Logistic Regression: Part 2
“Why include covariate
adjustment?”
Confounding, Mediation and
Attenuation
Robert Boudreau, PhD
Co-Director of Methodology Core
PITT-Multidisciplinary Clinical Research Center
for Rheumatic and Musculoskeletal Diseases
Confounding
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:
Outcomes:
Drug exposure, dose, duration
Blood pressure control (< 120/80)
Adverse events (fainting, mortality)
Risk Factors: Prior MI, BMI, Exercise(or lack of)
Criteria to be a Confounder
Confounder: 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 Confounder
Among people diagnosed with high BP and prescribed antiHTN drug
Take antiHTN
Drug Daily (Y,N)
Compare Rates of BP Control:
Blood Pressure
Control
( <120/80)
Those who take drug daily
vs Those who take it less frequently
Example of Confounder
Among people diagnosed with high BP and prescribed antiHTN drug
Daily Exercise
Take antiHTN
Drug Daily (Y,N)
Compare Rates of BP Control:
Blood Pressure
Control
( <120/80)
Those who take drug daily
vs Those who take it less frequently
1. A “cause” of the outcome
even in the unexposed group
Regular daily exercise contributes to lower blood pressure
Daily Exercise
Take antiHTN
Drug Daily (Y,N)
Compare Rates of BP Control:
Blood Pressure
Control
( <120/80)
Those who take drug daily
vs Those who take it less frequently
2. Correlated with Exposure
Regular daily exercisers are more likely to take their meds daily
Daily Exercise
Take antiHTN
Drug Daily (Y,N)
Compare Rates of BP Control:
Blood Pressure
Control
( <120/80)
Those who take drug daily
vs Those who take it less frequently
Confounder Diagram
Confounder
Exposure
Outcome
Example of Mediator
• Muscle weakness occurs in ~10% of statin users
In 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
Statin Drug
(to control lipids)
Muscle
Weakness
Mobility
Problems
General Interpretation
of Covariate Adjustment
E.g. Association of CRP levels with KneeOA
… adjusted for BMI
Interpretation:
 Add adjustment for BMI
 CRP differences (KneeOA vs Not)
between individuals with the same BMI

The proverbial “all other things being equal”
White Females: 2-Group Comparison
Using Dummy-coded Groups
* No OA is “referent” group (KneeOA=0);
proc reg data=kneeOA_vs_noOA;
model logCRP= KneeOA;
where female=1 and white=1;
run;
“No OA” mean
“kneeOA” mean
difference
from referent
Same p-value as equal
variance t-test
Note: Regression using Dummy (0, 1) for group variable (e.g. KneeOA=0,1)
In regression, equal (pooled) variance is assumed
ANCOVA (Analysis of Covariance)
Compare logCRP adjusted for BMI
proc reg data=kneeOA_vs_noOA;
model logCRP=KneeOA BMI;
where female=1 and white=1;
run;
Unadjusted diff (was 0.33)
has been attenuated
 BMI partially
“explains” this
difference

Note: Equal BMI slopes in each group is being modeled
Unadjusted
Mean Difference
{
Notice: At any BMI level,
the mean logCRP difference
between KneeOA vs Not
is smaller than the
unadjusted difference
Randomized Controlled Trials
Patients randomized
=> to different interventions
( e.g. type of drug, or dose, or to placebo group)
 Strength: balances risk factors across all groups
=> equal socio-demographic characteristics
=> equal health status, health behaviors
=> equal pre-clinical and clinical disease risk factors

 Balancing removes “arrow” from factors to “exposure”
 Eliminates biases in estimates of drug effect(s)
due to confounders
Randomized Controlled Trials
Weakness/limitations



Inclusion/exclusion criteria often results in study
population with fewer complications or comorbidities
than individuals living in the community
Sample sizes too small to identify adverse events with
low probabilities that can show up when drug goes to
market and is used by a large number of people
Rarely are products compared that were developed by
different pharmaceutical companies (pending: CER)
Non-Randomized Data Sources

