistent with those predicted under the model. Trace plots and posterior density plots indicated stable MCMC chain convergence and mean separability. We also computed posterior predictive p-values (PPP) for key summary statistics—including annual means and variances. The PPP values were centrally distributed (0.35–0.50), suggesting adequate model fit and no major misspecifications. Table 3 shows the performance measures (DIC and NLLK) of Poisson and negative binomial models with different numbers of clusters.

Table 3.

Latent cluster models comparison using DIC and NLLK

Model # Clusters Dbar pD DIC NLLK
Model 1 2 1452.7 1451.5 2904.1 795.9
(Poisson) 3 1281.3 1278.6 2559.8 712
4 1289.7 1287.1 2576.8 716.8
5 1285.7 1283.3 2569 721.2
6 1335.9 1333.2 2669.2 734.4
Model 2 2 1833.9 157.5 2991.4 979.7
(Negative binomial) 3 1832.5 155.4 2985 977.2
4 1831.3 153.6 2987.9 978.3
5 1831.4 153.6 3007.5 988
6 1832.5 153.9 3022.3 983.3
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DIC Deviance information criterion, NLLK Negative cross-validatory predictive log-likelihood, Dbar the posterior mean of the deviance, pD the effective number of parameters in the model

The findings indicated that the changes of DICs closely mirrored those of NLLKs within each model, demonstrating consistency between these two comparison measures. In addition, negative binomial specifications yielded substantially higher DIC and NLLK values than Poisson models, indicating that the Poisson distribution provided a better fit to our data. These patterns were robust across different numbers of clusters. We also compared the performance of the latent clustering models with models lacking spatial components as well as models incorporating conventional spatial correlation structures (see Supplement). Across all model specifications, the latent clustering model consistently achieved the lowest DIC and NLLK. While there are no strict cutoffs for DIC or NLLK differences, their interpretation is guided by the principle of parsimony—balancing model fit against complexity. In this context, the three-cluster Poisson model not only produced the lowest DIC (2559.8) and NLLK (712) but also offered the most straightforward interpretation. For these reasons, we selected the three-cluster Poisson model as the final specification. The clusters identified through the final model are mapped in Fig. 3. The names and numbers of the counties in each cluster are listed in Table S.1 in the supplementary file. Cluster one, with 27 counties, has the largest number of members. This cluster includes most of the north and central regions of Pennsylvania. Next comes cluster two with 25 counties, which are mainly distributed in southwestern and southeastern Pennsylvania. This group includes two major metropolitan areas (Pittsburg and Philadelphia) and their adjacent counties. These counties reported relatively lower MPOM rates than other counties in most time periods. The remaining 15 counties constituted cluster three, which primarily included counties in south central region of PA as well as several individual counties scattered in northeastern and northwestern Pennsylvania.

Fig. 3.

Fig. 3

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The distribution of the member counties in each spatial cluster

With respect to the relationship between MPOM and the area structural determinants, these three clusters exhibited different patterns (Fig. 4). For instance, while unemployment rates showed positive associations with MPOM for cluster one all the years (though non-significant), inverse associations were found for cluster two in 2010 and 2011. We also observed that the initially positive coefficient became negative for racial heterogeneity over years in cluster one. A similar trend was presented for the coefficients of poverty for cluster one (non-significant most of times though). In contrast, poverty positively correlated with MPOM all the years in cluster two but became non-significant after 2011. Moreover, population density showed divergent relations with MPOM cross clusters. Lower population densities predicted higher misuse outcomes in cluster one over time (significant in 2011 and 2012, and marginally significant in 2010 and 2013). However, the coefficients for population density for other two clusters remained negative or close to zero and nonsignificant for all the years. Interestingly, despite some minor variations, ascending trends of the association between MPOM and opioids prescription were shown in all three clusters. The coefficient estimates for cluster one and two in 2013 were significant. Detailed estimates of all coefficients can be found in the Table S.2 in the supplementary file.

Fig. 4.

Fig. 4

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The estimated coefficients and credible intervals (CI) of key risk factors by cluster and by year. Notes: The relationships between MPOM and the areal structural determinants exhibited different patterns in three clusters. The solid line is the estimated value of coefficients, the dash lines represent the range of 95% credible interval (CI, equivalent to the confidence interval in frequentist analysis, all of them >or <0 deemed as significant)

Plotting exceedance probability

To fully leverage Bayesian analysis, a map of hot spots for MPOM using the “exceedance probability” method [41] was created. The exceedance probability for a given area represents the probability that the estimated posterior relative risk surpasses a particular value (e.g., 1 indicates average risk, while 1.5 signifies 1.5 times the average risk). A probability that is notably high (e.g., 95% or more) for the estimated risk exceeding the given risk value signals the “significance” of the local risk. In this study, we used RR = 1 as the reference threshold, as the posterior relative risks were generally above 1 but rarely exceeded 1.25 in most years. Figure 5 illustrates the hotspots under different probability cutoffs (0.75–0.94, 0.95–0.98, and ≥ 0.99).

