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An Application of Doubly Robust Estimation JOHNSON
1. An Application of
Doubly Robust Estimation
Brian P. Johnson, MPH, Charles E. Gessert, MD, MPH,
Colleen M. Renier, BS, Jeanette A. Palcher, BA,
Adnan Ajmal, MBBS
HMORN conference, May 2, 2012
2. Background
• Angiotensin converting enzyme inhibitors (ACEIs)
and angiotensin receptor blockers (ARBs) are
FDA-approved for the treatment of hypertension
(HTN)1.
– Captopril was first FDA-approved ACEI in 1981.
(http://en.wikipedia.org/wiki/ACE_inhibitor, accessed April 23, 2012)
– Losartan was first FDA-approved ARB in 1995.
(http://en.wikipedia.org/wiki/Discovery_and_development_of_angiotensin_r
eceptor_blockers, accessed April 23, 2012)
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3. • A synthesis of the six practice guidelines in 2006
finds that, “[ACEIs] or ARBs are recommended for a
patient with HTN and comorbidities such as [heart
failure] HF, myocardial infarction (MI), diabetes
mellitus [(DM)], chronic kidney disease [(CKD)], and
recurrent stroke.1”
• Both ACEIs and ARBs are known to cause anemia.
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4. Study Overview
• In 2009, Dr. Ajmal initiated a retrospective study of
Essentia Health patient records to assess change in
Hgb within a population who had been prescribed
either ACEI or ARB between 2005 and 2009.
• Particularly interested in patients with CKD, which is
defined as a glomerular filtration rate (GFR) < 60
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5. Inclusion/Exclusion Criteria
(abbreviated)
• Inclusion criteria
– Prior primary care (PC) provided by Essentia Health (EH)
– Aged 40 to 70 years and initially prescribed ACEI or ARB,
but not both, by an EH PC physician
– Baseline and followup (F/U) Hgb values before and after
initiation of ACEI or ARB
– History of DM, CHF, and/or HTN
– Baseline GFR before and after initiation of ACEI or ARB
• Exclusion criteria
– Underlying conditions associated with anemia, or
– Other conditions or treatments that might affect Hgb level
during the F/U period
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7. Estimated Effects of Covariates
Outcome Model Logistic Model
Effect on F/U Hgb
in gm/dL (95% CI) OR of ARB*
Baseline Covariate Overall (N=741) (95% CI)
Treatment initiation date (years) -0.06 (-0.12, -0.00) 0.85 (0.72, 0.99)
Demographics
Age (years) 0.00 (-0.01, 0.01) 1.00 (0.98, 1.03)
Sex (female) -0.33 (-0.48, -0.19) 1.46 (1.01, 2.11)
Comorbidities
DM -0.03 (-0.17, 0.11) 1.09 (0.77, 1.55)
HTN 0.11 (-0.10, 0.32) 1.94 (1.05, 3.59)
CHF 0.39 ( 0.12, 0.67) 1.79 (0.94, 3.41)
CKD -0.16 (-0.34, 0.03) 1.15 (0.73, 1.80)
Laboratory
Hgb 0.60 ( 0.55, 0.65) 0.88 (0.77, 1.00)
* Odds of receiving ARB relative to odds of receiving ACEI
8. Evident Confounding
• CHF status infers an increase in F/U Hgb and more
CHF subjects were on ARBs
– Clinical explanation is that CHF patients are hemodiluted at
baseline and treatment for CHF increases Hgb
concentration
• More females were on ARBs than on ACEIs and F/U
Hgb differs per sex, even while accounting for
baseline Hgb
• Similar issues with HTN, baseline Hgb, and when
treatment was initiated
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9. Causal Inference
• Counterfactuals
– Suppose each individual in the population has a potential
outcome (e.g., F/U Hgb,) for each exposure (e.g., ACEI and
ARB.)
– Potential outcomes are estimated so as to be unbiased
• Average causal effect (ACE)
– The difference of the mean potential outcomes and mean of
the difference between potential outcomes
– If all confounders are measured, potential outcomes and
exposures are independent which permits unbiased
estimation of ACE
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10. • Estimate ACE by regression modeling
– Unbiased if regression model is correctly specified
• Estimate ACE by inverse probability weighting
– propensity to be exposed to one of the treatments is
captured by an estimated probability
– Unbiased if propensity model is correctly specified
• Doubly-robust (DR)
– Combine regression and propensity models
– Unbiased estimate of ACE if either model is correct
• Using SAS %dr macro of Funk et al. (2011)
(See http://www.unc.edu/~mfunk/dr)
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14. Average Causal Effect Estimates
Average
F/U Hgb Standard Confidence
Class of drug (gm/dL) Deviation Interval p-value
ACEI 14.31 1.43 (14.21, 14.42)
ARB 14.48 2.02 (14.33, 14.62)
Difference 0.16 2.06 ( 0.01, 0.31) 0.03
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15. Conclusion
• Causal estimates address the question, “what if
everyone were treated with ARB relative to if
everyone were treated with ACEI.”
• ACE can be estimated even when confounding
exists
• Estimated ACE suggests F/U Hgb is higher when
ARBs rather than ACEIs are prescribed, but the
mean difference may not be clinically meaningful.
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16. Further Research
• Variable and model selection, including interactions,
and sensitivity analysis
– Age, for example, doesn’t seem to be important, but it’s in
the models.
– Effect of baseline Hgb may be different for the sexes
• Use all cases, not just complete
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17. References
1. Miller AE, Cziraky M, Spinler SA. ACE inhibitors versus ARBs:
comparison of practice guidelines and treatment selection
considerations. Formulary. 2006;41:274–284.
2. Funk MJ, Westreich D, Wiesen C, Sturmer T, Brookhart MA,
Davidian M. Doubly robust estimation of causal effects.
Am J Epidemiol. Apr 1 2011;173(7):761-767.
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18. Bibliography
Lunceford JK, Davidian M. Stratification and weighting via the propensity
score in estimation of causal treatment effects: A comparative study. Stat
Med. Oct 15 2004;23(19):2937-2960.
Robins JM, Rotnitzky A, Zhao LP. Estimation of Regression Coefficients
When Some Regressors Are Not Always Observed.
J Amer Statistical Assoc. 1994;89(427):846-863.
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Notes de l'éditeur
Want stable PCP study population, aged 40 to 70, with a history of DM, CHF, and/or HTN, complete labs, and no confounding conditions.
Bivariate summaries. Difference in sex, HTN, and Hgb between the two groups. The difference is Hgb may be driven by the difference in sex, but it’s a difference nonetheless.
Multivariate models. Rows is red indicate the covariate has a significant effect and imbalance between the groups. Rows in orange indicate the covariate either has a significant effect or that there’s an imbalance between the groups.
Hard to ignore confounding with a clear conscience and the results may not be trustworthy.
The individual DR estimates are transparent, but the ACE in this form is not particularly intuitive.The z indicates treatment groupThe y is the actual FUP HgbThe p is the estimated probability, or propensity, of getting ARBThe m is the predicted FUP Hgb from the respective group
The ACE in this form is more intuitive, but the individual DR estimates are not transparent.Indicator functions are like switches.The mean of the numerators in the first terms, which are the residuals, are zero by definition, but the mean of the ratios are not. The mean of the difference of the ratios, however, is expected to be small if large or small values of p are not associated with large or small values of residuals. When this is true, the last two terms make the greater contribution to the ACE.Note that the first two terms honor the actual treatment received while the second make use of the concept of potential outcomes.
The starred subjects must be particularly like one or the other treatment groups.
