multifactorial population attributable fractions: approaches, examples, and issues to consider

Multifactorial Population Attributable Fractions: Approaches, Examples, and Issues to Consider

Deborah Rosenberg, PhD and Kristin Rankin, PhD

Epidemiology and Biostatistics

School of Public Health

University of Illinois at Chicago

Multifactorial Population Attributable Fractions:

Approaches, Examples, and Issues to Consider

Wednesday, May 30th, 3:15-5:00pm

Deborah Rosenberg, PhD Kristin Rankin, PhDResearch Associate Professor Research Assistant Professor

Division of Epidemiology and Biostatistics University of IL School of Public Health

Training Course in MCH Epidemiology

Background

In any multivariable analysis, the goal is to generate unconfounded / independent estimates of effect for each of many factors, taking into account the relationships among and intersection of those factors.

Different analytic approaches are required to obtain these mutually exclusive estimates according to whether ratio measures of association or population attributable fractions (PAFs) are of interest.

Background

In contrast to relative risks or odds ratiosthe PAF is a function of both the magnitude of association

and the prevalence of risk in the population

The crude PAF (Levin, 1953):

Extension to a multivariable PAF

or

Rothman Bruzzi

4

Risk Relative

1Risk Relative

Outcome with theThose Among

Exposed Proportion

k

0j j

j

j RR

1RRp

k

0j j

j

RR

p1

Background When estimating relative risks or odds ratios, independence

can be achieved through use of usual adjustment procedures to control for confounding:

“Does a risk factor confer excess risk of disease for an individual after holding all other factors constant?”

When estimating PAFs, usual adjustment does not result in mutually exclusive PAFs, nor does it address the dynamics of how the prevalence of risk factors might change in the population over time

“How much will eliminating a risk factor reduce the prevalence of disease in the population given that disease may still occur in the presence of other risk factors that have not yet been eliminated?”

5

Background

After adjustment, both ratio measures and PAFs may be overestimates because of residual confounding.

For PAFs, overestimation is of greater concern because simple adjustment assumes that only the factor of interest will be eliminated—its prevalence will be reduced to 0—while the prevalence of other factors remain constant.

Concern about the precision of PAF estimates is also critical since these measures directly speak to the potential impact of public health action

6

Background

Methods that go beyond the usual adjustment approach have been developed to handle the problem of obtaining mutually exclusive and mutually adjusted PAFs:

Modifiable risk factors are considered together as belonging to what might be called a “risk system”

− Expected disease reduction due to elimination of any one risk factor is quantified by acknowledging every possible sequence for eliminating all factors in the “risk system” over time.

− the maximum expected disease reduction due to elimination of all risk factors in the “risk system” can also be appropriately quantified

7

Organizing Factors into a Risk System: A Framework for Computing PAFs

“Adjusted” PAF: The PAF for eliminating a risk factor from a risk system after controlling for other factors (Miettenin, 1974)

Summary PAF: The PAF for the maximum expected disease reduction when all factors in a risk system are simultaneously eliminated (Bruzzi, 1985)

Component PAF: The separate PAF for every possible combination of exposure levels in the risk system (the set of joint and separate effects of risk factors)

8

Organizing Factors into a Risk System: A Framework for Computing PAFs

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

Average PAF: The PAF summarizing all possible sequences for eliminating a single modifiable risk factor (Eide and Gefeller, 1995)

9

Organizing Factors into a Risk System: A Framework for Computing PAFsThe Average PAF

The AvgPAF for a risk factor is both mutually exclusive and mutually adjusted

The sum of AvgPAFs for all modifiable risk factors in a system equals the summary PAF (sumPAF) for the risk system as a whole—the % of disease reduction expected if all of the factors are simultaneously and completely eliminated from the population

10

Example: Simultaneously Considering 3 Risk Factors for a Health OutcomeLet 3 factors be called M1, M2, and M3

The SummaryPAF for this “risk system” can be partitioned into seven component PAFs:

