Mixtures: Comparing approaches in Mixtures:
Comparing approaches in
epidemiology and toxicology
with a discussion of the July 2015 NIEHS Workshop Statistical Approaches for Assessing Health Effects of Environmental Chemical Mixtures in Epidemiology Studies
Chemical Mixtures in Epidemiology Studies
Thomas F. Webster
Th
F W bt
Boston University School of Public Health
[email protected]
13 January 2016
13
January 2016
SOT Joint Mixtures and Risk Assessment Specialty Sections
Mixtures are an important issue
“Traditionally, toxicological studies and
human health risk assessments* have
focused primarily on single chemicals.
However, people are exposed to a myriad
of chemical and nonchemical stressors
every day and throughout their lifetime…
It is imperative to develop methods to
assess the health effects associated with
complex exposures in order to minimize
their impact on the development of
disease.”
Carlin DJ, Rider CV, Woychik R, Birnbaum LS.
Unraveling the Health Effects of Environmental Mixtures: An NIEHS
Priority. Environ Health Perspect 2013; 121: A6-A8.
* and environmental epidemiology studies
2
Overview:
1. Review & compare approaches used to study health effects of mixtures: f
• Toxicology
• Epidemiology
p
gy
2. Discussion of the July 2015 NIEHS Workshop Statistical Approaches for Assessing Health Effects of Environmental
Approaches for Assessing Health Effects of Environmental Chemical Mixtures in Epidemiology Studies
I’m assuming most of you are more familiar with toxicology than epidemiology.
3
“Testing just one dose of just the top 1,000
hi h volume
high
l
chemicals
h i l
i
in
th
three‐way
combinations would require 166 million
different experiments.”
Estabrook & Tickner, 2001
 1000 

 ~ 1.7x108
 3 
‐> We probably cannot test out way out of b bl
f
this problem (“combinatorial explosion”)
N.B. There are also non‐chemical exposures
4
Two aspects of the mixtures problem:
1. What are the patterns of co‐exposure in real populations and what do they depend on (e.g., l i
d h d h d
d
(
demographics)? 2. What are the health impacts of mixtures (to p
(
which we are exposed)? a toxicology/pharmacology
a. toxicology/pharmacology
b. epidemiology
5
Two aspects of the mixtures problem:
1. What are the patterns of co‐exposure in real populations and what do they depend on (e.g., l i
d h d h d
d
(
demographics)?  Very important role for exposure science
6
Exposure Space
A multi‐dimensional representation of exposure
Each axes represents an exposure
Each point is a person
For real populations, large parts of exposure space will be p p
, g p
p
p
empty or sparse (not uniformly distributed)
• Some exposure are correlated; others are not
•
•
•
•
B
Simple 2D exposure space
A
7
Hierarchical Clustering of Serum Concentrations
More correlateed
One branch = PBDEs
O
b
h PBDE
Second branch = other
Two groups of PCBs
PBDEs
PCB‐lower MW
PCB‐higher MW
8
What else are we exposed to?
(b id what
(besides
h t we usually
ll look
l k for)
f )
Exposome
9
Exposure science yields important p
y
p
insights by studying real world exposures. exposures
e.g., not all possible mixtures occur,
co p e pa e s o co e a o s
complex patterns of correlations
 Informs toxicology & epidemiology
LOTS to be done here!
10
Two aspects of the mixtures problem:
1. What are the patterns of co‐exposure in real populations and how do they depend on l i
dh
d h d
d
demographics, etc? 2. What are the health impacts of mixtures (to p
(
which we are exposed)? a toxicology/pharmacology
a. toxicology/pharmacology b. epidemiology
11
2a. Toxicology/pharmacology
gy p
gy
i. Whole mixtures
Question: If we know the toxicity of a defined mixture (very highly correlated), can we estimate the toxicity of a “similar”
a similar mixture? How similar does it need to be?
mixture? How similar does it need to be?
(e.g., Arochlors)
12
2a. Toxicology/pharmacology
gy p
gy
i. Whole mixtures
Question: If we know the toxicity of a defined mixture (very highly correlated), can we estimate the toxicity of a “similar”
a similar mixture? How similar does it need to be?
mixture? How similar does it need to be?
