Logistic Regression: Part 2 Logistic Regression: Part 2

““Why include covariate Why include covariate adjustment?” adjustment?”

Confounding, Mediation and Confounding, Mediation and AttenuationAttenuation

Robert Boudreau, PhDRobert Boudreau, PhDCo-Director of Methodology CoreCo-Director of Methodology Core

PITT-Multidisciplinary Clinical Research Center PITT-Multidisciplinary Clinical Research Center for Rheumatic and Musculoskeletal Diseasesfor Rheumatic and Musculoskeletal Diseases

ConfoundingConfounding

Confounding is: a bias in the estimation of the effect of

exposure on disease or outcome due to inherent differences in risk between exposed and unexposed groups

Exposures: Drug exposure, dose, durationOutcomes: Blood pressure control (< 120/80)

Adverse events (fainting, mortality)

Risk Factors: Prior MI, BMI, Exercise(or lack of)

Criteria to be a ConfounderCriteria to be a ConfounderConfounder: The factor must be a cause of the disease or outcome, or a

surrogate measure of a cause, in unexposed people; factors satisfying this condition are called risk factors

be correlated, positively or negatively, with exposure in the study population. If the study population is classified into exposed and unexposed groups, this means that the factor has a different distribution (prevalence) in the two groups

not be an intermediate step in the causal pathway between the exposure and the disease

Example of ConfounderExample of Confounder

Take antiHTN Drug Daily

(Y,N)

Blood Pressure Control

( <120/80)

Among people diagnosed with high BP and prescribed antiHTN drug

Compare Rates of BP Control: Those who take drug daily vs Those who take it less frequently

Example of ConfounderExample of Confounder

Take antiHTN Drug Daily

(Y,N)

Blood Pressure Control

( <120/80)

Daily Exercise

Among people diagnosed with high BP and prescribed antiHTN drug

Compare Rates of BP Control: Those who take drug daily vs Those who take it less frequently

1.1. A “cause” of the A “cause” of the outcome outcome

even in the unexposed even in the unexposed group group

Take antiHTN Drug Daily

(Y,N)

Blood Pressure Control

( <120/80)

Daily Exercise

Regular daily exercise contributes to lower blood pressure

Compare Rates of BP Control: Those who take drug daily vs Those who take it less frequently

2. Correlated with 2. Correlated with ExposureExposure

Take antiHTN Drug Daily

(Y,N)

Blood Pressure Control

( <120/80)

Daily Exercise

Regular daily exercisers are more likely to take their meds daily

Compare Rates of BP Control: Those who take drug daily vs Those who take it less frequently

Confounder DiagramConfounder Diagram

Exposure Outcome

Confounder

Example of MediatorExample of Mediator

Statin Drug(to control

lipids)

Mobility Problems

Muscle Weakness

• Muscle weakness occurs in ~10% of statin usersIn a study evaluating the potential adverse side effects of statin use on mobility problems (may or may not be the case)

• Muscle weakness is in the pathway (= mediator)• Prior muscle weakness before statin use may also be a confounder

General Interpretation General Interpretation of Covariate Adjustmentof Covariate Adjustment

E.g. Association of CRP levels with KneeOAE.g. Association of CRP levels with KneeOA

… … adjusted for BMIadjusted for BMI

Interpretation:Interpretation: Add adjustment for BMIAdd adjustment for BMI

CRP differences (KneeOA vs Not)CRP differences (KneeOA vs Not)

between individuals between individuals with the same BMIwith the same BMI

The proverbial “all other things being The proverbial “all other things being equal”equal”

White Females: 2-Group White Females: 2-Group Comparison Using Dummy-Comparison Using Dummy-

coded Groupscoded Groups* No OA is “referent” group (KneeOA=0);

proc reg data=kneeOA_vs_noOA; model logCRP= KneeOA; where female=1 and white=1;run;

Note: Regression using Dummy (0, 1) for group variable (e.g. KneeOA=0,1) In regression, equal (pooled) variance is assumed

“No OA” mean

“kneeOA” mean difference

from referent

Same p-value as equalvariance t-test

ANCOVA (Analysis of ANCOVA (Analysis of Covariance)Covariance)

