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Threshold Dependence of Mortality Effects for Fine
and Coarse Particles in Phoenix, Arizona
Richard L. Smith a , Dan Spitzner a , Yuntae Kim b & Montserrat Fuentes b
a Department of Statistics , University of North Carolina , Chapel Hill , USA
b Department of Statistics , North Carolina State University , Raleigh , USA
Published online: 27 Dec 2011.
To cite this article: Richard L. Smith , Dan Spitzner , Yuntae Kim & Montserrat Fuentes (2000) Threshold Dependence of
Mortality Effects for Fine and Coarse Particles in Phoenix, Arizona, Journal of the Air & Waste Management Association,
50:8, 1367-1379, DOI: 10.1080/10473289.2000.10464172
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TECHNICAL PAPER
Smith, Spitzner, Kim, and Fuentes
ISSN 1047-3289 J. Air & Waste Manage. Assoc. 50:1367-1379
Copyright 2000 Air & Waste Management Association
Threshold Dependence of Mortality Effects for Fine and Coarse
Particles in Phoenix, Arizona
Richard L. Smith and Dan Spitzner
Department of Statistics, University of North Carolina, Chapel Hill
Yuntae Kim and Montserrat Fuentes
Department of Statistics, North Carolina State University, Raleigh
ABSTRACT
analysis of nonlinear pollution-mortality relationships, how-
ever, suggests that the true picture is more complicated than
that. For coarse particles, the evidence for any nonlinear or
threshold-based effect is slight. For fine particles, we found
evidence of a threshold, most likely with values in the range
of 20–25 µg/m3. We also found some evidence of interac-
tions of the PM effects with season and year.
Daily data for fine (<2.5 µm) and coarse (2.5–10 µm) par-
ticles are available for 1995–1997 from the U.S. Environ-
mental Protection Agency (EPA) research monitor in
Phoenix, AZ. Mortality effects on the 65 and over popula-
tion were studied for both the city of Phoenix and for a
region of about 50 mi around Phoenix. Coarse particles
in Phoenix are believed to be natural in origin and spa-
tially homogeneous, whereas fine particles are primarily
vehicular in origin and concentrated in the city itself. For
this reason, it is natural to focus on city mortality data
when considering fine particles, and on region mortality
data when considering coarse particles, and most of the
results reported here correspond to those assignments.
After allowing for seasonality and long-term trend
through a nonlinear (B-spline) trend curve, and also for me-
teorological effects based on temperature and specific hu-
midity, a regression of mortality was performed on PM using
several different measures for PM. Based on a linear PM ef-
fect, we found a statistically significant coefficient for coarse
particles, but not for fine particles, contrary to what is widely
believed about the effects of coarse and fine particles. An
The main effect here is an apparent seasonal interac-
tion in the coarse PM effect. An attempt was made to ex-
plain this in terms of seasonal variation in the chemical
composition of PM, but this led to another counterintuitive
result: the PM effect is highest in spring and summer, when
the anthropogenic concentration of coarse PM is lowest as
determined by a principal components analysis. There was
no evidence of confounding between the fine and coarse
PM effects. Although these results are based on one city
and should be considered tentative until replicated in other
studies, they suggest that the prevailing focus on fine rather
than coarse particles may be an oversimplification. The
study also shows that consideration of nonlinear effects
can lead to real changes of interpretation and raises the
possibility of seasonal effects associated with the chemical
composition of PM.
IMPLICATIONS
BACKGROUND AND DATA
The EPA standard for fine particles introduced in 1997
was based on the widespread belief that the most seri-
ous health effects occur for fine rather than coarse par-
ticles. The present study shows that coarse particles may
still have an effect and, therefore, should not be neglected.
It also confirms that fine particles have an effect, but in
this analysis, it is only observed above a threshold in the
region of 20–25 µg/m3; there appears to be no effect be-
low 15 µg/m3. Since the latter figure is the 1997 EPA stan-
dard for long-term average fine PM, the standard may
possibly be more stringent than needed. However, the
main message of the paper is that more study is needed
of the comparative effects of coarse and fine PM, of pos-
sible threshold or nonlinear relationships, and of the ef-
fect of variations in the chemical composition of PM.
In 1997, the U.S. Environmental Protection Agency (EPA)
introduced a new PM standard based on PM2.5 to supple-
ment an earlier standard based on PM10. The new stan-
dard was founded on the widely held belief that PM2.5 is
more directly injurious to human health than is PM10.
Nevertheless, although there has been widespread research
on the human health effects of PM10 based on time-series
analysis of daily mortality and morbidity counts,1–5 there
has been comparatively little direct comparison of the
epidemiologic effects of fine PM (i.e., PM2.5) and coarse
PM (PM10–PM2.5).
Schwartz et al.6 compared the effects of fine PM and
coarse PM on mortality using data from the Harvard “Six
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Smith, Spitzner, Kim, and Fuentes
Cities Study,” which involved an average of 8 years of
data at each of six cities, using dichotomous sampling
data collected every other day. In their study, they reported
a consistently stronger effect for fine particles than for
coarse particles. They also considered the possibility of
the “threshold effect” for fine particles by repeating the
analysis but restricting it to days on which the level of
PM2.5 was below either 25 or 30 µg/m3, and they reported
that even within those days there was still a statistically
significant association between PM2.5 and mortality.
However, Lipfert and Wyzga7 criticized this study,
arguing that the difference in results for coarse and fine
PM could have resulted from differential measurement
errors in the two series. Another study by Schwartz et al.8
reported that coarse particles did not have an adverse
health effect in Spokane, WA, a fact which could very likely
be explained by the fact that coarse particles in Spokane
are mostly natural dust and, therefore, far less toxic than
particles of industrial origin. Despite these studies, over-
all there has been much less direct epidemiologic com-
parison of fine and coarse PM than there has been of cases
where the two are combined into PM10 or TSP (total sus-
pended particulates). Of course, the main reason for this
is that daily PM2.5 data is available at only a very small
number of stations.