(e.g., Arochlors)
ii. Component based
Question: Can we predict the combined effect of a mixture from its components plus mechanistic information?
reduce combinatorial problem
13
Rephrase: (When & how) can we predict the dose response surface of a mixture from the
dose response surface of a mixture from the dose response curves of its components?
?
effect
A
effect
A
B B Individual dose response curves
Joint dose response surface
2D example
14
Main prediction approaches used by mixtures toxicologists based on models of “no
toxicologists, based on models of no interaction:
interaction:”
• Concentration addition (dose addition)
(
)
for compounds that act by similar mechanisms
• Independent
Independent action
action
for compounds that act by different mechanisms
Note:
Detailed mechanistic information: may allow predictions
Effect summation: not used by most mixtures toxicologists
effect A&B = effect A + effect B
effect A&B = effect A + effect B
15
Example: Toxic equivalence factors (TEFs):
• A special case of concentration addition
• Compounds act as if they are a dilute form of a potent reference compound: TEF = relative potency
• Dioxin‐like compounds (etc.)
p
(
)
• Provides a convenient summary measure of exposure
T t l ff ti d
Total effective dose = TEF
TEF1*X1 + TEF
TEF2*X2 + …
16
Toxic equivalence factors (TEFs):
Assumes same mechanism and “parallel” dose‐response curves (differing only in potency: shape & efficacy must be the same)
Individual components
Silva et al
Silva et al 17
Toxic equivalence factors (TEFs):
Assumes same mechanism and “parallel” dose‐response curves (differing only in potency: shape & efficacy must be the same)
Individual components
TEF model fits empirical mixture data TEF
model fits empirical mixture data
well compared with 2 other models
Silva et al
Silva et al CA=concentration addition
IA=independent action
ES=effect summation
18
Summary: Component‐based toxicology approach • Select compounds & doses for mixture
• Predict joint response from individual components
effect
effect
A
A
B B Individual dose response curves
Joint dose response surface
2D example
19
Two aspects of the mixtures problem:
1. What are the patterns of co‐exposure in real populations and what do they depend l
l i
d h d h d
d
on (e.g., demographics)? 2. What are the health impacts of mixtures (to p
(
which we are exposed)? a toxicology/pharmacology
a. toxicology/pharmacology
b. epidemiology
20
In some ways, epidemiologists have the opposite
(complementary) problem of toxicologists:
Epidemiologists
d
l
• study real world mixtures (
(vs. toxicologists & the huge number of possible mixtures to test)
g
g
p
)
Exposure space & outcome data
B
A
21
In some ways, epidemiologists have the opposite
(complementary) problem of toxicologists:
Epidemiologists
d
l
• study real world mixtures (
(vs. toxicologists & the huge number of possible mixtures to test)
g
g
p
)
• estimate response surfaces directly from data (vs. estimating it from dose‐response curves of components) Estimate response surface
Exposure space & outcome data
B
effect
A
B
A
22
Use of regression to estimate response surfaces from epi data: Very‐simple (2D) example using a traditional approach
Outcome & exposure data for each individual: (Yi, X1i, X2i) Yi   0  1 X1i   2 X 2i  12 X1i X 2i  i
outcome
Individual effects of exposures X1, X2
multiplicative multiplicative
interaction of X1, X2
error term
error term
Regression uses data from individual people (i) to estimate the parameters β0, β1, β2, β12
23
Some mixtures questions for epidemiologists
1. Variable selection: Which components of a mixture are important?
1
V i bl
l ti
Whi h
t f
i t
i
t t?
Challenges:
• Incomplete data on all relevant exposures
• Multiple comparisons
• Co‐pollutant confounding
24
Some mixtures questions for epidemiologists 1. Variable selection: Which components of a mixture are important?
1
V i bl
l ti
Whi h
t f
i t
i
t t?
2. Are there “interactions?”
“Additivity” vs. “interaction” (e.g., synergy, antagonism)
between multiple pollutants
Challenges:
Toxicologists, epidemiologists and statisticians do not mean mean
• Toxicologists, epidemiologists and statisticians do not
the same thing by additive, interaction, synergy, antagonism. • Difficult to examine without data spread across exposure space e g people with no exposure to either exposure to
space, e.g., people with no exposure to either, exposure to one, exposure to both
• Selection of agents to be examined & the many possible interactions
25
Some mixtures questions for epidemiologists
1. V
1
Variable selection: Which components of a mixture are important?
i bl
l ti
Whi h
t f
i t
i
t t?