Compare logCRP adjusted Compare logCRP adjusted for BMIfor BMIproc reg data=kneeOA_vs_noOA;

model logCRP=KneeOA BMI; where female=1 and white=1;run;

Note: Equal BMI slopes in each group is being modeled

Unadjusted diff (was 0.33)has been attenuated

BMI partially“explains” this

difference

{

UnadjustedMean

Difference

Notice: At any BMI level, the mean logCRP difference

between KneeOA vs Notis smaller than the

unadjusted difference

Randomized Controlled Randomized Controlled TrialsTrials

Patients Patients randomizedrandomized => to different interventions => to different interventions ( e.g. type of drug, or dose, or to placebo group)( e.g. type of drug, or dose, or to placebo group)

Strength:Strength: balances risk factors across all groups balances risk factors across all groups=> equal socio-demographic characteristics=> equal socio-demographic characteristics

=> equal health status, health behaviors=> equal health status, health behaviors => equal pre-clinical and clinical disease risk => equal pre-clinical and clinical disease risk

factorsfactors Balancing removes “arrow” from factors to Balancing removes “arrow” from factors to

“exposure”“exposure” Eliminates biases in estimates of drug effect(s)Eliminates biases in estimates of drug effect(s) due to confoundersdue to confounders

Randomized Controlled Randomized Controlled TrialsTrials

Weakness/limitationsWeakness/limitations

Inclusion/exclusion criteria often results in Inclusion/exclusion criteria often results in study population with fewer complications or study population with fewer complications or comorbidities than individuals living in the comorbidities than individuals living in the community community

Sample sizes too small to identify adverse Sample sizes too small to identify adverse events with low probabilities that can show up events with low probabilities that can show up when drug goes to market and is used by a when drug goes to market and is used by a large number of peoplelarge number of people

Rarely are products compared that were Rarely are products compared that were developed by different pharmaceutical developed by different pharmaceutical companies companies (pending: CER)(pending: CER)

Non-Randomized Data SourcesNon-Randomized Data Sources

Healthcare Utilization DatabasesHealthcare Utilization Databases (Medicare Part D, United HealthCare, (Medicare Part D, United HealthCare,

UPMC, VA)UPMC, VA)

=> selected outcomes=> selected outcomes => socio-demographics, comorbidities=> socio-demographics, comorbidities => historical health services utilization=> historical health services utilization (inpatient & outpatient)(inpatient & outpatient) => clinical information from electronic => clinical information from electronic

medical recordsmedical records => records of drug use (dose, Rx => records of drug use (dose, Rx

purchases) over timepurchases) over time

Non-Randomized Data SourcesNon-Randomized Data Sources Observational Longitudinal Cohort StudiesObservational Longitudinal Cohort Studies

(e.g. Framingham Heart Study – ongoing since (e.g. Framingham Heart Study – ongoing since 19481948

Health, Aging and Body Composition Study)Health, Aging and Body Composition Study)

=> Participants have annual (or periodic) clinic visits=> Participants have annual (or periodic) clinic visits => BMI, Strength Testing, Bone Density Scans, MRIs=> BMI, Strength Testing, Bone Density Scans, MRIs => Gait speed, Cognitive tests, Depression scales => Gait speed, Cognitive tests, Depression scales => Self-reported health (general, sleep probs, => Self-reported health (general, sleep probs,

anxiety, …)anxiety, …) => Drug use, dose, frequency => Drug use, dose, frequency (typically brown bag – “bring all meds you take” )(typically brown bag – “bring all meds you take” ) => Hospitalizations => Hospitalizations (MI, CHF, Stroke, Fractures …)(MI, CHF, Stroke, Fractures …)

Non-Randomized Data SourcesNon-Randomized Data SourcesAnalysis ChallengesAnalysis Challenges

Wide range of characteristics and measures Wide range of characteristics and measures Often longitudinal (collected at multiple timepoints)Often longitudinal (collected at multiple timepoints)

Confounding is extensive due to being Confounding is extensive due to being observationalobservational Similar issue in lab studies involving DAS-28 remission, Similar issue in lab studies involving DAS-28 remission,

assays, ELISA, ELISPOT, etc. assays, ELISA, ELISPOT, etc. following “physician following “physician preference” prescribing of drugs preference” prescribing of drugs

Must be addressed to obtain valid, unbiased Must be addressed to obtain valid, unbiased estimatesestimates

Proper selection of covariates for adjustment based Proper selection of covariates for adjustment based on clinical and subject matter expert knowledgeon clinical and subject matter expert knowledge

[1] MTX+Enbrel

[2] MTX+Humira

DAS drop > 1.2

Physician’s Criteria (unmeasured ?)

