Measurement and Modeling Issues withAdherence to Pharmacotherapy

M. Christopher Roebuck, M.B.A.Director, Health Economics

CVS Caremark

Teresa B. Gibson, Ph.D.Director, Health Outcomes

Thomson Reuters, Healthcare & Science

AMCP Educational Conference Workshop (W1)St. Louis, Missouri

Thursday, October 14, 201008:15-09:30

Outline

Measurement Issues:• Introduction to Adherence

• Calculation of Adherence Measures

• Defining “Adherent”: The 80% Threshold

• Handling Primary Non-Compliance

Modeling Issues:• Introduction to Adherence as Key Independent Variable

• Endogeneity/Selection Bias in Observational Studies

• Methods to Address Endogeneity/Selection Bias– Regression Adjustment– Propensity Score Matching– Instrumental Variables– Fixed Effects

Some Notes

• While we will largely focus on adherence (compliance), some issues raised will apply to persistence and other utilization patterns measures

• We rely on pharmacy claims data only for measurement, but…

• The presence of Rx fills does not necessarily indicate medication was consumed (in accordance with physician’s orders)

• The absence of an initial Rx fill does not guarantee medication wasn’t prescribed

• The absence of refills doesn’t mean patient wasn’t compliant (physician’s orders, free samples, cash purchase)

Measurement Issues

Introduction

• “Drugs don't work in patients who don't take them.”– C. Everett Koop, M.D.

• Need to measure if and how medications are taken

• Conduct analyses with these measures to answer research questions

• Adherence as a dependent variable:– What are the drivers of adherence?– How does pharmacy benefit design impact adherence?– Determine copay elasticity for Value-Based Insurance Design

• Adherence as an independent variable:– What is the impact of adherence on adverse health events?– Does adherence avert hospitalization and provide total healthcare cost savings?– Are adherent employees more productive?

Terminology and Definitions

• International Society for Pharmacoeconomics and Outcomes Research (ISPOR) Medication Compliance and Persistence Work Group1,2

• Medication compliance (adherence) defined as “the extent to which a patient acts in accordance with the prescribed interval and dose of a dosing regimen.”

– Measured over a period of time– Reported as a percentage (or proportion)

• Differs from other utilization pattern measures like persistence and gaps

Adherence Calculation

• Medication Possession Ratio (MPR)

• Can be calculated at drug, class, or condition levels

• Usually conditional on having at least 1 or 2 fills (more on this later)

• Time period (denominator) can be– variable (e.g., first fill to last fill + days’ supply)– fixed (e.g., annual)

• Indexed (person-specific windows) or calendar-based

• Since all days of medication supply are counted, values can exceed 1.00

Sum of Days of SupplyMPR

Number of Days in Period

Adherence Calculation

• Proportion of Days Covered (PDC)

• Each day with medication on hand counted once, thus, maximum PDC is 1

• Can be calculated at drug, class, or condition levels

• Usually conditional on having at least 1 or 2 fills (more on this later)

• Time period (denominator) can be– variable (e.g., first fill to last fill + days’ supply)– fixed (e.g., annual)

• Indexed (person-specific windows) or calendar-based

Sum of Unique Days with SupplyPDC

Number of Days in Period

Defining “Adherent”

• MPR/PDC measure adherence, so at what level is a patient “adherent”?

• Threshold of 0.80 is very common, but arbitrary

• Common approaches:– Retain continuous MPR/PDC, but this assumes linearity of response

• Is a move from 0.20 to 0.30 clinically equivalent to a move from 0.70 to 0.80?– As independent variable, use linear and squared terms to allow for curvature– Or categorized

• Preferably, start with theory of adherence based on pharmacological properties

• Could let data speak for themselves—perform nonparametric exploratory analysis

• One technique: STATA’s user-written command locpr3

– Semi-parametrically estimates proportion as function of 1 variable, graphs result– Estimates local linear regression @ 99 percentiles, smoothes results, and plots

