Decomposing the Variance: The Unique and Shared Associations of Fine and Ultrafine Particulate Matter Exposed during Pregnancy with Child Autism Spectrum Disorder

Abstract

While fine particulate matter (${\text{PM}}_{2.5}$) has been associated with autism spectrum disorder (ASD), few studies focused on ultrafine particles (${\text{PM}}_{0.1}$). Given that fine and ultrafine particles can be highly correlated due to shared emission sources, challenges remain to distinguish their health effects. In a retrospective cohort of 318,371 mother-child pairs (4,549 ASD cases before age 5) in Southern California, pregnancy average ${\text{PM}}_{2.5}$ and ${\text{PM}}_{0.1}$ were estimated using a California-based chemical transport model and assigned to residential addresses. The correlation between ${\text{PM}}_{2.5}$ and ${\text{PM}}_{0.1}$ was 0.87. We applied a two-step variance decomposition approach: first, decomposing ${\text{PM}}_{2.5}$ and ${\text{PM}}_{0.1}$ into the shared and unique variances using ordinary least squares linear regression (OLS) and Deming regression considering errors in both exposures; then assessing associations between decomposed ${\text{PM}}_{2.5}$ and ${\text{PM}}_{0.1}$ and ASD using Cox proportional hazard models adjusted for covariates. Prenatal ${\text{PM}}_{2.5}$ and ${\text{PM}}_{0.1}$ each was associated with increased ASD risk. OLS decomposition showed that associations were driven mainly by their shared variance, not by their unique variance. Results from Deming regression considering assumptions of measurement errors were consistent with those from OLS. This decomposition approach has potential to disentangle health effects of correlated exposures, such as ${\text{PM}}_{2.5}$ and ${\text{PM}}_{0.1}$ from common emissions sources.

Graphical Abstract

Introduction

Autism spectrum disorder (ASD) is a complex set of developmental disorders characterized by deficits in social interactions and communication, as well as the presence of restricted, repetitive, and stereotyped patterns of behaviors ¹. A recent review reported a global autism prevalence of approximately 1 in 100 children ². The estimated prevalence of ASD in the United States has shown a significant increase from 0.66% in 2002 to 2.78% in 2020 ^3,4. ASD imposes considerable lifelong emotional and social burden on affected children ⁵, their families ⁶, and economic burdens on society ⁷.

A growing number of studies has shown associations between prenatal air pollution exposures and ASD in offspring, with the most consistent findings for particulate matter (PM) ^8–11. PM is emitted directly to the atmosphere from a variety of sources, including vehicles, industrial sources, and biomass combustion. PM can also form in the atmosphere as a product of chemical reactions ¹². Due to the dynamic formation processes which involve nucleation, condensation, and coagulation, PM exhibits varying aerodynamic diameters broadly defined as coarse (with aerodynamic diameter < 10 μm; ${\text{PM}}_{10}$), fine (with aerodynamic diameter < 2.5 μm; ${\text{PM}}_{2.5}$) and ultrafine particles (with aerodynamic diameter < 0.1 μm; ${\text{PM}}_{0.1}$)¹². These differences in size give rise to distinct aerosol behaviors and toxicity profiles¹³. The shared variance between PM of different aerodynamic sizes may indicate common emission sources such as traffic exhaust and biomass burning ¹⁴. The unique variance may indicate distinct atmospheric processes. ${\text{PM}}_{0.1}$ can form in ambient air through nucleation, followed by coagulation and condensation into larger particles ¹⁵. Secondary aerosols like sulfate and nitrate, which are typically larger than 0.1 μm ¹⁶, may contribute to the unique variance of ${\text{PM}}_{2.5}$. Therefore, distinguishing the shared and unique variance of PM of different sizes can provide insights into the different mechanisms or components that may impact human health.

Recent toxicological and epidemiological studies reported that ambient ${\text{PM}}_{0.1}$ may have exerted greater toxic effects on health than coarse particles^17–19. The small size of ${\text{PM}}_{0.1}$ enables it to penetrate deep into the lungs and enter the systemic circulation, which may induce inflammation and oxidative stress¹⁷. Moreover, ${\text{PM}}_{0.1}$ may cross biological barriers²⁰, such as placenta²¹ and blood-brain barrier²², and enter the fetal bloodstream and developing fetal brain²¹. Animal studies have also provided evidence that PM0.1 can be a source of neurotoxicity that can alter microglia stimulation and impact neuronal activity and synaptic plasticity of developing brain ^23–25. Therefore, prenatal ${\text{PM}}_{0.1}$ exposure may have direct adverse health effects on fetal neurodevelopment. Since ${\text{PM}}_{0.1}$ is not regulated as a criteria pollutant and the modeling techniques for ${\text{PM}}_{0.1}$ exposures have only recently been developed, few epidemiological studies have examined the health effects of ${\text{PM}}_{0.1}$ during pregnancy. A recent study reported that prenatal ${\text{PM}}_{0.1}$ exposure was associated with asthma development in children²⁶. Specific to neurodevelopmental disorders such as ASD, a study from our group showed that aircraft emitted PM, primarily composed of ${\text{PM}}_{0.1}$, was associated with ASD in offspring²⁷. A recent case-control study has reported the association between increased ${\text{PM}}_{0.1}$ exposure in the second year of life and ASD development among children²⁸.