Is Physician A Confounder If Treatment Not Randomized ?

Compare DAS-28 response: [1] MTX+Enbrel (Th17 cytokines ?) [2] MTX+Humira

Health, Aging and Body Health, Aging and Body Composition (Health ABC) Composition (Health ABC) Longitudinal Cohort StudyLongitudinal Cohort Study

Observational study of 3075 men and womenObservational study of 3075 men and women age 70-79age 70-79 45% African-American45% African-American Pittsburgh, PA and Memphis, TNPittsburgh, PA and Memphis, TN Able to walk 1/4 mile and climb 10 steps Able to walk 1/4 mile and climb 10 steps (study eligibility (study eligibility

criteria)criteria) Designed to assess the relationship of weight and body Designed to assess the relationship of weight and body

composition tocomposition to incident weight related diseases andincident weight related diseases and DisabilityDisability

Baseline (Year 1) = 1997; Just completed Year 13 (2010); Baseline (Year 1) = 1997; Just completed Year 13 (2010); continuing …continuing …

Funded by NIH/NIA (National Institute on Aging) 1997 - Funded by NIH/NIA (National Institute on Aging) 1997 -

University of PittsburghUniversity of Pittsburgh University of Tennessee, MemphisUniversity of Tennessee, Memphis Coordinating Center: University of California, San FranciscoCoordinating Center: University of California, San Francisco Laboratory for Epidemiology, Demography and Biometry, Laboratory for Epidemiology, Demography and Biometry,

NIANIA

Health, Aging and Body Health, Aging and Body Composition Longitudinal Composition Longitudinal

Cohort StudyCohort StudyCentral Nervous System Drugs (CNS Central Nervous System Drugs (CNS

drugs)drugs) opioid receptor agonist analgesics, opioid receptor agonist analgesics,

antidepressants, antipsychotics, and antidepressants, antipsychotics, and benzodiazepine receptor agonistsbenzodiazepine receptor agonists

Clinical IndicationsClinical Indications self-reported sleep problemsself-reported sleep problems anxietyanxiety depressiondepression painpain

Health ABC: CNS Drug Health ABC: CNS Drug Ancillary StudyAncillary Study

Hanlon JT, Boudreau RM, Roumani YF, Hanlon JT, Boudreau RM, Roumani YF, Newman AB, Ruby CM, Wright RM, Newman AB, Ruby CM, Wright RM, Hilmer SN, Shorr RI, Bauer DC, Hilmer SN, Shorr RI, Bauer DC, Simonsick EM, Studenski SA. Simonsick EM, Studenski SA.

Number and dosage of central nervous Number and dosage of central nervous system medications on system medications on recurrent fallsrecurrent falls in in community elders: the Health, Aging and community elders: the Health, Aging and Body Composition study. Body Composition study.

J Gerontol A Biol Med Sci J Gerontol A Biol Med Sci 2009;64A(No.4):492-4982009;64A(No.4):492-498

Health, Aging and Body Health, Aging and Body Composition Longitudinal Composition Longitudinal

Cohort StudyCohort Study

Outcome:Outcome:

Falls in the previous yearFalls in the previous year

ValidatedValidated outcomeoutcome (numerous (numerous studies): studies): 2+ falls2+ falls

can use Logistic Regression for can use Logistic Regression for binary outcomebinary outcome

Anxiety is a ConfounderAnxiety is a Confounder

Take CNS drug (Y,N)

2+ Falls (Y,N)

Anxiety (Y,N)

Note: Each arrow will be statistically verified in the next 3 slides

HABC Year 2

CNS drug use is associated CNS drug use is associated withwith

higher rates of 2+ falls higher rates of 2+ falls (Bottom arrow)(Bottom arrow)

