symptoms over time and temperature. The
loess smoothing technique can accommodate
nonlinear and nonmonotonic patterns
between time (or temperature) and the health
outcome, offering a flexible nonparametric
modeling tool. In the loess smooth, each
observed value is replaced by a predicted
value, generated by a weighted regression of
values in a specified neighborhood (span)
around the value (7,8). Greater weight is
given to observations close to the middle of
the chosen span. This predicted value is the
smoothed estimate of the data point, and the
method is repeated over all observations. In
this manner, the underlying pattern of daily
symptoms over time is empirically determined,
and this function can then be added
to the model as a control variable. We chose a
span based on the Akaike Information
Criteria, which balances the bias and variance
incurred by the smoothing approach (7). The
optimal span was approximately 30% of the
data, or roughly 1 month for each of the
morbidity end points. However, the regression
results were generally insensitive to the
chosen span.
Finally, the effects of PM10 on the likelihood
of a new symptom (as opposed to the
probability of any day with a symptom) were
examined. A new symptom data set for each
individual for each symptom category
included only those days that followed a day
with no symptom in that category for that
individual. This is an effective manner to
examine a model where serial correlation is
minimized.