The Population Attributable Fraction (PAF) for Public Health Assessment: Epidemiologic Issues, Multivariable Approaches, and Relevance for Decision-Making

1
The Population Attributable Fraction (PAF) for
Public Health Assessment Epidemiologic Issues,
Multivariable Approaches, and Relevance for
Decision-Making

• Deborah Rosenberg
• Kristin Rankin
• Craig A. Mason
• Juan Acuña

2
Workshop Outline

• Overview of the Population Attributable Fraction
  (PAF)
• Methodological issues for the PAF in a
  multivariable context
• A simple example with 2 variables
• A modeling approach for a an example with 3
  variables
• Direct and indirect effectsthe special case when
  variables are in a causal pathway
• Issues for using the PAF for priority-setting,
  program planning, and to inform policy
• What we wont discuss
• Standard error and confidence interval estimation
• Statistical testing

3
The Population Attributable Fraction (PAF) for
Public Health Assessment Epidemiologic Issues,
Part I

• Deborah Rosenberg, PhD
• Research Assistant Professor
• Epidemiology and Biostatistics
• UIC School of Public Health

4
Overview of Attributable Risk Measures

• Measures based on Risk Differences
• Attributable Risk
• Attributable Fraction
• Pop. Attributable Risk
• Pop. Attributable Fraction

5
Overview of Attributable Risk Measures

• The PAF can also be computed as a function of the
  relative risk and the prevalence and distribution
  of exposure in the population
• directly in cohort and cross-sectional studies
• substituting the odds ratio as an estimate when
  appropriatein case control studies when
  disease is rare

6
Methodological Issues for the PAF in a
Multivariable Context

• In a multivariable context, the goal is to
  generate a PAF for each of multiple factors,
  taking into account relationships with other
  factors
• The sum of this set of PAFs should equal the
  aggregate PAF calculated for all of the factors
  combined

7
Methodological Issues for the PAF in a
Multivariable Context

• Generating mutually exclusive and mutually
  adjusted PAFs is not straightforward because of
  the overlapping distributions of exposure in the
  population
• Methods that go beyond the usual adjustment
  procedures, therefore, have to be used to address
  correlation between variables

8
Methodological Issues for the PAF in a
Multivariable Context

• In addition to different computational
  approaches, decisions about how variables will be
  considered may be different when focusing on the
  PAF than when focusing on the ratio measures of
  association
• Differentiating the handling of modifiable and
  non-modifiable risk factors
• Confounding and effect modification
• Handling factors in a causal pathway

9
Methodological Issues for the PAF in a
Multivariable Context

• Having an explicit conceptual framework / logic
  model is always important for multivariable
  analysis, and is particularly critical when
  focusing on the PAF because decisions about how
  to handle variables will not only influence the
  substantive interpretation of results, but will
  change computational steps as well.

10
Methodological Issues for the PAF in a
Multivariable Context

• Approaches to Generating PAFs
• Aggregate PAF The total PAF for many factors
  considered in a single risk system
• Component PAF The separate PAF for each
  combination of exposure levels in a risk system
• Sequential PAF The PAF considering one possible
  order for eliminating risk factors
• Average PAF The PAF summarizing all possible
  sequences for eliminating a risk factor

11
The simple case of 2 variables

• Smoking and Cocaine
• Crude RR 1.60 Crude RR 4.77

12
Smoking and Cocaine Organized into a Risk System

• Aggregate RR 1.88

13
Components of the Smoking-Cocaine Risk System

• Components
• RR5.89, both smoking and
  cocaine use
• 
  RR4.30, cocaine use only
• 
  RR1.36, smoking only
• There is a component for each combination of
  exposure levels in the risk system.