CNS drug use (overall): 14.8% (368/2693) CNS drug use (overall): 14.8% (368/2693) @Yr2@Yr2

Percent with 2+ fallsPercent with 2+ falls

CNS drug useCNS drug use No No 7.3% (169/2325) 7.3% (169/2325)

YesYes 13.6% (50/368) 13.6% (50/368) P<0.0001P<0.0001

0.136/(1-0.136)0.136/(1-0.136)

Odds-Ratio (OR) = ------------------- = 2.01Odds-Ratio (OR) = ------------------- = 2.01

0.073/(1-0.073) 0.073/(1-0.073)

Anxiety is associated withAnxiety is associated withhigher rates of 2+ fallshigher rates of 2+ falls

(Right diagonal arrow)(Right diagonal arrow)

Percent with 2+ fallsPercent with 2+ falls

AnxietyAnxiety No No 7.2% (130/1811) 7.2% (130/1811)

YesYes 10.1% (89/882) 10.1% (89/882) P=0.0095P=0.0095

0.101/(1-0.101)0.101/(1-0.101)

OR = ------------------- = 1.45OR = ------------------- = 1.45

0.072/(1-0.072) 0.072/(1-0.072)

Anxiety is associated withAnxiety is associated withhigher rates of CNS drug higher rates of CNS drug

use use (Left diagonal arrow)(Left diagonal arrow)

Percent with CNS drug usePercent with CNS drug use

AnxietyAnxiety No No 10.6% (206/1947) 10.6% (206/1947)

YesYes 20.3% (196/964) P<0.0001 20.3% (196/964) P<0.0001

OR = 2.16OR = 2.16

Anxiety is a ConfounderAnxiety is a Confounder

Take CNS drug (Y,N)

2+ Falls (Y,N)

Anxiety (Y,N)

HABC Year 2

Gender is not a Gender is not a confounderconfounder

Take CNS drug (Y,N)

2+ Falls (Y,N)

Gender (M, F)

HABC Year 2

Gender is not a confounderGender is not a confounder

Percent with CNS drug usePercent with CNS drug use

GenderGender M M 11.1% (146/1318) 11.1% (146/1318)

FF 16.4% (225/1375) P<0.0001 16.4% (225/1375) P<0.0001

Percent with 2+ FallsPercent with 2+ Falls

GenderGender M M 8.2% (108/1318) 8.2% (108/1318)

FF 8.1% (111/1375) 8.1% (111/1375) P=0.9082P=0.9082

22ndnd comparison => Rates of 2+ falls same by comparison => Rates of 2+ falls same by gendergender

Depression is a Depression is a ConfounderConfounder

Take CNS drug (Y,N)

2+ Falls (Y,N)

Depression (Y,N)

HABC Year 2

Smoking is not a Smoking is not a confounder,confounder,

but is associated with fallsbut is associated with falls

Take CNS drug (Y,N)

2+ Falls (Y,N)

Current Smoker (Y,N)

HABC Year 2

Multivariable Logistic Multivariable Logistic RegressionRegression

Model 1Model 1 (unadjusted) (unadjusted) OROR C.I. C.I. P-valueP-value

CNS drug useCNS drug use 2.01 (1.43, 2.81) <0.00012.01 (1.43, 2.81) <0.0001

Model 2Model 2

CNS drug useCNS drug use 2.02 (1.44, 2.83) < 0.00012.02 (1.44, 2.83) < 0.0001

FemaleFemale 0.94 (0.71, 1.24) 0.6595 0.94 (0.71, 1.24) 0.6595 (NS)(NS)

Model 3Model 3

CNS drug useCNS drug use 1.90 (1.44, 2.83) 0.00021.90 (1.44, 2.83) 0.0002

AnxietyAnxiety 1.35 (1.02, 1.80) 1.35 (1.02, 1.80) 0.03830.0383

Anxiety partially “explains” Anxiety partially “explains” apparent apparent

association of CNS drugs & association of CNS drugs & fallsfallsModel 1Model 1 (unadjusted) (unadjusted)OROR C.I. C.I. P-valueP-value

