Presentation on theme: "Day One: 8:30-12:00 Background and Overview"— Presentation transcript:
0Using the Population Attributable Fraction (PAF) to Assess MCH Population Outcomes Deborah Rosenberg, PhD and Kristin Rankin, PhDEpidemiology and BiostatisticsSchool of Public HealthUniversity of Illinois at Chicago
1Day One: 8:30-12:00 Background and Overview Basic Formulas and Initial ComputationsMoving Beyond Crude PAFs: Organizing Multiple Factors into a Risk SystemSummary, Component and “Adjusted” PAFs
2BackgroundEpidemiologists most commonly use ratio measures to estimate the magnitude of an association between a risk factor and an outcomeImpact measures, such as the Population Attributable Fraction (PAF), account for both the magnitude of association and the prevalence of risk in the populationPAFs are underused because of methodological concerns about how to appropriately account for the multifactorial nature of risk factors in the population
3BackgroundIn a multivariable context, the goal is to generate a PAF for each of multiple factors, taking into account relationships among the factorsGenerating 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 requiredWith 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
4Historical 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 wholep0 = prevalence of the outcome in the population as a wholep2 = prevalence of the outcome in the unexposed
5Historical 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 modificationBruzzi (1985)/Greenland and Drescher (1993)Summary PAF = Proportion of the disease that could be reduced by simultaneously eliminating multiple risk factors from the populationMethod for using regression modeling to generate PAFsBenichou and Gail (1990)Variance estimates for the adjusted and summary PAF based on the delta method
6Example: Summary PAF for Three Risk Factors for a Health Outcome Components of a risk system:complete crossclassification of factors
7Apportioning 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
8Apportioning the Summary PAF Eide 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 eliminatedFirst Sequential PAF = the “adjusted PAF” —the particular sequential PAF in which a risk factor is eliminated first before any other factors
9Apportioning the Summary PAF Ordering is imposed for eliminating risk factors from the population, while simultaneously controlling for all other factors in the modelEXAMPLE (Sequence #1):Eliminate A, then B, then CSequential 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
10Summary PAF Apportioned into Sequential PAFs for Sequence #1 Eliminate A, then B, then C
11Apportioning the Summary PAF Eide and Gefeller (1995/1998)Average PAF = Simple average of all sequential PAFsEqual 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 unknownBased on the Shapley-solution in Game TheoryMethod of fairly distributing the total profit gained by team members working in coalitions
12Apportioning the Summary PAF: The Average PAF Six Sequences for Three Risk FactorsSequence #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 AThere 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.
13Summary PAF Apportioned into Average PAFs for Three Risk Factors
14The Summary PAF: the Basis for Producing Multifactorial PAFs The Summary PAF can be apportioned into:component PAFs reflecting every possible combination of factors being consideredsequential PAFs reflecting pieces of one particular sequence in which risk factors might be eliminatedaverage PAFs reflecting estimates of the impact of eliminating multiple risk factors regardless of the order in which each is eliminated
15PAFs from Different Study Designs Cross-sectional:Prevalence and measure of effect estimated from same data sourceInterpretation: Proportion of prevalent cases that can be attributed to exposureCohort:Interpretation: Proportion of incident cases that can be attributed to exposureCase-Control:Prevalence of exposure among the cases must be used and the OR in place of the RR, using the rare disease assumption
16Methodological Issues for the PAF in a Multivariable Context In addition to different computational approaches, decisions about how variables will be considered may be different when focusing on the PAF as compared with focusing on the ratio measures of associationDifferentiating the handling of modifiable and unmodifiable factorsConfounding and effect modificationHandling factors in a causal pathway
17Analytic Considerations Variable SelectionModifiabilityUnmodifiable factors are only used as potential confounders or effect modifiers; PAFs not calculatedModifiable factors are factors that can possibly be altered with clear intervention strategiesClassification of risk factors as unmodifiable or modifiable depends on perspective and may alter results
18Analytic Considerations Model BuildingDifferential handling of unmodifiable and modifiable factorsLevels of measurementCoding choicesEffect modificationwithin modifiable factorsacross modifiable and unmodifiable factorswithin unmodifiable factorsSelection of a final model may not be based on statistical significance of the ratio measure of effectStratified modelsDefining the “significance” of PAFs
19Analytic Considerations Presentation and InterpretationAverage 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 diseaseThe 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
20Analytic Considerations 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 stepsVariance estimates for the average PAF are not yet available, either for random samples or for samples from complex designsCurrently, can only report 95% confidence intervals around crude, summary, and first sequential (adjusted) PAFsWhile the interpretation of average PAFs is strengthened by evidence of causality, an average PAF cannot itself establish causality
21Analytic Considerations As always, having an explicit conceptual framework / logic model is important for multivariable analysisConceptualization 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.
