using the population attributable fraction (paf) to assess mch population outcomes deborah...

Using the Population Attributable Fraction (PAF) to Assess MCH Population Outcomes

Deborah Rosenberg, PhD and Kristin Rankin, PhD

Epidemiology and Biostatistics

School of Public Health

University of Illinois at Chicago

Day One: 8:30-12:00

Background and Overview Basic Formulas and Initial Computations Moving Beyond Crude PAFs: Organizing

Multiple Factors into a Risk System Summary, Component and “Adjusted” PAFs

3

Background Epidemiologists most commonly use ratio measures

to estimate the magnitude of an association between a risk factor and an outcome

Impact measures, such as the Population Attributable Fraction (PAF), account for both the magnitude of association and the prevalence of risk in the population

PAFs are underused because of methodological concerns about how to appropriately account for the multifactorial nature of risk factors in the population

4

Background In a multivariable context, the goal is to generate a

PAF for each of multiple factors, taking into account relationships among the factors

Generating mutually exclusive and mutually adjusted PAFs is not straightforward given the overlapping distributions of exposure in the population; therefore methods that go beyond usual adjustment procedures are required

With appropriate methods, the PAF can be a tool for program planning and priority setting in public health since, unlike ratio measures, it permits sorting of risk factors according to their impact on an outcome

5

Historical Highlights

Levin’s PAF (1953) “Indicated maximum proportion of disease attributable

to a specific exposure” If an exposure is completely eliminated, then the

disease experience of all individuals would be the same as that of the “unexposed”

P(E) = prevalence of the exposure in the population as a whole p0 = prevalence of the outcome in the population as a whole p2 = prevalence of the outcome in the unexposed

0

20

p

pp

1)1RR(*)E(P

)1RR(*)E(PcrudePAF

6

Historical Highlights

Miettenin (1974) Adjusted PAF = Proportion of the disease that could be

reduced by eliminating one risk factor, after controlling for others factors and accounting for effect modification

Bruzzi (1985)/Greenland and Drescher (1993) Summary PAF = Proportion of the disease that could be

reduced by simultaneously eliminating multiple risk factors from the population

Method for using regression modeling to generate PAFs

Benichou and Gail (1990) Variance estimates for the adjusted and summary PAF

based on the delta method

7

Summary PAF = 0.457

Components of a risk system:

complete crossclassification of factors

0.0230.068

0.043

0.031

0.234

0.035

0.023

0.543

Factors A,B and C

Factor A Alone

Factor A and BFactor A and C

Factor B Alone

Factor B and C

Factor C AloneUnknown/Unexplained

Example: Summary PAF for Three Risk Factors for a Health Outcome

8

Apportioning the Summary PAF

The complete crossclassification of factors is not satisfactory because it fails to provide an overall estimate of impact for each risk factor.

Methodological work has been and is still being carried out to develop approaches that apportion the Summary PAF in a way that yields estimates of impact for each of a set of risk factors

9

Apportioning the Summary PAFEide and Gefeller (1995/1998)

Sequential PAF = Proportion of the disease that could be reduced by eliminating one risk factor from the population after some factors have already been eliminated

First Sequential PAF = the “adjusted PAF” —the particular sequential PAF in which a risk factor is eliminated first before any other factors

10

Apportioning the Summary PAF

Ordering is imposed for eliminating risk factors from the population, while simultaneously controlling for all other factors in the model

EXAMPLE (Sequence #1):Eliminate A, then B, then C

Sequential PAF* (A) = (A|B, C) Sequential PAF (B) = (A U B|C) – (A|B, C) Sequential PAF (C) = (A U B U C) – (A U B|

C)

*First Sequential or “adjusted” PAF

11

Summary PAF Apportioned into Sequential PAFs for Sequence #1

Eliminate A, then B, then C

Factor C=0.023

0.543

Factors A,B and C

Factor A Alone

Factor A and BFactor A and C

Factor B Alone

Factor B and C

Factor C AloneUnknown/Unexplained

Factor A=0.323

Factor B=0.111

12

Apportioning the Summary PAFEide and Gefeller (1995/1998)

Average PAF = Simple average of all sequential PAFs

Equal apportionment of risk over every possible sequence (removal orderings), since the order in which risk factors will be eliminated in the “real world” is an unknown

Based on the Shapley-solution in Game Theory Method of fairly distributing the total profit gained

by team members working in coalitions

13

Apportioning the Summary PAF:The Average PAFSix Sequences for Three Risk Factors

Sequence #1: Eliminate A, then B, then CSequence #2: Eliminate A, then C, then BSequence #3: Eliminate B, then A, then CSequence #4: Eliminate B, then C, then ASequence #5: Eliminate C, then A, then BSequence #6: Eliminate C, then B, then A

There are a total of 6 sequential PAFs for each of the three risk factors. The Average PAF for each factor, then, is the simple average of all 6.

14

Summary PAF Apportioned into Average PAFs for Three Risk Factors

0.290

0.090

0.543

0.078

Factor A

Factor B

Factor C

Unknown/Unexplained

15

The Summary PAF: the Basis for Producing Multifactorial PAFsThe Summary PAF can be apportioned into:

component PAFs reflecting every possible combination of factors being considered

sequential PAFs reflecting pieces of one particular sequence in which risk factors might be eliminated

average PAFs reflecting estimates of the impact of eliminating multiple risk factors regardless of the order in which each is eliminated

16

PAFs from Different Study DesignsCross-sectional:

Prevalence and measure of effect estimated from same data source

Interpretation: Proportion of prevalent cases that can be attributed to exposure

Cohort: Prevalence and measure of effect estimated from same

data source Interpretation: Proportion of incident cases that can be

attributed to exposure Case-Control:

Prevalence of exposure among the cases must be used and the OR in place of the RR, using the rare disease assumption

Interpretation: Proportion of incident cases that can be attributed to exposure

17

Methodological Issues for the PAFin a Multivariable ContextIn addition to different computational approaches, decisions about how variables will be considered may be different when focusing on the PAF as compared with focusing on the ratio measures of association

Differentiating the handling of modifiable and unmodifiable factors

Confounding and effect modification Handling factors in a causal pathway

18

Analytic Considerations

Variable Selection

Modifiability Unmodifiable factors are only used as potential

confounders or effect modifiers; PAFs not calculated Modifiable factors are factors that can possibly be

altered with clear intervention strategies

Classification of risk factors as unmodifiable or modifiable depends on perspective and may alter results

19

Analytic ConsiderationsModel Building

Differential handling of unmodifiable and modifiable factors Levels of measurement Coding choices Effect modification

– within modifiable factors– across modifiable and unmodifiable factors– within unmodifiable factors

Selection of a final model may not be based on statistical significance of the ratio measure of effect

Stratified models Defining the “significance” of PAFs

20

Analytic ConsiderationsPresentation and Interpretation

Average PAFs allow for the sorting of modifiable risk factors according to the potential impact of risk factor reduction strategies on an outcome in the population; Ratio measures only provide the magnitude of the association between a risk factor and a disease

The PAF is the proportion of an outcome that could be reduced if a risk factor is completely eliminated in the population – take care not to over-interpret findings

21


So, why isn’t the multifactorial PAF used more commonly in the analysis of public health data?

No known standard statistical packages to complete all of the steps

Variance estimates for the average PAF are not yet available, either for random samples or for samples from complex designs

Currently, can only report 95% confidence intervals around crude, summary, and first sequential (adjusted) PAFs

While the interpretation of average PAFs is strengthened by evidence of causality, an average PAF cannot itself establish causality

22


As always, having an explicit conceptual framework / logic model is important for multivariable analysis

Conceptualization is particularly critical when producing PAFs because decisions about variable handling and model building will determine the computational steps as well as influencing the substantive interpretation of results.