14
Components of the Smoking-Cocaine Risk System

• The aggregate PAF (PAFAGG) of
• variables in a risk system equals
• the sum of the component PAFs.
• 
  
• 
  

15
Components of the Smoking-Cocaine Risk System

• While the component PAFs of a risk system sum to
  the aggregate PAF for the system as a whole, they
  do not provide mutually exclusive measures of the
  PAF for each risk factor
• Here, the aggregate PAF 0.16,
• but the two factors are related
• some women are both smokers
• and cocaine users

16
The Adjusted PAF The Stratified Approach

• The PAF for eliminating an exposure
• controlling for other risk factors
• PAF considering potential effect modification
  (This assumption-free approach always applies)
• PAF assuming no effect modification

17
The Adjusted PAFThe PAF for Smoking,
Controlling for Cocaine Use

• RR1.37
• RR1.36

18
The Adjusted PAFThe PAF for Cocaine Use,
Controlling for Smoking

• RR4.33
• RR4.30

19
The Adjusted PAF

• While the usual adjustment methods control for
  other risk factors, the resulting adjusted PAFs
  still do not meet the criterion of summing to the
  aggregate PAF for all factors combined
• ?
• 0.0420.0620.0560.16 0.076 0.099 0.175

20
The Adjusted PAF

• The typical adjustment procedures result in a PAF
  that, by itself, represents an estimateperhaps
  unrealisticof the impact of eliminating one
  exposure in a risk system, controlling for the
  effects of other risk factors in the system
• The adjusted PAF becomes more useful when
  viewed as one element of a sequence for
  eliminating all risk factors in a system

21
Sequential PAFs (PAFSEQ) for theSmoking-Cocaine
Risk System

• For the smoking-cocaine risk system, there are 2
  possible sequences
• Eliminate smoking first, controlling for cocaine
  use, then eliminate cocaine use
• Eliminate cocaine use first, controlling for
  smoking, then eliminate smoking
• And within each sequence, there are two
  sequential PAFs

22
Sequential PAFs (PAFSEQ) for theSmoking-Cocaine
Risk System

• The PAFSEQ for eliminating smoking, controlling
  for cocaine use
• PAFSEQ (SC) 0.076
• The PAFSEQ for eliminating cocaine use after
  smoking has already been eliminated is the
  remainder of the Aggregate PAF
• PAFAGG PAFSEQ (SC) 0.16 0.076 0.084

23
Sequential PAFs (PAFSEQ) for theSmoking-Cocaine
Risk System

• The PAFSEQ for eliminating cocaine use,
  controlling for smoking
• PAFSEQ (CS) 0.099
• The PAFSEQ for eliminating smoking after cocaine
  use has already been eliminated is the remainder
  of the Aggregate PAF
• PAFAGG PAFSEQ (CS) 0.16 0.099 0.061

24
Sequential PAFs (PAFSEQ) for theSmoking-Cocaine
Risk System

• By definition, the sequential PAFs within the two
  possible sequences sum to the Aggregate PAF
• Smoking First Cocaine Use First
• 0.076 0.084 0.16 0.099 0.061 0.16

25
Average PAF (PAFAVG) for theSmoking-Cocaine Risk
System

• While the sequential PAFs for each sequence sum
  to the aggregate PAF, they still do not provide a
  summary comparison of the impact of smoking and
  cocaine use regardless of the order in which they
  are eliminated
• That is, regardless of the order of elimination,
  what would be the impact of eliminating smoking
  on average?

26
Average PAF (PAFAVG) for theSmoking-Cocaine Risk
System

• To calculate an average, the sequential PAFs are
  rearranged, grouping the two for smoking together
  and the two for cocaine together
• Eliminating smoking first, averaged with
  eliminating smoking second
• Eliminating cocaine use first, averaged with
  eliminating cocaine use second

27
Average PAF (PAFAVG) for theSmoking-Cocaine Risk
System

• Averaging Sequential PAFs
• Average PAF for Smoking
• Average PAF for Cocaine Use

28
Average PAFs for theSmoking-Cocaine Risk System

• The Average PAFs for each factor in the risk
  system are mutually exclusive and their sum
  equals the Aggregate PAF
• 0.0685 0.0915 0.16

29
Average PAFs for theSmoking-Cocaine Risk System

• The average PAF is perhaps most realistic since
  typically there are multiple interventions
  operating simultaneouslyrisk reduction
  activities are unordered and often intersect
• In addition, averages can be customizedinstead
  of a simple average, the sequential PAFs can be
  differentially weighted to reflect other
  unmeasured issues such as funding streams or
  political will