22Laying the Groundwork: An Example with Crude PAFs
23Overview of Attributable Risk Measures Measures based on Risk DifferencesAttributable RiskAttributable FractionPopulation Attributable RiskPopulation Attributable Fraction (PAF)
24Overview of Attributable Risk Measures General InterpretationAttributable Risk: The risk of an outcome attributed to a given risk factor among those with that factorAttributable Fraction: The proportion of cases of an outcome attributable to a risk factor in those with the given risk factorPop. Attributable Risk: The risk of an outcome attributed to a given risk factor in the population as a wholePop. Attributable Fraction (PAF): The proportion of cases of an outcome attributable to a risk factor in the population as a whole
26Overview of Attributable Risk Measures Various Formulas For the Crude PAF
27Example: Smoking and Low Birthweight Crude RR = = 1.606.25
28Example: Smoking and Low Birthweight Crude Association Interpretation of the RR v. the PAFWomen 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%
29Example: Cocaine and Low Birthweight Crude Association Crude RR = = 4.776.29
30Example: Cocaine and Low Birthweight Crude Association Interpretation of the RR v. the PAFWomen 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%
31Smoking and Low Birthweight Cocaine and Low Birthweight RR Compared to PAFNotice 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.
32Moving Beyond Crude PAFs Multivariable Approaches: Organizing Multiple Factorsinto a Risk System
33PAFs Based on Organizing Multiple Factors into a Risk System Summary PAF: The total PAF for many modifiable factors considered in a single risk systemComponent 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 systemSequential PAF: The PAF for eliminating a risk factor in a particular order from a risk system; sets of sequential PAFs comprise possible removal sequencesAverage PAF: The PAF summarizing all possible sequences for eliminating a risk factor
34Extension of Basic Formulas for Multifactorial PAFs = =Rothman Bruzzik=Number of unique exposure categories created with a complete cross-classification of independent variablespj=proportion of total cases that are in the “jth” unique exposure categoryRRj=Relative risk for the “jth” exposure level compared with the common reference groupImportant: Note that in these formulas, the pjs are column percents
35The Simple Case of 2 Binary Variables Organization into a Risk system
37The simple case of 2 binary variables Smoking and CocaineCrude RR = Crude RR = 4.77
38Smoking and Cocaine Organized into a Risk System If smoking and cocaine use were recoded as a single “substance use” variable:
39Components of each combination of risk factors in the smoking-cocaine risk system:pj* rpj* RRj*pj = column %**rpj = row %
40Component PAFs and Summary PAF for the Smoking-Cocaine Risk System Using Rothman’s formula:The Summary PAF is thesum of component PAFs+ = 0.16
41Component PAFs and Summary PAF for the Smoking-Cocaine Risk System Using Bruzzi’s formula:With Bruzzi’s formula, theSummary PAF is not builtfrom component PAFs
42Limitation of Component PAFs from the Smoking-Cocaine Risk System While 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 factorHere, the Summary PAF = 0.16,but the two factors overlap:the component PAFs still do notdisentangle smoking and cocainefor those who do both
43The “Adjusted” PAF: Obtaining a Single PAF for a Given Risk Factor The Stratified Approach: The PAF for eliminating arisk factor after controlling for other risk factorsWith 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
44The “Adjusted” PAF: Obtaining a Single PAF for a Given Factor The Stratified ApproachIf there is multiplicative effect modificationin 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.