23

Laying the Groundwork:

An Example with Crude PAFs

24

Measures based on Risk Differences

Attributable Risk

Attributable Fraction

Population Attributable Risk

Population Attributable Fraction (PAF)

Overview of Attributable Risk Measures

20 pp

1

21

p

pp

21 pp

0

20

p

pp

OUTCOME Freq Row Pct Yes No total

Risk Factor Yes

a p1

b n1

Risk Factor No

c p2

d n2

Total m1 p0

m2 N

25

Overview of Attributable Risk MeasuresGeneral Interpretation

Attributable Risk: The risk of an outcome attributed to a given risk factor among those with that factor

Attributable Fraction: The proportion of cases of an outcome attributable to a risk factor in those with the given risk factor

Pop. Attributable Risk: The risk of an outcome attributed to a given risk factor in the population as a whole

Pop. Attributable Fraction (PAF): The proportion of cases of an outcome attributable to a risk factor in the population as a whole

26

Overview of Attributable Risk Measures

Equivalent / Alternative Terminology

• Attributable Risk, Risk Difference • Attributable Fraction, Attributable Risk %

Attributable Proportion, Etiologic Fraction• Pop. Attributable Risk• Pop. Attributable Fraction, Population Attributable

Risk %, Etiologic Fraction, Attributable Risk

27

Overview of Attributable Risk MeasuresVarious Formulas For the Crude PAF

DP

E|DPDP

11Total

#

1Total

#

Risk Relativeexposed of

Risk Relativeexposed of

RiskRelative

1 RiskRelative

Cases Total

cases exposed of #

0

20

p

pp

1)1RR(*)E(P

)1RR(*)E(PcrudePAF


Risk Factor Yes

a p1

b n1

Risk Factor No

c p2

d n2

Total m1 p0

m2 N

28

Example: Smoking and Low Birthweight

Crude RR = 10.00 = 1.60

6.25

Freq LOW BIRTHWEIGHT Row Pct| yes | no |Total _______|________|________| smoke| 200 | 1800 | 2000 yes| 10.00 | 90.00 | _______|________|________| smoke| 500 | 7500 | 8000 no| 6.25 | 93.75 | _______|________|________| Total 700 9300 10000

PAR % =200

700

1.6 -1

1.6

100

10 7%. 107.06.1

16.1

700

200 PAFCrude

29

Example: Smoking and Low BirthweightCrude AssociationInterpretation of the RR v. the PAF

Women who smoke are at 1.6 times the risk of delivering a LBW infant compared to women who do not smoke.

10.7% of LBW births can be attributed to smoking. If smoking were eliminated, we would expect 75 fewer LBW births and the LBW rate would be reduced from 7% to 6.25%

30

Example: Cocaine and Low BirthweightCrude Association

Crude RR = 30.00 = 4.77

6.29

Freq LOW BIRTHWEIGHT Row Pct| yes | no |Total _______|________|________| cocaine| 90 | 210 | 300 yes| 30.00 | 70.00 | _______|________|________| cocaine| 610 | 9090 | 9700 no| 6.29 | 93.71 | _______|________|________| Total 700 9300 10000 102.0

77.4

177.4

700

90 PAFCrude

31

Example: Cocaine and Low BirthweightCrude AssociationInterpretation of the RR v. the PAF

Women who use cocaine are at 4.77 times the risk of delivering a LBW infant compared to women who do not use cocaine.

10.2% of LBW births can be attributed to cocaine use. If cocaine use were eliminated, we would expect 71 fewer LBW births and the LBW rate would thus be reduced from 7% to 6.29%

32

Smoking and Low BirthweightCocaine and Low Birthweight

RR Compared to PAF

Notice that although the relative risk for the association between cocaine and low birthweight is much greater than that for smoking and low birthweight, the PAF for each is quite similar—10.7 for smoking and 10.2 for cocaine.

33

Moving Beyond Crude PAFs

Multivariable Approaches:

Organizing Multiple Factors

into a Risk System

34

PAFs Based on Organizing Multiple Factors into a Risk System Summary PAF: The total PAF for many modifiable

factors considered in a single risk system Component PAF: The separate PAF for each

unique combination of exposure levels in a risk system

“Adjusted” PAF: The PAF for eliminating a risk factor first from a risk system

Sequential PAF: The PAF for eliminating a risk factor in a particular order from a risk system; sets of sequential PAFs comprise possible removal sequences

Average PAF: The PAF summarizing all possible sequences for eliminating a risk factor

35

Extension of Basic Formulas for Multifactorial PAFs

= =

Rothman Bruzzi

– k=Number of unique exposure categories created with a complete cross-classification of independent variables

– pj=proportion of total cases that are in the “jth” unique exposure category

– RRj=Relative risk for the “jth” exposure level compared with the common reference group

Important: Note that in these formulas, the pjs are column percents

RiskRelative

1 RiskRelative

Cases Total

cases exposed of #

k

0j j

j

j RR

1RRp

k

0j j

j

RR

p1

36

The Simple Case of 2 Binary Variables

Organization into a Risk system

10

11

12

13

m

gp

m

ep

m

cp

m

ap


Risk Factor 1 and 2

a p3

b n3

Only Risk Factor 1

c p2

d n2

Only Risk Factor 2

e p1

f n1

Neither (Reference)

g p0

h n0

Total m1 pTotal

m2 N

0

00

0

11

0

22

0

33

p

pRR

p

pRR

p

pRR

p

pRR

37

Equivalence of the Rothman and Bruzzi Formulas

1

1

2

2

3

3

1

1

2

2

3

3

11

1

22

2

33

3

1

1

2

2

3

3

1231

1

2

2

3

3

123

1231

1

2

2

3

3

01230

0

1

1

2

2

3

3

RR

RR

RR

RR

RR

RR

RR

RR

RR

RR

RR

RR

RRRR

RR

RRRR

RR

RRRR

RR

RR

RR

RR

RR

RR

RR

RRRRRRRR

RR

RR

RR

RR

RR

RRRRRR

1RRRRRR

1

1

RR

RR

RR

RR

RR

RR

RRRRRRRRRR

RR

RR

RR

RR

RR

RR

RR

1p

1p

1p

1p

1p

1p

pp

pp

pp0

1p

1p

1p

pppppp

pppppp

pppp1

1p

1p

1p

1p

pppp1

1p

1p

1p

1p

123123

11

22

33123

123123

123123

01230123

01230123

k

0j j

j

j RR

1RRp

k

0j j

j

RR

p1

38

The simple case of 2 binary variablesSmoking and Cocaine

Crude RR = 1.60 Crude RR = 4.77

107.06.1

16.1

700

200 PAFCrude

Freq LOW BIRTHWEIGHT Row Pct| yes | no |Total _______|________|________| cocaine| 90 | 210 | 300 yes| 30.00 | 70.00 | _______|________|________| cocaine| 610 | 9090 | 9700 no| 6.29 | 93.71 | _______|________|________| Total 700 9300 10000

102.077.4

177.4

700

90 PAFCrude

Freq LOW BIRTHWEIGHT Row Pct| yes | no |Total _______|________|________| smoke| 200 | 1800 | 2000 yes| 10.00 | 90.00 | _______|________|________| smoke| 500 | 7500 | 8000 no| 6.25 | 93.75 | _______|________|________| Total 700 9300 10000

PAR % =200

700

1.6 -1

1.6

100

10 7%.

