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

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

### Considering Poverty as Unmodifiable: Assessment: Calculating Sequential and/or Average PAFs for Smoking and Cocaine Use

### Considering Poverty Modifiable: LBW, Stratified by PovertyCalculating Sequential and/or Average PAFsfor Smoking, Cocaine Use, and Poverty

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

Workshop Outline Assessment:

- 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 effects—the 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 won’t discuss:
- Standard error and confidence interval estimation
- Statistical testing

Deborah Rosenberg, PhD

Research Assistant Professor

Epidemiology and Biostatistics

UIC School of Public Health

Overview of Attributable Risk Measures Assessment:

- Measures based on Risk Differences
- Attributable Risk =
- Attributable Fraction =
- Pop. Attributable Risk =
- Pop. Attributable Fraction =

Overview of Attributable Risk Measures Assessment:

- 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 appropriate—in case control studies when “disease” is rare

Methodological Issues for the PAF Assessment: 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

Methodological Issues for the PAF Assessment: 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

Methodological Issues for the PAF Assessment: 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

Methodological Issues for the PAF Assessment: 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.

Methodological Issues for the PAF Assessment: 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

The simple case of 2 variables Assessment:

- Smoking and Cocaine
- Crude RR = 1.60 Crude RR = 4.77

Smoking and Cocaine Organized into a Risk System Assessment:

- Aggregate RR = 1.88

Components of the Smoking-Cocaine Risk System Assessment:

- Components
- RR=5.89, both smoking and cocaine use
- RR=4.30, cocaine use only
- RR=1.36, smoking only
- There is a component for each combination of exposure levels in the risk system.

Components of the Assessment: Smoking-Cocaine Risk System

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

Components of the Assessment: 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

The “Adjusted” PAF: Assessment: 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

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

- RR=1.37
- +
- RR=1.36 =

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

- RR=4.33
- +
- RR=4.30 =

The “Adjusted” PAF: Assessment:

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

The “Adjusted” PAF: Assessment:

- The typical adjustment procedures result in a PAF that, by itself, represents an estimate—perhaps unrealistic—of 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

Sequential PAFs (PAF Assessment: SEQ) 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

Sequential PAFs (PAF Assessment: SEQ) for theSmoking-Cocaine Risk System

- The PAFSEQ for eliminating smoking, controlling for cocaine use:
- PAFSEQ (S|C) = 0.076
- The PAFSEQ for eliminating cocaine use after smoking has already been eliminated is the remainder of the Aggregate PAF
- PAFAGG – PAFSEQ (S|C) = 0.16 – 0.076 = 0.084

Sequential PAFs (PAF Assessment: SEQ) for theSmoking-Cocaine Risk System

- The PAFSEQ for eliminating cocaine use, controlling for smoking:
- PAFSEQ (C|S) = 0.099
- The PAFSEQ for eliminating smoking after cocaine use has already been eliminated is the remainder of the Aggregate PAF
- PAFAGG – PAFSEQ (C|S) = 0.16 – 0.099 = 0.061

Sequential PAFs (PAF Assessment: SEQ) 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

Average PAF (PAF Assessment: AVG) 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?

Average PAF (PAF Assessment: AVG) 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

Average PAF (PAF Assessment: AVG) for theSmoking-Cocaine Risk System

- Averaging Sequential PAFs
- Average PAF for Smoking:
- =
- Average PAF for Cocaine Use:
- =

Average PAFs for the Assessment: Smoking-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

Average PAFs for the Assessment: Smoking-Cocaine Risk System

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

In a Truly Multivariable Context Assessment:

- 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

Kristin Rankin, MSPH

Assistant Director of Research

CADE Research Data Management Group

UIC School of Public Health

PAF from Modeling Assessment:

- Why isn’t 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?

Advantages of Obtaining Estimates Assessment: 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

Using SAS PROC GENMOD Assessment:

- 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)

Modifiable and Unmodifiable Assessment: 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.

Case Study Assessment:

- 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.