30
In a Truly Multivariable Context

• The number of average PAFs equals the number of
  variables in a risk system. The number of
  sequences is a function of the number of
  variables and becomes large quickly as the number
  of variables increases.
• 2 variables 2 sequences
• 3 variables 6 sequences
• 5 variables 30 sequences
• Computation of the sequential PAFs becomes
  cumbersome and an automated modeling approach is
  needed

31
The Population Attributable Fraction (PAF) for
Public Health Assessment Epidemiologic Issues,
Part II

• Kristin Rankin, MSPH
• Assistant Director of Research
• CADE Research Data Management Group
• UIC School of Public Health

32
PAF from Modeling

• Why isnt the multivariable PAF used more
  commonly in the analysis of public health data?
• No known standard statistical packages to
  complete all steps
• What is the advantage of using modeling
  techniques over stratified analysis?

33
Advantages of Obtaining Estimates from Modeling

• Modeling is not as sensitive to sparse data in
  individual cells when there are many strata
• If you choose to consider confounding and effect
  modification in the same model, estimates are
  generated more easily
• Note Using an assumption-free approach, all
  variables are treated as effect modifiers

34
Using SAS PROC GENMOD

• With cross-sectional data, such as birth
  certificate data, you can use PROC GENMOD in SAS
  with log link and binomial or Poisson
  distribution to model the relative risks (RR) of
  factors
• As number of factors of interest increases, still
  only need one model to obtain relative risks for
  several different stratified relationships (using
  the Estimate statement in SAS)

35
Modifiable and Unmodifiable Risk Factors

• In addition, within one model, we can
  differentiate between those factors considered to
  be modifiable and those factors considered to be
  unmodifiable
• This differentiation has an impact on the
  resulting aggregate, sequential, and average PAFs.

36
Case Study

• Scenario You are asked to prioritize spending
  for interventions that target the high rate of lo
  birth weight (LBW) in your jurisdiction.
• Data You have a data set with relatively
  reliable data on smoking during pregnancy,
  cocaine use during pregnancy and poverty level.
• Method You would like to use one of the methods
  you just learned for calculating the PAFs for
  each of these factors.

37
Descriptive Statistics for Case Study
38
Component PAFs for Entire Risk System
39
Choose Your Own Adventure

• Would you consider each of the following
  variables unmodifiable or modifiable for
  preventing LBW?
• Smoking (1Smoking during pregnancy, 0No
  smoking)
• Cocaine (1Cocaine use during pregnancy, 0No
  cocaine)
• Poverty (1Below Federal Poverty Level, 0Above
  FPL)
• What type of PAF is most appropriate?
• Adjusted (only focused on one factor, controlling
  for others)
• Sequential (specifying one ordering for targeting
  factors)
• Average (account for all possible sequences of
  eliminating each factor)

40
Considering Poverty as UnmodifiableCalculating
Sequential and/or Average PAFs for Smoking and
Cocaine Use
41
SAS Code Obtaining Prevalence for Any Modifiable
Exposure vs LBW, Stratified by Poverty

• /Must first sort data set to use by variable
  below/
• proc sort
• by poverty
• run
• /Then, produce frequency tables for low birth
  weight (lbw) and any modifiable exposure
  (mod_exp), stratified by poverty/
• proc freq orderformatted
• tables lbwmod_exp/list nopercent
• /mod_exp1 if smoke1 or cocaine1/
• by poverty /Stratified by poverty/
• run

42
SAS Code Modeling to Obtain Stratified RRs for
Any Modifiable Exposure vs LBW

• /Binomial regression run below to obtain RRs/
• proc genmod title2 "Smoke and Cocaine,
  Stratified by Poverty"
• model lbw mod_exp poverty mod_exp
  poverty
• /mod_exp1 if woman has at least one
  of the modifiable
• exposures/
• / distbin linklog /Binomial
  distribution/
• estimate Smoke and/or Cocaine, where
  PovertyYes
• mod_exp 1 Poverty 0 mod_expPoverty
  1/exp/Stratified RR/
• estimate Smoke and/or Cocaine, where
  PovertyNo
• mod_exp 1 /exp /Stratified RR/
• run