39

Smoking and Cocaine Organized into a Risk SystemIf smoking and cocaine use were recoded as a single “substance use” variable: Freq | LOW BIRTHWEIGHT Row Pct | yes | no |Total _________|________|________| smoke and| 52 | 98 | 150 cocaine| 34.67 | 65.33 | _________|________|________| cocaine| 38 | 112 | 150 only| 25.33 | 74.67 | _________|________|________| smoke| 148 | 1702 | 1850 only| 8.00 | 92.00 | _________|________|________| neither| 462 | 7388 | 7850 | 5.89 | 94.11 | _________|________|________| Total 700 9300 10000

Freq | LOW BIRTHWEIGHT Row Pct | yes | no |Total __________|________|________| any smoke| 238 | 1912 | 2150 or cocaine| 11.07 | 88.93 | __________|________|________| neither| 462 | 7388 | 7850 | 5.89 | 94.11 | __________|________|________| Total 700 9300 10000

16.088.1

188.1

700

238

PAF Summary

40

Components of each

combination of

risk factors in the

smoking-cocaine

risk system:

pj* rpj* RRj

*pj = column %

**rpj = row %

Freq | LOW BIRTHWEIGHT Row Pct | yes | no |Total _________|________|________| smoke and| 52 | 98 | 150 cocaine| 34.67 | 65.33 | _________|________|________| cocaine| 38 | 112 | 150 only| 25.33 | 74.67 | _________|________|________| smoke| 148 | 1702 | 1850 only| 8.00 | 92.00 | _________|________|________| neither| 462 | 7388 | 7850 | 5.89 | 94.11 | _________|________|________| Total 700 9300 10000

RR = 5.89

062.089.5

189.5

700

52PAF

RR = 4.30

042.03.4

130.4

700

38PAF

RR = 1.36

056.036.1

136.1

700

148PAF

66.0700

462p

21.0700

148p

054.0700

38p

074.0700

52p

0

1

2

3

059.07850

462rp

08.01850

148rp

253.0150

38rp

347.0150

52rp

0

1

2

3

1059.0

059.0RR

36.1059.0

08.0RR

30.4059.0

253.0RR

89.5059.0

347.0RR

0

1

2

3

41

Component PAFs and Summary PAF for the Smoking-Cocaine Risk System

Using Rothman’s formula:

The Summary PAF is the

sum of component PAFs

+ +

+ = 0.16

062.089.5

189.5

700

52

3PAF

042.03.4

130.4

700

38

2PAF

056.036.1

136.1

700

148

1PAF

k

i j

j

j RR

RRp

0

1

0.01

11

700

462

0PAF

42

Component PAFs and Summary PAF for the Smoking-Cocaine Risk SystemUsing Bruzzi’s formula:

With Bruzzi’s formula, the

Summary PAF is not built

from component PAFs

k

0j j

j

RR

p1

16.0

8396.01

66.01544.00126.00126.01

1

66.0

36.1

21.0

30.4

054.0

89.5

074.01

43

Limitation of Component PAFs from the Smoking-Cocaine Risk SystemWhile the component PAFs of a risk system sum to the Summary PAF for the system as a whole, they do not provide mutually exclusive measures of the PAF for each risk factor

Here, the Summary PAF = 0.16,but the two factors overlap:the component PAFs still do not disentangle smoking and cocainefor those who do both

0.0620.056

0.042

0.84

44

The “Adjusted” PAF: Obtaining a Single PAF for a Given Risk FactorThe Stratified Approach: The PAF for eliminating a

risk factor after controlling for other risk factors

With the Rothman formula, data are organized into the more traditional strata set-up for adjustment:

Not assuming homogeneity, pj & RRj are stratum-specific:

Assuming homogeneity, Overall

strata of #

j

jj

Risk Relative

Risk Relative

strata all Cases, Total

cases exposed of

j

1#

Risk RelativeAdjusted

1 Risk RelativeAdjusted

strata all Cases, Total

strata all cases, exposed of #

45

The “Adjusted” PAF: Obtaining a Single PAF for a Given Factor

The Stratified Approach

If there is multiplicative effect modification

in the RR...

As usual, it is inappropriate to average widely varying stratum-specific RRs, say 3.0 and 0.90, because a single average would misrepresent the magnitude of the association, and sometimes, as in this example, misrepresent the direction of the association as well.

46



If there is not multiplicative effect modification

in the RR...

If there is no evidence of multiplicative effect modification and sample size permits, there is really nothing to be gained by not using stratum-specific estimates. Whichever formula is used, the result is a single “adjusted” PAF.

47


Reorganizing the data to

get an adjusted PAF with

Rothman’s formula


RR = 5.89

062.089.5

189.5

700

52PAF

RR = 4.30

042.03.4

130.4

700

38PAF

RR = 1.36

056.036.1

136.1

700

148PAF

COCAINE=YES Freq | LOW BIRTHWEIGHT Row Pct| yes | no |Total _______|________|________| smoke| 52 | 98 |150 yes| 34.67 | 65.33 | _______|________|________| smoke| 38 | 112 |150 no| 25.33 | 74.67 | _______|________|________| Total 90 210 300

COCAINE=NO Freq| LOW BIRTHWEIGHT Row Pct| yes | no |Total _______|________|________| smoke| 148 | 1702 |1850 yes| 8.00 | 92.00 | _______|________|________| smoke| 462 | 7388 |7850 no| 5.89 | 94.11 | _______|________|________| Total 610 9090 9700

48

The “Adjusted” PAF: The PAF for Smoking, Controlling for Cocaine Use*

RR=1.37 +

=

RR=1.36

*Using stratum-specific estimates

COCAINE=YES Freq | LOW BIRTHWEIGHT Row Pct| yes | no |Total _______|________|________| smoke| 52 | 98 |150 yes| 34.67 | 65.33 | _______|________|________| smoke| 38 | 112 |150 no| 25.33 | 74.67 | _______|________|________| Total 90 210 300

COCAINE=NO Freq| LOW BIRTHWEIGHT Row Pct| yes | no |Total _______|________|________| smoke| 148 | 1702 |1850 yes| 8.00 | 92.00 | _______|________|________| smoke| 462 | 7388 |7850 no| 5.89 | 94.11 | _______|________|________| Total 610 9090 9700

056.036.1

136.1

700

148PAF

020.037.1

137.1

700

52PAF

076.0

056.0020.0

Adjusted""PAF

49

The “Adjusted” PAF: The PAF for Cocaine Controlling for Smoking*

RR=4.33 +

=

RR=4.30

*Using stratum-specific estimates

SMOKE=YES Freq | LOW BIRTHWEIGHT Row Pct| yes | no |Total _______|________|________| cocaine| 52 | 98 | 150 yes| 34.67 | 65.33 | _______|________|________| cocaine| 148 | 1702 |1850 no| 8.00 | 92.00 | _______|________|________| Total 200 1800 2000

SMOKE=NO Freq | LOW BIRTHWEIGHT Row Pct| yes | no |Total _______|________|________| cocaine| 38 | 112 | 150 yes| 25.33 | 74.67 | _______|________|________| cocaine| 462 | 7388 |7850 no| 5.89 | 94.11 | _______|________|________| Total 500 7500 8000

057.033.4

133.4

700

52PAF

042.030.4

130.4

700

38PAF

099.0

042.0057.0

Adjusted""PAF

50

The “Adjusted” PAF: Obtaining a Single PAF for a Given Risk FactorUsing the Bruzzi formula, the “strata” are defined as each row of the risk system. In the smoking-cocaine risk system, then, there are 4 “strata”.