2. Are there “interactions?”
3. Cumulative effect: Quantify the net effect of groups of compounds using a summary measure (e.g., TEFs)
Challenges: Difficult to create summary measure: lack of biological
• Difficult to create summary measure: lack of biological knowledge, different mechanisms, etc.
• Simply adding exposures is driven by highest concentration exposure
26
Some difficulties for epidemiologists studying mixtures:
• Obtaining good exposure data at relevant time windows
‐ important problem; use of biospecimens
important problem use of biospecimens can sometimes help
can sometimes help
‐ analytical chemistry methods
‐ cost, volume of samples (e.g., blood), logistics
‐ short half‐life compounds
short half‐life compounds
‐ non‐chemical exposure
27
Some difficulties for epidemiologists studying mixtures:
• Obtaining good exposure data at relevant time windows
‐ important problem; use of biospecimens
important problem use of biospecimens can sometimes help
can sometimes help
‐ analytical chemistry methods
‐ cost, volume of samples (e.g., blood), logistics
‐ short half‐life compounds
short half‐life compounds
‐ non‐chemical exposure
• Cannot control exposure distribution except by selection of the population
‐ some exposures will be difficult to disentangle
‐ studying “interactions” needs different exposure combinations
28
Some difficulties for epidemiologists studying mixtures:
• Obtaining good exposure data at relevant time windows
‐ important problem; use of biospecimens
important problem use of biospecimens can sometimes help
can sometimes help
‐ analytical chemistry methods
‐ cost, volume of samples (e.g., blood), logistics
‐ short half‐life compounds
short half‐life compounds
‐ non‐chemical exposure
• Cannot control exposure distribution except by selection of the population
‐ some exposures will be difficult to disentangle
‐ studying “interactions” needs different exposure combinations
• Sample size
Sample size
29
Some difficulties for epidemiologists studying mixtures:
• Obtaining good exposure data at relevant time windows
‐ important problem; use of biospecimens
important problem use of biospecimens can sometimes help
can sometimes help
‐ analytical chemistry methods
‐ cost, volume of samples (e.g., blood), logistics
‐ short half‐life compounds
short half‐life compounds
‐ non‐chemical exposure
• Cannot control exposure distribution except by selection of the population
‐ some exposures will be difficult to disentangle
‐ studying “interactions” needs different exposure combinations
• Sample size
Sample size
• Possible confounding & other biases, e.g.
‐ hard but what epidemiologists are trained to do
‐ possibility of reverse causation with exposure biomarkers
possibility of reverse causation with exposure biomarkers
‐ confounding by correlated exposures
30
confounding by correlated exposures
Suppose:
A & B are highly correlated in a mixture (e.g., by common source U)
A causes the health outcome (Y), but B
causes the health outcome (Y) but B does not
does not
B
Y
U
A
Reality
31
confounding by correlated exposures
Suppose:
A & B are highly correlated in a mixture (e.g., by common source U)
A causes the health outcome (Y), but B
causes the health outcome (Y) but B does not
does not
Then:
If we only measure B, it will be associated with the health outcome
It may be difficult to separate the effects of A
ff
ff
f & B
B
U
A
Reality
Y
B
Y
Appearance
(if we only measure B)
32
Some difficulties for epidemiologists studying mixtures:
• Obtaining good exposure data at relevant time windows
‐ important problem; use of biospecimens
important problem use of biospecimens can sometimes help
can sometimes help
‐ analytical chemistry methods
‐ cost, volume of samples (e.g., blood), logistics
‐ short half‐life compounds
short half‐life compounds
‐ non‐chemical exposure
• Cannot control exposure distribution except by selection of the population
‐ some exposures will be difficult to disentangle
‐ studying “interactions” needs different exposure combinations
• Sample size
Sample size
• Possible confounding & other biases, e.g.
‐ hard but what epidemiologists are trained to do
‐ possibility of reverse causation with exposure biomarkers
possibility of reverse causation with exposure biomarkers
‐ confounding by correlated exposures
• Statistical issues, e.g.
