Utilizing Residential History to Examine Heterogeneous Exposure Trajectories: A Latent Class Mixed Modeling Approach Applied to Mesothelioma Patients

Abstract

Background:

Life-course exposure assessment, as opposed to a one-time snapshot assessment based on the address at cancer diagnosis, has become increasingly possible with available cancer patients' residential history data. To demonstrate a novel application of residential history data, we examined the heterogeneous trajectories of the nonasbestos air toxic exposures among mesothelioma patients, and compared the patients' residential locations with the spatiotemporal clusters estimated from the National Air Toxic Assessment (NATA) data.

Methods:

Patients' residential histories were obtained by linking mesothelioma cases diagnosed during 2011–2015 in the New York State (NYS) Cancer Registry to LexisNexis administrative data and inpatient claims data. To compare cancer risks over time, yearly relative exposure (RE) was calculated by dividing the NATA cancer risk at individual census tracts by the NYS average and subtracting 1. We used a latent class mixed model to identify distinct exposure trajectories among patients with a 15-year residential history prior to cancer diagnosis (n = 909). We further examined patient characteristics by the latent trajectory groups using bivariate comparisons and a logistic regression model. The spatiotemporal clusters of RE were generated based on all NATA data (n = 72,079) across the contiguous United States and using the SaTScan software.

Results:

The median number of addresses lived was 2 (IQR, 1–4), with a median residential duration of 8 years (IQR, 4.7–13.2 years). We identified 3 distinct exposure trajectories: persistent low exposure (27%), decreased low exposure (41%), and increased high exposure (32%). Patient characteristics did not differ across trajectory groups, except for race and Hispanic ethnicity (P < .0001) and residential duration (P = .03). Compared to their counterparts, non-Hispanic White patients had a significantly lower odds of belonging to the increased high exposure group (adjusted odds ratio, 0.14; 95% CI, 0.09–0.23) than the persistent low exposure and decreased low exposure groups. Patients in the increased high exposure group tended to reside in New York City (NYC), which was covered by one of the high-RE clusters. On the other hand, patients in the persistent low exposure group tended to reside outside of NYC within NYS, which was largely covered by 2 low-RE clusters.

Conclusion:

Using mesothelioma as an example, we quantified the heterogeneous trajectories of nonasbestos air toxic exposure based on patients' residential histories. We found that patients' race and ethnicity differed across the latent groups, likely reflecting the differences in patients' residential mobility before their cancer diagnoses. Our method can be used to study cancer types that do not have a clear etiology and may have a higher attributable risk due to environmental exposures as well as socioeconomic conditions.

Introduction

Using residential history to assess life-course environmental exposure, as opposed to a one-time snapshot exposure assessment (eg, exposure information at cancer diagnosis or at study baseline enrollment), has long been advocated in cancer epidemiology.^1-3 In the United States, previous studies have largely used self-reported residential history data to study the risk of developing cancer from exposures to air and water pollutants in the physical environment.^4-6 Obtaining residential history and incorporating such information into cancer epidemiological studies at scale (eg, using population-based data, such as those collected by the central cancer registries) has been a slow process in the United States, with a renewed interest in recent years.^7-15 For example, the recent linkage of address information from the LexisNexis administrative data with 11 cancer registries within the Surveillance, Epidemiology, and End Results (SEER) program of the National Cancer Institute (NCI) yielded a residential history data set for over 3 million cancer cases throughout the country.¹³ These encouraging developments have opened opportunities, such as applying innovative methods to examine the impact of physical and social environments across the cancer continuum by using residential history information.

Previously, we developed a method to construct the chronological profile of cancer risk from inhalation of ambient air toxics as well as risk associated with disadvantaged socioeconomic status (SES).¹⁶ We applied generalized linear regression models to compare the relative exposure in the past with that at cancer diagnosis, and explored the direction and the magnitude of exposure misclassification using mesothelioma patients as an example. Mesothelioma is a rare type of cancer with about 3,000 new cases diagnosed annually in the United States.^17-19 It is also an aggressive disease with a poor prognosis, as reflected by the late stage at diagnosis, a long latency period of 20 to 30 years, and a poor survival rate.^19-21 Malignant pleural mesothelioma, which represents over 80% of all mesothelioma cases, has a median diagnosis age of 72 years, and a 5-year relative survival rate of only 12%.^17,22