Case Study Data4

• Integrated pharmacy & medical claims data on 135,008 patients from 9 employers

• Annual panel dataset of adults continuously eligible from 7/1/05 through 6/30/08

• With one or more of the following conditions (sample size):– Hypertension: 112,757

– Diabetes: 42,080

– Dyslipidemia: 53,041

• For each of three 1-year observations,

• Calculated PDC by therapeutic class (TC)

• Rolled up to condition-level as PDC mean, weighted by TC days’ supply

PDC & Hospitalization: Functional Form

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PDC

Hypertension

PDC & Hospitalization: Functional Form

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Diabetes

PDC & Hospitalization: Functional Form

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PDC

Dyslipidemia

Zero Adherence

• Standard MPR/PDC measures require 1 or 2 fills (no initial 0s)

• Then, can either assume…– once on therapy must remain on therapy (subsequent 0 adherence allowed) or– clocked stopped once discontinued (no subsequent 0 adherence)

• Either approach requires an assumption about the physician’s treatment intent

• Similarly, requiring 1st fill assumes all patients prescribed medication initiated treatment

• Researcher should consider implications of these assumptions

• What is the population of interest?

Primary Non-Adherence

• What about patients who receive a prescription but do not fill?

• Primary non-adherence measurable with e-prescribing data and pharmacy claims

• Karter et al. (2009)5 report primary non-adherence rates for new prescriptions in a diabetic population (in San Francisco Bay area):

– Antihypertensives 3.2%; Cholesterol-lowering 8.5%; Antihyperglycemics 4.0%

• Moreover, they find 16%-22% fill only once in these conditions

• Liberman et al. (2010)6 find 34% primary non-adherent on dyslipidemics

• Fischer et al. (2010a)7 published primary non-adherence rates: hypertension (28.4%), hyperlipidemia (28.2%), and diabetes (31.4%)

• And, in an examination of nearly 1 million e-prescriptions, Fischer et al. (2010)8 estimate primary non-adherence rates of 20-24% for cardiovascular, endocrine, and metabolic agents

Primary Non-Adherence

• Important for inference, primary non-adherent patients may be a heterogeneous group (e.g., healthier?)

• No measurement alternative if only pharmacy claims data are available

• With medical data on hand, another approach is to assume diagnosed patients should be on therapy (as of diagnosis date)

• Appropriateness of this approach should take into account the condition– Perhaps ok for congestive heart failure, but maybe not for depression

• Depending on the research question and model, it may be worthwhile to try both approaches; may provide lower and upper bounds effect estimates

Comparing PDC Approaches: Hypertension

01

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PDC

Dx and Rx Required

01

02

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PDC

Only Dx Required

Hypertension

Comparing PDC Approaches: Diabetes

01

02

03

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0 .2 .4 .6 .8 1

PDC

Dx and Rx Required

01

02

03

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0 .2 .4 .6 .8 1

PDC

Only Dx Required

Diabetes

Comparing PDC Approaches: Dyslipidemia

01

02

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Pe

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0 .2 .4 .6 .8 1

PDC

Dx and Rx Required

01

02

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Pe

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0 .2 .4 .6 .8 1

PDC

Only Dx Required

Dyslipidemia

PDC & Hospitalization

• Estimated ordinary least squares models of hospitalization on PDC>=0.80 using two approaches

• Controls include: age, gender, region, Charlson Comorbidity Index, yearly time dummies

• Of course, sample sizes larger when only diagnosis is required

• Coefficients represent impact of optimal adherence on probability of hospitalization (p<0.01 for all)

• Larger reductions when primary non-compliant cohort included for hypertension, but smaller effects in diabetes & dyslipidemia