However, previous studies often treated ${\text{PM}}_{0.1}$ or ${\text{PM}}_{2.5}$ as single exposures and examined their isolated health associations, rather than considering the real world scenario where children are exposed to both ${\text{PM}}_{2.5}$ and ${\text{PM}}_{0.1}$, which can be highly correlated because of shared sources such as traffic²⁹. Therefore, it remains a challenge to distinguish their associations with health outcomes. The collinearity issue and inflated standard errors may present in the co-adjusted model with two highly correlated exposures³⁰. Therefore, we proposed a two-step variance decomposition approach using ordinary least squares (OLS) linear regression and Deming regression considering measurement errors in both exposures^31,32 as the first step to decompose two correlated ${\text{PM}}_{2.5}$ and ${\text{PM}}_{0.1}$ exposures into unique and shared variance. In the second step, we differentiated the associations of the health outcome with the shared variance and the unique variance that remained in their residuals. We leveraged a validated chemical transport model (CTM) ^14,33,34 for ${\text{PM}}_{2.5}$ and ${\text{PM}}_{0.1}$ exposures and a large retrospective birth cohort in Southern California to examine the associations between ASD in children with the shared and unique variance average ${\text{PM}}_{2.5}$ and ${\text{PM}}_{0.1}$ exposures during pregnancy.

Method

Study population

This study utilized a population-based retrospective birth cohort that included mothers with singleton deliveries (n=370,723) at Kaiser Permanente Southern California (KPSC) hospitals between January 1, 2001 and December 31, 2014. Information related to the mothers and children, including maternal residential addresses history and medical conditions, were extracted from high-quality integrated electronic medical records (EMR) maintained by KPSC. A total of 52,352 births were excluded due to (1) missing key covariates of gender, maternal race and ethnicity, and age at delivery (n=666); (2) maternal age <15 or >55 at delivery (n=159), an unusual age of pregnancy and high potential risk to children for this age of pregnancy; (3) incomplete maternal residential address during pregnancy or geocodes not suitable for air pollution exposure assignment (n=51,527) given that prenatal air pollution is our exposure of interest. The final data analysis included 318,371 mother-child pairs with complete data on residential estimates of ${\text{PM}}_{2.5}$ and ${\text{PM}}_{0.1}$ exposures (eFigure 1). Both KPSC and the University of Southern California Institutional Review Boards approved this study with waiver of individual subject consent.

ASD ascertainment

The outcome was ASD diagnosis before age 5. Children were followed from birth through EMR until clinical diagnosis of ASD, loss to follow-up, or age 5, whichever came first, as described previously ^35,36. The presence or absence of ASD in children was ascertained based on at least two clinical diagnoses using International Classification of Diseases, Ninth Revision (ICD- 9) codes 299.0, 299.1, 299.8, 299.9 from the EMR records before October 1, 2015 (the date of KPSC implementation of ICD-10 codes) and subsequently ICD-10 codes F84.0, F84.5, F84.9 F84.0, F84.3, F84.5, F84.8, F84.9. This methodology for ascertaining ASD diagnoses has been previously validated in the KPSC member population, with a positive predictive value of 87%³⁵, and has been employed in previous studies^36,37.

Air pollution exposure assessment

This analysis utilized the ${\text{PM}}_{0.1}$ and ${\text{PM}}_{2.5}$ mass concentrations with 4-km grid resolution generated by the UCD/CIT (University of California Davis/California Institute of Technology) Source Oriented chemical transport model (CTM). The UCD/CIT SO-CTM uses meteorological fields generated by the Weather Research and Forecast (WRF) model and geographically resolved emissions estimates from the California Air Resources Board (CARB), the Global Fire Emissions Database (GFED), and the Model of Emissions of Gases and Aerosols from Nature (MEGAN) to predict airborne PM concentrations. The model calculations track the size-resolved mass concentrations of the PM constituents in particle diameters ranging from 0.01 to 10 μm^14,33,34. The CTM calculations are based on fundamental equations of chemistry and physics that represent the production and destruction of pollutants in the atmosphere. The inputs to the CTM include detailed emissions inventories, meteorological fields, geographic fields, and chemical reaction mechanisms. Further details of the CTM used in the current study are provided elsewhere ²⁹. Concentrations predicted by the UCD/CIT SO-CTM were evaluated against ambient measurements at all available locations and times in previous studies. Predicted concentrations of ${\text{PM}}_{2.5}$ mass, ${\text{PM}}_{2.5}$ chemical components, and ${\text{PM}}_{0.1}$ mass exhibited excellent agreement with measurements (correlation coefficient R= 0.9 for ${\text{PM}}_{2.5}$ mass and 0.92 for ${\text{PM}}_{0.1}$ mass) ^14,33,34. Average exposures to ${\text{PM}}_{2.5}$ and ${\text{PM}}_{0.1}$ were assigned to maternal addresses during pregnancy. Exposures were time-weighted to account for changes of residential addresses during pregnancy. Because recent research found that postnatal air pollution exposure confounded ASD association with prenatal exposure ^28,38,39, we also assigned 1-year postnatal average ${\text{PM}}_{2.5}$ and ${\text{PM}}_{0.1}$ from residential addresses to assess potential confounding effects.

