Post on 17-Aug-2020
S 9. Supplement
S 9.1. Limits of detection and quantification
The chemical analysis procedure established the detection and quantification limits to create a min-imum signal-to-noise ratio of 3 and 10, respectively. This resulted in the limits presented in Table S.1.The amount of censoring for each municipality-drug combination is in Table S.2.
Meth MDMA Benzoylecgonine Methadone Hydrocodone Oxycodone
LOD 1.5 1.0 1.0 2.0 2.0 2.0LOQ 10.0 2.5 10.0 2.5 2.5 2.5
Note: Meth = methamphetamine
Table S.1: Detection and quantification limits (ng/L)
S 9.2. Sampled WWTPs
The 19 treatment plants contributing data for this analysis represent a convenience sample of diversesystems in the Northwest United States, specifically in the states of Washington and Oregon. The givenWWTP names are a mix of neighborhood names, city names, or collective names or otherwise convenientlabels that may or may not accurately reflect the catchment area served. We use the term “municipality”in general to indicate the WWTP and the area served. While most municipalities are along the mainnorth-south transportation corridor (US Interstate 5), several locations represent smaller cities or townsalong the coast or inland in the drier regions east of the Cascade mountain range. The relative populationsizes covered by each WWTP and their representative level of precipitation for 2009 are presented inFigure S.1. The final (average for Seattle and Renton; see Section 3.1) population estimates and thesource of those estimates, per the WWTP surveys, are in the second and third columns of Table S.2.
S 9.3. Sample data setup
Calculating a given sample’s index load requires four parameters: the measured concentration (column1 in Table S.3), the titration correction factor to account for titrating the sample to facilitate measurement(column 2), the day’s measured flow through the WWTP (column 3), and the day’s population estimate(column 6, constant in this example; see Section 3.1 for discussion of how this value might vary). The“Final Concentration” and “Final Load” columns (4 and 5) in the sample data setup are intermediatecalculations that represent the titration-corrected concentration and the product of this concentrationand the day’s volume.
For the third and fourth rows, the initial concentrations are censored. For estimating the mean indexload in the presence of censoring via a survival analysis method, the censoring must be represented asintervals to indicate the range the values could take. The final two columns, here labeled “Left” and“Right” (your software may prefer “Begin” and “End”, etc.), are what are inputted to the estimatingsoftware. For measurable observations, the two sides of this interval are the calculated index load. Forvalues below the level of detection (<LOD, where the LOD in the example is 1.5), the left side of theinterval is 0 and the right side is the LOD×titration factor×flow÷population÷(10002), to reflect thatthe initial concentration must be in the range of 0 to 1.5. For values below the level of quantification(<LOQ, where LOQ here is 10.0), we only know the initial concentration is between the LOD and theLOQ, and so the two sides of the interval reflect these values multiplied through: E.g., LOQ×titrationfactor×flow÷population÷(10002).
S 9.4. Robust retransformation
After maximum likelihood estimation, implemented with 50–80% censoring, we apply a robust retrans-formation to avoid retransformation bias as described by Helsel (2012), Kroll and Stedinger (1996), andShumway, Azari, and Kayhanian (2002). In order to create the distribution graphs in Figures 1, S.2, andS.3, we also apply Steps 1–4 below for cases with less than 50% censoring. Given data as in the exampleabove (Table S.3), the primary goal is to have an unbiased estimate of the mean of the data, and the
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ith
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mate
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on
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on
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erd
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sus
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erof
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ple
sav
aila
ble
for
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ysi
s.N
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tion
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mat
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ates
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ased
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ento
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ate
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ssal
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led
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her
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lati
ons
con
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t.
Tab
leS
.2:
Pop
ula
tion
esti
mate
san
dce
nso
rin
gof
sam
ple
sby
WW
TP
12
34
56
78
9
Mea
sure
dT
itra
tion
Fin
alF
inal
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exC
on
centr
atio
nC
orre
ctio
nF
low
Con
centr
atio
nL
oad
Loa
d(n
g/L
)F
acto
r(L
/d
ay)
(ng/
L)
(gra
ms)
Pop
ula
tion
(mg/
per
son
/day
)L
eft
Rig
ht
1005
.21.