In this study, we continued to explore new ways of using these residential history data from the same group of mesothelioma patients. In particular, we applied a case-only design and a novel statistical method (ie, a latent class mixed modeling approach^23-27) to the reconstructed cancer risk profile for exposure to ambient air toxics. It is not our intention to identify nonasbestos related exposure as a potential risk factor for mesothelioma, as mesothelioma is one of the few cancers with a known etiology, where asbestos exposure, especially in occupational settings, is the primary risk factor for the disease.^{18,20,21,28,29} Instead, we aimed to demonstrate a new approach to explore hidden exposure heterogeneities associated with patients' residential histories. As a side note, by using mesothelioma cases as an example, we provided some new insights into the heterogeneity of environmental exposures among these patients other than the commonly known patterns. Existing studies have been mainly focused on examining workplace asbestos exposure histories of mesothelioma patients.^19-21 Researchers have also used mesothelioma registries and questionnaires to incorporate residential history information into their analyses, hoping to understand the impact of known and unknown asbestos exposures among mesothelioma patients.^30-33 In contrast, only a few studies have examined nonasbestos exposures, such as air pollution and tobacco smoking, among mesothelioma patients.^18,34-36 No study has assessed the residential histories of mesothelioma patients and estimated nonasbestos exposure trajectories. Moreover, we also investigated whether patients' residential locations tended to be within spatiotemporal clusters (ie, hot or cold spots), which were estimated by using the National Air Toxic Assessment (NATA) data and the commonly used spatial epidemiologic methods implemented in the SaTScan software.³⁷ Findings from the current study can provide insights into applying novel methods to residential history data and studying other types of cancer with potentially a large contribution from physical environment exposures and social risks.

Methods

Data Sources and Study Population

Through an NCI-funded exploratory research project, we demonstrated the feasibility of reconstructing the residential history of 1,015 mesothelioma patients diagnosed between 2011 and 2015 and reported to the New York State (NYS) Cancer Registry.¹⁶ The sample size (and the proportion of the full sample) was 974 (96.0%), 952 (93.8%), 913 (90.0%), 839 (82.7%), and 444 (43.7%) for patients with available 5-year, 10-year, 15-year, 20-year, and 30-year residential histories prior to their cancer diagnoses, respectively. In the current study, we analyzed 913 patients with a 15-year residential history before their mesothelioma diagnoses. The choice of this subset was to strike a balance between having a sufficient number of patients from the original cohort and capturing a sufficient length of residential history. The study was approved by the institutional review boards at the NYS Department of Health (#1498055-1) and at the Icahn School of Medicine at Mount Sinai (IRB-19-02514).

Patient residential histories were constructed based on the address information from 3 data sources: (1) patient's street-level address at the time of cancer diagnosis collected in the NYS cancer registry database, (2) patient's street-level address at the time of hospitalization collected in the health insurance claims for the years 1982–2019 available in the New York Statewide Planning and Research Cooperative System (SPARCS) database,³⁸ and (3) patient's addresses provided by the LexisNexis, a commercial database that has been used in other studies.^10,12,39,40 The majority (5,696 of 5,795; 98.3%) of the unique address texts were valid and thus were successfully geocoded using 3 geocoders: the Automated Geospatial Geocoding Interface Environment system, which is a powerful geocoding platform for open use by US cancer registries^41,42; Google Maps; and the Census Geocoder. As the focus of the current analysis was to estimate the exposure history up to the time of cancer diagnosis, we included only geolocations where patients had resided prior to and at the time of their cancer diagnoses. Because the exposure data (details below) were only available at the census tract level, we mapped each address location to the corresponding census tract.

To assess patients' environmental exposures, we used estimates from the NATA data provided by the United States Environmental Protection Agency. The NATA estimate is a modeled lifetime cancer risk from inhalation of nonasbestos air toxins, which takes into account emission source types, meteorological conditions, and human activity patterns.⁴³ The national percentile ranking was available at census tract level for the calendar years 1996, 1999, 2002, 2005, 2011, and 2014. We matched the time of census tracts lived with the closest NATA years available. For example, for a census tract lived before 1997, we used the 1996 NATA estimate, and if a census tract was lived in 2015, then we used the 2014 NATA data.

Relative Exposure (RE)

Patient's cancer risk from exposure to nonasbestos air toxics was measured by a relative exposure (RE) with the NYS average as the reference. It was calculated by dividing the NATA percentile ranking of an individual census tract by the average percentile ranking for NYS and subtracting 1. The reason for using the RE was to overcome the inherent limitation of the NATA data. That is, it does not allow for a direct comparison of the NATA estimates (including the metric of cancer risk) across years due to methods changes (eg, the number and types of pollutants and models used) over time.⁴³ As the NATA's lifetime cancer risk estimate is based on ambient levels of a mixture of air toxics, the RE served as a composite indicator of the overall exposure to nonasbestos air toxics, rather than a specific type of air pollutant.

