Sensitivity Analysis for Residual Confounding

1
Sensitivity Analysis for Residual Confounding

• Sebastian Schneeweiss MD, ScD
• Division of Pharmacoepidemiology and
  Pharmacoeconomics
• Department of Medicine, Harvard Medical School,

2
Outline

• Residual Confounding and what we can do about it
• Simple sensitivity analysis Array Approach
• Study-specific analysis Rule Out Approach
• Using additional information External Adjustment

3
Unmeasured (residual) Confounding
smoking,healthy lifestyle, etc.
CU
CM
OREC
RRCO
Drug exposure
Outcome
RREO
4
Unmeasured Confounding in Claims Data

• Database studies are criticized for their
  inability to measure clinical and life-style
  parameters that are potential confounders in many
  pharmacoepi studies
• OTC drug use
• BMI
• Clinical parameters Lab values, blood pressure,
  X-ray
• Physical functioning, ADL (activities of daily
  living)
• Cognitive status

5
Strategies to Minimize Residual Confounding

• Choice of comparison group
• Alternative drug use that have the same perceived
  effectiveness and safety
• Multiple comparison groups
• Crossover designs (CCO, CTCO)
• Instrumental Variable estimation
• High dimensional proxy adjustment

6
Strategies to Discuss Residual Confounding

• Qualitative discussions of potential biases
• Sensitivity analysis
• SA is often seen as the last line of defense
• A) SA to explore the strength of an association
  as a function of the strength of the unmeasured
  confounder
• B) Answers the question How strong must a
  confounder be to fully explain the observed
  association
• Several examples in Occupational Epi but also for
  claims data

Greenland S et al Int Arch Occup Env Health
1994 Wang PS et al J Am Geriatr Soc 2001
7
Dealing with confounding
Confounding
Propensity scores

• Marginal Structural Models

Schneeweiss, PDS 2006
8
A simple sensitivity analysis

• The apparent RR is a function of the adjusted RR
  times the imbalance of the unobserved
  confounder
• After solving for RR we can plug in values for
  the prevalence and strength of the confounder

9
A made-up example

• Association between TNF-a blocking agents and NH
  lymphoma in RA patients
• Lets assume an observed RR of 2.0
• Lets assume 50 of RA patients have a more
  progressive immunologic disease
• and that more progressive disease is more
  likely to lead to NH lymphoma
• Lets now vary the imbalance of the hypothetical
  unobserved confounder

10
Bias by residual confounding
11
drugepi.org
12
Pros and cons of Array approach

• Very easy to perform using Excel
• Very informative to explore confounding with
  little prior knowledge
• Problems
• It usually does not really provide an answer to a
  specific research question
• 4 parameters can vary -gt in a 3-D plot 2
  parameter have to be kept constant
• The optical impression can be manipulated by
  choosing different ranges for the axes

13
Same example, different parameter ranges
14
Conclusion of Array Approach

• Great tool but you need to be honest to yourself
• For all but one tool that I present today
• Assuming conditional independence of CU and CM
  given the exposure status
• If violated than residual bias may be
  overestimated

Hernan, Robins Biometrics 1999
CU
CM
OREC
RRCO
Drug exposure
Outcome
RREO
15
More advanced techniques

• Wouldnt it be more interesting to know
• How strong and imbalanced does a confounder have
  to be in order to fully explain the observed
  findings?

RRCO
OREC
16
Example Psaty et al JAGS 199947749 CCB use
and acute MI. The issue Are there any
unmeasured factors that may lead to a preferred
prescribing of CCB to people at higher risk for
AMI?
OREC
ARR 1.57
ARR 1.30
RRCO
17
drugepi.org
18
Caution!

• Psaty et al. concluded that it is unlikely that
  an unmeasured confounder of that magnitude exists
• However, the randomized trial ALLHAT showed no
  association between CCB use and AMI
• Alternative explanations
• Joint residual confounding may be larger than
  anticipated from individual unmeasured
  confounders
• Not an issue of residual confounding but other
  biases, e.g. control selection?

19
Pros and cons of Rule Out Approach

• Very easy to perform using Excel
• Meaningful and easy to communicate interpretation
• Study-specific interpretation
• Problems
• Still assuming conditional independence of CU and
  CM
• Rule Out lacks any quantitative assessment of
  potential confounders that are unmeasured

20
External Adjustment

• One step beyond sensitivity analyses
• Using additional information not available in the
  main study
• Often survey information

21
Strategies to Adjust residual con-founding using
external information

• Survey information in a representative sample can
  be used to quantify the imbalance of risk factors
  that are not measured in claims among exposure
  groups
• The association of such risk factors with the
  outcome can be assess from the medical literature
  (RCTs, observational studies)

Velentgas et al PDS, 2007 Schneeweiss et al
Epidemiology, 2004
22
In our example
From Survey data in a subsample
From medical literature
CM
Rofecoxib
Acute MI
RREO
23
More contrasts
24
Sensitivity of Bias as a Function of a
Misspecified RRCD
Obesity (BMI gt30 vs. BMIlt30)
25
Sensitivity towards a misspecified RRCO from the
literature
OTC aspirin use (y/n)
26
drugepi.org
27
Limitations

• Example is limited to 5 potential confounders
• No lab values, physical activity, blood pressure
  etc.
• What about the unknow unknowns?
• To assess the bias we assume an exposuredisease
  association of 1 (null hypothesis)
• The more the truth is away from the null the more
  bias in our bias estimate
• However the less relevant unmeasured confounders
  become
• Validity depends on representativenes of sampling
  with regard to the unmeasured confounders
• We could not consider the joint distribution of
  confounders
• Limited to a binary world

28
Solving the Main Limitations

• Need a method
• That addresses the joint distribution of several
  unmeasured confounders
• That can handle binary, ordinal or normally
  distributed unmeasured confounders
• Lin et al. (Biometrics 1998)
• Can handle a single unmeasured covariate of any
  distribution
• But can handle only 1 covariate
• Sturmer, Schneeweiss et al (Am J Epidemiol 2004)
• Propensity score calibration
• Can handle multiple unmeasured covariates of any
  distribution

29
Summary

• Sensitivity analyses for residual confounding are
  underutilized although they are technically easy
  to perform
• Excel program for download (drugepi.org)
• The real challenge is the interpretation of your
  findings
• This is all summarized in Schneeweiss PDS 2007