Condition Rx & Dx Required

Dx Only Required

Hypertension N = 247,375

Coef = -0.059

N = 314,440

Coef = -0.068

Diabetes N = 83,642

Coef = -0.075

N = 115,637

Coef = -0.054

Dyslipidemia N = 103,064

Coef = -0.038

N = 142,944

Coef = -0.017

Modeling Issues

Medication Adherence and Outcomes

Medication Adherence Health Outcomes

• Admissions• ED Visits• Inpatient Spending• Medical Spending• Complications• Indirect Costs

The Value of Medication Adherence

Outcomeadherent – Outcomenon-adherent

Value of Medication Adherence

• Patients– Health– Work– Disease progression

• Payers– Health benefits– Productivity – Spending

• Practice– Disease progression– Compliance with therapeutic regimens– Complication rates

Adherence and Outcomes

Randomization relies on law of large numbers to create like comparison groups to compare means, and estimate the effects of adherence

Adherent

Non-Adherent

Outcome (e.g., # hospitalizations)

Adherence and Outcomes

With non-randomized data, there may be differences between those who are adherent and non-adherent

Adherent

Non-Adherent

Outcome (e.g., # hospitalizations)

Analytical Approaches

1. Randomized Controlled Trial

2. Natural Experiment– Group assignment according to an external, exogenous event

• Policy change, natural event– Difference-in-Differences– Regression Discontinuity

3. Instrumental Variables

4. Adjustment for Observable Differences– Regression Adjustment– Propensity Score Matching– Fixed Effects

Analytical Approaches

• In the absence of randomization the effect estimate of adherence on an outcome of interest cannot be interpreted as strictly causal, but correlational

Regression Adjustment

• Regression-adjusted differences– A common approach

– Adjusts for differences in observable characteristics

– Y = f(Adherent, X)

– Y = XB + u

Regression Adjustment Example

• Data Source– Thomson Reuters MarketScan Database– N=55,555 patients with Type 2 Diabetes on oral antidiabetic medications– Adherent is Percent of Days Covered (1=PDC 0.80; 0=PDC < 0.80)– Outcome is acute myocardial infarction rate (1/0 variable)

• Unadjusted Comparison of Means

• Regression Adjusted Comparison of Means– Pr(Complications|Adherent,X) = f(Adherent, sociodemographic, health plan,

provider, health status)– Logistic regression

Regression Adjusted Example: Results

0.0143

0.01360.0137

0.0158

0.0125

0.0130

0.0135

0.0140

0.0145

0.0150

0.0155

0.0160

Unadjusted Regression Adjusted

Adherent

Non-Adherent

Rates are similar (p=0.5821)

Adjusted OR: 0.861(p=0.073)

Rate of Acute Myocardial Infarction (N=55,555)

Considerations

• Adherent and nonadherent patients have different characteristics9,10,11

• Naïve differences may not accurately represent the actual adherence effect

• Is risk adjustment adequate to remove important biases?

• Selection Bias Issue: Adherence may be related to relevant, but omitted variables

– After adjusting for observed differences between groups, important differences may remain

• Examples of Bias – Differences in unobserved health status:

• If adherent patients are healthier and have correspondingly lower levels of utilization, then the effects of adherence may be biased upward

• If adherent patients are sicker and have correspondingly higher levels of utilization, then the effects of adherence may be biased downward

Addressing Selection Bias

1. Propensity Score Matching

2. Instrumental Variables

3. Fixed Effects

Propensity Score Matching

• Create a matched comparison group of patients who have characteristics that are similar to those in the treated group12

– Compare outcomes in treated group to matched comparison group

• Counterfactual• Estimate the effect on the treated as if they had been untreated (not observed)

• Matching is based on a propensity score– Matching on age, gender, location,… versus– Matching on a propensity score

Propensity Score Matching

To create the propensity score:

• One observation per individual

• Estimate the propensity score on the Xs (i.e., exposure equation)– Post-estimation predicted probability of treated (e.g., adherence) vs. untreated

(1/0 variable)– Logit or probit model

• Match based on the predicted propensity score– Types of matching (examples)