Descriptive Statistics for Case Study Assessment:

Component PAFs for Entire Risk System Assessment:

Choose Your Own Adventure Assessment:

- 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 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)

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 order=formatted;
- tables lbw*mod_exp/list nopercent;
- /*mod_exp=1 if smoke=1 or cocaine=1*/
- by poverty; /*Stratified by poverty*/
- run;

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_exp=1 if woman has at least one of the modifiable
- exposures*/
- / dist=bin link=log; /*Binomial distribution*/
- estimate “Smoke and/or Cocaine, where Poverty=Yes”
- mod_exp 1 Poverty 0 mod_exp*Poverty 1/exp;/*Stratified RR*/
- estimate “Smoke and/or Cocaine, where Poverty=No”
- mod_exp 1 /exp; /*Stratified RR*/
- run;

SAS Results: Elements of the PAF Modifiable Exposure vs LBWAGGfor Risk System, Stratified by Poverty

Poverty=Yes

Poverty=No

PAF Modifiable Exposure vs LBWAGG for Smoking and Cocaine Risk System, Considering Poverty Unmodifiable

Poverty=Yes

Poverty=No

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 order=formatted;
- tables lbw*smoke*cocaine/list nopercent;
- by poverty; /*Stratified by poverty*/
- run;

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
- smoke*cocaine smoke*poverty cocaine*poverty
- smoke*cocaine*poverty
- /*Every possible multiplicative term must be in model
- if using assumption-free, stratified approach*/
- /dist=bin link=log obstats; /*Binomial distribution*/
- /*ESTIMATE Statements in future slides should be inserted here*/
- run;

SAS Code: Estimate Statements to Obtain LBW, Stratified by PovertyStratified RRs for Smoking

- /*defining all possible parameter values for stratified model*/
- estimate “smoke, where cocaine=Yes and poverty=Yes”
- smoke 1 cocaine 0 poverty 0 smoke*cocaine 1 smoke*poverty 1
- cocaine*poverty 0 smoke*cocaine*poverty 1
- / exp; /* “exp” option gives relative risks from betas */
- estimate “smoke, where cocaine=Yes and poverty=No”
- smoke 1 cocaine 0 poverty 0 smoke*cocaine 1 smoke*poverty 0
- cocaine*poverty 0 smoke*cocaine*poverty 0
- / exp;
- estimate “smoke, where cocaine=No and poverty=Yes”
- smoke 1 cocaine 0 poverty 0 smoke*cocaine 0 smoke*poverty 1
- cocaine*poverty 0 smoke*cocaine*poverty 0
- /exp;estimate “smoke, where cocaine=No and poverty=No”
- smoke 1 cocaine 0 poverty 0 smoke*cocaine 0 smoke*poverty 0
- cocaine*poverty 0 smoke*cocaine*poverty 0
- / exp;

SAS Results: Elements of PAF LBW, Stratified by PovertySEQ for Smoking Removed First

Poverty=Yes

Poverty=No

Elements of LBW, Stratified by PovertyPAFSEQ for Smoking Removed First, Considering Poverty Unmodifiable

Poverty=Yes

Coke=Yes

Coke=No

Poverty=No

Coke=Yes

Coke=No

SAS Code: Estimate Statements to Obtain LBW, Stratified by PovertyStratified RRs for Cocaine

- estimate “Cocaine, where smoke=Yes and poverty=Yes”
- cocaine 1 smoke 0 poverty 0 cocaine*smoke 1 cocaine*poverty 1
- smoke*poverty 0 cocaine*smoke*poverty 1
- / exp e;
- estimate “Cocaine, where smoke=Yes and poverty=No”
- cocaine 1 smoke 0 poverty 0 cocaine*smoke 1 cocaine*poverty 0
- smoke*poverty 0 cocaine*smoke*poverty 0
- / exp e;
- estimate “Cocaine, where smoke=No and poverty=Yes”
- cocaine 1 smoke 0 poverty 0 cocaine*smoke 0 cocaine*poverty 1
- smoke*poverty 0 cocaine*smoke*poverty 0
- / exp e;
- estimate “Cocaine, where smoke=No and poverty=No”
- cocaine 1 smoke 0 poverty 0 cocaine*smoke 0 cocaine*poverty 0
- smoke*poverty 0 cocaine*smoke*poverty 0
- / exp e;

SAS Results: Elements of PAF LBW, Stratified by PovertySEQ for Cocaine Removed First

Poverty=Yes

Poverty=No

PAF LBW, Stratified by PovertySEQ for Cocaine Removed First, Considering Poverty Unmodifiable

Poverty=Yes

Smoke=Yes

Smoke=No

Poverty=No

Smoke=Yes

Smoke=No

PAF LBW, Stratified by PovertySEQ 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

PAF LBW, Stratified by PovertySEQ for Smoking and Cocaine,Considering Poverty as Unmodifiable

