An Application of Doubly Robust Estimation

HMORN conference, May 2, 2012

Brian P. Johnson, MPH, Charles E. Gessert, MD, MPH, Colleen M. Renier, BS, Jeanette A. Palcher, BA,

Adnan Ajmal, MBBS

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_receptor_blockers, accessed April 23, 2012)

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• 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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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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• 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

Inclusion/Exclusion Criteria(abbreviated)

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Subject Characteristics

  Class of drug  

Baseline Covariate

ACEI

(N=551)

ARB

(N=190) p-valueDemographics      

Age 57.36 +/- 7.73 57.85 +/- 7.65 0.45

Sex (female) 230 (41.7) 104 (54.7) <0.01

Comorbidities      

DM 191 (34.7) 72 (37.9) 0.43

HTN 481 (87.3) 176 (92.6) 0.05

CHF 29 (5.3) 18 (9.5) 0.06

CKD 85 (15.4) 39 (20.5) 0.11

Laboratory      

Hgb 14.65 +/- 1.42 14.29 +/- 1.52 <0.01

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  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

Estimated Effects of Covariates

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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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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• 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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Common formulation:

ACEDR1 – DR0;

Augmented Inverse Probability Weighted Estimator

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Alternate formulation:

ACE

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SubjectClass of drug F/U Hgb

DRestimate (ACEI)

DRestimate

(ARB)

DRtreatment

effect(ARB - ACEI)

10003* ACEI 14.4 14.19 14.39 0.2010005 ARB 17.3 15.06 24.19 9.1310008 ACEI 14.9 14.87 14.98 0.1110009 ACEI 16.7 16.89 16.06 -0.8310016* ARB 15.2 15.21 14.34 -0.8710022 ARB 13.0 13.27 11.83 -1.4410038 ACEI 14.0 13.56 15.46 1.9010039 ACEI 14.4 14.58 13.35 -1.2310047* ACEI 15.0 15.10 14.06 -1.0510048 ARB 14.1 13.40 15.12 1.72

Causal Effect Estimates(subset of subjects)

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Average Causal Effect Estimates

Class of drug

Average F/U Hgb (gm/dL)

Standard Deviation

ConfidenceInterval 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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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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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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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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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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