CNS drug useCNS drug use 2.01 (1.43, 2.81) <0.00012.01 (1.43, 2.81) <0.0001

Model 3Model 3 CNS drug useCNS drug use 1.90 (1.44, 2.83) 0.00021.90 (1.44, 2.83) 0.0002 AnxietyAnxiety 1.35 (1.02, 1.80) 0.03831.35 (1.02, 1.80) 0.0383

Notice: CNS drug use OR has been “attenuated”Notice: CNS drug use OR has been “attenuated” => CNS drug OR is smaller adjusted for => CNS drug OR is smaller adjusted for AnxietyAnxiety

=> Additional “odds-ratio” effect on => Additional “odds-ratio” effect on falls falls

(with or without Anxiety) OR=1.90(with or without Anxiety) OR=1.90

Covariates Considered in Covariates Considered in Health ABC CNS Drug StudyHealth ABC CNS Drug Study

SocioDemogs:SocioDemogs: race gender age site education race gender age site education LivingAloneLivingAlone

HealthBehaviorsHealthBehaviors: CurrentSmoker PastSmoker : CurrentSmoker PastSmoker CurrentDrinker PastDrinker Underweight Overweight CurrentDrinker PastDrinker Underweight Overweight ObeseObese

HealthStatus/comorbidities:HealthStatus/comorbidities: CHD CHF CVA Diabetes CHD CHF CVA Diabetes Hypertension Pulmonary PAD SomeLeak FrequentLeak Hypertension Pulmonary PAD SomeLeak FrequentLeak

Self-reported Fair/Poor Health Self-reported Fair/Poor Health Poor_to_CompletelyBlind Poor_to_CompletelyBlind

Hearing Impairment Hearing Impairment Indications for CNSIndications for CNS: SleepProblems Osteoarthritis: SleepProblems Osteoarthritis

MildPain ModeratePainOrWorse Anxiety Depression MildPain ModeratePainOrWorse Anxiety Depression Surrogate for disease severitySurrogate for disease severity: # of “Other” Rx Drugs: # of “Other” Rx Drugs

The most strongly The most strongly associated factorsassociated factors

(backwards stepwise regression)(backwards stepwise regression)

Model 1Model 1 (unadjusted) (unadjusted)OROR C.I. C.I. P-valueP-value CNS drug useCNS drug use 2.01 (1.43, 2.81) <0.00012.01 (1.43, 2.81) <0.0001

Model 4 (fully adjusted)Model 4 (fully adjusted) CNS drug useCNS drug use 1.81 (1.28, 2.57) 1.81 (1.28, 2.57) 0.00090.0009 DiabetesDiabetes 1.561.56 0.01460.0146 Some LeakSome Leak 1.431.43 0.04110.0411 FrequentLeakFrequentLeak 1.56 1.56 0.01470.0147 Poor-to-completely blind 2.49Poor-to-completely blind 2.49 0.00460.0046 AnxietyAnxiety 1.321.32 0.01860.0186# other Rx drugs# other Rx drugs 1.041.04 0.03080.0308

Health, Aging and Body Health, Aging and Body Composition Longitudinal Composition Longitudinal

Cohort StudyCohort StudyOutcomeOutcome 2 or more falls in the previous year2 or more falls in the previous year

“ “ in the previous 12 months have you fallen and in the previous 12 months have you fallen and landed on the floor or ground. ” For thoselanded on the floor or ground. ” For those

answering in the affirmative, they were asked, answering in the affirmative, they were asked,

“ “ how many times did you fall in the previous how many times did you fall in the previous 12 months. ” 12 months. ”

The choices were: 0, 1, 2-3, 4-5, 6 or moreThe choices were: 0, 1, 2-3, 4-5, 6 or more

ValidatedValidated outcomeoutcome (numerous studies): (numerous studies): 2+ 2+ fallsfalls

Thank you !Thank you !

Any Questions?Any Questions?

Robert Boudreau, PhDRobert Boudreau, PhDCo-Director of Methodology CoreCo-Director of Methodology Core

PITT-Multidisciplinary Clinical Research Center PITT-Multidisciplinary Clinical Research Center for Rheumatic and Musculoskeletal Diseasesfor Rheumatic and Musculoskeletal Diseases