M1 and M2 and M3

What is theproportion M1 and M2

of disease attributable M1 and M3

to each combination M2 and M3

of risk factors? M1 alone

M2 alone

M3 alone

11

Summary PAF Partitioned into 7 Component PAFs

3 Risk Factors

for an Outcome

Summary PAF

= 0.34

Component PAFs still fail to provide a

single estimate of the impact of each factor12

Example: Simultaneously Considering 3 Risk Factors for a Health OutcomeThe SummaryPAF for this “risk system” can be partitioned

six different ways into three sequential PAFs

Computation of sequential PAFs involves a series of subtractions of adjusted and/or summary PAFs based on repeatedly redefining the risk system and its corresponding Summary PAF in terms of particular combinations of risk factors

13

Example: Simultaneously Considering 3 Risk Factors for a Health OutcomeSix Sequences for Three Risk Factors

Sequence #1: Eliminate M1, then M2, then M3Sequence #2: Eliminate M1, then M3, then M2Sequence #3: Eliminate M2, then M1, then M3Sequence #4: Eliminate M2, then M3, then M1Sequence #5: Eliminate M3, then M1, then M2Sequence #6: Eliminate M3, then M2, then M1

For each factor, there are two 1st sequential PAFs, two 2nd sequential PAFs, and two 3rd Sequential PAFs.

14

Example: Simultaneously Considering 3 Risk Factors for a Health OutcomeEXAMPLE (Sequence #1):Eliminate M1, then M2, then M3

1st SeqPAF* (M1) = PAF(M1) adjusting for M2 & M3 and other covariates**

2nd SeqPAF (M2) = SumPAF(M1 & M2) adjusting for M3 and other covariates – PAF(M1) adjusting for M2 & M3 and other covariates

3rd SeqPAF (M3) = SumPAF (M1 & M2 & M3) – SumPAF(M1 & M2) adjusting for M3 and other covariates

*“adjusted” PAF **covariates are unmodifiable factors

15

Example: Simultaneously Considering 3 Risk Factors for a Health OutcomeEXAMPLE (Sequence #5):Eliminate M3, then M1, then M2

1st SeqPAF* (M3) = PAF(M3) adjusting for M1 & M2 and other covariates**

2nd SeqPAF (M1) = SumPAF(M3 & M1) adjusting for M2 and other covariates – PAF(M3) adjusting for M1 & M2 and other covariates

3rd SeqPAF (M2) = SumPAF(M1 & M2 & M3) – (SumPAF(M3 & M1) adjusting for M2 and other covariates

*“adjusted” PAF **covariates are unmodifiable factors

16

Summary PAF Partitioned into Sequential PAFs for Sequences #1 and #5

3 Risk Factors for an Outcome: Summary PAF = 0.34Sequential PAFs still fail to provide

a single estimate of the impact of each factor

17

Example: Simultaneously Considering 3 Risk Factors for a Health OutcomeIn general: the number of possible sequences is a function of the number of factors in the risk system and becomes large quickly as the number of variables increases.

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# of Risk Factors

# of Possible Removal Orderings / Sequences

Number of Unique Sequential PAFs for a factor

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

Example: Simultaneously Considering 3 Risk Factors for a Health OutcomeThe SummaryPAF for this “risk system” can be partitioned

into three average PAFs--one for each of the 3 factors

The sequences are broken apart, rearranging the sequential PAFs so that the six 1st, 2nd, and 3rd sequential PAFs for M1 are grouped together as are those for M2 and M3

The AveragePAF for each factor is then calculated as the simple arithmetic average across the 6 sequential PAFs for each factor

19

Example: Simultaneously Considering 3 Risk Factors for a Health OutcomeFor example, the Average PAF for M1 is the sum of the following

6 Sequential PAFs divided by 6:

The two 1st SeqPAFs for M1—Seq #1 & Seq #2= PAF(M1), adjusting** for M2 & M3 (multiplied by 2)

The two 2nd SeqPAFs for M1 —Seq #3 & Seq #5= (SumPAF(M2 & M1), adj. for M3) – PAF(M2) adj. for M1 & M3 = (SumPAF(M3 & M1), adj. for M2) – PAF(M3) adj. for M1 & M2