0767
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1424
1082
.318
.682
211
650.
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270.
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Tab
leS
.3:
Sam
ple
data
setu
pfo
rsu
bst
an
cew
ith
LO
Dof
1.5
ng/L
an
dL
OQ
of
10
ng/L
secondary goal to have a full hypothetical dataset to create boxplots. The robust retransformation isimplemented as follows:
Step 1 Take the estimated distribution of the transformed data and place the censored data in appro-priate places on the lower part of the distribution. These plotting positions or percentiles areessentially evenly spaced in the lower end of the distribution, on the transformed scale.
• Specifically, for each censored observation i among all c censored observations within the Nobservations, the plotting position p is given by
p =c
N×
i− 38
c + 14
(4)
where the i for observations below LOD come before the i for observations above LOD butbelow LOQ.
Step 2 Translate the percentiles into values on the transformed scale via the normal distribution quantilefunction.
Step 3 Individually re-transform these predicted values on the transformed scale to the original scale.
Step 4 Combine these predicted values with the original observed values (i.e. the uncensored values)into a new set of data.
Step 5 Calculate the mean of this hypothetical data.
S 9.5. Distributions and estimates for other analytes
Following the discussion of censoring, distribution, error components, and estimates for metham-phetamine and MDMA in the main text, here we present the graphical results for the other analytesconsidered: benzoylecgonine, methadone, hydrocodone, and oxycodone. In the boxplot graphs, the shad-ing of the box represents the amount of censoring for each municipality-drug combination, with darkerboxes indicating more complete data. The WWTPs are ordered by the completeness of the data andthen alphabetically. The background shading and label (Report censoring, MLE, KM, Complete data)indicate for groups of municipality-drugs what method was used to create the estimate in the corre-sponding estimates graphs. In the latter, the shading of the estimate indicator (the diamond) representsthe amount of censoring, and the dotted line the unweighted average estimate across the 19 WWTPs.WWTPs are ordered by the mean annual estimate.
S 9.6. Sensitivity of confidence intervals to changes in US
As described in the Discussion, our annual sampling error estimate of US = 10% came from a study ofsampling (or monitoring) uncertainty in a small European city (Ort et al., 2014a). That exercise involvedrepeated samples of N = 56 taken from over 1000 consecutive daily samples of benzoylecgonine (cocainemetabolite). With fewer than 56 samples in the current analysis, WWTP catchment area sizes of moreor less than 7000 users, and substances that may have more or less variation in use than cocaine, one mayquestion whether a different estimate of annual sampling error might change the results substantially.In Figure S.6, we present the estimates and confidence intervals for a single substance, MDMA, in whichwe have both doubled our sampling uncertainty RSD (top panel) and halved it (bottom panel). (Similargraphs for the other analytes are available upon request.) Compared to the bottom panel of Figure 2,we see that changing one of our four uncertainty parameters has small effects on the resulting CIs. Witha 5% uncertainty, Port Angeles MDMA becomes more clearly significantly higher than average, but weremain uncertain that Renton MDMA could not be essentially 0. With less certainty about the abilityof our 43 to 55 samples to represent the whole year—US = 20%—Port Angeles MDMA levels are clearlynot significantly different than the average, and Tacoma’s CI is more likely to overlap with any otherWWTP CI, but all except the Renton index load remain significantly greater than 0. Compared withboth the size of the CIs and the differences in estimated means, these changes in CI due to differentannual sampling uncertainties are relatively small.