RE Across Patient's Residential History

We calculated the yearly time-weighted-average (TWA) RE during the 15-year look-back window up to the year of cancer diagnosis. Patients who lived at a single address during an entire year were given the weight value of 1 for the yearly TWA measure. For patients who lived in multiple addresses in a year, the weights from these addresses summed to 1, with a higher weight assigned to addresses with a longer residential duration. To be consistent with the method used by other studies to calculate the duration of each address lived,^10-12,39,40 we used the first known date associated with a unique address as the starting time of this address, and used the start date of the next address in chronologically order as the end of the previous address. When we lacked any duration information for an address, we assumed a duration of 2.2 years, which was the median length of residency at an address among the original study population.¹⁶

Statistical Analyses

The main analysis was a 2-stage process. In the first stage, we identified the exposure trajectories and grouped patients with similar exposure histories into their own classes using a latent class linear mixed model. In the second stage, the identified trajectory class membership was used as the outcome variable in a logistic regression model to examine its associated patient-level characteristics.

We used a latent class linear mixed model to estimate the RE trajectories during the 15-year observation window. Linear mixed models are commonly used for longitudinal data with continuous outcomes (eg, RE in the current study) to account for within-subject correlations arise from repeated measures by incorporating random effects, which are assumed to be sampled from a single multivariate Gaussian distribution.^23,24,27 This homogenous assumption is relaxed in latent class linear models, which can incorporate non-normal random effects (eg, through a finite mixture of normal distributions rather than a single normal distribution).^23-27 In our model, RE was explained by time (a variable which indicated RE was at 1-, 2-, …, and 15-year prior to cancer diagnosis), squared time divided by 10 (for a potentially nonlinear time trend),²³ and age at cancer diagnosis, which was centered to 65 years (calculated as age at diagnosis minus 65). The random effects were grouped by unique participants. This model offered a way to account for the unobserved (latent) heterogeneity in the data and provided insights into how patients might have experienced different exposure trajectories, while the traditional linear mixed model assumed no presence of hidden subgroups. We tested 1-to 6-trajectory solutions, and chose the optimal number of trajectories based on commonly used measures, such as the Akaike information criterion (AIC; the lower the better), the Bayesian Information Criterion (BIC; the lower the better), entropy (the closer to 1 the better), the integrated complete-data likelihood (ICL; the lower the better), the number of patients in each trajectory group, and the class-membership posterior probabilities. In addition, we considered the optimal number of classes based on the stable “elbow” point of diminishing returns in model fit measures.⁴⁴

Once the trajectory class membership was established, we summarized descriptive statistics (eg, frequency, proportion, mean, standard deviation, median, and interquartile range) of the patient characteristics, most of which were collected at cancer diagnosis as a part of the routine cancer surveillance, including patient's age at cancer diagnosis, sex, race/ethnicity, cancer stage, and tobacco use status. We also summarized the characteristics related to patients' residential mobility, including the number of unique addresses lived, residential duration, and the Euclidean distance moved between addresses. We compared these patient characteristics by the trajectory group membership using χ² tests for categorical variables and Kruskal–Wallis tests for continuous variables. The same set of variables were used as explanatory variables in the logistic regression model. To minimize issues resulted from small cell sizes, we combined all patients whose race/ethnicity were not non-Hispanic White (NHW) into 1 aggregated group, “not NHW.” Thus, the not-NHW category included non-Hispanic Black, Hispanic, and patients in other race/ethnicity groups combined. This not-NHW group was then used as the reference to compare with the NHW group in the regression model. We also combined the persistent low exposure and decreased low exposure classes, since their REs were all below 0 (ie, lower than the NYS average), to avoid small cell size issues. We reported the adjusted odds ratio (aORs) and their 95% CIs. We implemented the trajectory modeling using the hlme function in the lcmm package²³ using R (version 4.0.2) with Rstudio (version 2022.02.03), and the logistic regression was implemented using SAS (version 9.4).

We also mapped the residential locations by the identified trajectory groups and assessed whether patients belonging to different trajectory groups tended to reside in different spatial clusters of high RE (hot spots) or low RE (cold spots) levels. The hot/cold spots were identified using a commonly used spatial epidemiological software, SaTScan (version 10.0.2).^37,45 Specifically, we first calculated the REs of cancer risk using all census tracts in the contiguous United States available in the NATA data (n = 72,079), similar to the RE estimates used for the mesothelioma sample. As such, the RE at each census tract was a relative measure in reference to the NYS average in a given year. We then used the space–time detection method with a normal probability model to identify clusters of high or low REs with the default settings, such as using a circular search window, a 999-random replication to obtain P values, and a Monte Carlo hypothesis testing approach.^37,45

Results

As shown in Table 1, the majority of the patients were NHW (89.6%), male (75.6%), and with a distant-stage tumor at the time of cancer diagnosis (65.0%). The mean age at diagnosis was 73.0 (SD, 11.9) years. On average, patients resided at 3 (SD, 2.3) addresses, with an average residential duration of 10.4 (SD, 8.4) years. The median distance moved among the entire study population was 8.2 (IQR, 1.6–133.2) miles. The time-weighted average REs had a median value of –0.16 (IQR, –0.43 to 0.18).