Covariates

We selected covariates a priori based on existing knowledge and past literature on air pollution exposures and ASD^11,27. Covariates included were child sex, maternal race/ethnicity, maternal age at delivery, parity, maternal education, maternal history of comorbidity [>=1 diagnosis of heart, lung, kidney, or liver disease; cancer], neighborhood disadvantage index (which was associated with ASD in this cohort ⁴⁰), birth year, and an indicator variable for season at conception (dry from April-October; wet from November-March). Birth year was included as a non-linear term with a penalized spline of 4 degrees of freedom based on Akaike Information Criterion (AIC).

Statistical Analysis

We applied Cox proportional hazards models adjusted for covariates to estimate hazard ratios (HRs) and 95% confidence intervals (CIs) for associations of ASD with exposure to pregnancy average ${\text{PM}}_{2.5}$ and ${\text{PM}}_{0.1}$. Separate models were fitted for ${\text{PM}}_{2.5}$ and ${\text{PM}}_{0.1}$, the HRs were scaled to their one standard deviation (SD) increase. Linearity of associations of ASD with ${\text{PM}}_{2.5}$ and ${\text{PM}}_{0.1}$ was examined using quintiles and no significant deviations from linearity were observed.

To distinguish the associations of ASD with the unique and shared variance of ${\text{PM}}_{2.5}$ and ${\text{PM}}_{0.1}$, we applied a two-step variance decomposition approach. Given that ${\text{PM}}_{2.5}$ and ${\text{PM}}_{0.1}$ have different measurement scales, we first scaled them by their SD for comparability. In Step 1 (variance decomposition), we fit two separate OLS linear regression models (equation 1–2):

$$P{M}_{2.5}={\alpha }_0+{\alpha }_{1}P{M}_{0.1}+e_{2.5}$$ (1)

$$P{M}_{0.1}={\beta }_0+{\beta }_{1}P{M}_{2.5}+e_{0.1}$$ (2)

to decompose ${\text{PM}}_{2.5}$ into predicted ${\text{PM}}_{2.5}$, $\left({\widehat{PM}}_{2.5}={\widehat{\alpha }}_0+{\widehat{\alpha }}_{1}P{M}_{0.1}\right)$ which represents the variance explained by ${\text{PM}}_{0.1}$, and ${\text{PM}}_{2.5}$ residuals $\left({\widehat{e}}_{2.5}\right)$ which contain the variance unexplained by ${\text{PM}}_{0.1}$. Similarly, ${\text{PM}}_{0.1}$ was decomposed into predicted ${\text{PM}}_{0.1}$, $\left({\widehat{PM}}_{0.1}={\widehat{\beta }}_0+{\widehat{\beta }}_{1}P{M}_{2.5}\right)$) which represents the variance explained by ${\text{PM}}_{2.5}$ and ${\text{PM}}_{0.1}$ residuals $\left({\widehat{e}}_{0.1}\right)$ which contain the variance unexplained by ${\text{PM}}_{2.5}$.

In Step 2 (outcome model estimation), we chose Cox regression modeling, which handles censoring in the birth cohort study design ⁴¹, as the outcome modeling framework to evaluate the association between decomposed prenatal PM exposures and ASD. We fit two separate Cox regression models adjusted for covariates: in Model 1, we included both ${\widehat{PM}}_{2.5}$ and ${\widehat{e}}_{2.5}$; in Model 2, we included both ${\widehat{PM}}_{0.1}$ and ${\widehat{e}}_{0.1}$. The coefficients for ${\widehat{PM}}_{2.5}$ and ${\widehat{PM}}_{0.1}$, respectively in Models 1 and 2 represent the association of the shared variance with the health outcome, while the coefficients for ${\widehat{e}}_{2.5}$ and ${\widehat{e}}_{0.1}$ refer to the associations between the unique variances of ${\text{PM}}_{2.5}$ and ${\text{PM}}_{0.1}$ with the health outcome.

As an alternative approach in Step 1, the variance decomposition, we also employed Deming regression^31,32, which accounts for the measurement errors in both the dependent and independent variables (shown in equation 3–4).

$$P{M}_{2.5}={\widehat{PM}}_{2.5}+{\epsilon }_{2.5}$$ (3)

$$P{M}_{0.1}={\widehat{PM}}_{0.1}+{\epsilon }_{0.1}$$ (4)

The Deming regression is generated based on the estimates of the expected (or predicted) values of ${\widehat{PM}}_{2.5}$ and ${\widehat{PM}}_{0.1}$ (equation 5)

$${\widehat{PM}}_{2.5}={\gamma }_0+{\gamma }_1{\widehat{PM}}_{0.1}$$ (5)

while assuming that the ratio between the errors variance ($\lambda$; equation 6) remains constant.