Smoking THEN Cocaine, Controlling for Poverty

Cocaine THEN Smoking, Controlling for Poverty

PAFSEQ2

PAFAGG=0.15

PAFAGG=0.15

PAFAGG=0.15

Average PAFs for Smoking and Cocaine, LBW, Stratified by PovertyControlling for Poverty

- Average PAF for Smoking
- PAFAVG: ((PAFSEQ1a+PAFSEQ2b)/2)
- PAFAVG : ((0.07 + 0.05 ) / 2) = 0.06
- Average PAF for Cocaine
- PAFAVG: ((PAFSEQ1b+PAFSEQ2a)/2)
- PAFAVG : ((0.10 + 0.08 ) / 2) = 0.09

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 order=formatted;
- tables lbw*mod_exp/list nopercent;
- /*mod_exp=1 if smoke=1 or cocaine=1 or poverty=1*/
- run;

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_exp=1 if woman has at least one of the
- modifiable exposures*/
- / dist=bin link=log; /*Binomial distribution*/
- estimate “Any Modifiable Exposure” mod_exp 1 / exp;
- run;

SAS Results: Elements of the PAF vs LBWAGG for Risk System (Smoking, Cocaine, Poverty)

SAS Code: Obtaining Prevalences for vs LBWSmoke, 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 order=formatted;
- tables lbw*smoke*cocaine*poverty/list nopercent;
- run;

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
- smoke*cocaine smoke*poverty cocaine*poverty
- smoke*cocaine*poverty
- /*Every possible multiplicative term must be in model
- if using assumption-free, stratified approach*/
- /dist=bin link=log obstats; /*Binomial Distribution*/
- /*ESTIMATE Statements in future slides should be inserted here*/
- run;

SAS Code: Estimate Statements to Obtain Poverty vs LBWStratified RRs for Smoking

- /*defining all possible parameter values for stratified model*/
- estimate “smoke, where cocaine=Yes and poverty=Yes”
- smoke 1 cocaine 0 poverty 0 smoke*cocaine 1 smoke*poverty 1
- cocaine*poverty 0 smoke*cocaine*poverty 1
- / exp; /* “exp” option gives relative risks from betas */
- estimate “smoke, where cocaine=Yes and poverty=No”
- smoke 1 cocaine 0 poverty 0 smoke*cocaine 1 smoke*poverty 0
- cocaine*poverty 0 smoke*cocaine*poverty 0
- / exp;
- estimate “smoke, where cocaine=No and poverty=Yes”
- smoke 1 cocaine 0 poverty 0 smoke*cocaine 0 smoke*poverty 1
- cocaine*poverty 0 smoke*cocaine*poverty 0
- /exp;estimate “smoke, where cocaine=No and poverty=No”
- smoke 1 cocaine 0 poverty 0 smoke*cocaine 0 smoke*poverty 0
- cocaine*poverty 0 smoke*cocaine*poverty 0
- / exp;

SAS Results: Elements of the PAF Poverty vs LBWSEQ for Smoking Removed First

SAS Results: Elements of PAF Poverty vs LBWSEQ for Smoking Removed First

PAF Poverty vs LBWSEQ for Smoking Removed First

Coke=Yes Poverty=Yes

Coke=No Poverty=Yes

Coke=Yes

Poverty=No

Coke=Yes

Poverty=No

SAS Code: Estimate Statements to Obtain Poverty vs LBWStratified RRs for Cocaine

estimate “Cocaine, where smoke=Yes and poverty=Yes”

cocaine 1 smoke 0 poverty 0 cocaine*smoke 1 cocaine*poverty 1

smoke*poverty 0 cocaine*smoke*poverty 1

/ exp e;

estimate “Cocaine, where smoke=Yes and poverty=No”

cocaine 1 smoke 0 poverty 0 cocaine*smoke 1 cocaine*poverty 0

smoke*poverty 0 cocaine*smoke*poverty 0

/ exp e;

estimate “Cocaine, where smoke=No and poverty=Yes”

cocaine 1 smoke 0 poverty 0 cocaine*smoke 0 cocaine*poverty 1

smoke*poverty 0 cocaine*smoke*poverty 0

/ exp e;

estimate “Cocaine, where smoke=No and poverty=No”

cocaine 1 smoke 0 poverty 0 cocaine*smoke 0 cocaine*poverty 0

smoke*poverty 0 cocaine*smoke*poverty 0

/ exp e;