Table 1.

Characteristics of the Study Population Overall and by the 3 Exposure Trajectory Groups

Variables	Persistent low exposure (n = 245; 27%)	Decreased low exposure (n = 373; (1%)	Increased high exposure (n = 295; 32%)	Overall (n = 913)
Age (y)
Mean (SD)	72.8 (11.6)	73.2 (12.0)	73.0 (11.9)	73.0 (11.9)
Median (IQR)	74 (67–81)	76 (66–82)	75 (66–82)	75 (66–82)
Sex
Male	190 (77.6%)	280 (75.1%)	220 (74.6%)	690 (75.6%)
Female	55 (22.4%)	93 (24.9%)	75 (25.4%)	223 (24.4%)
Race/ethnicity*
Non-Hispanic Black	NR	NR	29 (9.8%)	37 (4.1%)
Non-Hispanic White	244 (99.6%)	347 (93.0%)	227 (76.9%)	818 (89.6%)
Hispanic	NR	13 (3.5%)	28 (9.5%)	41 (4.5%)
Other	NR	NR	11 (3.7%)	17 (1.9%)
Cancer stage
Local	18 (7.3%)	37 (9.9%)	32 (10.8%)	87 (9.5%)
Regional	45 (18.4%)	50 (13.4%)	50 (16.9%)	145 (15.9%)
Distant	158 (64.5%)	248 (66.5%)	187 ((63.4%)	593 (65.0%)
Unknown	24 (9.8%)	38 (10.2%)	26 (8.8%)	88 (9.6%)
Tobacco use
Current	26 (10.6%)	41 (11.0%)	32 (10.8%)	95 (10.4%)
Former	129 (52.7%)	178 (47.7%)	50 (16.9%)	446 (48.9%)
Never	69 (28.2%)	130 (34.9%)	187 (63.4%)	298 (32.6%)
Unknown	21 (8.6%)	24 (6.4%)	26 (8.8%)	74 (8.1%)
Number of addresses lived
Mean (SD)	3.1 (2.2)	3.0 (2.3)	3.1 (2.2)	3.0 (2.3)
Median (IQR)	3 (1–4)	2 (1–4)	3 (1–4)	2 (1–4)
Average residential duration (years)*
Mean (SD)	9.4 (7.4)	11.1 (9.2)	10.6 (8.2)	10.4 (8.4)
Median (IQR)	6.9 (4.2–12.3)	8.2 (5.2–13.3)	8.3 (4.8–13.6)	8.0 (4.7–13.2)
Average Euclidean distance (miles) moved between addresses lived
Mean (SD)	146.4 (262.9)	130.3 (282.6)	93.9 (185.9)	122.9 (250.3)
Median (IQR)	8.7 (0.9–202.0)	8.9 (1.9–125.7)	7.1 (1.5–88.2)	8.2 (1.6–133.2)
Time-weighted-average relative exposure*
Mean (SD)	–0.60 (0.21)	–0.18 (0.20)	0.27 (0.19)	–0.15 (0.39)
Median (IQR)	–0.61 (–0.75 to –0.46)	–0.20 (–0.31 to –0.04)	0.30 (0.15–0.40)	–0.16 (–0.43 to 0.18)

IQR, interquartile range (25th–75th percentile); NR, not reportable due to cell size suppression of n<11.

^*Patient characteristics did not differ across the trajectory groups, except for race/ethnicity (P < .0001), average residential duration (P = .03), and time-weighted relative exposure (RE) (P < .0001). The duration, distance moved, and RE associated with each address were averaged within individual patients, respectively, before deriving the summary statistics shown.

We selected a 3-trajectory model as the optimal solution from models with 1 to 6 latent trajectories (Table 2). When choosing the optimal number of trajectories, we considered a combination of factors, including the best values on multiple model fit measures, the elbow point of diminishing returns in the model fit, the interpretability of the latent trajectories, the posterior probabilities of the class memberships, and the adequate sample size of different trajectory groups. The mean posterior probabilities for trajectory classes 1 to 3 were 91%, 91%, and 96%, respectively, which meant that, on average, the probability of patients belonging to the corresponding trajectory group was above 90%. The posterior probabilities of being above the 80% threshold for trajectories 1 to 3 were 79%, 83%, and 92%, respectively, which meant that the proportion of patients not ambiguously classified into their corresponding trajectory groups was greater than 79%.

Table 2.