45The “Adjusted” PAF: Obtaining a Single PAF for a Given Factor The Stratified ApproachIf there is not multiplicative effect modificationin 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.
46The “Adjusted” PAF: Obtaining a Single PAF for a Given Factor Reorganizing the data toget an adjusted PAF withRothman’s formula
47The “Adjusted” PAF: The PAF for Smoking, Controlling for Cocaine Use* RR==RR=1.36*Using stratum-specific estimates
48The “Adjusted” PAF: The PAF for Cocaine Controlling for Smoking* RR==RR=4.30*Using stratum-specific estimates
49The “Adjusted” PAF: Obtaining a Single PAF for a Given Risk Factor Using 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/rp2rp2/rp2rp3/rp4rp4/rp4
50For the Burzzi Formula: the RRj* and RRj~ RR= RR=1RR= RR=1
51The “Adjusted” PAF: Obtaining a Single PAF for a Given Risk Factor In the Bruzzi approach to “adjustment”, there are 3 different versions of the relative risks:RRj = the component RRsRRj* = 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 smokingRRj~ = 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
52The “Adjusted” PAF: Obtaining a Single PAF for a Given Risk Factor Using the Bruzzi method:PAF for Smoking,controlling for cocaine use.PAF for cocaine,controlling for smoking.
53The “Adjusted” PAF Obtaining a Single PAF for a Given Factor The Stratified ApproachNotice 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 vCrude v. “Adjusted” for cocaine:0.102 v
54Limitations 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≠= = 0.175
55Limitations 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
56Extension 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 observationsproc sort data=work.Orig_SampleLBW;by lbw smoke cocaine poverty;run;proc freq data=work.Orig_SampleLBW;tables lbw*smoke*cocaine*poverty/list;
57Extension to the Case of 3 Binary Variables LBW bySmoking,Cocaine useand Poverty
58Extension to the Case of 3 Binary Variables Data rearranged into “strata” in the Bruzzi sense...
59Component Prevalences and Relative Risks for a Risk System with Three Variables Prevalence and RR addedExample (first row):pj = 24 / 700 = RRj = [(24/59) / (175/4605)] = 10.70
60Unique Cross-Classifications of n Variables For binary variables, the # of strata k = 2n, where n=# variablesExample:Smoke (1=Yes, 0=No),Cocaine (1=Yes, 0=No),Poverty(1=Yes, 0=No)In general, K = the product ofthe # of levels for each variable;e.g. in Bruzzi, et al (1985):k = 2*3*3*4 = 72smokecocainepovertyyesnok = 23 = 8
61Component PAFs for Entire Risk System Summary PAF = 0.46
62Summary 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
63Using Modeling to Compute Summary and “Adjusted” PAFs Advantages of Modeling for Obtaining Intermediate Estimates for PAFs—as usual in comparison to stratified methodsModeling is not as sensitive to sparse data in individual cells when there are many strataIf you choose to consider confounding and effect modification in the same model, estimates are generated more easilyNote: 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)
64Assumption-Free Approach Using Fully Specified Model /*Binomial Regression – Directly estimate RRs*/proc genmod data=LBW desc;model lbw=smoke cocaine poverty smoke*cocainesmoke*poverty cocaine*povertysmoke*cocaine*poverty/dist=bin link=log;weight freq; run;/*Logistic Regression – ORs as estimates of RRs*/proc logistic data=LBW desc;smoke*cocaine*poverty;weight freq;run;
65Results from Fully-Specified Binomial Regression Model Response ProfileOrdered ValuelbwTotal Frequency170029300PROC GENMOD is modeling the probability that lbw='1'.Criteria For Assessing Goodness Of FitCriterionDFValueValue/DFDeviance8Scaled DeviancePearson Chi-SquareScaled Pearson X2Log Likelihood