43
SAS Results Elements of the PAFAGG for Risk
System, Stratified by Poverty
PovertyYes
PovertyNo
44
PAFAGG for Smoking and Cocaine Risk System,
Considering Poverty Unmodifiable
PovertyYes
PovertyNo
45
SAS Code Obtaining Prevalences for Smoke and
Cocaine vs LBW, Stratified by Poverty

• /Must first sort data set to use by variable
  below/
• proc sort
• by poverty
• run
• /Create a listing of the frequencies for each
  possible combination of smoke, poverty and lbw to
  calculate proportions/
• proc freq orderformatted
• tables lbwsmokecocaine/list nopercent
• by poverty /Stratified by poverty/
• run

46
SAS Code Modeling to Obtain RRs for Smoke and
Cocaine vs LBW, Stratified by Poverty

• /Binomial regression run below to obtain RRs/
• proc genmod
• title2 RRs for Smoke and Coke with LBW,
  controlling for Poverty"
• model lbw smoke cocaine poverty
• smokecocaine smokepoverty
  cocainepoverty
• smokecocainepoverty
• /Every possible multiplicative term
  must be in model
• if using assumption-free, stratified
  approach/
• /distbin linklog obstats /Binomial
  distribution/
• /ESTIMATE Statements in future slides should be
  inserted here/
• run

47
SAS Code Estimate Statements to Obtain
Stratified RRs for Smoking

• /defining all possible parameter values for
  stratified model/
• estimate smoke, where cocaineYes and
  povertyYes
• smoke 1 cocaine 0 poverty 0 smokecocaine 1
  smokepoverty 1
• cocainepoverty 0 smokecocainepoverty 1
• / exp / exp option gives relative risks
  from betas /
• estimate smoke, where cocaineYes and
  povertyNo
• smoke 1 cocaine 0 poverty 0 smokecocaine 1
  smokepoverty 0
• cocainepoverty 0 smokecocainepoverty 0
• / exp
• estimate smoke, where cocaineNo and
  povertyYes
• smoke 1 cocaine 0 poverty 0 smokecocaine 0
  smokepoverty 1
• cocainepoverty 0 smokecocainepoverty 0
• /expestimate smoke, where cocaineNo and
  povertyNo
• smoke 1 cocaine 0 poverty 0 smokecocaine 0
  smokepoverty 0
• cocainepoverty 0 smokecocainepoverty 0
• / exp

48
SAS Results Elements of PAFSEQ for Smoking
Removed First
PovertyYes
PovertyNo
49
Elements of PAFSEQ for Smoking Removed First,
Considering Poverty Unmodifiable
PovertyYes
CokeYes
CokeNo
PovertyNo
CokeYes
CokeNo
50
SAS Code Estimate Statements to Obtain
Stratified RRs for Cocaine

• estimate Cocaine, where smokeYes and
  povertyYes
• cocaine 1 smoke 0 poverty 0 cocainesmoke 1
  cocainepoverty 1
• smokepoverty 0 cocainesmokepoverty 1
• / exp e
• estimate Cocaine, where smokeYes and
  povertyNo
• cocaine 1 smoke 0 poverty 0 cocainesmoke 1
  cocainepoverty 0
• smokepoverty 0 cocainesmokepoverty 0
• / exp e
• estimate Cocaine, where smokeNo and
  povertyYes
• cocaine 1 smoke 0 poverty 0 cocainesmoke 0
  cocainepoverty 1
• smokepoverty 0 cocainesmokepoverty 0
• / exp e
• estimate Cocaine, where smokeNo and povertyNo
• cocaine 1 smoke 0 poverty 0 cocainesmoke 0
  cocainepoverty 0
• smokepoverty 0 cocainesmokepoverty 0
• / exp e

51
SAS Results Elements of PAFSEQ for Cocaine
Removed First
PovertyYes
PovertyNo
52
PAFSEQ for Cocaine Removed First, Considering
Poverty Unmodifiable
PovertyYes
SmokeYes
SmokeNo
PovertyNo
SmokeYes
SmokeNo
53
PAFSEQ for Smoking and Cocaine,Considering
Poverty as Unmodifiable