• Nearest neighbor• Caliper• Mahalanobis metric• Kernel

• Compare outcomes– Unadjusted– Regression Adjusted

Propensity Score Matching Example

• Comparison of complication rates between patients adherent to antidiabetic medications (PDC >= 0.80) and patients who are nonadherent to antidiabetic medications

• Exposure equation (logistic regression):

Pr(Adherent|X) = g(sociodemographics, health plan, provider, health status)

---> estimate propensity score

• Matching based on propensity score– N=30,190– Sample size is different (was N=55,555)

• Outcome equation (logistic regression):– Comparison of matched samples

• Adjusted• Unadjusted

Propensity Score Matching Example: Results

0.00910.0100

0.01360.0126

0.0000

0.0020

0.0040

0.0060

0.0080

0.0100

0.0120

0.0140

0.0160

Unadjusted Regression Adjusted

AdherentNon-Adherent

Rates are different (p<0.01)

Rate of Acute Myocardial Infarction (N=30,190)

Adjusted OR: 0.791(p=0.045)

Propensity Score Matching

Caliper MatchingMatch within common support

Considerations

• Observables• A good match

– Comparison of individual characteristics• For example, age distribution pre- and post- matching

– Reduction in bias– Which patients were matched in treatment and comparison group?

• Propensity scores as weights• Dose-response relationships• Regression adjustment after matching?

– If matching is perfect– If matching is imperfect

• Hidden bias may remain13 • Treatment group and available comparison group are very dissimilar

– Matches may be limited to the overlap in the distribution– Generalizability and conclusions

Instrumental Variables

• Y = f(Adherent, X)• Assume a linear relationship, f=1

• Instrumental variables (Z)14,15

1. Are correlated with treatment (adherence), and2. Are uncorrelated with outcome (Y), conditional on treatment (adherence)

• In this context, instrumental variables rely on finding variables (Z) that affect adherence but have no direct effect on outcome (Y)

– Randomization to adherence is an excellent instrument– In observational studies, need to find good instruments– Good instruments help isolate the effects of adherence on outcomes

Adherence and Outcomes

X

Z

AdherentOutcome (Y)

(e.g., # hospitalizations)

X: covariatesZ: instrumental variables

Y=outcome

Instrumental Variables

One of the most common methods is Two-Stage Least Squares (2SLS)

Y1 = 0 + 1Y2 + 2Z1 +u1 (1)• Y1 is the outcome• Y2 is endogenous• Z1 is a covariate

Y2 = 0 + 1Z2 + 2Z3 + v1 (2)• Z2 and Z3 are instrumental variables

• Equivalent to regressing• Y1 on Y2hat and Z1 (3)

Instrumental Variables Example

• Comparison of complication rates between patients adherent to antidiabetic medications (PDC >= 0.80) and patients nonadherent to antidiabetic medications

• Data Source: Thomson Reuters MarketScan Database (administrative claims and enrollment data)

• Two-Stage Residual Inclusion Model11,16

1. First Stage (Treatment)

Pr(Adherent|X,Z) = g(sociodemographics, health plan, provider, health status, benefit design)– Benefit design: e.g., prescription drug cost-sharing amount

2. Second Stage (Outcome)

Pr(Complications|X) = f(Adherent, sociodemographics, health plan, provider, health status, residual from first stage)

Instrumental Variables Example: Results

1. First Stage• Joint significance of instruments in first stage

equation p<0.01

2. Second Stage (Logistic Regression)

Outcome Adjusted Odds Ratio

Test of Exogeneity

(p-value)

Acute Myocardial Infarction

0.285

p=0.005

0.014

Instrumental Variables Example: Results

0.011

0.038

0

0.01

0.02

0.03

0.04

0.05

0.06

2SRI

AdherentNon-Adherent

Rate of Acute Myocardial Infarction (N=55,555)