Fig. 5.

Fig. 5

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Exceedance probability (75–100%) to have elevated MPOM relative risk (RR>1) by year (Hotspots). Notes: Exceedance probability for an area is the probability that the estimated posterior relative risk is greater than the average relative risk (using cutoff as <=0.74, 0.75–0.94.75.94, 0.95–0.98.95.98, >=0.99). The result suggests that north and central regions had higher SIRs of MPOM than south PA. Notably, two big metropolitan areas and their neighboring counties in the southwest and southeast conners of Pennsylvania showed quite lower MPOM risks than their rural/suburban counterparts in most years

Utilizing exceedance probabilities in mapping aids in identifying areas with unusually elevated risks, pinpointing spatial clusters of high-risk regions. Thus, mapping exceedance probabilities serves as a Bayesian approach for hotspot detection.

Figure 5 illustrates the probability distributions of estimated posterior MPOM risks surpassing average risks (RR = 1) for each year, categorized into specific probability ranges (with cutoffs at < = 0.74, 0.75–0.94, 0.95–0.98, >=0.99). This figure confirmed the increasing trend of MPOM from 2010 to 2013 in PA. It also clearly illustrated the disparity of MPOM risks between different regions of the state, which is that north and central regions had higher SIRs of MPOM than south PA. Notably, two big metropolitan areas and their neighboring counties in the southwest and southeast conners of Pennsylvania showed quite lower MPOM risks than their rural/suburban counterparts in most years. This pattern remained consistent and unaffected by the impact of extreme observations over time.

Discussion

This study illustrated markable spatial and temporal variations in county-level rates of MPOM and its associations with community environmental structure factors in PA. We first examined the overall incident rates of MPOM in Medicaid population during 2010–2013 in PA, which increased from 7.9% to 10.6% over the years. These rates are higher than the non-medical opioid use rates reported among ordinary pregnant women using CDC’s Pregnancy Risk Assessment Monitoring System data [8] and National Survey of Drug Use and Health data [9] (1.4% and 0.8%, respectively). Although this disparity may partially be due to the difference in the sensitivity between self-report method and algorithmic methods that consider prescription dosages, durations, and prescribing patterns, it clearly reflected the high-level MPOM risks for Medicaid enrolled women.

The temporal trend of MPOM in counties was also striking, demonstrating a rapid increase in MPOM rates across the state between 2010 and 2013. The mapping of crude SIRs and the estimated exceedance probability of MPOM each indicated that most Pennsylvania counties experienced a substantial increase in rates of MPOM. It is not unexpected since many previous reports demonstrated similar trends of various types of opioids related adverse events around that time [42–44]. However, while a previous study reported plateaued or even decreased patterns in opioid diversion and abuse nationally around 2011–2013 [36], the MPOM rates we observed in PA showed a continued upward pattern. A closer inspection revealed some variation in this rising trend in MPOM, including evidence of distinctive geographic patterns across the state. In general, northern and central counties in PA had higher MPOM rates than southern regions over the years. However, in 2013, the risks of MPOM in Allegheny Mountain area, which located in the west half of the southern central region, experienced noticeable increases. In contrast, the southeastern and southwestern regions of the state remained low risk areas at all times.

The cluster analysis showed that there were three distinctive spatial clusters in which the MPOM risks uniquely responded to key local environmental risk factors over time. It is noticeable that the members of cluster one were highly overlapped with the northern and central counties exhibiting high MPOM risks mentioned above. Compared with the counties in cluster two, these counties are more rural area with dispersed small towns and cities. While there were some fluctuations in the estimates of coefficients of major socio-economic factors, the one of population density were constantly negative and significant (or marginally significant) over time. It suggested that population density played a more important role in predicting MPOM in this group than other two clusters. It is plausible that the density of population negatively impacted the availability of health care service in these areas. Health care providers could be insufficient in these areas. The shortage of health care providers and the long distance to related facilities limits the access to qualified health care services, thus contributing the elevated MPOM risks. In contrast, the counties of cluster two spread around in southwestern and southeastern corners of the state, where the two biggest metropolitan areas (Philadelphia and Pittsburg) seated at the center of each region respectively. The areas in this cluster largely reflect affluent parts of the state and have relatively high employment rates. Unlike cluster one, the social structural factors, such as unemployment rates and poverty, showed more active influences on MPOM rates than population density. Counites in cluster three distributed like buffer areas between cluster one and cluster three. The patterns of estimated coefficients of covariates in cluster two are similar to the ones in cluster two in most instances, except the ones of unemployment and poverty in certain years. This could result from this cluster’s mixed geographical and environmental attributes between cluster one and cluster three. On one hand, areas in cluster three possess similar rural/suburban characteristics of cluster one, in which community environmental factors similarly impacted MPOM. On the other hand, many cluster three members are adjacent to two big metropolitan areas, thus having relatively easier access to health care service than areas in cluster one. It might explain why population density did not closely correlated with MPOM in cluster three.