The present study makes use of a new data source
from Phoenix, AZ. From 1995 to early 1998, the EPA lo-
cated a research monitoring platform in Phoenix, collect-
ing daily data from DFPSS, tapered element oscillating
microbalance (TEOM), and dichotomous samplers, to
determine both fine and coarse PM measurement as well
as particulate carbon and elemental concentration mea-
surement. These data have been described by the PM Re-
search Monitoring Network Data report for Phoenix, AZ,
February 1995–December 1997, produced by the EPA Na-
tional Exposure Research Laboratory, Research Triangle
Park, NC. Based on these data, we have calculated daily
fine and coarse PM data by averaging hourly measure-
ments from a TEOM monitor. Although the data contained
a small number of negative values, these were not re-
moved, as it seems likely that they result from the method
used to calculate hourly concentrations rather than from
simple recording error. Because it is common in this field
of research to use averages of up to 5 days of PM data as
an exposure measure, rather than just single daily read-
ings, we also calculated the k-day running averages, for
k = 2, 3, 4, and 5, of coarse and fine PM. In performing
this calculation, we followed the convention that if at
least one but less than k of the daily readings were avail-
able, we calculated a k-day average using all available days.
For most of the analysis to follow we used k = 3, and with
this convention, we had 1038 available days of fine PM
data and 1026 days of coarse PM data.
Climatic data for Phoenix have been downloaded from
the Web site of the National Climatic Data Center (NCDC)
in Asheville, NC. Although climatic data are also directly
available from the EPA report, we preferred to use the NCDC
data because of the wider range of variables available. Spe-
cifically, we made use of the following data available on a
daily basis: daily maximum temperature, daily minimum
temperature, and specific humidity, the latter calculated
from dew point and pressure. Daily deaths data were ob-
tained from the Arizona Health Services Department. Based
on these, we developed two series of daily deaths, one from
the city of Phoenix, and the other from a wider region of
about 50 mi around Phoenix, which includes other cities
such as Scottsdale, Mesa, and Tempe. We refer to this as
the “Phoenix region” data set. Both data sets were restricted
to residents, which avoids a possible bias due to seasonal
influx of temporary residents during the winter.
Some discussion needs to be given of the reasons for
considering separate city and regional data. There were
good a priori reasons, which the detailed analysis con-
firms, for expecting fine particles effects to be strongest
in the city data and coarse particles effects to be strongest
in the regional data. Fine particles in Phoenix are prima-
rily vehicular in origin, spatially heterogeneous, and con-
centrated in urban areas. We would not expect effects due
to downtown traffic to affect people living many miles
from the city or in other cities where the PM levels are
different from those in Phoenix. In contrast, coarse PM
in this region is believed to be primarily of natural origin
and spatially homogeneous. We therefore expect the ef-
fects of coarse PM to be homogeneous over the region,
and from a statistical point of view, we can expect to get
more precise estimates if we use a larger data set.
INITIAL DATA ANALYSIS
Previous time-series studies of air pollution and mortality
have made clear that there are both meteorological and
long-term trend and seasonality effects which must be
taken into account. Naturally, we find the same for the
current data set.
Figure 1 shows daily deaths for both the city and re-
gion, with a scatterplot smoother running through the data
points. The latter was obtained using the lowess function
in the statistical package S-Plus (MathSoft Inc.; Seattle, WA),
with f = 0.05 (this is a parameter controlling the amount of
smoothing). This plot shows a strong seasonal pattern and
possibly some additional long-term trend.
Figure 2 shows levels of 3-day averages of coarse PM
and fine PM, also with a scatterplot smoother. These are
shown in preference to 1-day values because the 3-day
values are the ones used in the more detailed analysis later
in this paper. A strong seasonal effect is clear here as well,
and possibly an overall increasing trend.
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Smith, Spitzner, Kim, and Fuentes
Figure 1. Daily deaths in (a) Phoenix city and (b) Phoenix region for the 3 years of the study, with a fitted smooth curve.
Initial studies of meteorological effects show that both
temperature and specific humidity are relevant, but the
effects may be nonlinear. With temperatures, some previ-
ous studies4,5 have suggested that a piecewise linear effect,
with different slopes on either side of some threshold value,
may fit the data better than a polynomial trend, and initial
exploratory regression analyses suggested that this might
be true here. Specifically, a model where the dependence
on daily maximum temperature tmax is of the form
(1)
with b1< 0, b1+ b2 > 0 and some threshold u, appears to
be a good fit. Exploration of u = 20, 25, 30, and 35 °C
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Smith, Spitzner, Kim, and Fuentes
(a) PM Coarse (3-Day Means)
(b) PM Fine (3-Day Means)
Figure 2. Three-day averages of (a) coarse PM and (b) fine PM (measured in µg/m3), with a fitted smooth curve.
led to u = 30 as the threshold chosen for subsequent
analysis. Other variables included were daily minimum
temperature, tmin; specific humidity, sh; and the square
of specific humidity, which we denote shsq. A com-
plete list of covariates used in the analysis, including
both these and the PM-based variables, is contained
in Table 1.
In addition, all the variables in Table 1, except day
and the mortality variables, are also considered in lagged
form; for instance, tmaxm means the value of tmax lagged
m days. We consider m = 0, 1, 2, 3, and 4; tmax0 is today’s
maximum temperature, tmax1 is yesterday’s, and so on.
For the seasonal and long-term trend, it is obvious
from Figure 1 that a simple polynomial or piecewise linear
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Smith, Spitzner, Kim, and Fuentes
Table 1. Description of variables used in analysis.
