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Bayesian hierarchical modeling of cardiac response to particulate matter exposure

Journal of Exposure Science & Environmental Epidemiology volume 21, pages 74–91 (2011)Cite this article

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Abstract

Studies have linked increased levels of particulate air pollution to decreased autonomic control, as measured by heart rate variability (HRV), particularly in susceptible populations such as the elderly. In this study, we use data obtained from the 1998 USEPA epidemiology-exposure longitudinal panel study of elderly adults in a Baltimore retirement home to examine the relationship between HRV and PM2.5 personal exposure. We consider PM2.5 personal exposure in the aggregate and personal exposure to the components of PM2.5 as estimated in two ways using receptor models. We develop a Bayesian hierarchical model for HRV as a function of personal exposure to PM2.5, which integrates HRV measurements and data obtained from personal, indoor and outdoor PM2.5 monitoring and meteorological data. We found a strong relationship between decreased HRV (HF, LF, r-MSSD and SDNN) and total personal exposure to PM2.5 at a lag of 1 day. Using personal exposure monitoring (PEM) apportionment results, we examined the relative importance of ambient and non-ambient personal PM2.5 exposure to HRV and found the effect of internal non-ambient sources of PM2.5 on HRV to be minimal. Using the PEM apportionment data, a consistent effect of soil at short time scales (lag 0) was found across all five HRV measures, and an effect of sulfate on HRV was seen for HF and r-MSSD at the moving average of lags 0 and 1 days. Modeling of ambient site apportionment data indicated effects of nitrate on HRV at lags of 1 day, and moving averages of days 0 and 1 and days 0–2 for all but the ratio LF/HF. Sulfate had an effect on HRV at a lag of 1 day for four HRV measures (HF, LF, r-MSSD, SDNN) and for LF/HF at a moving average of days 0–2.

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Acknowledgements

We thank John Creason (USEPA) and Debra Walsh (USEPA) for their assistance with health measures data, as well as Charles Rodes and the staff of RTI International for their collection of field exposure data. The authors thank the reviewer for insightful comments on the manuscript.

Author information

Authors and Affiliations

  1. Nicholas School of the Environment and Earth Sciences, Duke University, Durham, 27708-0251, North Carolina, USA

    Sandra J Mcbride

  2. National Exposure Research Laboratory, USEPA, Research Triangle Park, 27711, North Carolina, USA

    Gary A Norris & Ron W Williams

  3. National Health and Environmental Effects Research Laboratory, USEPA, Research Triangle Park, 27711, North Carolina, USA

    Lucas M Neas

Authors
  1. Sandra J Mcbride
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  2. Gary A Norris
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  3. Ron W Williams
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  4. Lucas M Neas
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Corresponding author

Correspondence to Ron W Williams.

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The authors declare no conflict of interest.

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Disclaimer

This paper is now being subjected to external peer review and has not been cleared for publication by the US Environmental Protection Agency. The US Environmental Protection Agency through its Office of Research and Development funded and conducted the research described herein through contract 3D-5925-WATX and 4D-5895-WATX to Dr. Sandra McBride. Mention of trade names or commercial products does not constitute endorsement or recommendation for use.

Appendix A

Appendix A

WinBUGS code

model;

{

## model for first 119 obs with both HRV and PM personal mmts

## separate loop for first observation since this is a lag 1 model and

## an observation at time 0 is not available; see defn of errorfirst.

for (obsnum in 1:1){

## measurement error model for observed HRV observations

Z[obsnum]∼dnorm(H[obsnum],tau.H);

## regression equation for unknown HRV

H[obsnum] <- beta[Person[obsnum]]+Hcoef[1]+Hcoef[2]*age[obsnum]+Hcoef[3]*cvcompro[obsnum]+Hcoef[4]*sex[obsnum]+Hcoef[5]*M.P.tot.lag1[obsnum]+Tcoef[1]*a.temp1[day.num[obsnum]]+Tcoef[2]*a.temp2[day.num[obsnum]]+Tcoef[3]* a.temp3[day.num[obsnum]]+Tcoef[4]*a.temp4[day.num[obsnum]]+error[obsnum];

## first observation of error is set to be random and is the same for all individuals

error[obsnum]<-errorfirst;

## measurement error model for observed PM2.5

Y.P.lag1[obsnum]∼dnorm(M.P.tot.lag1[obsnum],tau.M.P.tot);

## unknown total personal PM2.5 exposure as sum of ambient and

## non-ambient components

M.P.tot.lag1[obsnum]<-M.P.NA.lag1+M.P.A.lag1[obsnum];