Healthcare Utilization Databases
(Medicare Part D, United HealthCare, UPMC, VA)
=> selected outcomes
=> socio-demographics, comorbidities
=> historical health services utilization
(inpatient & outpatient)
=> clinical information from electronic medical records
=> records of drug use (dose, Rx purchases) over time
Non-Randomized Data Sources

Observational Longitudinal Cohort Studies
(e.g. Framingham Heart Study – ongoing since 1948
Health, Aging and Body Composition Study)
=> Participants have annual (or periodic) clinic visits
=> BMI, Strength Testing, Bone Density Scans, MRIs
=> Gait speed, Cognitive tests, Depression scales
=> Self-reported health (general, sleep probs, anxiety, …)
=> Drug use, dose, frequency
(typically brown bag – “bring all meds you take” )
=> Hospitalizations
(MI, CHF, Stroke, Fractures …)
Non-Randomized Data Sources
Analysis Challenges

Wide range of characteristics and measures


Often longitudinal (collected at multiple timepoints)
Confounding is extensive due to being observational

Similar issue in lab studies involving DAS-28 remission, assays,
ELISA, ELISPOT, etc. following “physician preference”
prescribing of drugs

Must be addressed to obtain valid, unbiased estimates

Proper selection of covariates for adjustment based on
clinical and subject matter expert knowledge
Is Physician A Confounder
If Treatment Not Randomized ?
Physician’s Criteria (unmeasured ?)
[1] MTX+Enbrel
[2] MTX+Humira
Compare DAS-28 response:
(Th17 cytokines ?)
DAS drop > 1.2
[1] MTX+Enbrel
[2] MTX+Humira
Health, Aging and Body Composition
(Health ABC) Longitudinal Cohort Study




Observational study of 3075 men and women
 age 70-79
 45% African-American
 Pittsburgh, PA and Memphis, TN
 Able to walk 1/4 mile and climb 10 steps (study eligibility criteria)
Designed to assess the relationship of weight and body composition to
 incident weight related diseases and
 Disability
Baseline (Year 1) = 1997; Just completed Year 13 (2010); continuing …
Funded by NIH/NIA (National Institute on Aging) 1997  University of Pittsburgh
 University of Tennessee, Memphis
 Coordinating Center: University of California, San Francisco
 Laboratory for Epidemiology, Demography and Biometry, NIA
Health, Aging and Body Composition
Longitudinal Cohort Study
Central Nervous System Drugs (CNS drugs)
 opioid receptor agonist analgesics,
antidepressants, antipsychotics, and
benzodiazepine receptor agonists
Clinical Indications
 self-reported sleep problems
 anxiety
 depression
 pain
Health ABC: CNS Drug Ancillary Study
Hanlon JT, Boudreau RM, Roumani YF, Newman
AB, Ruby CM, Wright RM, Hilmer SN, Shorr RI,
Bauer DC, Simonsick EM, Studenski SA.
Number and dosage of central nervous system
medications on recurrent falls in community
elders: the Health, Aging and Body Composition
study.
J Gerontol A Biol Med Sci 2009;64A(No.4):492-498
Health, Aging and Body Composition
Longitudinal Cohort Study
Outcome:


Falls in the previous year
Validated outcome (numerous studies): 2+ falls
 can use Logistic Regression for binary outcome
Anxiety is a Confounder
HABC Year 2
Anxiety (Y,N)
Take CNS drug
(Y,N)
2+ Falls (Y,N)
Note: Each arrow will be statistically verified in the next 3 slides
CNS drug use is associated with
higher rates of 2+ falls (Bottom arrow)
CNS drug use (overall): 14.8% (368/2693) @Yr2
CNS drug use
Percent with 2+ falls
No 7.3% (169/2325)
Yes 13.6% (50/368) P<0.0001
0.136/(1-0.136)
Odds-Ratio (OR) = ------------------- = 2.01
0.073/(1-0.073)
Anxiety is associated with
higher rates of 2+ falls
(Right diagonal arrow)
Anxiety
Percent with 2+ falls
No 7.2% (130/1811)
Yes 10.1% (89/882) P=0.0095
0.101/(1-0.101)
OR = ------------------- = 1.45
0.072/(1-0.072)
Anxiety is associated with
higher rates of CNS drug use
(Left diagonal arrow)
Anxiety
Percent with CNS drug use
No 10.6% (206/1947)
Yes 20.3% (196/964) P<0.0001
OR = 2.16
Anxiety is a Confounder
HABC Year 2
Anxiety (Y,N)
Take CNS drug
(Y,N)
2+ Falls (Y,N)
Gender is not a confounder
HABC Year 2
Gender (M, F)
Take CNS drug
(Y,N)
2+ Falls (Y,N)
Gender is not a confounder
Gender
Gender
M
F
Percent with CNS drug use
11.1% (146/1318)
16.4% (225/1375) P<0.0001
M
F
Percent with 2+ Falls
8.2% (108/1318)
8.1% (111/1375) P=0.9082
2nd comparison => Rates of 2+ falls same by gender
Depression is a Confounder
HABC Year 2
Depression (Y,N)
Take CNS drug
(Y,N)
2+ Falls (Y,N)
Smoking is not a confounder,
but is associated with falls
HABC Year 2
Current Smoker (Y,N)
Take CNS drug
(Y,N)
2+ Falls (Y,N)
Multivariable Logistic Regression
Model 1 (unadjusted) OR
C.I.
P-value
CNS drug use
2.01 (1.43, 2.81) <0.0001
Model 2
CNS drug use
Female
Model 3
CNS drug use
Anxiety
2.02 (1.44, 2.83) < 0.0001
0.94 (0.71, 1.24) 0.6595 (NS)
1.90 (1.44, 2.83) 0.0002
1.35 (1.02, 1.80) 0.0383
Anxiety partially “explains” apparent
association of CNS drugs & falls
Model 1 (unadjusted)
CNS drug use
OR
C.I.
P-value
2.01 (1.43, 2.81) <0.0001
Model 3
CNS drug use
Anxiety
1.90 (1.44, 2.83) 0.0002
1.35 (1.02, 1.80) 0.0383
Notice: CNS drug use OR has been “attenuated”
=> CNS drug OR is smaller adjusted for Anxiety
=> Additional “odds-ratio” effect on falls
(with or without Anxiety) OR=1.90
Covariates Considered in
Health ABC CNS Drug Study





SocioDemogs: race gender age site education LivingAlone
HealthBehaviors: CurrentSmoker PastSmoker CurrentDrinker
PastDrinker Underweight Overweight Obese
HealthStatus/comorbidities: CHD CHF CVA Diabetes
Hypertension Pulmonary PAD SomeLeak FrequentLeak
Self-reported Fair/Poor Health Poor_to_CompletelyBlind
Hearing Impairment
Indications for CNS: SleepProblems Osteoarthritis
MildPain ModeratePainOrWorse Anxiety Depression
Surrogate for disease severity: # of “Other” Rx Drugs
The most strongly associated factors
(backwards stepwise regression)
Model 1 (unadjusted)
CNS drug use
OR
C.I.
P-value
2.01 (1.43, 2.81) <0.0001
Model 4 (fully adjusted)
CNS drug use
1.81 (1.28, 2.57)
Diabetes
1.56
Some Leak
1.43
FrequentLeak
1.56
Poor-to-completely blind 2.49
Anxiety
1.32
# other Rx drugs
1.04
0.0009
0.0146
0.0411
0.0147
0.0046
0.0186
0.0308
Health, Aging and Body Composition
Longitudinal Cohort Study
Outcome
 2 or more falls in the previous year
“ in the previous 12 months have you fallen and
landed on the floor or ground. ” For those
answering in the affirmative, they were asked,
“ how many times did you fall in the previous 12
months. ”
The choices were: 0, 1, 2-3, 4-5, 6 or more

Validated outcome (numerous studies): 2+ falls
Thank you !
Any Questions?
Robert Boudreau, PhD
Co-Director of Methodology Core
PITT-Multidisciplinary Clinical Research Center
for Rheumatic and Musculoskeletal Diseases