66Results from Fully-Specified Binomial Regression Model Analysis of Parameter EstimatesParameterDFEstimateStandard ErrorChi-SquarePr >ChiSqIntercept10.0741<.0001smoke0.58690.138617.94cocaine1.82010.214072.36poverty0.84470.093182.27smoke*cocaine0.29021.180.2769smoke*poverty0.18368.350.0039cocaine*poverty0.29515.380.0204smoke*cocaine*poverty0.64940.40202.610.1062Scale1.00000.0000
67Component and Summary PAFs from Fully-specified Model Discuss Worksheet B in Supplementary Excel File:Summary PAFs from Fully Specified Models
68Re-examining Fully-Specified Model Analysis of Parameter EstimatesParameterDFEstimateStandard ErrorChi-SquarePr >ChiSqIntercept10.0741<.0001smoke0.58690.138617.94cocaine1.82010.214072.36poverty0.84470.093182.27smoke*cocaine0.29021.180.2769smoke*poverty0.18368.350.0039cocaine*poverty0.29515.380.0204smoke*cocaine*poverty0.64940.40202.610.1062Non-significant interaction terms could be dropped from model
69Reduced Modelproc genmod data=LBW desc;model lbw=smoke cocaine poverty smoke*poverty cocaine*poverty/dist=bin link=log;weight freq; run;Analysis of Parameter EstimatesParameterDFEstimateStandard ErrorChi-SquarePr > ChiSqIntercept10.0712<.0001smoke0.51690.125117.08cocaine1.63690.1482121.99poverty0.81110.090380.60smoke*poverty0.16435.870.0154cocaine*poverty0.20122.870.0905Non-significant interaction term could be dropped from model
70Analysis of Parameter Estimates Final Modelproc genmod data=LBW desc;model lbw=smoke cocaine poverty smoke*poverty / dist=bin link=log;weight freq; run;Analysis of Parameter EstimatesParameterDFEstimateStandard ErrorChi-SquarePr > ChiSqIntercept10.0704<.0001smoke0.57410.120322.79cocaine1.43720.0980214.96poverty0.77870.088477.69smoke*poverty0.15689.280.0023
71Component and Summary PAFs from Final Reduced Model Model Discuss Worksheet C in Supplementary Excel File:Summary PAFs from Final Reduced Models
72Exercise 1 Discussion of Exercise 1 Day One: 1:00-3:15Exercise 1Discussion of Exercise 1
73Day One: 3:15-5:00Overview of Sequential and Average PAFs: Example with 2 modifiable risk factorsCase study with 3 factors:-2 modifiable factors, 1 unmodifiable factor-3 modifiable factorsIntroduction of Exercise 2
74Sequential PAFs (PAFSEQ) for the Smoking-Cocaine Risk System For the smoking-cocaine risk system, there are 2 possible sequences:Eliminate smoking first, controlling for cocaine use, then eliminate cocaine useEliminate cocaine use first, controlling for smoking, then eliminate smokingAnd within each sequence, there are two sequential PAFs
75Sequential PAFs (PAFSEQ) for the Smoking-Cocaine Risk System The PAFSEQ for eliminating smoking, controlling for cocaine use:PAFSEQ1a (S|C) = 0.076The PAFSEQ for eliminating cocaine use after smoking has already been eliminated is the remainder of the Summary PAFPAFSEQ1b =PAFSUM – PAFSEQ1a (S|C) = 0.16 – = 0.084
76Sequential PAFs (PAFSEQ) for the Smoking-Cocaine Risk System The PAFSEQ for eliminating cocaine use, controlling for smoking:PAFSEQ2a (C|S) = 0.099The PAFSEQ for eliminating smoking after cocaine use has already been eliminated is the remainder of the Summary PAFPAFSEQ2b =PAFSUM – PAFSEQ2a (C|S) = 0.16 – = 0.061
77Sequential PAFs (PAFSEQ) for the Smoking-Cocaine Risk System By definition, the sequential PAFs within the two possible sequences sum to the Summary PAFSmoking First Cocaine Use First= = 0.16
78Average PAF (PAFAVG) for the Smoking-Cocaine Risk System While 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 eliminatedThat is, regardless of when cocaine might be eliminated, what would the impact of eliminating smoking be on average?