The two 3rd SeqPAFs for M1 —Seq #4 & Seq #6= (SumPAF(M1 & M2 & M3) – SumPAF(M2 & M3), adj. for M1

**Adjustment also includes covariates

20

Summary PAF Partitioned into Average PAFs for Three Risk Factors The avgPAF for a factor is the simple average of all of

that factor’s seqPAFs

With 3 factors, the avgPAF

3 Risk Factors for an Outcome

Summary PAF = 0.34

The Average PAF is a single estimate of the impact

of each risk factor

21

6

seqPAFs 6 all

Example: Smoking, Cocaine Use and Low Birthweight

22

Example: Smoking, Cocaine Use, and Low Birthweight: Crude Associations

Crude RR = 10.00 = 1.60 Crude RR = 30.00 = 4.77 6.25 6.29

23

107.06.1

16.1

700

200 PAFCrude

102.077.4

177.4

700

90 PAFCrude

Smoking and Cocaine Organized into a Risk SystemIf smoking and cocaine use were recoded as a single “substance use” variable:

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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

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

25

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

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

26

0.0620.056

0.042

0.84

Coc Sm/Coc Sm

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

The 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

27

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 #

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

Reorganizing the data to

get an adjusted PAF with

Rothman’s formula

28

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

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

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

RR=1.37 +

= RR=1.36

*Using stratum-specific estimates

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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

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

RR=4.33 +

=

RR=4.30

*Using stratum-specific estimates

30

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

Limitations of the “Adjusted” PAF:

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

31

0.825

0.0760.099

0.0620.056

0.042

0.84

Sequential PAFs (PAFSEQ) for theSmoking-Cocaine Risk System

For the smoking-cocaine risk system, there are 2 possible sequences:

1. Eliminate smoking first (a), controlling for cocaine use, then eliminate cocaine use (b)

2. Eliminate cocaine use first (a), controlling for smoking, then eliminate smoking (b)

And within each sequence, there are two sequential PAFs

32


1. The 1st sequential PAF for eliminating smoking first, controlling for cocaine use (the “adjusted” PAF):

PAFSEQ1a (S|C) = 0.076

2. The 2nd sequential PAF 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

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1. The 1st sequential PAF for eliminating cocaine use first, controlling for smoking (the “adjusted” PAF:

PAFSEQ2a (C|S) = 0.099

2. The 2nd PAF 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

34


By definition, the sequential PAFs within the two possible sequences sum to the Summary PAF, but they still do not provide single measures of the impact of smoking or cocaine use regardless of the order in which they are eliminated

Smoking First Cocaine Use First

0.076 + 0.084 = 0.16 0.099 + 0.061 = 0.1635

0.84

0.076

0.084

0.84

0.099

0.061

Average PAF (PAFAVG) for theSmoking-Cocaine Risk System

To obtain a single estimate, the sequential PAFs are rearranged, grouping the two for smoking together and the two for cocaine together and then calculating an average for each factor:

1. Eliminating smoking first, averaged with eliminating smoking second

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

36

Average PAF (PAFAVG) for theSmoking-Cocaine Risk System

Averaging Sequential PAFs

Average PAF for Smoking:

=

Average PAF for Cocaine Use:

=

37

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

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

38

0.09

0.07

0.84

Model Building Issues and Strategies

in the Context of

Estimating and Reporting PAFs

39

40

Modeling to Generate AvgPAFs

Regression modeling is a flexible and efficient method for obtaining the series of relative risks needed for calculating seqPAFs as the number of variables being considered increases.

As an intermediate step in estimating avgPAFs, the modeling process will differ from that for estimating ratio measures of association:

Variable selection and organization Level of Measurement & choice of reference groups Confounding and effect modification Model building strategies for choosing a final model

41

Variable Selection and OrganizationClassifying factors as modifiable or unmodifiable

When modeling to estimate relative risks or odds ratios, explicit differentiation between modifiable and unmodifiable factors is not necessary, although this differentiation is certainly conceptually important.