Measures Used to Identify the Optimal Trajectory Groups

A. Model fit measures
Number of classes	loglik	AIC	BIC	SABIC	entropy	ICL
1	899.084	–1776.170	–1723.180	–1758.120	1.000	–1723.180
2	1009.231	–1990.460	–1923.030	–1967.490	0.835	–3665.170
3	1116.696	–2199.390	–2117.510	–2171.500	0.834	–3804.880
4	1150.770	–2261.540	–2165.210	–2228.720	0.819	–3802.420
5	1178.634	–2311.270	–2200.480	–2273.530	0.808	–3797.400
6	1184.910	–2317.820	–2192.580	–2275.160	0.804	–3757.740

B. Mean of posterior probabilities in each class in the optimal model with 3 trajectory classes
	%class1 (PLE)	%class2 (DLE)	%class3 (IHE)
	PLE	DLE	IHE
class1 (PLE)	91	9	0
class2 (DLE)	6	91	3
class3 (IHE)	0	4	96

C. Posterior probabilities of being above a threshold (%) in the optimal model with 3 trajectory classes
Threshold	class1 (PLE)	class2 (DLE)	class3 (IHE)
prob>0.7	88.57	88.20	94.58
prob>0.8	78.78	82.84	92.20
prob>0.9	70.20	71.85	87.80

AIC, Akaike information criterion (the lower the better); BIC, Bayesian information criterion (the lower the better); DLE, decreased low exposure; entropy (the closer to 1 the better); ICL, integrated complete-data likelihood (the lower the better); IHE, increased high exposure; Loglik, maximum log-likelihood (the higher the better); PLE, persistent low exposure; SABIC, sample-size-adjusted BIC (the lower the better); prob, probability. Class1, class2, and class3 represent persistent low exposure, decreased low exposure, and increased high exposure, respectively.

We interpreted these 3 distinct trajectories of REs as persistent low exposure (n = 245; 27%), decreased low exposure (n = 373; 41%), and increased high exposure (n = 295; 32%) (Figure 1, Table 1). Unsurprisingly, RE values differed significantly by exposure trajectory groups (P < .0001), with the highest RE found in the increased high exposure group (Table 1, Figure 2). In addition, levels of RE by the trajectory groups in Figure 1 show that the lowest REs were among patients in the persistent low exposure group, while the highest REs were among patients in the increased high exposure group.

Figure 1.

Weighted Marginal Prediction of Exposure Trajectory Classes

We interpreted these 3 distinct trajectories of relative exposure as “persistent low exposure” for class 1, “decreased low exposure” for class 2, and “increased high exposure” for class 3.The dots in the figure show the fitted values of class-specific marginal and subject-specific mean relative exposure (RE) evolution over time. The line and the shaded band showed the observed class-specific mean RE evolutions with time and its 95% confidence bounds, respectively. The class-specific mean evolutions were weighted by the class-membership probabilities. The “low” and “high” designations in the naming of the trajectory groups reflected that the RE values of addresses in class 1 and class 2 were both below 0 (lower than the New York State average), while those in class 3 were above 0 (higher that the state average). The terms “increased” and “decreased” in the trajectory names reflected the trend over time.

Figure 2.

Bivariate Comparisons of Patient Characteristics (Continuous Variables) by the Exposure Trajectory Classes

Trajectory classes 1, 2, and 3 represent “persistent low exposure,” “decreased low exposure,” “increased high exposure,” respectively.

Patient characteristics did not differ across the 3 trajectory groups, except for race/ethnicity (P < .0001) and the average residential duration (P = .03; Table 1, Figure 2). The proportion of NHW patients was the highest in the persistent low exposure group (99.6%) and lowest in the increased high exposure group (76.9%). Consistent with the bivariate comparison result, the logistic regression model also showed a significant association between the race/ethnicity variable and the trajectory class membership (Table 3). NHW patients (vs the aggregated group of the remaining patients who were not NHW) had lower odds (aOR, 0.14; 95% CI, 0.09–0.23) of belonging to the increased high exposure trajectory group than in the reference group (ie, combined persistent low exposure and decreased low exposure trajectory groups).

Table 3.

Factors Associated with Belonging to the Increased High Exposure Trajectory Class Compared to the Persistent Low and Decreased Low Exposure Classes

Variable	Adjusted OR (95% CI)
Age	1.01 (0.995–1.02)
Sex (female vs male)	1.11 (0.78–1.58)
Race/ethnicity (NHW vs not NHW)	0.14 (0.09–0.23)
Cancer stage
Local vs distant	1.33 (0.81–2.17)
Regional vs distant	0.76 (0.44–1.30)
Other vs distant	1.12 (0.75–1.68)
Tobacco use
Former vs current	1.20 (0.71–2.02)
Never vs current	1.05 (0.61–1.80)
Other vs current	1.69 (0.84–3.40)
Number of tracts lived	1.06 (0.98–1.15)
Average duration lived	1.01 (0.99–1.03)
Average distance moved	0.998 (0.999–1.000)

NHW, non-Hispanic White; not NHW, individuals whose race/ethnicity are not non-Hispanic White (eg, Hispanic, non-Hispanic Black, Asian, Pacific Islander, and American Indian/Alaskan Native persons, as well as those of unknown of mixed races); OR, odds ratio. P < .0001 for race/ethnicity comparison; P = .01 for average distance moved. P > .05 for all the remaining variables.