‐ highly correlated exposures hi hl
l t d
‐ multiple comparisons
‐ lack of standard methods
33
Use of regression to estimate response surfaces: very‐simple (2D) example Yi   0  1 X1i   2 X 2i  12 X1i X 2i   ' Z  i
outcome
Individual effects of exposures X1, X2
error term
multiplicative control
interaction confounders
of X1, X2
Some potential problems with this model and its assumptions:
• continuous Y
34
Use of regression to estimate response surfaces: very‐simple (2D) example Yi   0  1 X1i   2 X 2i  12 X1i X 2i   ' Z  i
outcome
Individual effects of exposures X1, X2
error term
multiplicative control
interaction confounders
of X1, X2
Some potential problems with this model and its assumptions:
• continuous Y
• linear relationship of outcome to exposures
35
Use of regression to estimate response surfaces: very‐simple (2D) example Yi   0  1 X1i   2 X 2i  12 X1i X 2i   ' Z  i
outcome
Individual effects of exposures X1, X2
error term
multiplicative control
interaction confounders
of X1, X2
Some potential problems with this model and its assumptions:
• continuous Y
• linear relationship of outcome to exposures
• multiplicative interaction term
36
Use of regression to estimate response surfaces: very‐simple (2D) example Yi   0  1 X1i   2 X 2i  12 X1i X 2i   ' Z  i
outcome
Individual effects of exposures X1, X2
error term
multiplicative control
interaction confounders
of X1, X2
Some potential problems with this model and its assumptions:
• continuous Y
• linear relationship of outcome to exposures
• multiplicative interaction term
• won
won’tt work well if exposures are highly correlated (colinearity)
work well if exposures are highly correlated (colinearity)
• even this simple model requires a fair amount of data and some spread across exposure space
• becomes more difficult with more exposure variables (variable (
selection), non‐linear models, etc.
37
September 26-27, 2011
Chapel Hill, NC
““Another area that requires collaboration is the development off
better statistical methods for assessing the effects of multipollutant
exposures
p
in epidemiological
p
g
studies. Overall,, mixtures studies
require novel and sophisticated mathematical, statistical,
computational, and analytical tools, which will be dependent on
continuous collaboration among the various disciplines.
disciplines ”
Carlin et al. 2013
38
39
Goals and Approach of the Workshop
Workshop Goals:
• Identify and compare different approaches and methods for analysis of mixtures data
• Foster collaborations between workshop participants
• Inform the development of a long term coordinated NIEHS mixtures research program
Workshop Structure: Data Challenge
•
•
•
•
3 datasets used by all participants
Participants analyzed data prior to workshop Short presentations at meeting
Panel discussion of strengths and limitations
Include expertise in biostatistics, epidemiology, toxicology, exposure science and risk assessment
40
Simulated data sets (answers known by organizing committee, but not participants)
Simulated Data Set #1
Simulated Data Set #2
Data per subject:
p
j
Data per subject:
p
j
N=500
Y = 1 continuous outcome variable
7 continuous exposure variables
1 binary confounder
N=500
Y = 1 continuous outcome variable
14 continuous exposure variables
3 covariates (binary, continuous)
Simulated data sets (answers known to organizing committee, but not participants)
Simulated Data Set #1
Simulated Data Set #2
Data per subject:
p
j
Data per subject:
p
j
N=500
Y = 1 continuous outcome variable
7 continuous exposure variables
1 binary confounder
N=500
Y = 1 continuous outcome variable
14 continuous exposure variables
3 covariates (binary, continuous)
Key Features/Challenges:
Key Features/Challenges:
• High correlation between some exposures (based on real serum data)
• Biologically based model: non‐linear associations with outcome
associations with outcome
• Toxicologic interactions
• Different directions of effect
o g co ou d g by
• SStrong confounding by Z
• Small amount of random noise
• High
High correlation between some correlation between some
exposures (based on real serum data)
• Linear associations between outcome & p
exposures
• No interactions between exposures
• Same direction of effect
• Strong modification by one covariate
• Moderate amount of random noise
Real World Dataset (real epidemiologic data “warts
(real epidemiologic data, warts & all
& all”, simplified)
simplified)
Features of dataset :
• Prospective cohort of mothers and children (n=270)
• Y = Mental Development Index (MDI) at 1‐3 years of age
• Xs = serum levels of 14 PCBs, 4 PBDEs, 4 organochlorine pesticides l l f
hl i
i id
• Zs = Child sex, mom age, education, race, and smoking during pregnancy
Key findings from single‐exposure analyses:
• Chemicals within a given class more correlated than across classes
• Several PBDEs associated with decreased MDI
• Several PCBs associated with increased MDI
43
Questions Addressed by Participants for Data Sets • Which exposures contribute to the outcome? Are there any that do not? (Qualitative)
h d
? (Q li i )
• Which exposures contributed to the outcome and by how much? (Quantitative)
• Is there evidence of “interaction”* or not?