For the PAF for smoking, controlling for cocaine use,the 4 ps are the 4 columnpercents and the 4 RRs are:

rp1/rp2 rp2/rp2 rp3/rp4 rp4/rp4


RR = 5.89

062.089.5

189.5

700

52PAF

RR = 4.30

042.03.4

130.4

700

38PAF

RR = 1.36

056.036.1

136.1

700

148PAF

51

For the Burzzi Formula: the RRj* and RRj~

RR=1.37 RR=1

RR=1.36 RR=1


RR = 5.89

062.089.5

189.5

700

52PAF

RR = 4.30

042.03.4

130.4

700

38PAF

RR = 1.36

056.036.1

136.1

700

148PAF


RR = 5.89

062.089.5

189.5

700

52PAF

RR = 4.30

042.03.4

130.4

700

38PAF

RR = 1.36

056.036.1

136.1

700

148PAF


RR = 5.89

062.089.5

189.5

700

52PAF

RR = 4.30

042.03.4

130.4

700

38PAF

RR = 1.36

056.036.1

136.1

700

148PAF


RR = 5.89

062.089.5

189.5

700

52PAF

RR = 4.30

042.03.4

130.4

700

38PAF

RR = 1.36

056.036.1

136.1

700

148PAF

52

The “Adjusted” PAF: Obtaining a Single PAF for a Given Risk FactorIn the Bruzzi approach to “adjustment”, there are 3 different

versions of the relative risks:

RRj = the component RRs

RRj* = the RRs for combinations of covariates in the absence of the factor being 'adjusted‘—in this simple example, these are the 2 RRs not involving smoking

RRj~ = the RRs for the factor being 'adjusted' conditioned on combinations of the covariates—in this simple example, these are the 2 RRs for smoking in the presence and absence (conditioned) on cocaine use. These are the “stratum-specific” RRs in the classic stratified set-up

53

The “Adjusted” PAF: Obtaining a Single PAF for a Given Risk FactorUsing the Bruzzi method:

PAF for Smoking,

controlling for cocaine use.

PAF for cocaine,

controlling for smoking.

078.0

922.01

66.01544.0054.0054.01

1

66.0

36.1

21.0

1

054.0

37.1

074.01

10.0

90.01

66.021.0126.0017.01

1

66.0

1

21.0

3.4

054.0

33.4

074.01

54

The “Adjusted” PAF Obtaining a Single PAF for a Given Factor


Notice that controlling for confounding typically reduces the PAF, just as it typically reduces the relative risk or odds ratio.

Crude v. “Adjusted” PAF for smoking:

0.107 v. 0.076

Crude v. “Adjusted” for cocaine:

0.102 v. 0.099

55

Limitations of the “Adjusted” PAF:While adjustment methods control for other risk factors, the resulting adjusted PAFs still are not mutually exclusive and they do not meet the criterion of summing to the Summary PAF for all factors combined

≠

0.042+0.062+0.056=0.16 0.076 + 0.099 = 0.175

0.825

0.0760.099

0.0620.056

0.042

0.84

56

Limitations of the “Adjusted” PAF:Adjustment procedures result in a PAF that taken by itself represents an estimate—perhaps unrealistic—of the impact of eliminating one exposure first in a risk system, controlling for other factors, but not considering that some of those other factors may also be eliminated.

The “adjusted” PAF becomes more useful when it is considered as one element of a set of possible sequences for addressing all of the risk factors in a risk system—HOLD THIS THOUGHT

57

Extension to the Case of 3 Binary Variables

Example: SAS Code for reformatting individual-level data for the outcome and risk factors of interest into k observations

proc sort data=work.Orig_SampleLBW;by lbw smoke cocaine poverty;

run;

proc freq data=work.Orig_SampleLBW; tables lbw*smoke*cocaine*poverty/list;

run;

58


LBW by

Smoking,

Cocaine use

and Poverty

lbw smoke cocaine poverty Freq Cumulative Frequency

yes yes yes yes 24 24

yes yes yes no 28 52

yes yes no yes 80 132

yes yes no no 68 200

yes no yes yes 19 219

yes no yes no 19 238

yes no no yes 287 525

yes no no no 175 700

no yes yes yes 35 735

no yes yes no 63 798

no yes no yes 775 1573

no yes no no 927 2500

no no yes yes 50 2550

no no yes no 62 2612

no no no yes 2958 5570

no no no no 4430 10000

59


smoke cocaine poverty Casesj Controlsj Totalj

yes yes yes 24 35 59

yes yes no 28 63 91

yes no yes 80 775 855

yes no no 68 927 995

no yes yes 19 50 69

no yes no 19 62 81

no no yes 287 2958 3245

no no no 175 4430 4605

Data rearranged into “strata” in the Bruzzi sense...

60

Component Prevalences and Relative Risks for a Risk System with Three Variables

smoke cocaine poverty Casesi Controlsi Totali Pj RRj

yes yes yes 24 35 59 0.034 10.70

yes yes no 28 63 91 0.040 8.10

yes no yes 80 775 855 0.114 2.46

yes no no 68 927 995 0.097 1.80

no yes yes 19 50 69 0.027 7.25

no yes no 19 62 81 0.027 6.17

no no yes 287 2958 3245 0.410 2.33

no no no 175 4430 4605 0.250 1.00

Prevalence and RR added

Example (first row):pj = 24 / 700 = 0.034 RRj = [(24/59) / (175/4605)] = 10.70

61

Unique Cross-Classifications of

n VariablesFor binary variables, the # of strata k = 2n, where n=# variables

Example:

Smoke (1=Yes, 0=No),

Cocaine (1=Yes, 0=No),

Poverty(1=Yes, 0=No)

In general, K = the product of

the # of levels for each variable;

e.g. in Bruzzi, et al (1985):

k = 2*3*3*4 = 72 k = 23 = 8

smoke cocaine poverty

yes yes yes

yes yes no

yes no yes

yes no no

no yes yes

no yes no

no no yes

no no no

62

Component PAFs for Entire Risk System

0.0430.035

0.068

0.2340.543

0.023

0.0230.031

Smoke Alone

Smoke and Coke

Smoke and Poverty

Poverty Alone

Coke and Poverty

Coke Alone

All exposures

Unknown

Summary PAF = 0.46

63

Summary and Adjusted PAFs for a 3 Factor Risk System

Discuss Worksheet A in Supplementary Excel File Component, Adjusted and Summary PAF

calculations for smoke, cocaine, and poverty

64

Using Modeling to Compute Summary and “Adjusted” PAFs

Advantages of Modeling for Obtaining Intermediate Estimates for PAFs—as usual in comparison to

stratified methods

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 (but this method breaks down quickly as there are more variables in the risk system)

65

Assumption-Free Approach Using FullySpecified Model/*Binomial Regression – Directly estimate RRs*/

proc genmod data=LBW desc; model lbw=smoke cocaine poverty smoke*cocaine smoke*poverty cocaine*poverty smoke*cocaine*poverty/dist=bin link=log;weight freq; run;

/*Logistic Regression – ORs as estimates of RRs*/proc logistic data=LBW desc; model lbw=smoke cocaine poverty smoke*cocaine smoke*poverty cocaine*poverty smoke*cocaine*poverty;weight freq;run;

66

Results from Fully-Specified Binomial Regression Model

PROC GENMOD is modeling the probability that lbw='1'.