79Average PAF (PAFAVG) for the Smoking-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 secondEliminating cocaine use first, averaged with eliminating cocaine use second
80Average PAF (PAFAVG) for the Smoking-Cocaine Risk System Averaging Sequential PAFsAverage PAF for Smoking:=Average PAF for Cocaine Use:
81Average PAFs for the Smoking-Cocaine Risk System The Average PAFs for each factor in the risk system are mutually exclusive and their sum equals the Summary PAF:= 0.16
82Case 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.
83Modifiable and Unmodifiable Risk Factors Using a Modeling ApproachWithin one model, we can differentiate between those factors considered to be modifiable and those factors considered to be unmodifiableWhile 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
84Decisions 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)
86Case Study Part I Considering Poverty as Unmodifiable Calculating Sequential and/or Average PAFs for Smoking and Cocaine UseConsidering Poverty as Unmodifiable
87Sequential PAFs for the Smoking-Cocaine-Poverty Risk System, Considering Poverty as Unmodifiable With 3 factors, but only 2 of them modifiable, there are 2 possible sequences:Eliminate smoking first, controlling for cocaine use and poverty, then eliminate cocaine useEliminate cocaine use first, controlling for smoking and poverty, then eliminate smokingAnd within each sequence, there are two sequential PAFs
88SAS 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*/
89Discuss Worksheets D and E in Supplementary Sequential PAFs for the Smoking-Cocaine-Poverty Risk System, Considering Poverty as UnmodifiableDiscuss Worksheets D and E in SupplementaryExcel File:Calculations for 1st Sequential PAFs, Summary PAFs, and Average PAFs for Smoking and Cocaine, Controlling for Poverty
90PAFSEQ for Smoking and Cocaine, Considering Poverty as Unmodifiable Sequence 1: Smoking, THEN CocainePAFSEQ1a: (S | C U P)=PAFSEQ1b : (C U S | P) – (S | C U P) =0.156 – 0.074= 0.082Sequence 2: Cocaine, THEN SmokingPAFSEQ2a : (C | S U P) = 0.098PAFSEQ2b: (S U C | P) – (C | S U P) == 0.058The Summary PAF includes only smoking and cocaine, since poverty is unmodifiable.
91PAFSEQ for Smoking and Cocaine, Considering Poverty as Unmodifiable Smoking THEN Cocaine, Controlling for PovertyCocaine THEN Smoking, Controlling for PovertyPAFSEQ2PAFSUM=0.156PAFSUM=0.156PAFAGG=0.15
92Average PAF (PAFAVG)Eide (1995): Based on Game Theory according to Cox’s Theorem (1984) for risk allocation (attributable risk among the exposed),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 systemNote: Average PAF is sometimes called the “partial” attributable fraction
93Average PAFs for Smoking and Cocaine, Controlling for Poverty Average PAF for SmokingPAFAVG: ((PAFSEQ1a+PAFSEQ2b)/2)PAFAVG : (( ) / 2) = 0.066Average PAF for CocainePAFAVG: ((PAFSEQ1b+PAFSEQ2a)/2)PAFAVG : (( ) / 2) = 0.090
94Considering Poverty as Modifiable Case Study Part IICalculating Sequential and/or Average PAFs for Smoking, Cocaine Use, and PovertyConsidering Poverty as Modifiable
95Sequential PAFs (PAFSEQ) for the Smoking-Cocaine Risk System For the smoking-cocaine-poverty risk system, there are 6 possible sequences:Smoking, cocaine use, povertySmoking, poverty, cocaine useCocaine use, smoking, povertyCocaine use, poverty, smokingPoverty, smoking, cocaine usePoverty, cocaine use, smokingAnd within each sequence, there are three sequential PAFs
96SAS 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*/
97Sequential PAFs n=4, n!= 4x3x2x1 = 24 unique sequences Q: How many unique sequences will there be for removing risk factors from the risk system?A: n!, where n=# of modifiable risk factors in systemEx: n=3, n!= 3x2x = unique sequencesn=4, n!= 4x3x2x1 = 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.
