Estimating the Effects of Two Classes of Drugs on Hemoglobin

with a Doubly Robust Method

APHA conference, October 30, 2012

Brian P. Johnson, MPH, Charles E. Gessert, MD, MPH, Colleen M. Renier, BS, Adnan Ajmal, MBBS

Presenter Disclosures

The following personal financial relationships with commercial interests relevant to this presentation existed during the past 12 months:

Brian P. Johnson, MPH

No relationships to disclose

Outline• Background

– Study Overview

• Moviation– Subject Characteristics and Estimated Effects of Covariates– Evident Confounding

• Causal Inference– Augmented Inverse Probability Weighted Estimator– Causal Effect Estimates– Average Causal Effect Estimates

• Conclusion• Further Research

3

Background

• Angiotensin converting enzyme inhibitors (ACEIs) and angiotensin receptor blockers (ARBs) are FDA-approved for the treatment of hypertension (HTN)1.

4

• ACEIs or ARBs are recommended for patients with HTN and comorbidities such as heart failure (HF), myocardial infarction, diabetes mellitus (DM), chronic kidney disease (CKD), and recurrent stroke.1

• Both ACEIs and ARBs are known to cause anemia.

5

Study Overview

• Retrospective study 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 ml/min/1.73 m2

6

• 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)

7

• Complete-case ANCOVA for F/U Hgb with treatment as a factor

• Covariates

Planned Analysis

8

Treatment initiation date (years)Age (years)Sex (female)Diabetes mellitus (DM)Hypertension (HTN)

Congestive heart failure (CHF)Chronic kidney disease (CKD)Baseline Hgb

  Outcome Model Logistic Model

 Effect on F/U Hgb

in g/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

10

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

11

• Estimation of ACE– Regression modeling

• Unbiased if correctly specified

– Inverse probability weighting• Propensity to be exposed to one of the

treatments is captured by an estimated probability

• Unbiased if correctly specified

– Doubly-robust (DR)• Combine regression and propensity models• Unbiased if either model is correct• Using SAS %dr macro of Funk et al. (2011)2

12

Common formulation:

ACEDR1 – DR0;

Augmented Inverse Probability Weighted Estimator

13

Alternate formulation:

ACE

14

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)

15

Average Causal Effect Estimates

Class of drugAverage F/U Hgb in g/dL (95% CI*) p-value

ACEI 14.31 (14.21, 14.42)  ARB 14.48 (14.32, 14.62)  Difference 0.17 ( 0.00, 0.31) 0.0360

16

* Bootstrap BCa3

Conclusion

• The ACE can be estimated in the presence of confounding*.

• Estimated ACE suggests F/U Hgb is higher when ARBs rather than ACEIs are prescribed, but the mean difference may not be clinically meaningful.

* Assuming all confounders are in the model.

17

Further Research

• Variable and model selection– Traditional response-based– Focused information criteria of Claeskens et al.

(2003)

• All-case analysis– Davidian et al. (2005) address missing outcomes

from a randomized trial with counter factual approach. This could be extended to the same for an observational study.

18

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.

3. Efron B, Tibshirani RJ. An Introduction to the Bootstrap. Boca Raton: Chapman & Hall; 1993.

19

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.

Claeskens G, Hjort NL. The Focused Information Criterion. J Amer Statistical Assoc. 2003;98(464):900-945.

Davidian M, Tsiatis AA, Leon S. Semiparametric Estimation of Treatment Effect in a Pretest–Posttest Study with Missing Data. Statistical Science. 2005;20(3):261-301.

20