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Sensitivity Analysis for Residual Confounding

Sensitivity Analysis for Residual Confounding. Sebastian Schneeweiss MD, ScD Division of Pharmacoepidemiology and Pharmacoeconomics Department of Medicine, Harvard Medical School,. Outline. Residual Confounding and what we can do about it Simple sensitivity analysis: Array Approach

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Sensitivity Analysis for Residual Confounding

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  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. Unmeasured Confounders Measured Confounders Unmeasurable Unmeasured, but measurable in substudy Design Analysis • Standardization • Stratification • Regression • Restriction • Matching Design Analysis • 2-stage sampl. • Ext. adjustment • Imputation • Instrumental variable • Proxy analysis • Sensitivity analysis • Cross-over • Active comparator (restriction) 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 • Let’s assume an observed RR of 2.0 • Let’s assume 50% of RA patients have a more progressive immunologic disease • … and that more progressive disease is more likely to lead to NH lymphoma • Let’s 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 -> 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 • Wouldn’t it be more interesting to know • How strong and imbalanced does a confounder have to be in order to fully explain the observed findings? OREC RRCO

  16. Example: Psaty et al: JAGS 1999;47:749 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. [smoking,aspirin, BMI, etc.] CU OREC RRCO 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 >=30 vs. BMI<30)

  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 exposure–disease 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

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