Page 432 - Contributed Paper Session (CPS) - Volume 2

CPS1916 Erica P. et al.
of the study is given in Sinharay et al. (2017). The association between
metabolite levels and TRAP exposures was assessed in van Veldhoven et al.
(2018) in a mixed model framework, including random effects for the
individual, as well as for the location and time point of each measurement.
Fixed effects were sex, age, body mass index (BMI), caffeine intake and health
group, as well as annual and instantaneous measurements of the exposure of
interest. Five exposures were considered separately, namely black carbon
(CBLK), nitrogen dioxide (NO2), particulate matter (PM10 and PM25) and ultra-
fine particles (UFP).
The model was fitted on each of the 5749 measured metabolic features
and results were then corrected for multiple testing using a Bonferroni-
corrected significance level. We formulated the same model using a Bayesian
framework and included an additional component to model the presence of
measurement error. We assumed a classical measurement error for the
different pollutants, i.e. that the exposure variable Z can be observed only via
a proxy W, such that
W = Z + U

With ~ (0, )
2

Such formulation was included in the model by adding a latent variable for
the exposure, namely a normally distributed variable with mean equal to 0 and
variance equal to the error variance and resulting in the following hierarchical
structure:

A vague gamma prior was used for the error variance, with shape and scale
parameters equal to 0.0001. Informative priors were used as well, based on
previous knowledge of the error variance on similar pollutants.
To model the presence of a Berkson measurement error, we assumed that
Z=W+U. It is a different scenario than the one depicted in the previous section,
as the observed variance is actually less than the real one, as opposed to a
classical framework where the presence of the error leads to an increase in the
observed variance of a variable. In the presence of a Berkson measurement
error, the expected attenuation of the effect of the error-prone variable is
lower, as the bias is not expected to propagate to the estimates of the
regression parameters (Carroll et al., 2006).

421 | I S I W S C 2 0 1 9