$$\lambda ={\sigma }_{{\epsilon }_{2,5}}^2/{\sigma }_{{\epsilon }_{0.1}}^2$$ (6)

Unlike OLS regression where we fitted two separate models, based on a single Deming regression model of ${\text{PM}}_{2.5}\sim {\text{PM}}_{0.1}$, ${\text{PM}}_{2.5}$ was decomposed into predicted ${\text{PM}}_{2.5}$ $\left({\widehat{PM}}_{2.5}\right)$ and residuals of ${\text{PM}}_{2.5}$ $\left({\widehat{\epsilon }}_{2.5}\right)$ and ${\text{PM}}_{0.1}$ was decomposed into predicted ${\text{PM}}_{0.1}$ $\left({\widehat{PM}}_{0.1}\right)$ and residuals of ${\text{PM}}_{0.1}$ $\left({\widehat{\epsilon }}_{0.1}\right)$. The Deming regression model of ${\text{PM}}_{0.1}\sim {\text{PM}}_{2.5}$ gives equivalent results. Details of Deming regression are provided in the eMethods under the Deming regression subsection.

In Deming regression, we refer to the ${\widehat{PM}}_{2.5}$ (or ${\widehat{PM}}_{0.1}$) as “shared variance”, and the residuals of ${\text{PM}}_{2.5}$ $\left({\widehat{\epsilon }}_{2.5}\right)$ and residuals of ${\text{PM}}_{0.1}$ $\left({\widehat{\epsilon }}_{0.1}\right)$ as “unique variance”. Given that Deming regression requires a hyperparameter specifying the ratio of measurement error variances $(\lambda )$, we assessed the sensitivity to this hyperparameter by a varying set of values from 0.5 to 2 with 0.1 increment. In Step 2, outcome model estimation, similar to the OLS approach, we fitted two separate Cox regression models: one with predicted ${\widehat{PM}}_{2.5}$ and residuals of ${\text{PM}}_{2.5}$ $\left({\widehat{\epsilon }}_{2.5}\right)$ and the other one with predicted ${\widehat{PM}}_{0.1}$ and residuals of ${\text{PM}}_{0.1}$ $\left({\widehat{\epsilon }}_{0.1}\right)$

To assess the robustness of the results, we conducted three sensitivity analyses: (1) Since ${\text{PM}}_{0.1}$ is a subset of ${\text{PM}}_{2.5}$, we conducted analysis by subtracting the ${\text{PM}}_{0.1}$ mass from ${\text{PM}}_{2.5}$ mass $\left({\text{PM}}_{0.1-2.5}={\text{PM}}_{2.5}-{\text{PM}}_{0.1}\right)$ and examined the associations of shared and unique variance between ${\text{PM}}_{0.1}$ and ${\text{PM}}_{0.1\text{-}2.5}$ during pregnancy and ASD; (2) Heteroscedasticity in residuals of regression models, i.e, the variance of residuals varies with the level of the predicted value, can lead to biased estimates and confidence intervals. To address possible bias due to heteroscedasticity in residuals, we used weighted Deming regression ⁴², with weights the inverse of the variances of the residual for each subject; (3) To address the potential confounding by postnatal PM exposures, the Cox regression models for ASD with OLS and Deming regression decomposed pregnancy average ${\text{PM}}_{2.5}$ and ${\text{PM}}_{0.1}$ were further adjusted for 1-year postnatal average ${\text{PM}}_{2.5}$ or ${\text{PM}}_{0.1}$, respectively.

Two-sided statistical tests were used $(\alpha =0.05)$ and 95% confidence intervals (CIs) were reported. Deming regression was implemented using mcr library⁴³. All analyses were performed using R Statistical Software (version 4.2)⁴⁴. R codes are available at https://github.com/lindayu0408/Deming-regression.

Results

During follow-up, 4,549 (1.4%) children were diagnosed with ASD by age 5 (Table 1). Among children with ASD diagnoses, 3,695 (81.2%) were boys. Mothers of children with ASD were slightly older at delivery (31.28 years, SD=5.71) than mothers of children without ASD (30.18 years, SD=5.79). Compared to children without ASD, children with ASD had greater proportions of nulliparous mothers and mothers with a history of comorbidities.

Table 1.