• Sequence 1 Smoking, THEN Cocaine
• PAFSEQ1a (S CP) 0.07
• PAFSEQ1b (CS P S CP) (0.15 0.07)
  0.08
• Sequence 2 Cocaine, THEN Smoking
• PAFSEQ2a (C SP) 0.10
• PAFSEQ2b (SC P C SP) (0.15 - 0.10) 0.05

54
PAFSEQ for Smoking and Cocaine,Considering
Poverty as Unmodifiable
Smoking THEN Cocaine, Controlling for Poverty
Cocaine THEN Smoking, Controlling for Poverty
PAFSEQ2
PAFAGG0.15
PAFAGG0.15
PAFAGG0.15
55
Average PAFs for Smoking and Cocaine,Controlling
for Poverty

• Average PAF for Smoking
• PAFAVG ((PAFSEQ1aPAFSEQ2b)/2)
• PAFAVG ((0.07 0.05 ) / 2) 0.06
• Average PAF for Cocaine
• PAFAVG ((PAFSEQ1bPAFSEQ2a)/2)
• PAFAVG ((0.10 0.08 ) / 2) 0.09

56
Considering Poverty ModifiableCalculating
Sequential and/or Average PAFsfor Smoking,
Cocaine Use, and Poverty
57
SAS Code Obtaining Prevalences for Any
Modifiable Exposure vs LBW

• /Produce frequency tables for low birth weight
  (lbw) and any modifiable exposure (mod_exp)/
• proc freq orderformatted
• tables lbwmod_exp/list nopercent
• /mod_exp1 if smoke1 or cocaine1 or
  poverty1/
• run

58
SAS Code Modeling to Obtain RR for Any
Modifiable Exposure vs LBW

• /Binomial regression run below to obtain RRs/
• proc genmod
• title2 Any Modifiable Exposure (Smoke, Cocaine
  and/or Poverty"
• model lbw mod_exp
• /mod_exp1 if woman has at least one
  of the
• modifiable exposures/
• / distbin linklog /Binomial
  distribution/
• estimate Any Modifiable Exposure
  mod_exp 1 / exp
• run

59
SAS Results Elements of the PAFAGG for Risk
System (Smoking, Cocaine, Poverty)
60
SAS Code Obtaining Prevalences for Smoke,
Cocaine and Poverty vs LBW

• /Create a listing of the frequencies for each
  possible combination of smoke, cocaine, poverty
  and lbw to calculate proportions/
• proc freq orderformatted
• tables lbwsmokecocainepoverty/list
  nopercent
• run

61
SAS Code Modeling to Obtain RRs for Smoke,
Cocaine and Poverty vs LBW

• /Binomial regression run below to obtain RRs/
• proc genmod
• title2 RRs for Smoke, Coke, and Poverty with
  LBW"
• model lbw smoke cocaine poverty
• smokecocaine smokepoverty
  cocainepoverty
• smokecocainepoverty
• /Every possible multiplicative term
  must be in model
• if using assumption-free, stratified
  approach/
• /distbin linklog obstats /Binomial
  Distribution/
• /ESTIMATE Statements in future slides should be
  inserted here/
• run

62
SAS Code Estimate Statements to Obtain
Stratified RRs for Smoking

• /defining all possible parameter values for
  stratified model/
• estimate smoke, where cocaineYes and
  povertyYes
• smoke 1 cocaine 0 poverty 0 smokecocaine 1
  smokepoverty 1
• cocainepoverty 0 smokecocainepoverty 1
• / exp / exp option gives relative risks
  from betas /
• estimate smoke, where cocaineYes and
  povertyNo
• smoke 1 cocaine 0 poverty 0 smokecocaine 1
  smokepoverty 0
• cocainepoverty 0 smokecocainepoverty 0
• / exp
• estimate smoke, where cocaineNo and
  povertyYes
• smoke 1 cocaine 0 poverty 0 smokecocaine 0
  smokepoverty 1
• cocainepoverty 0 smokecocainepoverty 0
• /expestimate smoke, where cocaineNo and
  povertyNo
• smoke 1 cocaine 0 poverty 0 smokecocaine 0
  smokepoverty 0
• cocainepoverty 0 smokecocainepoverty 0
• / exp