98Discuss Worksheets F and G in Supplementary Sequential PAFs for the Smoking-Cocaine-Poverty Risk System, Considering Poverty as ModifiableDiscuss Worksheets F and G in SupplementaryExcel File:Calculations for 1st Sequential PAFs, Summary PAFs, and Average PAFs for Smoking,Cocaine, and Poverty
99PAFSEQ for Smoking Removed First Sequence 1: Smoking, THEN Cocaine, THEN PovertyPAFSEQ1a: (S | C U P) = 0.074PAFSEQ1b: (S U C | P) – (S | C U P) = – =PAFSEQ1c: (S U C U P) – (S U C | P) = – =Sequence 2: Smoking, THEN Poverty, THEN CocainePAFSEQ2a: (S | P U C)= 0.074PAFSEQ2b: (S U P | C) – (S | P U C) = – =PAFSEQ2c: (S U P U C) – (S U P | C) = – =
100PAFSEQ for Smoking Removed First Smoking THEN Cocaine, THEN PovertySmoking THEN Poverty, THEN CocainePAFSEQ2
101PAFSEQ for Cocaine Removed First Sequence 3: Cocaine, THEN Smoking, THEN PovertyPAFSEQ3a: (C | S U P)= 0.098PAFSEQ3b: (C U S | P) – (C | S U P) = – = 0.058PAFSEQ3c: (C U S U P) – (C U S| P) = – = 0.286Sequence 4: Cocaine, THEN Poverty, THEN SmokingPAFSEQ4a : (C | P U S)= 0.098PAFSEQ4b: (C U P | S) – (C | P U S) = – = 0.257PAFSEQ4c: (C U P U S) – (C U P | S) = – = 0.086
102PAFSEQ for Cocaine Removed First Cocaine THEN Smoking, THEN PovertyCocaine THEN Poverty, THEN SmokingPAFSEQ2
103PAFSEQ for Poverty Removed First Sequence 5: Poverty, THEN Smoking, THEN CocainePAFSEQ5a: (P | S U C) = 0.275PAFSEQ5b: (P U S | C) – (P | S U C) = – = 0.108PAFSEQ5c: (P U S U C) – (P U S | C) = – = 0.058Sequence 6: Poverty, THEN Cocaine, THEN SmokingPAFSEQ6a: (P | C U S)= 0.275PAFSEQ6b: (P U C | S) – (P | C U S) = – = 0.080PAFSEQ6c: (P U C U S) – (P U C | S) = – = 0.086
104PAFSEQ for Poverty Removed First Poverty THEN Smoking, THEN CocainePoverty THEN Cocaine THEN SmokingPAFSEQ2
105PAFAVG 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) (0.086)) / 6) =Average PAF for Cocaine(PAFSEQ1b +PAFSEQ2c+PAFSEQ3a+PAFSEQ4a+PAFSEQ5c+PAFSEQ6b) / 6PAFAVG = (2(0.098) (0.058)) / 6 =Average PAF for PovertyPAFAVG = (PAFSEQ1c+PAFSEQ2b+PAFSEQ3c+PAFSEQ4b+PAFSEQ5a+PAFSEQ6a) / 6PAFAVG = (2(0.275) (0.286)) / 6 =
106Average PAFs for all possible models Smoke and Coke, Controlling for PovertySmoke and CokeSmoke, Coke and PovertyPAFSUM=0.16PAFSUM=0.156PAFSUM=0.441
107Smoke and Coke, Controlling for Poverty Average PAFs for all possible models – with no interaction term for smoke*povertySmoke and Coke, Controlling for PovertySmoke and CokeSmoke, Coke and PovertyPAFSUM=0.160PAFSUM=0.155PAFSUM=0.393
108Average PAFs stratified by poverty PAFSUM=0.088PAFSUM=0.245Poverty = YesPoverty = No
110Day Two: 8:00-12:00 Exercise 2 and Discussion of Exercise 2 Brief ReviewModel Building IssuesExercise 3
111ReviewThe 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 outcomeThe 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.