## unknown personal PM2.5 of ambient origin as product of infiltration

## and unknown ambient PM2.5

M.P.A.lag1[obsnum]<-gamma1*PMC[day.num[obsnum]];

}

## loop for remaining 118 observations for which both HRV and PM2.5 are

## available (same code as above except for defn of “error[obsnum]”)

for (obsnum in 2:119){

Z[obsnum]∼dnorm(H[obsnum],tau.H);

H[obsnum] <- beta[Person[obsnum]]+Hcoef[1]+Hcoef[2]*age[obsnum]+Hcoef[3]*cvcompro[obsnum]+Hcoef[4]*sex[obsnum]+Hcoef[5]*M.P.tot.lag1[obsnum]+Tcoef[1]*a.temp1[day.num[obsnum]]+Tcoef[2]*a.temp2[day.num[obsnum]]+Tcoef[3]*a.temp3[day.num[obsnum]]+Tcoef[4]*a.temp4[day.num[obsnum]]+error[obsnum];

##Definition of error term in terms of previous observations

##Indicator variable “Frst” indicates whether this observation

##is the first in the time series for a given individual.

error[obsnum]<-Frst[obsnum]*errorfirst+(1−Frst[obsnum])*(exp(−alpha*delta[obsnum])*error[obsnum-1]);

Y.P.lag1[obsnum]∼dnorm(M.P.tot.lag1[obsnum],tau.M.P.tot);

M.P.tot.lag1[obsnum]<-M.P.NA.lag1+M.P.A.lag1[obsnum];

M.P.A.lag1[obsnum]<-gamma1*PMC[day.num[obsnum]];

}

### model for remaining measurements with HRV only, no personal PM mmts

for (obsnum in 120:658){

Z[obsnum]∼dnorm(H[obsnum],tau.H);

H[obsnum] <- beta[Person[obsnum]]+Hcoef[1]+Hcoef[2]*age[obsnum]+Hcoef[3]*cvcompro[obsnum]+Hcoef[4]*sex[obsnum]+Hcoef[5]*M.P.tot.lag1[obsnum]+Tcoef[1]*a.temp1[day.num[obsnum]]+Tcoef[2]*a.temp2[day.num[obsnum]]+Tcoef[3]*a.temp3[day.num[obsnum]]+Tcoef[4]*a.temp4[day.num[obsnum]]+error[obsnum];

error[obsnum]<-Frst[obsnum]*errorfirst+(1−Frst[obsnum])*(exp(−alpha*delta[obsnum])*error[obsnum-1]);

M.P.tot.lag1[obsnum]<-M.P.NA.lag1+M.P.A.lag1[obsnum];

M.P.A.lag1[obsnum]<-gamma1*PMC[day.num[obsnum]];

}

## random subject-specific effect

for (i in 1:56){

beta[i]∼dnorm(0.0,tau.b);

}

## non-ambient PM2.5 personal

M.P.NA.lag1∼dnorm(mu.MPNA,tau.MPNA);

## personal sulfur measurements are X.Ind

## gamma1 is the infiltration factor

for (i in 1:N.sulfur){

X.Ind[i]∼dnorm(Sulfur.Ind[i],tau.meas.sulfurInd);

Sulfur.Ind[i]<-gamma1*SulfurC[day.num.sulfur[i]]+errgamma1;

}

## submodel for outdoor sulfur; mean is linear function of meteorology

## outdoor sulfur measurements are X.C

## separate models for day 1 and days 2–29 since for day 1

## a mean of sulfur at day 0 is needed; this is set to be random

for (t in 1:1){

X.C[t]∼dnorm(SulfurC[t],tau.meas.sulfurC);

SulfurC[t]∼dnorm(mu.sulfurC[t],tau.mean.sulfurC);

mu.sulfurC[t] <- Scoef[1]+Scoef[2]*humid[t]+Scoef[3]*humid.lag1[t]+Scoef[4]*vws[t]+Scoef[5]*vws.lag1[t]+Scoef[6]*temp[t]+Scoef[7]*temp.lag1[t]+rho.sulfurc*mu.sulfurc.t0+eps.sulfur;

}

for (t in 2:29){

X.C[t]∼dnorm(SulfurC[t],tau.meas.sulfurC);