Of 2,782 unique addresses, 2,317 (83.3%) were in NYS, spanning 1,493 census tracts. The proportion of New York City (NYC) addresses was 0.5%, 6.6%, and 74.8% for the trajectory classes 1, 2, and 3, respectively. Among the 818 NHW patients, 207 (25.3%) resided in NYC at one time, including 94 (11.5%) who resided exclusively in NYC within the 15 years prior to cancer diagnosis. In comparison, of the remaining 95 not-NHW patients, 71 (74.8%) resided in NYC at one time and 41 (43.1%) resided exclusively in NYC. These results were consistent with the distribution of patient residential locations and hot/cold spots of REs across the contiguous United States as shown in Figure 3a. Furthermore, NYS-focused distribution in Figure 3b shows that patients in the increased high exposure group tended to live in NYC, while patients in the persistent low exposure group tended to live outside of NYC.

Figure 3.

The Distribution of Patient Residential Locations (Dots) by the 3 Relative Exposure (RE) Trajectory Classes (Persistent Low, Decreased Low, and Increased High Exposure) in Relation to the Distribution of Hot/Cold Spots of High/Low RE Clusters Across the Continuous United States (a), and in New York State (b)

Hot/cold spot RE clusters were identified using a SaTScan space-time analysis based on data from all census tracts (n = 72,079) in the National Air Toxics Assessment (NATA) for the contiguous United States. Details of the hot/cold spots were shown in Table 4. To protect confidentiality, points in the map are not shown at the exact locations.

Also shown in Figure 3, the SaTScan analysis found a total of 7 significant clusters (all P < .001), which included 4 high-RE clusters (ie, hot spots) and 3 low-RE clusters (ie, cold spots). One of the high-RE clusters centered in NYC (40.774858 N, 73.980666 W, cluster III), with a radius of 24.18 kilometers. The mean RE within this particular hot spot was 0.61, while areas outside of NYC had a mean RE of -0.19 (Table 4). The mean RE of this NYC hot spot was also higher than the mean REs found in the other 2 hot spots (0.25 and 0.32 in clusters II and III, respectively). On the other hand, a large portion of NYS excluding NYC tended to be covered by 2 low-RE clusters, one (cluster IV) over the Great Lakes region and the other (cluster VI) over the New England region (Figure 3, Table 4). Therefore, areas within NYC tended to have a higher air toxic exposure than the non-NYC area in the state.

Table 4.

Details of the 7 Spatial Clusters of Relative Exposure (RE) Identified from the SaTScan Analysis Based on All Census Tract in the National Air Toxics Assessment (NATA) Data (n = 72,079) for the Contiguous United States

	Cluster type	General regions covered	Cluster centroid	Cluster radius (km)	Mean RE inside the cluster	Mean RE outside of the cluster	Time frame
Cluster I	High	Southeast region	31.667244 N, 88.650140 W	842.20	0.25	–0.23	2011/1/1 to 2014/12/31
Cluster II	High	West region	32.664751 N, 117.147814 W	528.22	0.32	–0.20	2011/1/1 to 2014/12/31
Cluster III	High	New York City area	40.774858 N, 73.980666 W	24.18	0.61	–0.19	2011/1/1 to 2014/12/31
Cluster IV	Low	Great Lakes region	44.042897 N, 82.941870 W	443.61	–0.52	–0.16	2011/1/1 to 2014/12/31
Cluster V	Low	Northwest region	45.173773 N, 108.711004 W	1054.14	–0.61	–0.17	1999/1/1 to 2005/12/31
Cluster VI	Low	New England region	44.941764 N, 72.219544 W	450.32	–0.52	–0.17	2011/1/1 to 2014/12/31
Cluster VII	High	Pittsburg area	40.417762 N, 79.892146 W	21.38	0.56	–0.18	2011/1/1 to 2014/12/31

RE at each census tract was a relative measure in reference to the New York State average in 1996, 1999, 2002, 2005, 2011, and 2014, which were the years of corresponding available NATA data.