SAS Results: Elements of the PAF Poverty vs LBWSEQ for Cocaine Removed First

SAS Results: Elements of the PAF Poverty vs LBWSEQ for Cocaine Removed First

PAF Poverty vs LBWSEQ for Cocaine Removed First

Poverty=Yes

Smoke=No

Poverty=Yes

Smoke=Yes

Poverty=No

Smoke=Yes

Poverty=No

Smoke=No

SAS Code: Estimate Statements to Obtain Poverty vs LBWStratified RRs for Poverty

- estimate “Poverty, where Smoke=Yes and Cocaine=Yes”
- poverty 1 smoke 0 cocaine 0 poverty*smoke 1
- poverty*cocaine 1 smoke*cocaine 0 poverty*smoke*cocaine 1
- / exp e;
- estimate “Poverty, where Smoke=Yes and Cocaine=No”
- poverty 1 smoke 0 cocaine 0 poverty*smoke 1
- poverty*cocaine 0 smoke*cocaine 0 poverty*smoke*cocaine 0
- / exp e;
- estimate “Poverty, where Smoke=No and Cocaine=Yes”
- poverty 1 smoke 0 cocaine 0 poverty*smoke 0
- poverty*cocaine 1 smoke*cocaine 0 poverty*smoke*cocaine 0
- / exp e;
- estimate “Poverty, where Smoke=No and Cocaine=No”
- poverty 1 smoke 0 cocaine 0 poverty*smoke 0
- poverty*cocaine 0 smoke*cocaine 0 poverty*smoke*cocaine 0
- / exp e;

SAS Results: Elements of the Poverty vs LBWPAFSEQ for Poverty Removed First

SAS Results: Elements of the PAF Poverty vs LBWSEQ for Poverty Removed First

PAF Poverty vs LBWSEQ for Poverty Removed First

Smoke=Yes

Cocaine=No

Smoke=Yes

Cocaine=Yes

Smoke=No

Cocaine=Yes

Smoke=No

Cocaine=No

Elements for Calculation of Factors Removed Second and Third Poverty vs LBW

- 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:
- SC|P = 0.15
- SP|C = 0.37
- CP|S = 0.37

PAF Poverty vs LBWSEQ 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

PAF Poverty vs LBWSEQ for Smoking Removed First

Smoking THEN Cocaine, THEN Poverty

Smoking THEN Poverty, THEN Cocaine

PAFSEQ2

PAFAGG=

0.46

PAFAGG=

0.46

PAF Poverty vs LBWSEQ 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

PAF Poverty vs LBWSEQ for Cocaine Removed First

Cocaine THEN Smoking, THEN Poverty

Cocaine THEN Poverty, THEN Smoking

PAFSEQ2

PAFAGG=

0.46

PAFAGG=

0.46

PAFAGG=

0.46

PAF Poverty vs LBWSEQ 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

PAF Poverty vs LBWSEQ for Poverty Removed First

Poverty THEN Smoking, THEN Cocaine

Poverty THEN Cocaine THEN Smoking

PAFSEQ2

PAFAGG=

0.46

PAFAGG=

0.46

PAF Poverty vs LBWAVG for Smoking, Cocaine and Poverty

- Average PAF for Smoking
- PAFAVG: ((PAFSEQ1a+PAFSEQ3b+PAFSEQ4c+PAFSEQ5b)/4)
- PAFAVG : ((0.07 + 0.05 + 0.09 + 0.10 ) / 4) = 0.08
- Average PAF for Cocaine
- PAFAVG: ((PAFSEQ1b+PAFSEQ2c+PAFSEQ3a+PAFSEQ6b)/4)
- PAFAVG : ((0.08 + 0.08 + 0.10 + 0.09 ) / 4) = 0.09
- Average PAF for Poverty
- PAFAVG: ((PAFSEQ1c+PAFSEQ2b+PAFSEQ4b+PAFSEQ5a)/4)
- PAFAVG : ((0.31 + 0.31 + 0.27 + 0.28 ) / 4) = 0.29

Average PAFs for all possible models Poverty vs LBW

Smoke and Coke, Controlling for Poverty

Smoke and Coke

Smoke, Coke and Poverty

PAFAGG=0.16

PAFAGG=0.46

PAFAGG=0.15

Summary Poverty vs LBW

- 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

Selected Articles for Additional Reading Poverty vs LBW

- 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.
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Contact Information Poverty vs LBW

- Deborah Rosenberg
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- Kristin Rankin
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