MLE
KM
Com
plet
e da
ta
0.442.23.9mg/person/day
Kla
mat
h Fa
llsO
ntar
ioP
ort A
ngel
esO
lym
pia
Ben
dG
rant
s P
ass
Lako
taR
edon
doS
eattl
eTr
i−C
ityC
orva
llis
Por
tland
Eug
ene
Abe
rdee
nE
vere
ttH
erm
isto
nP
asco
Ren
ton
Taco
ma
BE
NZ
OY
LEC
GO
NIN
E b
ox s
hadi
ng:
80%
cen
sore
d50
% c
enso
red
No
cens
orin
g
KM
Com
plet
e da
ta
0.0280.140.25mg/person/day
Cor
valli
sR
ento
nA
berd
een
Eug
ene
Gra
nts
Pas
sK
lam
ath
Falls
Oly
mpi
aP
ortla
ndS
eattl
eTr
i−C
ityP
asco
Por
t Ang
eles
Ben
dE
vere
ttH
erm
isto
nLa
kota
Ont
ario
Red
ondo
Taco
ma
ME
TH
AD
ON
E
Fig
ure
S.2
:B
enzo
yle
cgon
ine
(top
)an
dm
eth
ad
on
e(b
ott
om
)in
dex
load
dis
trib
uti
on
(mg/p
erso
n/d
ay)
KM
Com
plet
e da
ta
0.0310.150.27mg/person/day
Oly
mpi
aR
ento
nC
orva
llis
Por
t Ang
eles
Pas
coLa
kota
Eug
ene
Gra
nts
Pas
sK
lam
ath
Falls
Tri−
City
Sea
ttle
Por
tland
Abe
rdee
nTa
com
aR
edon
doB
end
Eve
rett
Her
mis
ton
Ont
ario
HY
DR
OC
OD
ON
E b
ox s
hadi
ng:
80%
cen
sore
d50
% c
enso
red
No
cens
orin
g
KM
Com
plet
e da
ta
0.0630.310.57mg/person/day
Por
tland
Oly
mpi
aC
orva
llis
Pas
coB
end
Eve
rett
Her
mis
ton
Lako
taR
edon
doTr
i−C
ityS
eattl
eR
ento
nA
berd
een
Por
t Ang
eles
Eug
ene
Gra
nts
Pas
sK
lam
ath
Falls
Ont
ario
Taco
ma
OX
YC
OD
ON
E
Fig
ure
S.3
:H
yd
roco
don
e(t
op
)an
doxyco
don
e(b
ott
om
)in
dex
load
dis
trib
uti
on
(mg/p
erso
n/d
ay)
0.170.851.5mg/person/day
Kla
mat
h Fa
llsG
rant
s P
ass
Oly
mpi
aA
berd
een
Por
t Ang
eles
Cor
valli
sP
ortla
ndP
asco
Sea
ttle
Eve
rett
Ont
ario
Ben
dH
erm
isto
nE
ugen
eTr
i−C
ityR
ento
nLa
kota
Red
ondo
Taco
ma
5355
4454
5252
4355
5354
5246
4253
5248
5050
52N
T
mea
n (0
% c
enso
red)
mea
n (6
0% c
enso
red)
95%
CI
aver
age
mea
n
BE
NZ
OY
LEC
GO
NIN
E
0.0130.0650.12mg/person/day
Pas
coH
erm
isto
nC
orva
llis
Ren
ton
Oly
mpi
aE
ugen
eS
eattl
eA
berd
een
Gra
nts
Pas
sP
ort A
ngel
esB
end
Ont
ario
Lako
taK
lam
ath
Falls
Tri−
City
Por
tland
Red
ondo
Taco
ma
Eve
rett
5254
5255
5353
4652
5254
5540
5048
4350
5352
53N
ME
TH
AD
ON
E
Fig
ure
S.4
:B
enzo
yle
cgon
ine
(top
)an
dm
eth
ad
on
e(b
ott
om
)in
dex
load
mea
nw
ith
95%
con
fid
ence
inte
rval
(mg/p
erso
n/d
ay)
0.00810.040.073mg/person/day
Ren
ton
Oly
mpi
aR
edon
doB
end
Eug
ene
Taco
ma
Por
t Ang
eles
Tri−
City
Kla
mat
h Fa
llsG
rant
s P
ass
Sea
ttle
Lako
taP
asco
Por
tland
Cor
valli
sH
erm
isto
nA
berd
een
Ont
ario
Eve
rett
4650
5253
3453
5443
5552
5052