Response Profile

OrderedValue

lbw

TotalFrequency

1 1 700

2 0 9300

Criteria For Assessing Goodness Of Fit

Criterion DF Value Value/DF

Deviance 8 4816.8235 602.1029

Scaled Deviance 8 4816.8235 602.1029

Pearson Chi-Square 8 9999.9937 1249.9992

Scaled Pearson X2 8 9999.9937 1249.9992

Log Likelihood -2408.4117

67

Results from Fully-Specified Binomial Regression Model

Analysis of Parameter Estimates

Parameter DF Estimate Standard Error

Chi-Square

Pr >ChiSq

Intercept 1 -3.2701 0.0741 1945.31 <.0001

smoke 1 0.5869 0.1386 17.94 <.0001

cocaine 1 1.8201 0.2140 72.36 <.0001

poverty 1 0.8447 0.0931 82.27 <.0001

smoke*cocaine 1 -0.3155 0.2902 1.18 0.2769

smoke*poverty 1 -0.5306 0.1836 8.35 0.0039

cocaine*poverty 1 -0.6844 0.2951 5.38 0.0204

smoke*cocaine*poverty 1 0.6494 0.4020 2.61 0.1062

Scale 0 1.0000 0.0000

68

Component and Summary PAFs from Fully-specified ModelDiscuss Worksheet B in Supplementary Excel File:

Summary PAFs from Fully Specified Models

69

Re-examining Fully-Specified Model

Non-significant interaction terms could be dropped from model



Chi-Square

Pr >ChiSq

Intercept 1 -3.2701 0.0741 1945.31 <.0001

smoke 1 0.5869 0.1386 17.94 <.0001

cocaine 1 1.8201 0.2140 72.36 <.0001

poverty 1 0.8447 0.0931 82.27 <.0001

smoke*cocaine 1 -0.3155 0.2902 1.18 0.2769

smoke*poverty 1 -0.5306 0.1836 8.35 0.0039

cocaine*poverty 1 -0.6844 0.2951 5.38 0.0204

smoke*cocaine*poverty

1 0.6494 0.4020 2.61 0.1062

70

Reduced Model



Chi-Square Pr > ChiSq

Intercept 1 -3.2506 0.0712 2083.76 <.0001

smoke 1 0.5169 0.1251 17.08 <.0001

cocaine 1 1.6369 0.1482 121.99 <.0001

poverty 1 0.8111 0.0903 80.60 <.0001

smoke*poverty 1 -0.3981 0.1643 5.87 0.0154

cocaine*poverty 1 -0.3407 0.2012 2.87 0.0905

Non-significant interaction term could be dropped from model

proc genmod data=LBW desc; model lbw=smoke cocaine poverty smoke*poverty cocaine*poverty/dist=bin link=log;weight freq; run;

71

Final Model



Chi-Square Pr > ChiSq

Intercept 1 -3.2341 0.0704 2110.99 <.0001

smoke 1 0.5741 0.1203 22.79 <.0001

cocaine 1 1.4372 0.0980 214.96 <.0001

poverty 1 0.7787 0.0884 77.69 <.0001

smoke*poverty 1 -0.4778 0.1568 9.28 0.0023

proc genmod data=LBW desc; model lbw=smoke cocaine poverty smoke*poverty / dist=bin link=log;weight freq; run;

72

Component and Summary PAFs from Final Reduced Model ModelDiscuss Worksheet C in Supplementary Excel File:

Summary PAFs from Final Reduced Models

Day One: 1:00-3:15

Exercise 1 Discussion of Exercise 1

Day One: 3:15-5:00

Overview of Sequential and Average PAFs: Example with 2 modifiable risk factors

Case study with 3 factors:

-2 modifiable factors, 1 unmodifiable factor

-3 modifiable factors Introduction of Exercise 2

75

Sequential PAFs (PAFSEQ) for theSmoking-Cocaine Risk SystemFor the smoking-cocaine risk system, there are 2 possible sequences:

1. Eliminate smoking first, controlling for cocaine use, then eliminate cocaine use

2. Eliminate cocaine use first, controlling for smoking, then eliminate smoking

And within each sequence, there are two sequential PAFs

76

Sequential PAFs (PAFSEQ) for theSmoking-Cocaine Risk System1.The PAFSEQ for eliminating smoking, controlling

for cocaine use:

PAFSEQ1a (S|C) = 0.076

2.The PAFSEQ for eliminating cocaine use after smoking has already been eliminated is the remainder of the Summary PAF

PAFSEQ1b =

PAFSUM – PAFSEQ1a (S|C) = 0.16 – 0.076 = 0.084

77

Sequential PAFs (PAFSEQ) for theSmoking-Cocaine Risk System1. The PAFSEQ for eliminating cocaine use,

controlling for smoking:

PAFSEQ2a (C|S) = 0.099

2. The PAFSEQ for eliminating smoking after cocaine use has already been eliminated is the remainder of the Summary PAF

PAFSEQ2b =

PAFSUM – PAFSEQ2a (C|S) = 0.16 – 0.099 = 0.061

78

Sequential PAFs (PAFSEQ) for theSmoking-Cocaine Risk SystemBy definition, the sequential PAFs within the two possible sequences sum to the Summary PAF

Smoking First Cocaine Use First

0.076 + 0.084 = 0.16 0.099 + 0.061 = 0.16

0.84

0.076

0.084

0.84

0.099

0.061

79

Average PAF (PAFAVG) for theSmoking-Cocaine Risk SystemWhile the sequential PAFs for each sequence sum to the Summary PAF, they still do not provide a overall comparison of the impact of smoking and cocaine use regardless of the order in which they are eliminated

That is, regardless of when cocaine might be eliminated, what would the impact of eliminating smoking be on average?

80

Average PAF (PAFAVG) for theSmoking-Cocaine Risk SystemTo calculate an average, the sequential PAFs are rearranged, grouping the two for smoking together and the two for cocaine together:

1. Eliminating smoking first, averaged with eliminating smoking second

2. Eliminating cocaine use first, averaged with eliminating cocaine use second

81

Average PAF (PAFAVG) for theSmoking-Cocaine Risk System

Averaging Sequential PAFs

Average PAF for Smoking:

=

Average PAF for Cocaine Use:

=

2

PAF C|SPAF SUMSEQ S|CPAFSEQ 07.0

2

0.0610.076

09.02

0.0840.099

2

PAF S|CPAF SUMSEQ C|SPAFSEQ

82

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 Summary PAF:

0.0685 + 0.0915 = 0.16

0.09

0.07

0.84

83

Case Study: Example with Three Factors Scenario: You are asked to prioritize spending

for interventions that target the high rate of low 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.

84

Modifiable and Unmodifiable Risk Factors

Using a Modeling Approach

Within one model, we can differentiate between those factors considered to be modifiable and those factors considered to be unmodifiable

While this does not change the model, this differentiation has an impact on the resulting summary, sequential, and average PAFs due to how relative risks are calculated

85

Decisions for PAF Analysis

Would you consider each of the following variables unmodifiable or modifiable for preventing LBW? Smoking (1=Smoking during pregnancy, 0=No smoking) Cocaine (1=Cocaine use during pregnancy, 0=No cocaine) Poverty (1=Below Federal Poverty Level, 0=Above FPL)

What type(s) of PAF is/are 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)

86

Descriptive Statistics for Case Study Frequency and Percent of LBW by Each

Covariate

Frequency (Row %) Low Birth Weight

yes no Total

Smoke

yes 200 (10.0%) 1800 (90.0%) 2000

no 500 (6.2%) 7500 (93.8%) 8000

Cocaine

yes 90 (30.0%) 210 (70.0%) 300

no 610 (6.3%) 909 (93.7%) 9700

Poverty

yes 410 (9.7%) 3818 (90.3%) 4228

no 290 (5.0%) 5482 (95.0%) 5772

Total 700 9300 10000

87

Case Study Part I

Calculating Sequential and/or Average PAFs for Smoking and Cocaine Use

Considering Poverty as Unmodifiable

88

Sequential PAFs for theSmoking-Cocaine-Poverty Risk System, Considering Poverty as UnmodifiableWith 3 factors, but only 2 of them modifiable, there are 2 possible sequences:

1.Eliminate smoking first, controlling for cocaine use and poverty, then eliminate cocaine use

2.Eliminate cocaine use first, controlling for smoking and poverty, then eliminate smoking

And within each sequence, there are two sequential PAFs

89

SAS Code: Obtaining Prevalences and Beta Estimates for Smoke, Cocaine and Poverty/*Create a listing of the frequencies for each possible combination of smoke, coke, poverty for LBW cases to calculate proportions*/proc freq order=formatted; tables poverty*smoke*cocaine/list nopercent; where lbw=1;run;

/*Binomial regression to obtain RRs*/proc genmod;title2 “RRs for Smoke and Coke with LBW, controlling for Poverty";model lbw = smoke cocaine poverty smoke*poverty

/dist=bin link=log obstats; /*Binomial distribution*/

run;

90

Discuss Worksheets D and E in Supplementary

Excel File:

Calculations for 1st Sequential PAFs, Summary PAFs, and Average PAFs for Smoking and Cocaine,

Controlling for Poverty

Sequential PAFs for theSmoking-Cocaine-Poverty Risk System, Considering Poverty as Unmodifiable

91

PAFSEQ for Smoking and Cocaine,Considering Poverty as UnmodifiableSequence 1: Smoking, THEN Cocaine

PAFSEQ1a: (S | C U P)= 0.074

PAFSEQ1b : (C U S | P) – (S | C U P) =

0.156 – 0.074= 0.082

Sequence 2: Cocaine, THEN Smoking

PAFSEQ2a : (C | S U P) = 0.098

PAFSEQ2b: (S U C | P) – (C | S U P) =

0.156 - 0.098= 0.058

The Summary PAF includes only smoking and cocaine, since poverty is unmodifiable.

92

0.074

0.082

0.844

Seq PAF Smoke Seq PAF Coke Unknown 0.07

0.08

0.85

Seq PAF Smoke Seq PAF Coke Unknown

PAFSEQ2Smoking THEN

Cocaine, Controlling for

Poverty

Cocaine THEN Smoking,

Controlling for Poverty

PAFSUM=0.156

PAFAGG=0.15

0.058

0.098

0.844

Seq PAF Coke Seq PAF Smoke Unknown

PAFSUM=0.156

PAFSEQ for Smoking and Cocaine,Considering Poverty as Unmodifiable

93

Average PAF (PAFAVG)

Eide (1995): Based on Game Theory according to Cox’s Theorem (1984) for risk allocation (attributable risk among the exposed)

w

SEQAVG wiPAFn

PAF ,

!

1

Note: Average PAF is sometimes called the “partial” attributable fraction

where “n” is the number of modifiable risk factors in the risk system, “w” is the number of unique removal sequences for all variables in risksystem and “i” represents a specific variable in the system

,

94

Average PAFs for Smoking and Cocaine,Controlling for Poverty Average PAF for Smoking

PAFAVG: ((PAFSEQ1a+PAFSEQ2b)/2)

PAFAVG : ((0.074 + 0.058 ) / 2) = 0.066

Average PAF for Cocaine

PAFAVG: ((PAFSEQ1b+PAFSEQ2a)/2)

PAFAVG : ((0.098 + 0.082 ) / 2) = 0.090

95

Case Study Part II

Calculating Sequential and/or Average PAFs for Smoking, Cocaine Use, and Poverty

Considering Poverty as Modifiable

96

Sequential PAFs (PAFSEQ) for theSmoking-Cocaine Risk SystemFor the smoking-cocaine-poverty risk system, there are 6 possible sequences:

1. Smoking, cocaine use, poverty

2. Smoking, poverty, cocaine use

3. Cocaine use, smoking, poverty

4. Cocaine use, poverty, smoking

5. Poverty, smoking, cocaine use

6. Poverty, cocaine use, smoking

And within each sequence, there are three sequential PAFs

97

SAS Code: Obtaining Prevalences and Beta Estimates for Smoke, Cocaine and Poverty/*Create a listing of the frequencies for each possible

combination of smoke, coke, poverty for LBW cases to calculate proportions*/proc freq order=formatted; tables poverty*smoke*cocaine/list nopercent; where lbw=1;run;

/*Binomial regression to obtain RRs*/proc genmod;title2 “RRs for Smoke and Coke with LBW, controlling for Poverty";model lbw = smoke cocaine poverty smoke*poverty

/dist=bin link=log obstats; /*Binomial distribution*/

run;

98

Sequential PAFsQ: How many unique sequences will there be for removing risk factors from the risk system?

A: n!, where n=# of modifiable risk factors in system

Ex: n=3, n!= 3x2x1 = 6 unique sequences

n=4, n!= 4x3x2x1 = 24 unique sequencesn=5, n!= 5x4x3x2x1 = 120 unique sequencesetc…

To calculate the PAFSEQ for factors removed second and third in a 3 variable risk system, it is necessary to compute the PAF for every pair of two factors combined, adjusting for the third factor. These are intermediate Summary PAFs.

99

Discuss Worksheets F and G in Supplementary

Excel File:

Calculations for 1st Sequential PAFs, Summary PAFs, and Average PAFs for Smoking,

Cocaine, and Poverty

Sequential PAFs for theSmoking-Cocaine-Poverty Risk System, Considering Poverty as Modifiable