• What is the effect of joint exposure to the mixture? (Qualitative)
• What is the joint dose‐response function?
* state definition of interaction you used
44
Response and Types of Methods Used
• Received 31 abstracts
• Many different approaches, for example:
Many different approaches, for example:
Exposure–Response Surface Estimation Strategies Bayesian Kernel Machine Regression (BKMR)
Bayesian Kernel Machine Regression (BKMR)
Exposure Space Smoothing (ESS)
Bayesian Additive Regression Tree (BART)
Variable Selection Strategies
Variable
Selection Strategies
Shrinkage (LASSO/LARS)
Weighted Quantile Sum (WQS) Regression
Bayesian Estimation of Weighted Sum
Classification and Prediction Strategies
Principal Component Analysis (PCA)
Variable Selection and Multivariate Adaptive Regression
p
g
Splines
p
((MARS))
Classification and Regression Trees (CART)
45
Examples of methods
Yi   0  1 X1i   2 X 2i  12 X1i X 2i   ' Z  i
outcome
Individual effects of exposures X1, X2
error term
multiplicative control
multiplicative
interaction confounders
of X1, X2
g(Y )i  0  f (X1,..., X p )   ' Z  i
smooth function of exposures
flexible interaction
2 exposure
2
exposure–response
response surface estimation strategies surface estimation strategies
• Bayesian Kernel Machine Regression (BKMR)
• Exposure Surface Smoothing (ESS)
Y
X1
X2
Observations on Model Performance Across Datasets
Question
Simulated
Dataset #1
Simulated
Dataset #2
Real‐world Dataset† Identified correct exposures?
Most
Many (for subset of X)
NA
Identified correct
Identified
correct
direction of X‐Y
associations?
Most
Most
Identified correct f
interactions?*
Some
Some
Estimated joint Estimated
joint
exposure effect?
Few
Few
NA
NA
NA
*Interaction with other X (dataset 1) or covariate Z3 (dataset 2)
† Correct answer not known. 47
Real world data set
Real world data set
• A number of methods identified PBDE congeners (inverse association) and PCB congeners (positive association). • Sensitivity of results to pre‐treatment of data (e.g., influential points
48
Key Observations/Recommendations
• Many approaches are available:
– Relatively easy to implement (e.g., using R packages)
• Comparison across methods is difficult outside the context of i
h d i diffi l
id h
f
a specific mixtures question
• Results varied across methods depending on the properties of the data sets; there did not appear to be any clear overall winner
• Variable selection/reduction is important
• Some limitations of the data (sample size, co‐pollutant correlation, missing exposures) cannot be solved with statistical models alone
• Need greater integration of toxicological and exposure science information
49
Next Steps, Tentative Plans
•
•
•
•
•
•
Continuing analysis of results of workshop
Commentary and review articles underway
Mixtures “portal”
Future “Data Challenges”
Consortium & other collaborative efforts
Statistical methods development still needed
50
Please visit the workshop website for access to:
• Simulated datasets
• Abstracts
• Statistical code
http://www.niehs.nih.gov/about/visiting/events/
pastmtg/2015/statistical/index cfm
pastmtg/2015/statistical/index.cfm
51
Summary:
• Exposure science, toxicology and epidemiology can provide complementary information for understanding mixtures.
• These three fields have different definitions of interaction.
• New methods are being developed for analyzing health effects of mixtures in epidemiology.
effects of mixtures in epidemiology.
• Successful workshop with a unusual format that generated great interest and enthusiasm.