Characteristics of children, with and without ASD diagnosis

Characteristics	Children, No. (%) or mean [SD]
	Overall (n = 318,371)	With ASD (n= 4,549)	Without ASD (n= 313,822)
Sex = Male (%)	162,985 (51.2)	3,695 (81.2)	159,290 (50.8)
Maternal age at delivery, mean [SD], years Parity; N (%)	30.20 (5.79)	31.28 (5.71)	30.19 (5.79)
0	111,854 (35.1)	1,843 (40.5)	110,011 (35.1)
1	104,428 (32.8)	1,490 (32.8)	102,938 (32.8)
>=2	84,091 (26.4)	901 (19.8)	83,190 (26.5)
Unknown	17,998 (5.7)	315 (6.9)	17,683 (5.6)
Maternal Education; N(%)
High school or lower	112,045 (35.2)	1,335 (29.3)	110,710 (35.3)
Some college	94,417 (29.7)	1,472 (32.4)	92,945 (29.6)
College graduate or higher	108,871 (34.2)	1,708 (37.5)	107,163 (34.1)
Unknown	3,038 (1.0)	34 (0.7)	3,004 (1.0)
Race/ethnicity; N (%)
Non-Hispanic white	80,909 (25.4)	953 (20.9)	79,956 (25.5)
Non-Hispanic black	29,752 (9.3)	446 (9.8)	29,306 (9.3)
Hispanic	161,318 (50.7)	2,299 (50.5)	159,019 (50.7)
Asian/Pacific Islander	39,854 (12.5)	739 (16.2)	39,115 (12.5)
Other	6,538 (2.1)	112 (2.5)	6,426 (2.0)
Any history of maternal comorbiditiesa; N (%)	46,647 (14.7)	838 (18.4)	45,809 (14.6)
Neighborhood disadvantage index mean [SD]b	0.19 (1.85)	0.16 (1.88)	0.19 (1.85)
Year of birth; N (%)
2001–2004	78,236 (24.6)	817 (18.0)	77,419 (24.7)
2005–2009	111,064 (34.9)	1,307 (28.7)	109,757 (35.0)
2010–2014	129,071 (40.5)	2,425 (53.3)	126,646 (40.4)
Pregnancy average ${\text{PM}}_{2.5}$ (μg/m3)	14.17 (4.15)	13.43 (4.00)	14.18 (4.15)
Pregnancy average ${\text{PM}}_{0.1}$ (μg/m3)	1.10 (0.47)	1.03 (0.46)	1.10 (0.47)

^*Abbreviations: SD, standard deviation.

^a>=1 diagnosis of heart, lung, kidney, or liver disease; cancer.

^bCensus tract level neighborhood disadvantage index. Higher values represent more disadvantaged neighborhoods

The levels of ${\text{PM}}_{2.5}$ and ${\text{PM}}_{0.1}$ decreased over time (eFigure 2). The average exposure of ${\text{PM}}_{2.5}$ and ${\text{PM}}_{0.1}$ during pregnancy were 14.17 μg/m³ (SD = 4.15) and 1.10 μg/m³ (SD = 0.47), respectively. Although pregnancy average ${\text{PM}}_{0.1}$ accounts for only 7.5% mass of ${\text{PM}}_{2.5}$ (ranging from 2.1% to 19.1% over participants in the study cohort), the two exposures were highly correlated (r=0.87) (eTable 1).

Our analysis of single pollutant pregnancy average ${\text{PM}}_{2.5}$ and ${\text{PM}}_{0.1}$ revealed that each was associated with ASD diagnosis before age 5 with HRs of 1.08 (95% CI 1.02, 1.14, per SD=4.15 μg/m³ increase for ${\text{PM}}_{2.5}$) and 1.07 (95% CI 1.02, 1.12, per SD=0.47 μg/m³ increase for ${\text{PM}}_{0.1}$), respectively (Table 2). The OLS linear regression models for variance decomposition showed that 76% of the variance in pregnancy average ${\text{PM}}_{2.5}$ was explained by pregnancy average ${\text{PM}}_{0.1}$ and vice versa (eTable 2). Outcome models with OLS decomposed variance (Table 2) showed that only the predicted ${\text{PM}}_{2.5}$ (${\widehat{PM}}_{2.5}$; the variance explained by ${\text{PM}}_{0.1}$) or predicted ${\text{PM}}_{0.1}$ (${\widehat{PM}}_{0.1}$; the variance explained by ${\text{PM}}_{2.5}$) were significantly associated with higher risk of ASD diagnosis with HRs of 1.09 (95% CI 1.03, 1.16, per SD=4.15 μg/m³ increase for predicted ${\text{PM}}_{2.5}$) and 1.09 (95% CI 1.02, 1.16, per SD=0.47 μg/m³ increase for predicted ${\text{PM}}_{0.1}$). The residuals of ${\text{PM}}_{2.5}$ or ${\text{PM}}_{0.1}$ were not associated with ASD [HRs of 1.04 (95% CI 0.96, 1.13, per SD=4.15 μg/m³ increase for ${\text{PM}}_{2.5}$ residuals) and 1.04 (95% CI 0.98, 1.12, per SD=0.47 μg/m³ increase for ${\text{PM}}_{0.1}$ residuals)].

Table 2.