100

PAFSEQ for Smoking Removed FirstSequence 1: Smoking, THEN Cocaine, THEN Poverty

PAFSEQ1a: (S | C U P) = 0.074

PAFSEQ1b: (S U C | P) – (S | C U P) = 0.156 – 0.074 = 0.082

PAFSEQ1c: (S U C U P) – (S U C | P) = 0.441 – 0.156 = 0.286

Sequence 2: Smoking, THEN Poverty, THEN Cocaine

PAFSEQ2a: (S | P U C)= 0.074

PAFSEQ2b: (S U P | C) – (S | P U C) = 0.383 – 0.074 = 0.310

PAFSEQ2c: (S U P U C) – (S U P | C) = 0.441 – 0.383 = 0.058

101

PAFSEQ2Smoking THEN Cocaine, THEN

Poverty

Smoking THEN Poverty, THEN

Cocaine

0.559

0.074

0.082

0.286

Seq PAF Smoke Seq PAF Coke Seq PAF Poverty Unknown

0.559

0.31

0.074

0.058

Seq PAF Smoke Seq PAF Poverty Seq PAF Coke Unknown

0.10

0.05

0.54

0.31

Seq PAF Coke Seq PAF Smoke Seq PAF Poverty Unknown

PAFSEQ for Smoking Removed First

102

PAFSEQ for Cocaine Removed FirstSequence 3: Cocaine, THEN Smoking, THEN Poverty

PAFSEQ3a: (C | S U P)= 0.098

PAFSEQ3b: (C U S | P) – (C | S U P) = 0.156 – 0.098 = 0.058

PAFSEQ3c: (C U S U P) – (C U S| P) = 0.441 – 0.156 = 0.286

Sequence 4: Cocaine, THEN Poverty, THEN Smoking

PAFSEQ4a : (C | P U S)= 0.098

PAFSEQ4b: (C U P | S) – (C | P U S) = 0.355 – 0.098 = 0.257

PAFSEQ4c: (C U P U S) – (C U P | S) = 0.441 – 0.355 = 0.086

103

PAFSEQ for Cocaine Removed First

0.559

0.098

0.058

0.286


PAFSEQ2Cocaine THEN

Smoking, THEN Poverty

Cocaine THEN Poverty, THEN

Smoking

0.10

0.05

0.54

0.31


0.257

0.098

0.559

0.086

Seq PAF Coke Seq PAF Poverty Seq PAF Smoke Unknown

104

PAFSEQ for Poverty Removed FirstSequence 5: Poverty, THEN Smoking, THEN Cocaine

PAFSEQ5a: (P | S U C) = 0.275

PAFSEQ5b: (P U S | C) – (P | S U C) = 0.383 – 0.275 = 0.108

PAFSEQ5c: (P U S U C) – (P U S | C) = 0.441 – 0.383 = 0.058

Sequence 6: Poverty, THEN Cocaine, THEN Smoking

PAFSEQ6a: (P | C U S)= 0.275

PAFSEQ6b: (P U C | S) – (P | C U S) = 0.355 – 0.275 = 0.080

PAFSEQ6c: (P U C U S) – (P U C | S) = 0.441 – 0.355 = 0.086

105

0.08

0.275

0.559

0.086

Seq PAF Poverty Seq PAF Coke Seq PAF Smoke Unknown

PAFSEQ for Poverty Removed First

PAFSEQ2Poverty THEN

Smoking, THEN Cocaine

Poverty THEN Cocaine THEN

Smoking

0.10

0.05

0.54

0.31


0.559

0.275

0.108

0.058

Seq PAF Poverty Seq PAF Smoke Seq PAF Coke Unknown

106

PAFAVG for Smoking, Cocaine and Poverty(6 Sequential PAFs in each Average, 4 are Unique)

Average PAF for SmokingPAFAVG =(PAFSEQ1a +PAFSEQ2a+PAFSEQ3b+PAFSEQ4c+PAFSEQ5b+PAFSEQ6c) / 6PAFAVG = (2(0.074) + 0.058 + 0.108 + 2(0.086)) / 6) = 0.081

Average PAF for CocainePAFAVG =(PAFSEQ1b +PAFSEQ2c+PAFSEQ3a+PAFSEQ4a+PAFSEQ5c+PAFSEQ6b) / 6 PAFAVG = (2(0.098)+0.082+0.080+2(0.058)) / 6 = 0.079

Average PAF for PovertyPAFAVG = (PAFSEQ1c+PAFSEQ2b+PAFSEQ3c+PAFSEQ4b+PAFSEQ5a+PAFSEQ6a) / 6 PAFAVG = (2(0.275)+0.310+0.257+2(0.286)) / 6 = 0.281

107

0.281

0.081

0.079

0.559

Avg PAF Smoke Avg PAF CokeAvg PAF Poverty Unknown

0.09

0.84

0.07

Average PAFs for all possible models

0.090

0.85

0.066

0.077

0.090

0.289

0.545


Smoke and Coke Smoke and Coke, Controlling for

Poverty

Smoke, Coke and Poverty

PAFSUM=0.16 PAFSUM=0.156 PAFSUM=0.441

108

0.0570.081

0.2550.607


0.092

0.840

0.068

Average PAFs for all possible models – with no interaction term for smoke*poverty

0.064

0.091

0.000

0.845

0.077

0.090

0.289

0.545


Smoke and Coke Smoke and Coke, Controlling for

Poverty

Smoke, Coke and Poverty

PAFSUM=0.160 PAFSUM=0.155 PAFSUM=0.393

109

0.067

0.912

0.021

0.123

0.757

0.120

Poverty = Yes Poverty = No

0.077

0.090

0.289

0.545


Average PAFs stratified by poverty

PAFSUM=0.088 PAFSUM=0.245

110

Introduction of Exercise 2

Day Two: 8:00-12:00

Exercise 2 and Discussion of Exercise 2 Brief Review Model Building Issues Exercise 3

112

Review

The Population Attributable Fraction (PAF) could be a useful tool to inform priority-setting and development of targeted interventions in public health since it estimates the potential impact of risk reduction in the population on the occurrence of a health outcome

The PAF incorporates both a measure of association between a risk factor and an outcome and the prevalence of the risk factor in the population as a whole.

113

Review The Summary PAF is the proportion of an

outcome that could be reduced bysimultaneously eliminating from the population all modifiable factors in a risk system.

The Summary PAF can be partitioned into: Component PAFs Sequential PAFs corresponding to a particular

removal sequence Average PAFs

The modifiable factors in the risk system can be “adjusted” both for each other and for other unmodifiable factors

114

Review

Partitioning of the Summary PAF

for a Risk System

Component PAFs Sequential PAFs for Average PAFs

One Possible Sequence

115

Review The component PAFs reflect every combination of the

modifiable factors in the risk system and do not yield any factor-specific PAF

Sequential PAFs yield factor-specific PAFs, but these factor-specific PAFs vary across the possible removal sequences; the first sequential PAF in any sequence is what is commonly called the “adjusted” PAF

Component PAFs and Sequential PAFs for a given sequence are not mutually exclusive estimates of the impact of eliminating modifiable factors regardless of whether and when other modifiable factors are also eliminated.

116

ReviewThe number of possible sequences is a function of the number of variables in the risk system and becomes large quickly as the number of variables increases.

Number of Risk Factors

Number of Possible Removal Orderings / Sequences

Number of Unique Sequential PAFs

2 2! = 2 2

3 3! = 6 4

4 4! = 24 8

5 5! = 120 16

6 6! = 720 32

7 7! = 5,040 64

117

Review The number of average PAFs equals the number of

variables in a risk system.

Average PAFs, by considering every possible sequence, yield mutually exclusive estimates, making comparisons of the potential impact of risk reduction intervention strategies possible

The average PAF may be a better measure of impact than the first sequential (“adjusted”) PAF since typically there are multiple interventions operating simultaneously—risk reduction activities are unordered and often intersect

118

Review

Sequence X: Factor M1Mn, controlling for UM1UMz

PAFSEQXa: (M1| M2 U U Mn U UM1 U U UMz)

(“adjusted” PAF for M1)

PAFSEQXb: (M1 U M2 | M3 U U Mn U UM1 U U UMz)

– (M1| M2 U U Mn U UM1 U U UMz)

PAFSEQXn: M1 U U Mn | UM1 U U UMz)

– (M1 U U Mn-1 | Mn U UM1 U U UMz)

The 2nd, 3rd, to n-1th sequential PAFs are the remainders from intermediate Summary PAFs; the nth sequential PAF is the remainder from the total Summary PAF

119

Review

Computation of the sequential PAFs within particular removal sequences becomes cumbersome as the number of variables, both modifiable and unmodifiable increases

Intermediate Summary PAFs are required for differing subsets of modifiable variables in a risk system

120

Review

Whether computing crude, “adjusted”, summary, or sequential PAFs, and whether using a stratified or modeling approach, some form of either the Rothman or Bruzzi formulas can be used.

k

0j j

j

j RR

1RRp

k

0j j

j

RR

p1

121

Model Building Issues and Strategies

in the Context of Estimating PAFs

Reporting PAFs

122

Model Building Issues and Strategies Within one model, we can differentiate between those factors considered to be modifiable and those factors considered to be unmodifiable

The differentiation between modifiable and unmodifiable variables may change the final model since this differentiation has an impact on decisions as to whether the variable is included in a final model

In addition, the resulting summary, sequential, and average PAFs will vary depending on which variables are designated as modifiable because of how relative risks are calculated

123


Variable Selection

Modifiability Unmodifiable factors are only used as potential

confounders or effect modifiers; PAFs not calculated Modifiable factors are factors that can possibly be

altered with clear intervention strategies

Being in the pool of modifiable factors not only influences final PAF estimates, but also may change level of measurement, choice of reference level, and handling of confounding and effect modification