Table 5 shows the proportion of addresses within each of the 3 RE trajectory groups by the hot/cold spot RE clusters identified from the SaTScan analysis. At the national level, 67.2% of the addresses in the increased high exposure group were located within hot-spot clusters. In contrast, 71.0% of the addresses in the persistent low exposure group were covered by cold-spot clusters. Within NYS, 74.6% of the increased high exposure addresses were in the NYC hot spot, while 82.6% of the persistent low exposure addresses were within cold spots.

Table 5.

Proportions of Addresses from the 3 Relative Exposure (RE) Trajectory Groups by Hot/Cold Spot RE Clusters

	Trajectory groups	Overall (%)	Cold spots (%)	Hot spots (%)	Neither (%)
All addresses within the contiguous United States	Increased high exposure	33.3	7.0	67.2	25.8
	Decreased low exposure	39.4	52.2	10.1	37.6
	Persistent low exposure	27.4	71.0	7.9	21.1
All addresses within New York State	Increased high exposure	33.5	6.5	74.6	18.9
	Decreased low exposure	39.8	59.6	5.1	35.4
	Persistent low exposure	26.7	82.6	0.5	16.9

Hot/cold spot RE clusters were based on all census tracts (n=72,079) in the National Air Toxics Assessment (NATA) data for the contiguous United States. Details of the hot/cold spots were shown in Table 4.

Discussion

When analyzing mesothelioma patients' residential histories spanning 15 years prior to their cancer diagnoses, we found that the trajectory pattern of exposures to nonasbestos air toxics was not homogeneous. In addition, patients' residential histories, their related exposures, and exposure trajectories differed by race and ethnicity. The identified nonasbestos exposure patterns were not intended for studying the disease etiology of mesothelioma. Rather, our findings provide some new insights into the heterogeneity of environmental exposures among mesothelioma patients other than the commonly known asbestos exposure patterns. More importantly, this study demonstrated an innovative approach that can be used to study cancer types that do not have a clear etiology and may have a higher risk from environmental exposures. This method can also be applied to examine exposure heterogeneity in social risks, such as low SES, and their impact on patient outcomes across the cancer continuum.

We identified 3 clear trajectory patterns of exposure histories to nonasbestos air toxics: persistent low exposure, decreased low exposure, and increased high exposure. They corresponded to lateral, downward, and upward changes of exposures over time. In addition, we found patients' race and ethnicity differed across the 3 trajectory groups, with NHW patients being less likely to be in the increased high exposure group than patients of other races/ethnicities. To further elucidate the identified heterogeneity, we compared our mesothelioma patients' residential locations with the hot/cold spots of REs identified using the national NATA data. We found that patients within the persistent low exposure class tended to live outside of NYC, the largest metropolitan urban city in the United States, which also tends to have a higher air toxic exposure than the non-NYC area in NYS. The opposite was seen for patients belonging to the increased high exposure group. These results are consistent with the general demographic distributions of NHW and not-NHW groups, where a higher proportion of not-NHW individuals tend to concentrate in NYC than in the rest of NYS. We also found that, compared to patients in the other 2 trajectory groups, patients in the persistent low exposure trajectory group had a significantly shorter residential duration, suggesting that these patients may move more frequently. However, comparisons of patients across the 3 trajectory groups shows that these patients were similar in other characteristics, including the number of unique addresses lived. Taken together, the observed differences in the proportion of race/ethnicity and residential durations by exposure trajectory groups are likely reflecting the differences in patients' residential mobility. For instance, patients in the persistent low exposure group tend to have a lateral mobility (ie, moving among places with similar levels of low exposure levels to nonasbestos air toxics). While investigating the reasons of moving is beyond the scope of the current paper, future studies should examine factors (eg, family, job, housing, SES, and health related factors) associated with the moves that occurred both before and after cancer diagnosis, as well as how these moves impact patient's cancer care delivery and health outcomes.

The current study also suggests that the extent of exposure misclassification may vary by trajectory groups when using the exposure at cancer diagnosis for past exposures. For example, our mesothelioma patients in the persistent low exposure group experienced a lower variability in their exposure levels than those in the increased high exposure and decreased low exposure groups. Consequently, using the exposure level at cancer diagnosis and assuming a constant exposure history may be more reasonable for patients in the persistent low exposure group than patients in the other 2 groups. Nevertheless, regardless of the trajectory assignment, all 3 groups showed some variations during the 15-year look-back window and thus all patients would be susceptible to exposure misclassification. In particular, using the snapshot of exposure level at cancer diagnosis is likely to overestimate patients' past exposures for those in the increased high exposure group and underestimate them for patients in the other 2 trajectory groups.