When modeling is an intermediate step in estimating avgPAFs, the question of modifiability must be tackled from the start, since variable handling proceeds differently according to how variables are classified.

42


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; these are the factors in the “risk system”

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

43


Both broad and narrow definitions of modifiability may be reasonable, with some researchers computationally treating all variables as modifiable, including factors such as race/ethnicity, age, and poverty; others treat as modifiable only factors that reflect a much narrower perspective on modifiability

How close should the connection be between classification as modifiable

and public health interventions?

44

Level of Measurement and Reference Groups

For unmodifiable factors, decisions about level of measurement, categorization schemes, and choice of reference groups can be made with the same considerations relevant to any epidemiologic modeling process.

For modifiable factors for which avgPAFs will be computed, however, level of measurement is constrained since avgPAFs are discrete measures anchored to levels, or categories, of exposure.

45


Modifiable factors are in effect treated as dichotomous, comparing “any” to “no” risk. This mirrors the interpretation of a PAF as the proportion of disease reduction given complete elimination of exposure.

Defining the reference group as “lower risk” rather than “no” risk is one way to pull back from reporting an unrealistic maximum impact. For example:

>= 2 days exercise, rather than >= 5 days exercise

<=1 medical risk factor rather than 0 medical risks

46


Continuous or ordinal variable:

the “j” relative risks will be exponentiated multiples of a beta coefficient for each observed value.

the “unexposed”, or reference group, will include only those with the single lowest value of the variable; conversely, those with any other value will be considered “exposed”

With the single lowest value as the reference group, the proportion of exposed will likely be artificially high (an ordinal variable with a few levels will typically have a broader (more inclusive) reference group)

47


Dummy variables—whether a recoded continuous or ordinal variable

or a nominal variable with k categories:

the “j” relative risks are computed from separate beta coefficients corresponding to the k-1 categories

for the special case of dichotomous variables, a single relative risk is computed from a single beta coefficient

48

Level of Measurement and Reference Groups With dummy variables, the analyst can choose

between reporting category-specific avgPAFs or an avgPAF for the summation over all categories. Note that while it is not possible to obtain a single ratio measure for a set of dummies, it is possible to obtain a single avgPAF.

If public health programming differs by exposure category, then using dummy variables and reporting dummy-specific avgPAFs may be more appropriate than summing over all categories.

49

1. no prenatal care, and 2. inadequate prenatal care

Modifiable

3. adequate+ (high end) prenatal care Unmodifiable

with adequate prenatal care as the reference group


Dummy variables may also be used to break up a single construct into modifiable and unmodifiable parts. Using prenatal care as an example, dummy variables might be:

50

Confounding and Effect Modification

• For each modifiable factor, confounding by all other modifiable and unmodifiable factors should be assessed. This is no different than assessment of confounding in any model when precise estimation of multiple “exposures” is of interest

• Accounting for effect modification, however, is related to whether it is present within the pool of unmodifiable factors, across modifiable and unmodifiable factors, or within the pool of modifiable factors

51


Within unmodifiable factors—use product terms or ignore the interaction if it does not have an impact on the measures of association for the modifiable factors

—this may depend on the pattern and strength of the confounding effect of the interacting unmodifiable factors on the factors in the risk system

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

52


Within modifiable factors—use either product terms or common reference coding to create a set of dummy variables

--even insignificant interaction among modifiable factors might be modeled in order to obtain the most precise joint and separate effects of the factors in the risk system

--stratified modeling should not be used, since it would not be possible to compute an avgPAF for the modifiable factor defining the strata

53

Model Building Strategies and Choosing a Final Model

Unmodifiable factors should remain in a model only if they are confounders or effect modifiers of the modifiable factors in the risk system—their independent association with the outcome is not of interest

Modifiable factors should remain in a model based on the size and reliability of the avgPAFs computed for them; parsimony is not as important when building a model to obtain avgPAFs, so variables with insignificant RRs/ORs may be included in a final model if the PAFs based on them are meaningfully large.


Possible Model building strategies

1. Build separate models for each modifiable factor plus the complete set of unmodifiable factors, assessing the results for the “adjusted” PAF (there is no avgPAF with only one modifiable factor in the model).