SulfurC[t]∼dnorm(mu.sulfurC[t],tau.mean.sulfurC);

mu.sulfurC[t] <- Scoef[1]+Scoef[2]*humid[t]+Scoef[3]*humid.lag1[t]+Scoef[4]*vws[t]+Scoef[5]*vws.lag1[t]+Scoef[6]*temp[t]+Scoef[7]*temp.lag1[t]+rho.sulfurc*mu.sulfurC[t−1]+eps.sulfur;

}

## submodel for outdoor PM2.5 observations

## outdoor PM2.5 measurements are Y.C

for (t in 1:1){ ## for PM2.5

Y.C[t]∼dnorm(PMC[t],tau.meas.pmc);

PMC[t]∼dnorm(mu.pmc[t],tau.mean.pmc);

mu.pmc[t] <- PMCcoef[1]+PMCcoef[2]*humid[t]+PMCcoef[3]*humid.lag1[t]+PMCcoef[4]*vws[t]+PMCcoef[5]*vws.lag1[t]+PMCcoef[6]*dow[t]+ rho.pmc * mu.pmc.t0+eps.pmc;

}

for (t in 2:29){

Y.C[t]∼dnorm(PMC[t],tau.meas.pmc);

PMC[t]∼dnorm(mu.pmc[t],tau.mean.pmc);

mu.pmc[t] <- PMCcoef[1]+PMCcoef[2]*humid[t]+PMCcoef[3]*humid.lag1[t]+PMCcoef[4]*vws[t]+PMCcoef[5]*vws.lag1[t]+PMCcoef[6]*dow[t]+ rho.pmc * mu.pmc[t−1]+eps.pmc;

}

##############

### PRIORS ###

##############

## coefficients in regression equation for HRV

for (i in 1:5) {

Hcoef[i]∼dnorm(0.0,1.0E−2);

}

## error term in regression equation for HRV

alpha∼dunif(0.0,20.0);

tau.H <- pow(sigma.tau.H,−2);

sigma.tau.H∼dunif(0.0,100.0);

## scale parameter for random subject effect

tau.b <- pow(sigma.tau.b,−2);

sigma.tau.b∼dunif(0.0,100.0);

errorfirst∼dnorm(0,1.0E−2);

## coefficients in cubic splines for temperature

for (i in 1:4){

Tcoef[i]∼dnorm(0.0,1.0E−2);

}

## scale parameter for measured personal sulfur

tau.meas.sulfurInd<-pow(sigma.tau.meas.sulfurInd,−2);

sigma.tau.meas.sulfurInd∼dunif(0.0, 100.0);

## scale parameter for total personal PM2.5 exposure

tau.M.P.tot<-pow(sigma.tau.M.P.tot,−2);

sigma.tau.M.P.tot∼dunif(0.0, 100.0);

## parameters in non-ambient personal PM2.5 exposure

mu.MPNA∼dnorm(5.0,1.0E−2);

tau.MPNA<-pow(sigma.tau.MPNA,−2);

sigma.tau.MPNA∼dunif(0.0, 100.0);

## infiltration factor

gamma1∼dbeta(1.0,1.0);

errgamma1∼dnorm(0.0,1.0E−2);

## priors for terms in model for outdoor sulfur

eps.sulfur∼dnorm(0.0,1.0E−2);

rho.sulfurc∼dunif(−1,1);

mu.sulfurc.t0∼dnorm(2.3,1.0E−2);

for (i in 1:7){

Scoef[i]∼dnorm(0.0,1.0E−2);

}

tau.meas.sulfurC<-pow(sigma.tau.meas.sulfurC,−2);

sigma.tau.meas.sulfurC∼dunif(0.0,100.0);

tau.mean.sulfurC<-pow(sigma.tau.mean.sulfurC,−2);

sigma.tau.mean.sulfurC∼dunif(0.0, 100.0);

## priors for terms in model for outdoor PM2.5

eps.pmc∼dnorm(0.0,1.0E−2);

rho.pmc∼dunif(−1,1);

mu.pmc.t0∼dnorm(18,1.0E−2);

for (i in 1:6){

PMCcoef[i]∼dnorm(0.0, 1.0E−2);

}

tau.meas.pmc<-pow(sigma.tau.meas.pmc,−2);

sigma.tau.meas.pmc∼dunif(0.0,100.0);

tau.mean.pmc<-pow(sigma.tau.mean.pmc,−2);

sigma.tau.mean.pmc∼dunif(0.0,100.0);

}

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Mcbride, S., Norris, G., Williams, R. et al. Bayesian hierarchical modeling of cardiac response to particulate matter exposure. J Expo Sci Environ Epidemiol 21, 74–91 (2011). https://doi.org/10.1038/jes.2009.58

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