We observed that some individual counties, such as Bradford and Crawford in Cluster 3, were scattered away from the main body of their cluster. This phenomenon might not be fully explained by their location in buffer zones between Clusters 1 and 3. The scatteredness of these counties suggests that maternal prescription opioid misuse (MPOM) is influenced not only by geographic contiguity but also by broader sociodemographic, economic, and healthcare system factors that transcend simple spatial adjacency. For example, noncontiguous counties may nonetheless share similar prescribing environments, socioeconomic vulnerabilities, or healthcare access challenges that align them into the same latent risk profile. This is consistent with the purpose of Bayesian latent-cluster models, which can guide further detection of shared underlying structures even when they are not geographically adjacent.

Although some studies reported that opioid misuse related adverse outcomes began to decline after 2012, our analysis did not detect such dropping or flattening patterns in PA. The continuing increase in opioid prescriptions could be responsible for this. As we observed, the total number of opioids prescriptions in PA continued increasing until 2012 (167,510 to 173,789), and only had a slight decline in 2013 (172,295), which has a lagged peaking time compared with the national flatten and decline phenomena in opioid prescriptions starting at 2011 [36]. This lagging may explain the continued rising trend of MPOM during 2013. Looking at the changes in coefficient of total opioid prescribed, despite some minor variation, ascending trends are found in all three clusters. By 2013, estimated coefficient for two major clusters (cluster one and two) were positive and significant, indicating the positive association between MPOM and total amount of opioid medications. With continuously rising consumption of opioid prescriptions in PA, the MPOM rates kept growing through 2013. Essentially, our findings enforced the evidence of boosting effect of opioid prescriptions on MPOM.

This study illustrates the benefits of a Bayesian based cluster analysis approach to investigate opioid misuse outcomes involving varying local environment structural determinants. The advantage of such an approach is to allow flexible temporal and cluster specific variation in the association between the outcome and related risk factors. The differential temporal trends and magnitudes of the estimated coefficients of multiple environmental factors for MPOM suggest that the shaping of MPOM was heterogenous across time and space. There was no single universal pattern suiting all the areas in PA. This variation may be due to the spatial differences in local community structures, geological characters, or available resources. Also, temporally, with increased awareness of the threat of opioid epidemic, many local/state measures have been taken to reduce opioid related adverse events, such as promoting MAT services, enforcing prescription monitoring systems, implementing rural health supporting program, and strengthen community assisting network. In many cases, such factors were unevenly distributed and difficult to measure. With the assistance of the introduced cluster analysis, it is possible to detect space specific patterns of MPOM incident risk and its relationship with key local areal risk factors. This can help provide more tailed insights to MPOM prevention policy. For example, it may be more important to improving the accessibility of qualified rural health services (e.g., expand rural hospital model and increase the density of MAT cites) in north-central areas than in other areas. It also makes sense to pay more attention to reduce MPOM prone socio-economic factors on MPOM in metropolitan setting than in rural areas. Finally, it suggests that reducing inappropriate prescribing practices and promoting alternative pain management strategies is critical to reduce MPOM in all areas in PA.

In terms of clinical and public health implications, our findings suggest that strategies to address MPOM should not be restricted to geographically contiguous regions alone but instead targeted toward clusters of counties that share common risk environments. Clinically, this implies the need for prenatal care providers to be particularly vigilant in counties characterized by high prescribing rates, elevated poverty, or limited behavioral health resources, regardless of where those counties are located within the state. From a public health perspective, cluster-based targeting can guide the allocation of prevention resources, screening programs, and treatment capacity to counties with similar risk profiles, even if they are spatially dispersed. In this way, our study provides a framework for identifying “communities of risk” that may benefit from coordinated intervention strategies beyond traditional geographic boundaries.