The associations between pregnancy average ${\text{PM}}_{2.5}$, ${\text{PM}}_{0.1}$ and ASD diagnosis

Single Pollutant	HR (95% CI)
${\text{PM}}_{2.5}$ per SD=4.15 μg/m3 increase	1.08 (1.02, 1.14)
${\text{PM}}_{0.1}$ per SD=0.47 μg/m3 increase	1.07 (1.02, 1.12)
OLS Decomposed Variance
${\text{PM}}_{2.5}$ per SD=4.15 μg/m3 increase
Predicted ${\text{PM}}_{2.5}$ a	1.09 (1.03, 1.16)
Residuals of ${\text{PM}}_{2.5}$ a	1.04 (0.96, 1.13)
${\text{PM}}_{0.1}$ per SD=0.47 μg/m3 increase
Predicted ${\text{PM}}_{0.1}$ b	1.09 (1.02, 1.16)
Residuals of ${\text{PM}}_{0.1}$ b	1.04 (0.98, 1.12)

Abbreviations: CI, confidence interval; HR, hazard ratio; SD, standard deviation

^a${\text{PM}}_{2.5}$ was decomposed into predicted ${\text{PM}}_{2.5}$ (the variance explained by ${\text{PM}}_{0.1}$) and residuals (the variance not explained by ${\text{PM}}_{0.1}$) using OLS linear regression where ${\text{PM}}_{2.5}$ is the dependent variable and ${\text{PM}}_{0.1}$ is the independent variable. HRs for predicted ${\text{PM}}_{2.5}$ and residuals were all scaled to one SD increase in ${\text{PM}}_{2.5}$.

^b${\text{PM}}_{0.1}$ was decomposed into predicted ${\text{PM}}_{0.1}$ (the variance explained by ${\text{PM}}_{2.5}$) and residuals (the variance not explained by ${\text{PM}}_{2.5}$) using OLS linear regression where ${\text{PM}}_{0.1}$ is the dependent variable and ${\text{PM}}_{2.5}$ is the independent variable. HRs for predicted ${\text{PM}}_{0.1}$ and residuals were all scaled to one SD increase in ${\text{PM}}_{0.1}$.

The fitted slopes and intercepts of Deming regression models between pregnancy average ${\text{PM}}_{2.5}$ and ${\text{PM}}_{0.1}$ with varying ratios of error variances for these two exposures are shown eTable 3. Deming regression yielded a larger shared variance between ${\text{PM}}_{0.1}$ and ${\text{PM}}_{2.5}$ than OLS regression (88% vs. 75%) (eTables 2 & 4). Similar to the results using OLS, only the shared variance between ${\text{PM}}_{2.5}$ and ${\text{PM}}_{0.1}$, as represented by predicted ${\text{PM}}_{2.5}$ and predicted ${\text{PM}}_{0.1}$, was significantly associated with higher likelihood of ASD. No significant association was observed with the unique variance, as represented by the residuals of ${\text{PM}}_{2.5}$ or ${\text{PM}}_{0.1}$ (Figure 1). These associations remained largely unchanged across different values of the ratios of error variances.

Figure 1.

ASD risk associated with decomposed ${\text{PM}}_{2.5}$ and ${\text{PM}}_{0.1}$ using Deming regression with varying ratios of error variances

Abbreviations: HR, hazard ratio

Note: Pregnancy average ${\text{PM}}_{2.5}$ and ${\text{PM}}_{0.1}$ were scaled to their SD. Scaled prenatal ${\text{PM}}_{2.5}$ (a) and (b) and ${\text{PM}}_{0.1}$ (c) and (d) were decomposed into predicted values (shared variance) and residuals (unique variance) using Deming regression with scaled ${\text{PM}}_{0.1}$ as the independent variable and scaled ${\text{PM}}_{2.5}$ as the dependent variable based on a set of ratios of error variances values.

In sensitivity analyses, (1) the findings with ${\text{PM}}_{0.1\text{-}2.5}$ and ${\text{PM}}_{0.1}$ were almost identical to the main analysis showing that the shared variance, not the unique variance, was associated with ASD (eFigure 3). (2) The outcome models using the decomposed parameters of weighted Deming regression provided findings consistent with the main analysis (eFigure 4). (3) Associations between 1-year postnatal ${\text{PM}}_{2.5}$, ${\text{PM}}_{0.1}$ and ASD were not statistically significant [HR=1.03 (95% CI 0.98, 1.09) per SD=3.78 μg/m³ increase for ${\text{PM}}_{2.5}$; HR=1.04 (95% CI 0.99, 1.09) per SD=0.45 μg/m³ increase for ${\text{PM}}_{0.1}$], adjusted for covariates. In models co-adjusted for 1-year postnatal ${\text{PM}}_{2.5}$ or ${\text{PM}}_{0.1}$ exposures, the positive associations between ASD and the shared variance of pregnancy average ${\text{PM}}_{2.5}$ and ${\text{PM}}_{0.1}$ remained statistically significant. The unique variance still showed non-significant associations with ASD (eTable 5 and eFigure 5).

Discussion

${\text{PM}}_{2.5}$ and ${\text{PM}}_{0.1}$ can be highly correlated due to shared emission sources such as traffic²⁹, food cooking, and biomass combustion. Therefore, it is challenging to distinguish their associations with health outcomes in large population studies. We illustrated the application of a variance decomposition approach utilizing OLS linear regression and Deming regression to examine the associations between ASD and highly correlated prenatal ${\text{PM}}_{2.5}$ and ${\text{PM}}_{0.1}$ exposures. We found that the shared variance between prenatal exposure to ${\text{PM}}_{2.5}$ and ${\text{PM}}_{0.1}$ were significantly associated with ASD, while the unique variance remaining in the residuals of ${\text{PM}}_{2.5}$ and ${\text{PM}}_{0.1}$ was not associated with ASD.