112ReviewThe Summary PAF is the proportion of an outcome that could be reduced by simultaneously eliminating from the population all modifiable factors in a risk system.The Summary PAF can be partitioned into:Component PAFsSequential PAFs corresponding to a particular removal sequenceAverage PAFsThe modifiable factors in the risk system can be “adjusted” both for each other and for other unmodifiable factors
113Partitioning of the Summary PAF ReviewPartitioning of the Summary PAFfor a Risk SystemComponent PAFs Sequential PAFs for Average PAFsOne Possible Sequence
114ReviewThe component PAFs reflect every combination of the modifiable factors in the risk system and do not yield any factor-specific PAFSequential 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” PAFComponent 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.
115ReviewThe 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 FactorsNumber of Possible Removal Orderings / SequencesNumber of Unique Sequential PAFs22! = 233! = 644! = 24855! = 1201666! = 7203277! = 5,04064
116ReviewThe 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 possibleThe 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
117Review 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
118ReviewComputation of the sequential PAFs within particular removal sequences becomes cumbersome as the number of variables, both modifiable and unmodifiable increasesIntermediate Summary PAFs are required for differing subsets of modifiable variables in a risk system
119ReviewWhether 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.
120Model Building Issues and Strategies in the Context of Estimating PAFs Reporting PAFs
121Model Building Issues and Strategies Within one model, we can differentiate between those factors considered to be modifiable and those factors considered to be unmodifiableThe 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 modelIn 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
122Model Building Issues and Strategies Variable SelectionModifiabilityUnmodifiable factors are only used as potential confounders or effect modifiers; PAFs not calculatedModifiable factors are factors that can possibly be altered with clear intervention strategiesBeing 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
123Model Building Issues and Strategies Differential handling ofunmodifiable and modifiable factorsLevels of measurement:Modifiable variables cannot be continuousModifiable variables can be ordinal or nominalSets of dummy variables can be used, but for modifiable factors it means there will be a separate PAF for each dummy variableUnmodifiable 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
124Model Building Issues and Strategies Choice of Reference Level for ComparisonSince 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
125Model Building Issues and Strategies Reference Groups for Modifiable FactorsMore restrictive level of the reference group could lead to both a higher prevalence of exposure and stronger measure of effect, resulting in an inflated PAFImportance of distinguishing between never exposed and formerly exposedUse conceptual framework and balance evidence with realistic goals
126Model Building Issues and Strategies Effect modificationwithin modifiable factors—use either a product term or could use common reference coding to create a set of dummy variablesacross 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 stratificationwithin 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
127Model Building Issues and Strategies 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.
128Model Building Issues and Strategies Criteria 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 modelCriteria forModifiable Risk FactorsStaying in a Model1st Sequential PAF95% CI Does Not Include 095% CI Includes 0SignificantRR / ORClose to the null?Far from the nullNot Significant
129Model Building Issues and Strategies 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 factorsThe 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
130Model Building Issues and Strategies Possible Model building strategiesBuild models with one modifiable factor at a time plus the unmodifiable factorsBuild models with subsets of modifiable factors that are within a domain (substantively related) plus the unmodifiable factorsBuild models starting with all modifiable and unmodifiable factors, and then use a manual backward elimination approach
131Moving 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 criteriaCalculate average PAFs for all modifiable factors in the final model, but report only those with values above some threshold, e.g. 2%, 5%, 10%?
132Moving from Modeling to Reporting of PAFs 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
133Moving from Modeling to Reporting of PAFs 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)
134Moving from Modeling to Reporting of PAFs Variance 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 reliabilityThe 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?
137Presentation of Sequential PAFs for the Smoke, Coke and Poverty Risk System
138Interpretations of Sequential PAFs from the Smoke- Coke- Poverty Risk System PAFSEQ (smoking 3rd, after coke and poverty) =0.09An 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 womenThe 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
139Interpretation of Average PAFs from the Smoke, Coke, and Poverty Risk System PAFAVG (Smoking) = 0.06On 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 povertyPAFAVG (Cocaine) = 0.09On 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.
140Presentation Issues to consider Is there any time when displaying stratified PAFs would be appropriate?Targeting an intervention to a particular risk groupDisplaying the interaction effects between variablesOthers?
141Interpretation 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: 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 factorcan 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
142Interpretation Issues to Consider 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.Assumes all biases are absentAssumes 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
143Interpretation Issues to Consider Rothman 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.