Our previous study of mesothelioma patients with varied residential history lengths, which assumed no heterogeneity in exposure trajectories among patients, showed a difference of up to 15 percentage points in the yearly RE associated with air toxics between earlier addresses and the address at cancer diagnosis.¹⁶ The method we used in the previous study was a traditional general estimated equation model, which is commonly used for longitudinal data, such as ours where the yearly RE estimate was available for the same mesothelioma patient over multiple time points during the 15-year period prior to cancer diagnosis. The focus there was to capture the average RE variation over time assuming a homogeneous RE profile among all patients. In the current study, we used a latent class mixed modeling approach, which belongs to a family of latent process methods that have been increasingly used to capture the heterogeneity in treatment responses and behavioral development in clinical and psychosocial studies.^23-26 Here, we focused on the relationship between REs and the underlying latent trend among subgroups. This method allowed us to capture the variability in the shape and level of REs across trajectory groups. The finding of 3 class trajectories over 1 class trajectory suggests that individuals may follow distinctive exposure trajectories or belong to different subgroups rather than all belonged to 1 homogeneous group.

Expanding from our previous work, the current study suggests that there exist heterogeneous exposure misclassification patterns tied to different exposure trajectories as well. These findings may have important implications in examining cancer risks when comparing cancer patients and their noncancer counterparts, such as those in a case-control or a cohort study. For example, if more cases are from an increased high exposure trajectory group while more controls are from a decreased low exposure or a persistent low exposure trajectory group, then the relative risk or odds ratio based on the exposure at cancer diagnosis may be overestimated. On the other hand, if more cases were from a decreased low exposure group or a persistent low exposure group while more controls are from an increased high exposure trajectory group, then the relative outcome–exposure association based on the snapshot exposure at cancer diagnosis would be underestimated. Therefore, future studies should consider the heterogeneity in exposure trajectories when estimating exposure-outcome associations.

The study has a few limitations. First, our findings may be unique to the mesothelioma patients studied, as these patients were likely to have different occupational, socioeconomic, and demographic factors, as well as residential mobility patterns from patients diagnosed with other types of cancer. For example, the predominant majority of mesothelioma patients in our study were NHW. This also contributed to the uncommon magnitude of aOR and their relatively wide 95% CIs seen in the regression model results. In addition, patients in NYS may also differ from patients in other states, as NYS is a large populous state with dynamic migration patterns. For example, a recent study on all cancer patients from 11 registries (representing 11 states) in the NCI's SEER program showed that cancer patients in NYS had the highest state-to-state move rates within the most recent 5-year period.¹³ Future examinations using different patient populations, particularly those with cancer types that are more germane to nonasbestos air toxics, are needed. Second, our exposure estimate was based on the NATA data at the census tract level for 6 specific years, which did not consider border (or overflow) effects. Incorporating environmental exposure data with refined geographic and time resolutions and applying spatial disag-gregation or downscaling methods should improve the quality of exposure estimates. Finally, the patient residential history included may be incomplete and the missingness of the address information may differ by patients characteristics, including race and ethnicity, as previous studies using LexisNexis have shown.^10,14,39 On the other hand, we were able to identify the patient residential history information from 3 data sources, which may have mitigated this problem to a certain degree, though the cancer registry data only contained patients' address information at the time of cancer diagnosis, and the SPARCS data were only for those who had inpatient admissions in NYS during the study period. Additional analysis using those with a 20-year residential history also yielded a 3-class solution and supported the main finding that NHW patients were more likely to be in the persistent low exposure and decreased low exposure groups (data not shown). Finally, while we were able to identify 3 trajectory groups in the first stage of the analysis, the uncertainty of the class membership was not incorporated in the second stage of the analysis, which warrants further exploration with more advanced statistical models. The current model also assumed a linear relationship between the outcome (RE) and a Gaussian latent variable, which may be a strong assumption.⁴⁶ Future studies should also explore the differences between linear and nonlinear latent models in estimating trajectory groups and the impact of different group membership assignments in the second stage analysis. Along the same vein, the hot/cold spots were identified using a circular search window (default settings and computationally efficient), while the true hot/cold spots may be irregularly shaped.

Conclusions

As residential history information becomes more and more readily available, there is a growing interest in using this information to facilitate cancer surveillance and epidemiological studies. We quantified the heterogeneous experiences of cancer risks associated with exposures to ambient air toxics among a cohort of NYS mesothelioma patients, and found that patient race and ethnicity differed across the identified exposure trajectories. Comparisons of the patient residential locations to the spatiotemporal hot/cold spots of exposures, identified based on the NATA data, revealed that the observed differential trajectory patterns were likely a reflection of differences in patients' residential mobility prior to their cancer diagnoses. We used mesothelioma patients for illustrative purposes, acknowledging that the method was not developed for the purposes of identifying the etiology of mesothelioma. Overall, we demonstrated an innovative method of combining latent class mixed modeling and spatiotemporal scan statistics. This method can be applied to all cancer types to understand patient exposure history to pollutants and social risks, as well as their relationships with cancer incidence, treatment, and survival.