DETAILS OF REGRESSION ANALYSIS
For the first part of the analysis, several different values
of K, ranging from 8 to 48, were tried in eq 2, and for
each, meteorological variables from Table 1 (and their
lagged values) were selected by backward selection, using
hypothesis tests with size 0.1 to decide whether to retain
the meteorological variables (in other words, a meteoro-
logical variable was retained whenever the p value for that
variable was smaller than 0.1). The resulting models were
compared by a variety of model selection devices, includ-
ing PRESS, AIC, and BIC.11 In general, PRESS and AIC be-
have similarly and tend to favor models with larger
numbers of parameters, while BIC selects models with
fewer parameters. This behavior was seen here, as the
optimal value of K when selected by PRESS or AIC was 40
for the regional data and 24 for the city data; when se-
lected by BIC, it was 16 and 12, respectively. Although
this leaves open the question of which K we should actu-
ally use, one point in favor of the smaller K was that the
backward selection procedure in that case selected more
meteorological variables, and that seemed desirable in
principle, so that the resulting model included both me-
teorological terms and a long-term trend. Therefore, the
BIC values were adopted for further analysis, with meteo-
rological variables given in Tables 2 and 3. The subsequent
results in the paper are not overly sensitive to the precise
model chosen at this stage of the analysis, a point we re-
turn to later.
After selecting an initial model to represent the
long-term trend and meteorological components, dif-
ferent PM variables based on Table 1, together with
lagged values, were added to the model one at a time,
in an attempt to ascertain what the strongest effect
would be. At this point in the analysis, it emerged that,
taken as linear terms, those based on coarse PM con-
tributed more statistically significant effects than those
based on fine PM. For example, using the regional data,
any one of p1c0, p2c0, or p3c0 was statistically signifi-
cant, with t statistics (ratio of parameter estimate to
standard error) of 3.5, 3.6, and 3.2, respectively. For a
large data set such as this, the t distribution effectively
coincides with a normal distribution, so any t value
larger than 2 is statistically significant at level 0.05, and
the values quoted here are significant at levels 0.001 or
smaller. Results for coarse particles in the city of Phoe-
nix are similar, but with larger standard errors leading
to smaller t values; for example, the t value for p3c0 is
2.0. In contrast, no analysis based on fine PM for either
the city or the region produced a t statistic larger than
1.2, which is not statistically significant.
day
Number of days (1 = Feb 1, 1995; 1065 = Dec 31, 1997)
mortc
mortr
tmax
tmin
sh
Elderly nonaccidental mortality in city
Elderly nonaccidental mortality in region
Daily maximum temperature
Daily minimum temperature
Daily mean specific humidity
Larger of tmax–30 and 0
Square of sh
tg30
shsq
p1c
p2c
p3c
p4c
p5c
p1f
Daily coarse particles level (PM10–PM2.5)
2-day averages of p1c
3-day averages of p1c
4-day averages of p1c
5-day averages of p1c
Daily fine particles level (PM2.5)
2-day averages of p1f
p2f
p3f
3-day averages of p1f
p4f
4-day averages of p1f
p5f
5-day averages of p1f
function will not be adequate, and the solution adopted
here is a B-spline representation, which represents the
estimated function as a continuous sequence of cubic
polynomials of the form
(2)
where B(·) is the B-spline basis function.4,9 In effect, this
represents the trend as a linear combination of K inde-
pendent functions, with coefficients ck estimated from the
data, and whose smoothness may be controlled by vary-
ing the value of K. Note that eq 2 effectively ensures that
the “knots” of the B-spline representation, given the value
of K, are uniformly distributed throughout the 1065 days
for which data are available.
The final “initial data analysis” issue is the form of de-
pendence of mortality on the regression terms. In the
present paper, this has been achieved by a linear regression
of the square root of daily mortality on the long-term trend,
meteorological, and PM-based variables. The choice of a
square root transformation was made after a comparison
with a logarithmic transformation and with no transfor-
mation, using methods similar to Atkinson, section 6.2.10
The square root transformation was clearly superior to the
other two transformations in every comparison made.
To summarize the results of this section, the model
adopted is a linear regression in which the dependent
variable is the square root of daily mortality in either the
city of Phoenix or the Phoenix region, and the linear re-
gression terms are long-term trends modeled by eq 2, to-
gether with a subset of the meteorological and PM-based
variables in Table 1, lagged from 0 to 4 days.
At this stage, therefore, our conclusion is that there
may be a significant result due to coarse PM, but there is
no sign of any due to fine PM.
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Smith, Spitzner, Kim, and Fuentes
Table 2. Meteorological variables used in analysis of Phoenix region data. Suffixes denote lags. The
Figure 3 shows the result of this analy-
sis, in which the response to PM as a piecewise
linear function is plotted together with the con-
fidence bands. Plots are shown for coarse PM
for the region data and for fine PM for the city
data. The results show a contrast between the
cases of coarse and fine PM. For coarse PM (left-
hand half of the plot), there is no significant
change in slope on either side of the thresh-
old, except for threshold 10, which is rather
meaningless in view of the shortage of coarse
PM data (and very wide confidence bands on
the coefficient) below this threshold. In con-
model also included a long-term trend based on eq 2, with K = 24.
tmax1
tmin0
sh1
tg301
tg302
shsq1
shsq3
Table 3. Meteorological variables used in analysis of Phoenix city data, together with long-term trend
based on eq 2 with K = 16.
tmax2
tmin1
tmin3
sh1
tg300
shsq1
Nonlinear Dependence for Coarse and Fine PM
The picture becomes considerably more complicated,
however, if the possibility of a nonlinear PM response is
taken into consideration. For most of the following dis-
cussion, for reasons explained earlier, we used regional
data when looking at coarse PM and city data when look-
ing at fine PM. The results for coarse PM on the city data
were similar to those for the regional data, but with much
wider confidence bands, making it harder to characterize
the form of the relationship. In contrast, it was impos-
sible to find any effect, linear or nonlinear, relating fine
PM to regional mortality. As noted already, however, this
is only to be expected based on what is known about the
sources of PM, so it seems reasonable to concentrate on
the city data when looking for fine PM effects.