5342
5455
5252
54N
T
mea
n (0
% c
enso
red)
mea
n (6
0% c
enso
red)
95%
CI
aver
age
mea
n
HY
DR
OC
OD
ON
E
0.0220.110.2mg/person/day
Pas
coO
lym
pia
Kla
mat
h Fa
llsP
ortla
ndC
orva
llis
Lako
taR
edon
doTa
com
aA
berd
een
Eve
rett
Ben
dH
erm
isto
nO
ntar
ioR
ento
nS
eattl
eE
ugen
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i−C
ityG
rant
s P
ass
Por
t Ang
eles
5153
5352
5355
4346
5350
5355
4854
5054
4253
52N
OX
YC
OD
ON
E
Fig
ure
S.5
:H
yd
roco
don
e(t
op
)an
doxyco
don
e(b
ott
om
)in
dex
load
mea
nw
ith
95%
con
fid
ence
inte
rval
(mg/p
erso
n/d
ay)
>80
%ce
nsor
ing
10%50%90%●
●
●
●
●
●
0.0030.0150.027
mg/person/day
Abe
rdee
nO
ntar
ioLa
kota
Kla
mat
h Fa
llsO
lym
pia
Por
tland
Red
ondo
Sea
ttle
Eug
ene
Taco
ma
Her
mis
ton
Pas
coG
rant
s P
ass
Tri−
City
Cor
valli
sR
ento
nB
end
Por
t Ang
eles
Eve
rett
4352
5552
5353
5254
5252
4346
4854
5055
5553
50N
● ●
< L
OD
< L
OQ
MD
MA
, SA
MP
LIN
G U
NC
ER
TAIN
TY
= 2
0%
>80
%ce
nsor
ing
10%50%90%
●
●
●
●
●
●
0.0030.0150.027
mg/person/day
Abe
rdee
nO
ntar
ioLa
kota
Kla
mat
h Fa
llsO
lym
pia
Por
tland
Red
ondo
Sea
ttle
Eug
ene
Taco
ma
Her
mis
ton
Pas
coG
rant
s P
ass
Tri−
City
Cor
valli
sR
ento
nB
end
Por
t Ang
eles
Eve
rett
4352
5552
5353
5254
5252
4346
4854
5055
5553
50N
● ●
< L
OD
< L
OQ
MD
MA
, SA
MP
LIN
G U
NC
ER
TAIN
TY
= 5
%
Fig
ure
S.6
:M
DM
Ain
dex
load
mea
nw
ith
95%
con
fid
ence
inte
rval
(mg/p
erso
n/d
ay)
base
don
an
nu
al
sam
plin
ger
ror
of
20%
(top
)an
d5%
(bott
om
)
S 9.7. Observation variability and population size
Figure S.7: Variability of daily drug loads [as coefficient of variation (CV)] vs. population size (P, in 1000s) in five differentcatchments for different substances (duration of studies in days: 1©=1369, 2©=311, 3©=28, 4©=239, 5©=28/35). Reasonsfor CVs exceeding 0.8 in theses studies are: i) observations below limit of quantification (heroin) and ii) pronounced intra-week variability (MDMA). Such a regular weekend effect causes a high CV but does not imply that more samples wouldbe needed for the same acceptable uncertainty. Adapted from European Monitoring Centre for Drugs and Drug Addiction(2016).
Reference
European Monitoring Centre for Drugs and Drug Addiction, Assessing Illicit Drugs in
Wastewater: Advances in Wastewater-based Drug Epidemiology (Insights 22), 2016,
Publications Office of the European Union; Luxembourg, http://dx.doi.org/10.2810/6622.