63
SAS Results Elements of the PAFSEQ for Smoking
Removed First
64
SAS Results Elements of PAFSEQ for Smoking
Removed First
65
PAFSEQ for Smoking Removed First
CokeYes PovertyYes
CokeNo PovertyYes
CokeYes PovertyNo
CokeYes PovertyNo
66
SAS Code Estimate Statements to Obtain
Stratified RRs for Cocaine
estimate Cocaine, where smokeYes and
povertyYes cocaine 1 smoke 0 poverty 0
cocainesmoke 1 cocainepoverty 1 smokepoverty
0 cocainesmokepoverty 1 / exp e estimate
Cocaine, where smokeYes and povertyNo
cocaine 1 smoke 0 poverty 0 cocainesmoke 1
cocainepoverty 0 smokepoverty 0
cocainesmokepoverty 0 / exp e estimate
Cocaine, where smokeNo and povertyYes cocaine
1 smoke 0 poverty 0 cocainesmoke 0
cocainepoverty 1 smokepoverty 0
cocainesmokepoverty 0 / exp e estimate
Cocaine, where smokeNo and povertyNo cocaine
1 smoke 0 poverty 0 cocainesmoke 0
cocainepoverty 0 smokepoverty 0
cocainesmokepoverty 0 / exp e
67
SAS Results Elements of the PAFSEQ for Cocaine
Removed First
68
SAS Results Elements of the PAFSEQ for Cocaine
Removed First
69
PAFSEQ for Cocaine Removed First
PovertyYes SmokeNo
PovertyYes SmokeYes
PovertyNo SmokeYes
PovertyNo SmokeNo
70
SAS Code Estimate Statements to Obtain
Stratified RRs for Poverty

• estimate Poverty, where SmokeYes and
  CocaineYes
• poverty 1 smoke 0 cocaine 0 povertysmoke 1
• povertycocaine 1 smokecocaine 0
  povertysmokecocaine 1
• / exp e
• estimate Poverty, where SmokeYes and
  CocaineNo
• poverty 1 smoke 0 cocaine 0 povertysmoke 1
• povertycocaine 0 smokecocaine 0
  povertysmokecocaine 0
• / exp e
• estimate Poverty, where SmokeNo and
  CocaineYes
• poverty 1 smoke 0 cocaine 0 povertysmoke 0
• povertycocaine 1 smokecocaine 0
  povertysmokecocaine 0
• / exp e
• estimate Poverty, where SmokeNo and CocaineNo
• poverty 1 smoke 0 cocaine 0 povertysmoke 0
• povertycocaine 0 smokecocaine 0
  povertysmokecocaine 0
• / exp e

71
SAS Results Elements of the PAFSEQ for Poverty
Removed First
72
SAS Results Elements of the PAFSEQ for Poverty
Removed First
73
PAFSEQ for Poverty Removed First
SmokeYes CocaineNo
SmokeYes CocaineYes
SmokeNo CocaineYes
SmokeNo CocaineNo
74
Elements for Calculation of Factors Removed
Second and Third

• To calculate the PAFSEQ for factors removed
  second and third, you will first need the
  sub-PAFAGG for every combination of two factors
  combined, stratified by the third factor.
• Sub-PAFAGG
• SCP 0.15
• SPC 0.37
• CPS 0.37

75
PAFSEQ for Smoking Removed First

• Sequence 1 Smoking, THEN Cocaine, THEN Poverty
• PAFSEQ1a (S CP) 0.07
• PAFSEQ1b (SC P S CP) (0.15 0.07)
  0.08
• PAFSEQ1c (SCP SC P) (0.46 0.15) 0.31
• Sequence 2 Smoking, THEN Poverty, THEN Cocaine
• PAFSEQ2a (S PC) 0.07
• PAFSEQ2b (SP C S PC) (0.38 0.07)
  0.31
• PAFSEQ2c (SPC SP C) (0.46 0.38) 0.08

76
PAFSEQ for Smoking Removed First
Smoking THEN Cocaine, THEN Poverty
Smoking THEN Poverty, THEN Cocaine
PAFSEQ2
PAFAGG 0.46
PAFAGG 0.46
77
PAFSEQ for Cocaine Removed First