At this stage of the analysis, it was decided to con-
centrate on p3c0 and p3f0 (3-day averages with no time
lags; in other words, the average of today’s, yesterday’s,
and the day before yesterday’s values) as the main PM
variables of interest. This decision was based both on the
results of the previous section and on general experience
of this field of research, which has shown that 2- or 3-day
averages of PM very often give a more reliable indication
of epidemiologic effects than do single-day values.
There are, however, numerous ways in which we can
look for nonlinear effects, and in this section we consider
three of them. All models fitted include the same meteo-
rological and long-term trend terms as in the preceding
section.
trast, for fine PM, although there is no significant effect
when represented as a linear term, when piecewise lin-
ear terms are selected, there are some significant results.
In particular, the plots for thresholds 20 and 25 show
that for either of these, the fine PM effect above the
threshold is statistically significant, though the effect
below the threshold is not. The t statistics for the effect
above the threshold were 2.4 and 2.7, respectively, for
thresholds 20 and 25.
It is possible to give a firmer characterization of the
effects in Figure 3 by formally testing the null hypothesis
of a linear PM effect against the alternative hypothesis of
a piecewise linear effect with threshold as shown. For the
five plots based on coarse PM, the p values of the test
statistics are all in excess of 0.5, indicating no threshold
effect. For the five plots based on fine PM, the p values
(top to bottom) are 0.06, 0.05, 0.007, 0.005, and 0.33. For
thresholds 20 and 25, in particular, this provides strong
evidence that a piecewise linear fit improves on a simple
linear fit.
B-Spline Analysis
The second nonlinear method tried was to represent the
PM (coarse or fine) effect as a B-spline representation, simi-
lar to the formula given in eq 2 for the time-dependent
effect. For this analysis, the number of knots was fixed at
K = 4, which is large enough to display a nonlinear effect
if there is one; for a much larger K than that, the random-
ness in estimating the coefficients of the individual
B-spline terms (equivalent to ck in eq 2) would be so large
as to render the results meaningless. The meteorological
and long-term trend terms in the model were the same as
in the linear analysis.
Results were expressed as relative risks (RR), using the
long-term mean PM value as a reference level for which
RR = 1. This was 13.0 for fine PM and 33.6 for coarse PM.
Pointwise 95% confidence bands were computed using
the standard errors and covariances of parameter estimates
in the regression analysis. Unfortunately, confidence
bands computed by this method tend to be very wide,
Piecewise Linear Analysis
The first nonlinear method tried was a piecewise linear
method, similar to the model adopted in eq 1 for tem-
perature. For each of several possible thresholds, separate
linear trends were estimated below and above the thresh-
old, together with 95% confidence intervals. An early
example of the idea of looking at separate linear trends
below and above a threshold was the paper by Ostro,12 in
which he applied this method to data from London in
the 1950s and in 1960.
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Smith, Spitzner, Kim, and Fuentes
Figure 3. Piecewise linear estimates of the coarse PM effect for the region and the fine PM effect for the city plotted for different thresholds.
Volume 50 August 2000
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Smith, Spitzner, Kim, and Fuentes
but they were included in the plots because they give at
least a rough indication of the extent to which various
nonlinearities in the plot may be regarded as true effects
rather than just artifacts of the data. Figure 4 shows these
plots for both coarse (regional data) and fine PM (city data).
In Figure 4a, for coarse PM in the region, it can be
seen that the sharpest increase in the nonlinear curve
occurs between 20 and 40 µg/m3, though there also ap-
pears to be a second sharp rise over 60 µg/m3. Overall,
however, the results of this plot do not contradict a simple
overall linear effect. In contrast, in Figure 4b, for fine
PM, there appears to be a clear change in the slope some-
where in the region of 20 µg/m3, and the accompanying
confidence bands show that this is statistically signifi-
cant. This may be evidence of a threshold effect or at
least a significantly nonlinear relationship, which con-
trasts sharply with our earlier finding of no relationship
at all.
deaths was whether this approach copes adequately with
the problems of overdispersion and serial correlation that
sometimes arise in studies involving Poisson regression.2
Overdispersion refers to the property that variances of the
observed responses are larger than those which would hold
if the data were truly independent Poisson counts. In the
case of a square root transformation, the variance is very
nearly stabilized to a constant value of 0.25. An observed
variance larger than that is, therefore, an indication of
overdispersion. Other studies typically indicate an
overdispersion in the region of 1.05–1.1 (i.e., 5–10% larger
than the Poisson variance).
For fine particles, the estimated residual variance was
0.2715. Dividing by 0.25, this therefore corresponds to
an overdispersion of 1.09. For coarse particles, the corre-
sponding residual variance is 0.2816, or an overdispersion
of 1.13. These results are, therefore, at the high end of the
accepted range of overdispersions, which may indicate
some additional source of variability that has not been
taken into account.
Diagnostics for the B-Spline Analysis
A number of the standard regression diagnostics11 were
computed for the fitted models with the B-spline repre-
sentation for the PM effect. These serve as a check on
whether the model is a reasonable fit to the data. Such
diagnostics could have been computed for all the models
fitted, but we focused on this one because of all the mod-
els considered, the one involving a nonlinear PM effect
appeared to provide the best overall fit to the data.
One issue raised by our decision to concentrate on
linear regression with a square root transformation of
Serial correlations have been calculated based on the
studentized residuals. For fine particles, the first three
values are 0.034, 0.035, and 0.103. To judge the signifi-
cance of these, a common rule of thumb is to compare
them with 2/N0.5, where N is the sample size on which
the serial correlations are based. In this case, 2/N0.5 = 0.062,
which means that the third-order autocorrelation is sig-
nificant. However, none of the other autocorrelations is
significant. The results for the model based on coarse par-
ticles fitted to the region data are similar: serial correla-
tions 0.055, 0.037, 0.084, ... so
that the third value is again
significant, but none of the
others are. We do not have a
ready explanation for this.