124

Model Building Issues and StrategiesDifferential handling of

unmodifiable and modifiable factors

Levels of measurement: Modifiable variables cannot be continuous Modifiable variables can be ordinal or nominal Sets of dummy variables can be used, but for

modifiable factors it means there will be a separate PAF for each dummy variable

Unmodifiable variables can be at any level of measurement, although if there is effect modification with a modifiable factor, recoding into categories will be necessary for continuous variables

125


Choice of Reference Level for Comparison

Since PAFs quantify the impact of complete elimination of a risk factor, it may be more realistic to define reference groups that pull back from this maximum:

Some Examples: >= 2 days exercise, rather than >= 5 days exercise

<=1 medical risk factor rather than 0 medical risks

126

Model Building Issues and StrategiesReference Groups for Modifiable Factors

More restrictive level of the reference group could lead to both a higher prevalence of exposure and stronger measure of effect, resulting in an inflated PAF

Importance of distinguishing between never exposed and formerly exposed

Use conceptual framework and balance evidence with realistic goals

127

Model Building Issues and StrategiesEffect modification

– within modifiable factors—use either a product term or could use common reference coding to create a set of dummy variables

– across modifiable and unmodifiable factors—this might point to doing modeling stratified by the unmodifiable factor involved in the interaction; if the unmodifiable variable is continuous, it would have to be recoded into categories for stratification

– within unmodifiable factors—use a product term or ignore the interaction if it does not have an impact on the measures of association for the modifiable factors

128


Parsimony is not as important when building a model as a step toward obtaining average PAFs; that is, variables with insignificant RRs / ORs may be included in a final model if the resulting PAFs based on them are meaningfully large.

129

Model Building Issues and StrategiesCriteria for selection of variables for a final model:

The prevalence estimates themselves might also be used in to inform decisions about which variables will stay in a model

Criteria for Modifiable Risk Factors

Staying in a Model

1st Sequential PAF

95% CI Does Not Include 0

95% CI Includes 0

Significant RR / OR

Close to the null ? ?Far from the null ? ?

Not SignificantRR / OR

Close to the null ? ?Far from the null ? ?

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For unmodifiable factors, statistical significance may be more important as it is one component of indicating the presence of confounding of the effects of the modifiable factors

The prevalence of the unmodifiable factors in the population is not of interest since they are not part of the risk system for which PAFs are being estimated

131

Model Building Issues and StrategiesPossible Model building strategies

Build models with one modifiable factor at a time plus the unmodifiable factors

Build models with subsets of modifiable factors that are within a domain (substantively related) plus the unmodifiable factors

Build models starting with all modifiable and unmodifiable factors, and then use a manual backward elimination approach

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Moving from Modeling to Reporting of PAFs

For any model building strategy:

Choose final pool of modifiable factors based on the significance of the first sequential PAFs and 95% CIs, or some other explicitly decided upon criteria

Calculate average PAFs for all modifiable factors in the final model, but report only those with values above some threshold, e.g. 2%, 5%, 10%?

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Even with careful choice of reference levels, average PAFs are probably over-estimates of the expected reduction in an outcome since they assume that all of the factors in a risk system can be completely eliminated from the population

134


Average PAFs can be refined by differentially weighting removal sequences to reflect issues such as funding streams or political will, since in reality not all removal sequences are equally likely, or by incorporating measures of uptake and efficacy of public health interventions

(this is beyond the scope of this training)

135

Moving from Modeling to Reporting of PAFsVariance estimates for Average PAFs need to be developed and then a consensus needs to be reached for the interpretation of resulting confidence intervals.

As always, narrower CIs will mean increased reliability

The CIS across multiple PAFs will undoubtedly overlap. What will this mean for informing the prioritization process across modifiable factors?

Will a CI with a lower bound < 1 mean a factor is not significant and therefore not a priority?

136

Presentation and Interpretation

137

0.035 0.0310.043

0.068

0.023 0.023Ref

0.234

0

0.05

0.1

0.15

0.2

0.25

0.3

Co

mp

on

ent

PA

F

Smoke=YCoke=Y

Smoke=YCoke=N

Smoke=NCoke=Y

Smoke=NCoke=N

Component PAFs for Smoke and Coke, Stratified by Poverty

Poverty=No

Poverty=Yes

Total PAF=0.457

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Presentation of Sequential PAFs for the Smoke, Coke and Poverty Risk System

0.07

0.31

0.54

0.08

Seq PAF Smoke Seq PAF Poverty Seq PAF Coke Unknown

1

2

3

0.10

0.27

0.54

0.09


0.10

0.27

0.54

0.09


1

2

3

1

139

Interpretations of Sequential PAFs from the Smoke- Coke- Poverty Risk System PAFSEQ (smoking 3rd, after coke and poverty) =0.09

An additional nine percent of LBW cases can be attributed to smoking after cocaine use and poverty have already been eliminated from the population of pregnant women

The expectation is that an additional 63 cases (0.09*700) of LBW in this sample of pregnant women would have been prevented had smoking been eliminated from the population after the elimination of cocaine and poverty

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Interpretation of Average PAFs from the Smoke, Coke, and Poverty Risk System PAFAVG (Smoking) = 0.06

On average, regardless of the order in which risk factors are removed from the risk system, the expectation is that six percent of LBW cases would be prevented if smoking is eliminated from the population, while also considering the impact of cocaine and poverty

PAFAVG (Cocaine) = 0.09

On average, nine percent of LBW cases would be prevented by the additional elimination of cocaine exposure from the population after a random collection of exposures has already been eliminated.

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Presentation Issues to consider

Is there any time when displaying stratified PAFs would be appropriate?

Targeting an intervention to a particular risk group

Displaying the interaction effects between variables

Others?

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Interpretation Issues to ConsiderPAF should not be mis-interpreted as the percent of

diseased who have the risk factor of interest or the percent of cases for which an identifiable risk factor can be found. Example: PAF for impact of 10 factors on breast

cancer=0.25.

Incorrect: Although various risk factors have been identified as causes of breast cancer, the fact remains that in 75% of all breast cancer no identifiable risk factor

can be found.

Incorrect: Only 25 percent of breast cancer cases can be attributed to one or more risk factors, meaning that the majority of cancers occur in women with no risk factors.

Rockhill, et al., 1998

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Interpretation Issues to ConsiderRothman: With a PAF of 25%, the following interpretation is not completely true: 25% of disease would be reduced if X risk factor were eliminated.

1) Assumes all biases are absent

2) Assumes that absence of risk factor would not expand person-years at risk, which could subsequently lead to more cases (in the case of competing risks)

Rothman, & Greenland, 1998

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Interpretation Issues to ConsiderRothman Example 1: PAF=0.25 for smoking in relation to coronary deaths.Elimination of smoking could lead to less lung cancer deaths,

which would lead to more people living long enough to die by coronary heart disease. Therefore, “25% fewer coronary deaths would have occurred had these doctors not smoked” is a little misleading.

Rothman Example 2: PAF=0.20 for spermicide in relation to Down’s syndromeElimination of spermicide use could lead to more pregnancies,

which would lead to more Down’s syndrome cases. Therefore, “20% fewer Down’s syndrome cases would have occurred had the couple not used spermicide” is a little misleading.

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Exercise 3

Day Two: 1:00-2:00

Discuss Exercise 3

Day Two: 2:00-4:30

Interactive Model Building:

Demonstration and Exercise

using the population attributable fraction (paf) to assess mch population outcomes deborah...

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