A substantial body of epidemiological evidence has shown associations between pregnancy air pollution exposure, especially ${\text{PM}}_{2.5}$, and children’s health outcomes such as birth weight, respiratory health, and neurodevelopment^45,46. However, limited studies have focused on prenatal exposure to ultrafine particles, which can have more detrimental effects due to their ability to more readily translocate to the systemic circulation and cross biological barriers such as the placenta²¹ and blood-brain barrier²². A recent prospective study in the United States has reported the association between prenatal ultrafine particles and childhood asthma development and the association was found to be independent of ${\text{PM}}_{2.5}$ ²⁶. Another study in Canada found that prenatal exposure to ultrafine particles was associated with cancer incidence diagnosed before 6 years of age after adjusting for ${\text{PM}}_{2.5}$ ⁴⁷. In these two studies, ${\text{PM}}_{2.5}$ mass and ultrafine particles measures (particle number concentrations) were weakly correlated, therefore, collinearity and overadjustment were not a concern in the co-adjusted models. Nonetheless, challenges remain in distinguishing the potential health effects of fine and ultrafine particles, particularly in the real-world scenarios where they tend to be highly correlated. A recent California based case-control study of 660 ASD cases applied Bayesian kernel machine regression (BKMR) to the joint effects of highly-correlated ${\text{PM}}_{0.1}$ and ${\text{PM}}_{0.1\text{-}2.5}$, and other gaseous pollutants on ASD ²⁸. That study reported null associations between ${\text{PM}}_{0.1}$ and ${\text{PM}}_{0.1\text{-}2.5}$ during pregnancy and ASD ²⁸. BKMR is computationally intensive for a large cohort like ours. Instead, the variance decomposition approach is applicable to datasets of any large size and can provide a straightforward interpretation of the associations related to the shared and unique variance of highly correlated exposures.

The OLS residual decomposition approach was applied to examine the independent effects of ${\text{PM}}_{2.5}$ constituents on health outcomes while adjusting for ${\text{PM}}_{2.5}$ mass⁴⁸. The key advantage of extracting residuals using linear regression is that it helps avoid collinearity issues which may occur in the co-adjusted outcome model. However, the interpretation of estimated associations between the health outcome and the decomposed exposure (predicted values and residuals) warrants clarification. In this study, we focused on highly correlated ${\text{PM}}_{0.1}$ and ${\text{PM}}_{2.5}$ and their potential associations with ASD. Since the predicted values of ${\text{PM}}_{2.5}$ and ${\text{PM}}_{0.1}$ from both OLS regression and Deming regression models were associated with ASD, this reflects the association with the shared variance between ${\text{PM}}_{0.1}$ and ${\text{PM}}_{2.5}$. The residuals of the OLS model represent the variance in the dependent variable that was unexplained by the variance in the independent variable. As described in Mostofsky et al. ⁴⁸, the association with the residuals of ${\text{PM}}_{2.5}$ from the first OLS decomposition model can be interpreted as the association of total ${\text{PM}}_{2.5}$ holding ${\text{PM}}_{0.1}$ constant; similarly, the association with the residuals of ${\text{PM}}_{0.1}$ from the second decomposition OLS model can be interpreted as the association of ${\text{PM}}_{0.1}$ holding total ${\text{PM}}_{2.5}$ constant. In this study, neither of these two residuals were associated with ASD, suggesting that variance represented by residuals were not associated with ASD. However, the effect size estimates for the residuals were positive in both analyses, albeit with wide confidence intervals. The interpretation of the association with residuals warrants caution because only about 24% of the exposure variance remained in the residuals (eTable 2), limiting the power to examine the associations between residuals and the health outcome.

Since a greater fraction of ${\text{PM}}_{0.1}$ is composed of primary particulate matter compared to ${\text{PM}}_{2.5}$ ⁴⁹, the common associations observed for the shared variance of ${\text{PM}}_{2.5}$ and ${\text{PM}}_{0.1}$ suggests that primary particles emitted directly to the atmosphere may be more strongly associated with the risk of ASD than secondary particulate matter formed in the atmosphere through chemical reactions. Primary particles often consist of black carbon (BC), organic carbon (OC), and directly emitted metals. In our previous studies of this cohort, we found that ${\text{PM}}_{2.5}$ components of BC, OC, and metals (Cu, Fe, and Mn) were associated with increased risk of ASD ^50,51. A recent study also reported associations of traffic-related metals (Barium and Zinc) and BC with ASD ⁵², which were consistent with our previous study in this cohort showing associations between near-road air pollution and ASD ⁵³. Among secondary particles, sulfates showed consistent associations with ASD while findings on nitrates-ASD associations were inconsistent using different exposure models of PM components ⁵⁰.