There are also a num-
ber of diagnostics aimed at de-
termining whether any of the
observations are particularly
influential on the final results.
There are several of these that
tend to work in a similar way,
so we concentrated on one,
namely, DFFITS.10,11 According
to criteria originally given by
Belsley et al.,13 DFFITS indi-
cates an influential observa-
tion at a value 2(p/N)0.5, where
N is the sample size and p is
PM (µg/m3)
PM (µg/m3)
the number of parameters in
the model. In the case of the
fine particles analysis, p was
0.295, and there were 65 values
Figure 4. Nonlinear estimates of RR (relative to the mean PM variable), together with pointwise 95%
confidence bands. (a) Coarse PM effect–regional deaths data. (b) Fine PM effect–city deaths data.
1374 Journal of the Air & Waste Management Association
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Smith, Spitzner, Kim, and Fuentes
(out of the 1014 for which DFFITS could be calculated)
which exceeded that in absolute value, the largest abso-
lute value being –0.6196. This is a little difficult to inter-
pret, but we have examined whether outlying values of
DFFITS correspond to outlying observations of PM, and
no clear pattern emerges. The picture for coarse particles
is similar, with 55 values of DFFITS exceeding the cut-off
value of 0.327, the largest absolute value being –0.5853,
but extreme values of DFFITS again do not correspond to
extreme values of the PM variable of interest.
In practice, we have assumed u to lie on a discrete
grid (10, 11, 12, ..., 35 for fine PM and 0, 2, 4, ..., 70 for
coarse PM) and have computed posterior densities by sum-
ming the values of eq 6 over this grid, renormalizing so
that the overall sum of probabilities is 1. The results are
shown in Figure 5. These results may be interpreted as an
overall probabilistic statement about the location of the
threshold based on the data available.
We have already seen that the strongest evidence for
a threshold is in Figure 4b, for fine PM in the city of Phoe-
nix, with less strong evidence in Figure 4a (coarse PM in
the region). Results in Figure 5 confirm this, but also give
new insights into the strength of evidence for the exist-
ence of a threshold.
Overall, there are a number of features here that might
justify further exploration, but none that casts serious
doubt on the correctness of the model.
Bayesian Analysis for Threshold Selection
One can take the analysis of the previous section some-
what further by looking specifically for a threshold effect
of the form
For coarse PM, Figure 5a shows a peak in the poste-
rior density around 20 µg/m3, but it is not a very strong
peak, and the posterior density does not tend to 0 near
u = 0, which suggests that there may in fact be no thresh-
old at all.
(3)
For fine PM, Figure 5b shows a very clear peak in the
posterior density near u = 22 µg/m3, with the posterior
density near 0 outside the range of 15–30. Although the
results have been calculated on the assumption of a uni-
form prior distribution for u, the general form of this plot
(with a much higher posterior density in the range of
15–30 than outside that range) will not be very sensitive
to this, provided a prior density is adopted that is consis-
tent with reasonable prior belief over a wide range of val-
ues of u. Thus, in this case we deduce strong evidence in
favor of the existence of a threshold.
where p is a PM variable (coarse or fine) and u is the thresh-
old. The purpose of this section was to see how far we
could go toward formally selecting the best value of u to
be consistent with the formula in eq 3.
Conditionally on u, the dependence between the vec-
tor of responses Y and the matrix of covariates X (which
includes long-term trend, meteorology, and PM variables)
is a linear model of the form
(4)
SENSITIVITY ANALYSES
in which the matrix of covariates X(u), the regression pa-
rameters b(u), and the residual variance v(u) > 0 all depend
on the threshold parameter u, and I is the identity ma-
trix. If we take a Bayesian point of view, assuming a joint
prior density for (u, b(u), v(u)) of the form
As a check on the sensitivity of the main results in this
paper to some of the modeling assumptions made at the
beginning, they were repeated with the following changes:
(1) the choice of K (number of knots in the B-spline rep-
resentation) was made by AIC rather than BIC; (2) the
size of the hypothesis tests performed at the backward
selection stage was increased from 0.10 to 0.15 (the effect
of this will be to include more meteorological variables in
the analysis); and (3) the meteorological modeling was
confined to temperature-based variables (no humidity),
that is, tmax, tmin, and tg30 (see Table 1), together with
their lagged values.
(5)
for some upper bound umax on the permissible values of u,
then by combining eqs 4 and 5 and integrating out b(u)
and v(u), the marginal density of Y given u is of the form
(6)
We shall not present detailed results of this, but the
following are the main conclusions. An AIC-based selec-
tion of K led to K = 40 for the region data and K = 20 for
the city data. With these changes to the model, both coarse
and fine PM effects are a little weaker than those in the
preceding analysis, but the qualitative results are the
same—there is a significant linear effect for coarse PM in
the region and a significant nonlinear effect for fine PM
in the city.
Here, n is the number of observations, q is the number of
regressors in the linear model eq 4, and G(u)2 is the con-
ventional error sum of squares for the linear regression
model eq 4 with u treated as fixed. Bayesian inference for
u may, therefore, be based directly on the conditional
density in eq 6, renormalizing the probabilities so that
the posterior density of u integrates to 1.