52
Workshop Planning Committee
Joe Braun, Danielle Carlin, Jennifer Collins, Caroline Dilworth, Chris Gennings, Kim Gray, Russ Hauser, Jerry Heindel, Heather Henry, Bonnie Joubert, Helena Kennedy, Richard Kwok, Andreas K
Kortenkamp, Katie Pelch, Cynthia Rider, Thad Shug, k
K i P l h C hi Rid Th d Sh
Kyla Taylor, Claudia Thompson, Bill Suk, Tom Webster
Other Acknowledgements
• Participants in workshop
• SOT Mixtures Specialty Session
• Superfund Research Program
53
Suggested Further Reading
• Howard GJ, Webster TF. Contrasting Theories of Interaction in Epidemiology and Toxicology. Environ Health Perspect 2013; 121:1–6. • Braun JM, Gennings C, Hauser R, Webster TF. What can Epidemiological Studies Tell Us about the Impact of Chemical
Epidemiological Studies Tell Us about the Impact of Chemical Mixtures on Human Health? Environ Health Perspect 2016; 124: A6‐9.
• Future publications coming out of the NIEHS workshop
Future publications coming out of the NIEHS workshop
54
Is the combination of A and B “synergistic?”
outcom
me
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
Control
A
B
A&B
If you’re an epidemiologist, think of the outcome as a risk (with no confounding or bias)
56
Is the combination of A and B “synergistic?”
outcom
me
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
Control
A
B
Answer:
• Epidemiology: Yes
E id i l
Y
• Mixtures toxicologist: Can’t tell
without more information
A&B
Why?
57
Toxicology/pharmacology & Epidemiology agree on one thing 
Evaluating synergy and antagonism crucially depends on the a uat g sy e gy a d a tago s c uc a y depe ds o t e
definition of no interaction (“additivity”)
synergy (greater than expected)
No interaction (expected under definition of no interaction)
antagonism (less than expected)
58
Toxicologists, epidemiologists (and statisticians) h
have different definitions of non‐interaction ff
f
f
(“additive”).
• Th
They therefore judge synergy & antagonism using different th f
j d
& t
i
i diff
t
criteria.
• Definitions cannot be right or wrong. The real question is whether they are useful.
• Need to specify the definition you are using.
Is the combination of A and B “synergistic?”
0
0.35
35
outcome
0.3
0 25
0.25
0.2
0.15
0.1
0.05
0
Control
A
B
R00
R01
R10
In epidemiology:
A&B
R11
synergy, because (R11-R00)>(R10-R00)+(R01-R00)
effect A&B > effect A + effect B
60
Is the combination of A and B “synergistic?”
0
0.35
35
outcome
0.3
0 25
0.25
0.2
0.15
0.1
0.05
0
Control
A
B
R00
R01
R10
In epidemiology:
A&B
R11
synergy, because (R11-R00)>(R10-R00)+(R01-R00)
effect A&B > effect A + effect B
•
•
Equivalent to effect summation in toxicology, generally not used
by mixtures toxicologists
61
Derived from non-interaction of causes
So why do toxicology and epidemiology give y
gy
p
gy g
different answers here?
• Epidemiology: Look at the sum of the effects
• Toxicology: Additional information: Suppose that A and B obey TEFs. Look at the the sum of the doses (weighted by TEF )
TEFs).
• These give different results when dose‐response curves are non‐linear
(N.B. Toxicologists have a few definitions of no interaction, depending on mechanism).
Linear dose‐response curve
• A and B have TEFs: can be shown on the same dose‐response curve
• the incremental effect of B
the incremental effect of B does NOT depend on A
does NOT depend on A (epidemiology: (epidemiolog
“causal independence”)
N interaction.
No
i t
ti
A
B
Consequence:
q
• TEF result = effect summation
• Epidemiology & toxicology agree: no interaction
Non‐linear dose response curve
the incremental effect of B
the
incremental effect of B depends on A
depends on A (epidemiology: (epidemiology: “causal
causal interdependence”)
TEF
Nonlinear DRC
Effect summation
A
B
Consequence:
• TEFs predicts larger effect than effect summation
TEFs predicts larger effect than effect summation
• Epidemiology: interaction
• Toxicology: no interaction
WARNING Use of the following words—interaction, additive,
synergy, antagonism—may lead to severe confusion.
Avoid with alcohol.
alcohol Casual use of these words by
graduate students in a qualifying exam is particularly
hazardous: make sure you know the field of the person
asking
ki the
h question,
i
as toxicologists,
i l i
epidemiologists
id i l i and
d
statisticians do not mean the same thing by these terms.