Conventional OLS linear regression models assume that random errors only exist in the dependent variable, not in the independent variable. This assumption does not hold because both ${\text{PM}}_{0.1}$ and ${\text{PM}}_{2.5}$ were modeled estimates predicted with error. Deming regression is an errors-in-variables model assuming errors in both the dependent and the independent variables³¹. It has been widely used in clinical chemistry to assess the consistency between two measurement approaches⁵⁴. We applied this approach in an environmental epidemiology study to decompose the variance between two highly correlated exposures into shared and unique variance. The OLS linear regression aims to minimize the sum of squares of vertical residuals (or horizontal residuals when swapping the dependent and independent variable), where the Deming regression minimizes the sum of squares of oblique residuals based on the ratio of error variances (see eMethods Deming regression section). The two OLS linear regression models can be regarded as the two extreme cases where the ratio of error variances is close to 0 and infinity. Therefore, findings based on Deming regression decomposition are complementary to OLS and provide additional evidence to help draw inference relating to shared and unique sources of correlated exposures on outcomes.

One critical assumption of Deming regression is that the ratio of error variances remains constant at all levels of the dependent and independent variables values^31,32. In clinical chemistry, the measurement errors are often estimated by multiple repeated measurements within each subject⁵⁵. In environmental epidemiology, this assumption provides an opportunity to incorporate exposure model uncertainty into the health effects analysis. There are a limited number of continuous ${\text{PM}}_{2.5}$ monitors with large spatial distances between them, and few monitors for ${\text{PM}}_{0.1}$, therefore, the actual measurement errors can hardly be estimated. In addition, the exposures were assigned to residential addresses without considering time-activity patterns which also introduce complexity in estimating the measurement errors in the exposures to ${\text{PM}}_{2.5}$ and ${\text{PM}}_{0.1}$. Consequently, we tested the sensitivity to this ratio of error variances by a varying set of possible values, and the findings remained consistent. In addition, it is possible that the ratio of error variances may vary depending on the levels of exposures. In other words, the ratio of error variances can be a function of exposure levels and this function can be incorporated into the optimization process to minimize the sum of squared residuals with varying ratios of error variances. However, this adaptation is not a routine feature of Deming regression in current statistical software. Moreover, Deming regression assumes homoscedasticity in the residuals. Therefore, we also conducted weighted Deming regression⁴² using the inverted squared values of the measurement data, and the findings were consistent with those of the standard Deming regression.

We acknowledge some limitations of this study. The 4 km spatial resolution may be coarse to resolve sharp ${\text{PM}}_{0.1}$ spatial gradients from local sources, such as traffic exhaust, which decreases markedly with distance from roads. While ${\text{PM}}_{2.5}$ is considered a regional pollutant, averaging ${\text{PM}}_{0.1}$ to a 4 km resolution may miss some unique variance of ${\text{PM}}_{0.1}$, leaving more of the shared variance between ${\text{PM}}_{2.5}$ and ${\text{PM}}_{0.1}$. However, the CTM models for ${\text{PM}}_{0.1}$ capture regional trends in Southern California ²⁹. With future advancements in modeling ultrafine particles at finer spatial scales, our variance decomposition approach may more effectively distinguish the effects between ${\text{PM}}_{2.5}$ and ${\text{PM}}_{0.1}$. In addition, we focused on the associations with pregnancy PM exposures. Given that early signs of autism may appear before age 2 ^56,57, we co-adjusted 1-year postnatal average PM in sensitivity analyses. Although the significant positive associations between the shared variance of pregnancy average ${\text{PM}}_{2.5}$ and ${\text{PM}}_{0.1}$ remained after adjusting for 1-year postnatal average ${\text{PM}}_{2.5}$ or ${\text{PM}}_{0.1}$, it remains a challenge to address both the temporal correlation between prenatal and early postnatal exposures and the high correlation among pollutants sharing similar sources simultaneously. Distributed lag models (DLM) have been applied to address the potential temporal autocorrelation to identify sensitive windows^11. Further investigation is needed to see if the variance decomposition approaches (e.g. OLS and Deming regression) can be combined with DLM to identify sensitive exposure windows for highly correlated pollutants.

Conclusion

In this study, we illustrated the application of variance decomposition approach to examine the association of a health outcome with the shared or unique variance of two correlated environmental exposures. We also highlighted the potential use of Deming regression in environmental epidemiology to examine the independent effects of two highly correlated exposures on health outcomes while considering measurement errors in both exposures. Using a large birth cohort in Southern California as a case study, we found that the shared variance of pregnancy exposure to ${\text{PM}}_{2.5}$ and ${\text{PM}}_{0.1}$ measured by a California-based chemical transport model was significantly associated with ASD. No association was found with the unique variance in the residuals from these models. These approaches have potential to disentangle shared and unique health effects of correlated environmental exposures due to common emissions sources.

Highlights.

• A large cohort study to evaluate associations between ${\text{PM}}_{2.5}$ and ${\text{PM}}_{0.1}$ and ASD

• Decompose highly correlated ${\text{PM}}_{2.5}$ and ${\text{PM}}_{0.1}$ into shared and unique variance

• An application of Deming regression assuming measurement errors in ${\text{PM}}_{2.5}$ and ${\text{PM}}_{0.1}$

• Shared variance between prenatal ${\text{PM}}_{2.5}$ and ${\text{PM}}_{0.1}$ was associated with ASD