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Journal of the Air & Waste Management Association 1375

Smith, Spitzner, Kim, and Fuentes
We should note, however, that
the trend and seasonal variation
must not be overmodeled. During
the AIC analysis for the city data,
it was noted that K = 48 gives an
AIC value not very different from
the optimal value K = 20, but when
the fine particles analysis was re-
peated with this value of K, the re-
sults were entirely different, several
of the linear coefficients appearing
significantly negative. The inter-
pretation of this result would ap-
pear to be that local fluctuations
of the order of 3 weeks (the inter-
val between knots in this analysis)
are short enough to be confounded
with the fine particles effect, lead-
ing to incorrect estimates for the
Threshold u
Threshold u
Figure 5. Posterior densities for threshold. (a) Coarse PM effect–regional deaths data. (b) Fine PM
latter. This serves as a warning
against indiscriminate reliance on
AIC or indeed on any “black box”
statistical criterion.
effect–city deaths data.
PM were unusually low during the first half of 1995. To
test whether this had any influence on the results, 4 “years”
were defined corresponding to February–June 1995 (year
INTERACTIONS
Another question we have considered is the possibility of
an interaction between the PM effect and either season
or year. If there are different effects in different seasons or
years, this could be an indication that the true relation-
ship is more complicated than simple cause and effect.
As an example, a seasonal interaction model for
coarse PM was defined as follows. Instead of a single re-
gressor for coarse PM, four variables were defined, one
for each season. For example, “winter coarse PM” is the
coarse PM value during the winter months (December,
January, and February) and 0 for the remainder of the
year. Spring, summer, and fall coarse PM values were
defined similarly. The main regression analysis of the
paper, for the region data, was rerun, producing the re-
sults in Table 4. Also shown for comparison are the mean
levels of coarse PM for each season.
It can be seen from Table 4 that the coarse PM effect is
really only significant during the spring and summer
months. It is possible that this could be an artifact of what
is really a nonlinear relationship between PM and mortal-
ity, but we doubt this because (1) our previous studies
showed no sign of this, and (2) it appears that if it were due
to a nonlinear relationship, it is the wrong way round—
the high PM coefficient occurs during seasons when the
mean coarse PM level is low. Below, we offer another ex-
planation for the seasonal variation in the PM coefficient.
The possibility of an interaction by year was suggested
by Figure 2, where it can be seen that both coarse and fine
1), July 1995–June 1996 (year 2), July 1996–June 1997 (year
3), and July–December 1997 (year 4). A year effect was esti-
mated using exactly analogous methodology to that just
described for the season effect. In the case of coarse PM, it
indeed turns out that the effect is lowest in year 1, but
when the overall significance of the coarse PM × year in-
teraction was tested using an F test, it was not significant
(p value = 0.07). In contrast, the F test for a seasonal inter-
action was significant, with a p value of 0.004.
In the case of fine PM, there was again evidence of a
seasonal interaction when modeled as a linear effect, but
in this case it does appear to be a proxy for the threshold
dependence noted earlier in the paper. When the seasonal
interaction model was fitted based on a threshold model,
with separate effects below and above a threshold of
25 µg/m3, the seasonal effect disappeared. A year interac-
tion effect was noted even in the threshold model, with a
significant negative coefficient below the threshold in year
1. In this case, an F test for the overall presence of a year
interaction effect in the threshold model was significant,
with a p value of 0.016. However, this is not as significant
as the previously noted seasonal effect for coarse PM, and
since it is rather hard to explain a negative dependence
between fine PM and mortality, we feel this is much more
likely to be an artifact of some kind.
It is not yet known whether there is any natural expla-
nation for the seasonal interaction effect that was found
for coarse PM. One possibility is that this effect might be
1376 Journal of the Air & Waste Management Association
Volume 50 August 2000

Smith, Spitzner, Kim, and Fuentes
associated with seasonal variations in the chemical com-
position of PM. In addition to the TEOM data used through-
out this paper, we have the air pollution data broken down
into 44 chemical elements (excluding carbon) that are con-
stituents of coarse PM. We removed elements that are typi-
cally below the detection limit. This analysis was based on
about 300 days of data, and the elements used in the study
were Al, Si, S, Ci, K, Ca, Ti, Mn, Fe, Cu, Zn, and Pb. A prin-
cipal components analysis of the constituent elements of
coarse PM showed that the crustal elements (Al, Si, K, Ca,
Ti, Mn, and Fe) explain 55% of the variation of coarse PM,
the anthropogenic elements (Fe, Cu, Zn, and Pb) explain
30%, and the elements of marine origin (Cl [NaCl, Na was
not measured]) explain 5%. Table 5 shows a breakdown by
season of the means of three principal components corre-
sponding to each of these groups.
primary pollutant for the region data. Then, however,
whichever was the primary pollutant, the other was also
included as a co-pollutant, and the coefficient of the pri-
mary pollutant was re-estimated in this case. The results
are in the last two columns of Table 4. In no case does the
estimate for the primary pollutant change significantly
as a result of including the co-pollutant.
The last conclusion is reassuring in that it is consis-
tent with fine and coarse particles being essentially sepa-
rate pollutants having distinct effects. Note, however, that
we have not studied possible confounding of either fine
or coarse particles with gaseous pollutants such as O3 or
SO2, and since past studies have suggested confounding
between PM and gaseous co-pollutants,3 it would seem
worthwhile to consider that aspect as well.
The results in Table 5 suggest that the composition
of coarse PM differs throughout the year, with the crustal
elements highest and the anthropogenic elements lowest
in spring and summer. If this were the explanation for
the seasonal interaction, however, the implication would
be that crustal, rather than anthropogenic, elements were
responsible for the PM mortality associations. This result
seems counterintuitive and suggests that we do not yet
fully understand the seasonal interactions.
A final effect that has been examined is the possibility
of confounding between coarse and fine particles. In all
models studied before now, coarse and fine particles have
been treated separately, with one or the other included,
but not both at the same time. If the regression coefficients
were to change dramatically when both pollutants were
included in the same model, that would further compli-
cate the interpretation of the results. Fortunately, the evi-
dence on this point is that the coefficients do not change
very much. To make a specific comparison, piecewise lin-
ear effects were fitted for both fine and coarse particles (sepa-
rately) based on threshold u = 25. They were then all
included together to examine how the coefficients changed.