2. Build a combined model including all modifiable factors selected from the initial models along with all unmodifiable factors that were confounders or effect modifiers in any of those models.

3. Drop unmodifiable factors if their status as confounders or effect modifiers changes in the combined model and drop modifiable factors if their avgPAF does not meet the researcher’s criteria for inclusion

54


Possible Model building strategies

Alternatively, a first step might be to build models with subsets of substantively related modifiable variables, assessing the results for the avgPAFs for the variables in each subset, with steps two and three for building a combined model and revisiting the status of unmodifiable factors proceeding as previously described.

55

Interpretation Issues to Consider

PAF 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: the Summary PAF for the impact of 10 factors on breast cancer=0.25.

Incorrect: While many risk factors have been identified as causes of breast cancer, 75% of all breast cancer cases do not have an identifiable risk factor.

Incorrect: Only 25 percent of breast cancer cases can be attributed to one or more risk factors; 75% of breast cancers occur in women with no risk factors.

56Rockhill, et al., 1998

Interpretation Issues to ConsiderIncorrect: The pie should represent 100% of subjects with PAL, not 100% of all subjects.

Oppermann, et al., 2004 57


Rothman: 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)

58Rothman, & Greenland, 1998


Rothman Example 1: PAF=0.25 for smoking in relation to coronary deaths.Elimination of smoking could lead to fewer lung cancer deaths, which would lead to more people living long enough to die from coronary heart disease. Therefore, “25% fewer coronary deaths would have occurred had these doctors not smoked” is somewhat 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 somewhat misleading.

59


Causality takes on a prominent role when attributable risk measures are reported since these measures claim that a health outcome can be reduced given full or partial elimination of one or more risk factors. Differentiating between modifiable and unmodifiable factors only indirectly addresses causality, but public health interventions are often appropriately focused on factors that can be changed in the population even when strict causal criteria are not met or causality has yet to be established.

60

Limitations in available software packages: computation of only the 1st sequential (adjusted) PAF

with 95% CIs, but not the average PAF (AFLOGIT in STATA)

computation of avgPAFs but only for certain study designs, e.g. not case-control

computation of avgPAFs, but only accommodates dichotomous variables and handles all factors as modifiable – no adjustment for unmodifiable covariates

Variance estimates for the adjusted and summary PAF were derived by Benichou and Gail (1990) based on the delta method, but fully flexible variance estimation of the avgPAF is still not available

61

Variance Estimation and Confidence IntervalsOnce variance estimates for Average PAFs are fully incorporated into statistical software, interpretation of resulting confidence intervals will become important.

As always, narrower CIs will mean increased reliability of the point estimate of the avgPAF

The CIs across multiple avgPAFs will undoubtedly overlap. What will the overlap imply about the prioritization process across modifiable factors?

Will a CI with a lower bound < 0 mean a factor is not significant and therefore not a priority?

62

Review and Final Comments

Methodological advances might include:

differentially weighting removal sequences prior to computing Average PAFs in order to reflect funding streams or political will, since in reality not all removal sequences are equally likelyincorporating measures of uptake and efficacy of the public health interventions aimed at particular risk factors

63


Potential Impact Fraction (PIF)*: the estimation of impact; Incorporates the practicalities of interventions

Success Rate = Proportion of affected individuals whose risk status will change due to participation in the intervention programs

Relative Efficacy=Extent to which a successful risk-factor change results in a reduction of risk to the level of persons never exposed

PIF = avgPAF x Success Rate x Relative Efficacy*Morgenstern, et al (1982); Butlers, et al (1997)

64

Review and Final CommentsPIFs and Impact Numbers:

Increasing Participation in Sports as a Strategy to Reduce Overweight among Adolescent Females

65

Review and Final Comments 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

66


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.

67


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 an outcome

Typically, 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

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

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multifactorial population attributable fractions: approaches, examples, and issues to consider

Documents

prevalence of risk factors

risk system

modifiable risk factors

excess risk of disease

factors constant

factors miettenin

prevalence of disease

exclusive pafs