• Sequence 3 Cocaine, THEN Smoking, THEN Poverty
• PAFSEQ3a (C SP) 0.10
• PAFSEQ3b (CS P C SP) (0.15-0.10) 0.05
• PAFSEQ3c (CSP CS P) (0.46 - 0.15) 0.31
• Sequence 4 Cocaine, THEN Poverty, THEN Smoking
• PAFSEQ4a (C PS) 0.10
• PAFSEQ4b (CP S C PS) (0.37 - 0.10) 0.27
• PAFSEQ4c (CPS CP S) (0.46 - 0.37) 0.09

78
PAFSEQ for Cocaine Removed First
Cocaine THEN Smoking, THEN Poverty
Cocaine THEN Poverty, THEN Smoking
PAFSEQ2
PAFAGG 0.46
PAFAGG 0.46
PAFAGG 0.46
79
PAFSEQ for Poverty Removed First

• Sequence 5 Poverty, THEN Smoking, THEN Cocaine
• PAFSEQ5a (P SC) 0.28
• PAFSEQ5b (PS C P SC) (0.38 0.28)0.10
• PAFSEQ5c (PSC PS C) (0.46 - 0.38)0.08
• Sequence 6 Poverty, THEN Cocaine, THEN Smoking
• PAFSEQ6a (P CS) 0.28
• PAFSEQ6b (PC S P CS) (0.37 - 0.28) 0.09
• PAFSEQ6c (PCS PC S) (0.46 - 0.37) 0.09

80
PAFSEQ for Poverty Removed First
Poverty THEN Smoking, THEN Cocaine
Poverty THEN Cocaine THEN Smoking
PAFSEQ2
PAFAGG 0.46
PAFAGG 0.46
81
PAFAVG for Smoking, Cocaine and Poverty

• Average PAF for Smoking
• PAFAVG ((PAFSEQ1aPAFSEQ3bPAFSEQ4cPAFSEQ5b)/4)
  
• PAFAVG ((0.07 0.05 0.09 0.10 ) / 4)
  0.08
• Average PAF for Cocaine
• PAFAVG ((PAFSEQ1bPAFSEQ2cPAFSEQ3aPAFSEQ6b)/4)
  
• PAFAVG ((0.08 0.08 0.10 0.09 ) / 4)
  0.09
• Average PAF for Poverty
• PAFAVG ((PAFSEQ1cPAFSEQ2bPAFSEQ4bPAFSEQ5a)/4)
  
• PAFAVG ((0.31 0.31 0.27 0.28 ) / 4)
  0.29

82
Average PAFs for all possible models
Smoke and Coke, Controlling for Poverty
Smoke and Coke
Smoke, Coke and Poverty
PAFAGG0.16
PAFAGG0.46
PAFAGG0.15
83
Summary

• Partitioning methods allow
• Precise (accurate) estimation of the population
  attributable fraction
• Mutually exclusive estimates that make
  comparisons of the potential impact of
  intervention strategies among factors possible

84
Selected Articles for Additional Reading

• Benichou, J. (2001). A review of adjusted
  estimators of attributable risk. Statistical
  Methods in Medical Research 10 195-216.
• Eide, G., Gefeller, O. (1995). Sequential and
  average attributable fractions as aids in the
  selection of prevention strategies. Journal of
  Clinical Epidemiology 48(5) 645-655.
• Gefeller, O., Land, M., Eide, G. (1998).
  Averaging Attributable Fractions in the
  Multifactorial Situation Assumptions and
  Interpretation. Journal of Clinical Epidemiology
  51(5) 437-441.
• Land, M., Vogel, C., Gefeller, O. (2001).
  Partitioning methods for multifactorial risk
  attribution. Statistical Methods in Medical
  Research 10 217-230.
• Rothman, K.J. and Greenland, S. Modern
  Epidemiology. Philadelphia Lippincott Williams
  Wilkins, 2nd ed, 1998 295.

85
Contact Information

• Deborah Rosenberg
• drose_at_uic.edu
• Kristin Rankin
• krankin_at_uic.edu