In Table 6, regression parameter estimates and their
standard errors are shown both for fine and coarse par-
ticles, below and above the threshold. As with earlier stud-
ies, the results indicate fine particles are the primary
pollutant for the city data and coarse particles are the
DISCUSSION
A number of aspects of this analysis raise further points
for discussion. The study is based on only 3 years of data
at a single site; many other studies are based on either a
much longer series or on combining data from many
sites.14 This is a limitation, pointing toward the need for
more studies of these issues.
Other recent studies have examined both of the pri-
mary issues in this paper, the existence of thresholds and
the comparisons of fine and coarse particles. In particu-
lar, ours is not the only study to suggest that the effect of
coarse particles may be equal to or greater than that of
fine particles. For example, Ostro et al.15 showed in the
case of some California data, which are dominated by
coarse particles, that there is still a significant effect using
PM10 as a regressor, which challenges the notion that there
is no particulate-based effect in cases where the particles
are primarily coarse.8 Castillejos et al.16 have compared
fine and coarse particles effects in data from Mexico City,
finding, as we have here, that the coarse particles effect
can by no means be neglected. There are also other re-
cent studies on thresholds. Cakmak et al.17 have consid-
ered the possible effect of measurement error on the
estimation of a threshold. Daniels et al.18 have examined
the existence of a threshold in PM10 data across the 20
largest cities of the United States, the same database as in
Dominici et al.14 Their preliminary results suggest the ab-
sence of a threshold in PM10 data for all-cause
mortality, though there is clearly a need for
Table 4. Interactions of coarse PM and season.
more detailed research on the best way to
combine data from different cities.
Season
Mean Coarse PM
Estimate
Standard Error
t Statistic
p Value
Lipfert and Wyzga7 discussed the pos-
sible role of differential measurement error
in the attribution of mortality effects to a
single pollutant. Specifically, they argued
that the results of Schwartz et al.,6 which
claimed a stronger effect for fine particles,
Winter
Spring
Summer
Fall
33.6
28.9
31.6
39.3
0.0036
0.0139
0.0063
0.0023
0.0023
0.0026
0.0026
0.0022
1.5
5.3
2.4
1.0
0.13
0.0001
0.018
0.3
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Journal of the Air & Waste Management Association 1377

Smith, Spitzner, Kim, and Fuentes
Table 5. Breakdown by season of mean level of each of the three principal groups
ASU West, and Estrella Park) are, respectively, 0.85, 0.88,
0.93, and 0.76 for coarse PM and 0.64, 0.90, 0.91, and
0.74 for fine PM. Thus, in the case of Higley, the correla-
tion of coarse PM with the Phoenix station is clearly higher
than that of fine PM, while for the other three stations,
the correlations are about the same for coarse and fine
PM. This is, inevitably, inconclusive about whether coarse
particles are indeed more homogeneously distributed than
fine particles, but the results are qualitatively very differ-
ent from those reported by Lipfert and Wyzga7 for Phila-
delphia, for instance.
of elements (standardized to overall mean 0 for each component).
Season
Crustal
Anthropogenic
Marine
Winter
Spring
Summer
Fall
–0.144
–0.278
0.004
0.503
–0.323
–0.483
0.222
–0.589
0.073
0.41
0.245
0.03
could be the result of fine particles being more accurately
measured than coarse particles in the six-cities data set.
We have no direct evidence on measurement error in
the Phoenix data set, but we have no reason to think
that it acts differentially in favor of either coarse or fine
particles.
CONCLUSIONS
The original purpose of this study was to compare the
effects of coarse and fine PM on mortality in Phoenix.
Knowledge of the dominant origins of PM (natural dust
for coarse, vehicular emissions for fine) suggested that the
effects would be primarily concentrated on the city of
Phoenix for fine PM, but would be apparent throughout
the region for coarse PM, and this was largely confirmed
by the statistical analysis. Linear regressions for coarse and
fine PM, taking into account meteorological and trend/
seasonal effects, led us to conclude that there is a signifi-
cant effect for coarse PM but not for fine PM, contrary to
the prevailing orthodoxy in this field. The results were
rather different, however, when nonlinear effects were
taken into consideration.
The question of measurement error also arises in the
difference between ambient monitor measurements and
the personal exposure of individuals. There have been
some studies of the effect of imputing personal expo-
sures—for example, Dominici et al.19 have proposed a
mathematical modeling approach to this, but it also ap-
pears from their paper that currently available data on
personal exposure are quite limited and do not distin-
guish between fine and coarse particles. Another issue
related to this topic is the effect of spatial variation. Lipfert
and Wyzga7 reported on various studies in the eastern
United States in which fine particles were more homoge-
neously distributed than were coarse particles. As noted
at the beginning of this paper, we believe that in Phoe-
nix, coarse particles are more homogeneously distributed
than are fine particles. Direct data to support this point
are limited, but we do have data on fine and coarse par-
ticles from the city of Phoenix and from four other loca-
tions within the Phoenix region used in this paper.
Measuring correlations of logarithms of PM concentra-
tion to improve numerical stability of the results, we found
that the spatial correlations between the Phoenix down-
town site and four other sites in the region (Higley, Tempe,
Three different methods were used to study non-
linear effects: (1) a piecewise linear effect below and
above a threshold, (2) a smooth nonlinear effect based
on a cubic spline representation, and (3) formal selec-
tion of a threshold by Bayesian means. None of the three
methods led to any conclusions that contradicted a lin-
ear effect for coarse PM, but in the case of fine PM, there
was clear evidence for a change of slope somewhere in
the region of 20–25 µg/m3. The conclusion is that fine
PM may indeed have an effect at high levels, but only
above the current EPA standard for the long-term mean
of 15 µg/m3.