Our study has some limitations to mention. First, this study can only provide a general picture of the trends and patterns of MPOM and its association with county-level environment structural variables. While counties provide a meaningful balance between data availability, confidentiality, and statistical stability, analyses at finer geographic scales (e.g., ZIP codes or census tracts) could offer additional insights into local variation in maternal prescription opioid misuse. The findings can neither be used to interpret the dynamics of MPOM at the incident or individual-level. Further research on the smaller spatial unit or incident/individual-level is warranted to obtain a more comprehensive picture of MPOM generating mechanism. Second, this study focuses on legitimate opioid prescriptions, which may ignore the effect of illicit opioid usage on the MPOM. Some illegally distributed medication (e.g., fentanyl without prescription) and heroin, could have potential impact on MPOM risks. Nevertheless, pregnant women and those enrolled in Medicaid are most likely to abuse prescription opioids than other forms of opioid misuse [15, 45]; are at higher risk of reporting non-medical use of prescription opioids [16] and access prescription opioids directly from medical sources than other populations [16, 46, 47], which may minimize this concern. Another limitation of this study is that the data span 2010–2013 and do not extend to more recent years. However, this period represents a critical stage of the opioid epidemic, when prescription opioids were the dominant driver of misuse before the transition to heroin and fentanyl in later years. By focusing on this window, our analysis provides valuable historical insight into the formative stage of the crisis and its associations with maternal health and community-level factors. Future work should apply these methods to more recent, multi-source datasets as they become available, to examine how these dynamics have evolved.

Beyond Bayesian spatiotemporal approaches, recent advances in artificial intelligence offer promising opportunities to enhance geospatial health research. In particular, Explainable Geospatial Machine Learning (XGeoML) has emerged as a framework that balances predictive performance with interpretability, a critical feature in public health applications where transparency is essential [48]. Other AI-driven methods, such as spatially adaptive deep learning and graph neural networks (GNNs), provide powerful tools for capturing nonlinear spatial dependencies and complex interactions that may be difficult to model with conventional techniques. While these methods were beyond the scope of the present study, future research could benefit from hybrid frameworks that integrate Bayesian modeling with AI-based approaches, thereby leveraging the interpretability of Bayesian inference alongside the scalability and flexibility of machine learning. Such integration may offer deeper insights into spatial heterogeneity and more robust predictions for informing policy and intervention planning.

Conclusion

This study demonstrates the utility of the Bayesian hierarchical spatio-temporal clustering approach when analysing opioid misuse outcome involving space and time dynamic information. With the assistance of this latent clustering analytic method, it is possible to detect space specific patterns of MPOM incident risk and its relationship with key local areal risk factors. The findings increase our understanding of the trend of MPOM in Pennsylvania and provide a more comprehensive picture about the factors associated with MPOM. The varying relationships between MPOM and areal structural determinants have important implications for state and county MPOM prevention measures. Differentiated prevention measures suited in local areal environments should be considered.

Supplementary Information

Supplementary Material 1. (70KB, docx)

Acknowledgements

Does not apply to this study.

Abbreviations

MPOM

Maternal prescription opioid misuse

MAX

Medicaid analytic extract

MCMC

Markov chain monte carlo

NAS

Neonatal abstinence syndrome

MAT

Medication-assisted treatment

RHM

Rural hospital model

SIR

Standardized incident ratios

ACS

American community survey

DIC

Deviance information criterion

NLLK

Negative cross-validatory predictive Log-LiKelihood

Authors’ contributions

XX: conceptualization, methodology, investigation, resources, writing original draft, review and editing, visualization, supervision, project administration. CM: conceptualization, methodology, review and editing, supervision, project administration. CC: conceptualization, methodology, review and editing, visualization, supervision, project administration.

Funding

This research was supported in part by two seed grant awards from the Institute for Computational and Data Sciences and from the Social Science Research Institute at the Pennsylvania State University.

Data availability

The data that support the findings of this study are available from the Centers for Medicare and Medicaid Services (CMS) Virtual Research Data Center, but restrictions apply to the availability of these data, which were used under the Data Use Agreement for the current study, and so are not publicly available. Aggregated data without the risk of revealing individual information could be available upon request. Please contact the Penn State Data Accelerator for data requests ([evidence2impact@psu.edu](mailto: evidence2impact@psu.edu)).

Declarations

Ethics approval and consent to participate

Study approval was obtained from the Penn State Institutional Review Board. Consent to participate is not applicable because: (1) All of the data are existing secondary data, (2) The MAX data used are already deidentified, (3) All data are aggregated and present at county-level.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.

Footnotes

1

Expected number of MPOM = the number of delivered women in county i at year t/total number of delivered women in PAInline graphictotal number of women with MPOM during 2010–2013 in PA.

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

Supplementary Material 1. (70KB, docx)

Data Availability Statement

The data that support the findings of this study are available from the Centers for Medicare and Medicaid Services (CMS) Virtual Research Data Center, but restrictions apply to the availability of these data, which were used under the Data Use Agreement for the current study, and so are not publicly available. Aggregated data without the risk of revealing individual information could be available upon request. Please contact the Penn State Data Accelerator for data requests ([evidence2impact@psu.edu](mailto: evidence2impact@psu.edu)).

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