Additional analyses suggested there could be signifi-
cant interactions in the PM effect with season and year.
The strongest effect was a seasonal interaction for coarse
PM, the effect being significant only in spring and summer.
An attempt was made to explain this in terms of the chemi-
cal constituents of coarse PM, and it was found that crustal
elements of coarse PM were highest and anthropogenic
elements lowest in spring and summer. If interpreted caus-
ally, however, this result would imply that crustal and
not anthropogenic sources of PM are primarily respon-
sible for deaths, which does not seem a very plausible
conclusion. A more reassuring conclusion was that there
was no evidence of any confounding between fine and
coarse PM.
Table 6. Interactions of fine and coarse PM.
Primary Pollutant Estimate
Std. Err.
Estimate
Std. Err.
With Co-Pollutant
Without Co-Pollutant
Fine particles,
below threshold
Fine particles,
–0.006
0.050
0.005
–0.010
0.042
0.005
above threshold
Coarse particles,
below threshold
Coarse particles,
above threshold
0.018
0.019
0.0003
0.0065
0.0062
0.0019
0.0008
0.0068
0.0003
0.0021
1378 Journal of the Air & Waste Management Association
Volume 50 August 2000

Smith, Spitzner, Kim, and Fuentes
7. Lipfert, F.; Wyzga, R. Daily Mortality and Size-Fractionated Particu-
late Matter in Six U.S. Metropolitan Areas: The Implications of Mea-
surement and Modeling Uncertainties; J. Air & Waste Manage. Assoc.
1997, 47, 517-523.
8. Schwartz, J.; Norris, G.; Larson, T.; Sheppard, L.; Caiborne C.; Koenig,
J. Episodes of High Coarse Particles Concentration Are Not Associ-
ated with Increased Mortality; Environ. Health Perspect. 1999, 107,
339-342.
9. Green, P.J.; Silverman, B.J. Nonparametric Regression and Generalized
Linear Models: A Roughness Penalty Approach; Chapman and Hall: Lon-
don, 1994.
10. Atkinson, A.C. Plots, Transformations and Regression; Oxford Univer-
sity Press: Oxford, UK, 1985.
These results, being based on a single city and for a
comparatively short time period, cannot be regarded as
definitive. Nevertheless, they carry clear implications that
contradict those of (very few) previous studies of these
kinds of questions, in particular, the paper of Schwartz et
al.6 The story about the comparative effects of coarse and
fine PM is by no means concluded, and this paper also
shows that it is worthwhile to consider nonlinear or
threshold-based effects as well as the possibility of sea-
sonal interaction.
11. Neter, J.; Kutner, M.H.; Nachtsheim, C.J.; Wasserman, W. Applied Lin-
ear Statistical Models, 4th ed.; Irwin: Chicago, IL, 1996.
12. Ostro, B. A Search for a Threshold in the Relationship of Air Pollu-
tion to Mortality: A Re-Analysis of Data on London Winters; Environ.
Health Perspect. 1984, 58, 397-399.
13. Belsley, D.A.; Kuh, E.; Welsch, R.E. Regression Diagnostics; Wiley: New
York, 1980.
ACKNOWLEDGMENTS
This work was supported in part by EPA Cooperative Agree-
ment CR 825173-01-1 to the University of Washington,
as a subcontract to the National Institute of Statistical
Sciences, Research Triangle Park, NC, and by EPA Coop-
erative Agreement CR 827737-01-0 to Smith. The authors
would like to thank Merlise Clyde, Peter Guttorp, Garry
Norris, and Larry Cox for assistance with the data and
advice about the analysis.
14. Dominici, F.; Samet, J.M.; Zeger, S.L. Combining Evidence on Air
Pollution and Daily Mortality from the 20 Largest U.S. Cities: A Hier-
archical Modeling Strategy; J.R. Statist. Soc. 2000, 163, in press.
15. Ostro, B.; Hurley, S.; Lipsett, M.J. Air Pollution and Daily Mortality in
the Coachella Valley, California: A Study of PM10 Dominated by Coarse
Particles; Environ. Res. 1999, 81, 231-238.
16. Castillejos, M.; Borja-Aburto, V.; Dockery, D.W.; Gold, D.R.; Loomis,
D. Airborne Coarse Particles and Mortality; Inhal. Toxicol. 2000, 12
(Suppl. 1), 61-72.
17. Cakmak, S.; Burnett, R.T.; Krewski, D. Methods for Detecting and
Estimating Population Threshold Concentrations for Air Pollution-
Related Mortality with Exposure Measurement Error; Risk Anal. 1999,
19, 487-496.
18. Daniels, M.J.; Dominici, F.; Samet, J. Estimating PM10-Mortality Dose
Response Curves and Threshold Levels: An Analysis of Daily Time
Series for the 20 Largest U.S. Cities. Preprint, Johns Hopkins Univer-
sity, 2000.
19. Dominici, F.; Zeger, S.L.; Samet, J.M. A Measurement Error Model for
Time-Series Studies of Air Pollution and Mortality; Biostatistics, in
press.
DISCLAIMER
This paper has not been subjected to the U.S. Environ-
mental Protection Agency’s internal peer review system
and no endorsement by the Agency should be implied or
inferred.
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About the Authors
Yuntae Kim is a graduate student and Montserrat Fuentes
is an assistant professor, Department of Statistics, North
Carolina State University, Raleigh, NC. Dan Spitzner is a
graduate student and Richard L. Smith is a professor, De-
partment of Statistics, University of North Carolina, Chapel
Hill, NC 27599-3260. Correspondence about this paper
should be addressed to Richard Smith at the above ad-
dress or by e-mail at rls@email.unc.edu.
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Journal of the Air & Waste Management Association 1379