Considerations

• Instruments– Strong/Weak17

– Good/Bad• “That Instrument is Lousy!”18

• Tests of Instruments- Significance in the first stage equation- Theoretical relationship- Tests of overidentification

• In the reduced form Y=f(X,Z), interpretation of estimated coefficient on Z

• Caution: Use of instrumental variables may affect efficiency– Standard error estimates

• Examples of instruments– Distance to a provider of care19

– Patient blood type20

Fixed Effects

• Panel data (aka cross-sectional time series; longitudinal; repeated measures) allows for the use of fixed effects modeling

• With two time periods, one can estimate a first-differenced model:

• Notice that first-differencing all variables (dependent and independent) eliminates unobservables ( ) constant across time periods

• Thus, unobservable confounders that would otherwise bias treatment (adherence) effect estimates are also removed

• With more than two time periods, the first-difference model is transformed; instead within-person means are subtracted from each observation (mathematically comparable to first-differencing)

1 0 1 0 1 0( ) ( ) ( ) ( )it it it it it it i iY Y X X A A

Fixed Effects Example: PDC & Hospitalization

• Estimated linear fixed effects models of hospitalization on PDC>=0.80, compared to OLS

• Controls include: Charlson Comorbidity Index, yearly time dummies

• Coefficients represent impact of optimal adherence on probability of hospitalization (p<0.01 for all)

• Fixed effects results are smaller in absolute value across three conditions; naïve models would overstate reductions in hospitalization from adherence

• “Healthy user bias” possible

Condition OLS Fixed Effects

Hypertension Coef = -0.068 Coef = -0.041

Diabetes Coef = -0.054 Coef = -0.027

Dyslipidemia Coef = -0.017 Coef = -0.012

Considerations

• Fixed effects models cannot include covariates constant over time (e.g., gender), although one can interact them with other dynamic variables

• Adequate within-subject variation necessary for identification of effects

• Fixed effects are less efficient than random effects because between-subject variation is “discarded”

• Only time-invariant unobservables are removed as potential confounders; endogeneity from time-varying characteristics could still persist

• Can be combined with IV to assist with remaining endogeneity

Questions?

M. Christopher Roebuck, MBADirector, Health EconomicsCVS Caremark

(410) 215-8380mroebuck@mindspring.com

Teresa B. Gibson, Ph.D.Director, Health Outcomes

Thomson Reuters

(734) 913-3481 teresa.gibson@thomsonreuters.com

References

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2. Peterson, AM; Nau, DP; Cramer, JA; Benner, J; Gwadry-Sridhar, F; Nichol, M. 2007. “A Checklist for Medication Compliance and Persistence Studies Using Retrospective Databases.” Value in Health 10(1):3-12.

3. Nichols, A. 2008. –LOCPR- user-written STATA command available for download at: http://fmwww.bc.edu/repec/bocode/l/locpr.ado.

4. Roebuck, MC; Liberman, JN; Gemmill-Toyama, M; Brennan, TA. In Review. “Impact of Medication Adherence in Chronic Vascular Disease on Health Services Utilization and Cost.” Health Affairs.

5. Karter, AJ; Parker, MM; Moffet, HH; Ahmed, AT; Schmittdiel, JA; Selby, JV. 2009. “New Prescription Medication Gaps: A Comprehensive Measure of Adherence to New Prescriptions.” Health Services Research 44:1640-1661.

6. Liberman, JN; Hutchins, DS; Popiel, RG; Patel, MH; Jan, SA; Berger, SE. 2010. “Determinants of Primary Non-Adherence in Asthma Controller and Dyslipidemia Pharmacotherapy.” American Journal of Pharmacy Benefits 2(2): 1-10.

7. Fischer, MA; Stedman, MR; Lii, J; Vogeli, C; Shrank, WH; Brookhart, MA; Weissman, JS. 2010a. “Primary Medication Non-Adherence: Analysis of 195,930 Electronic Prescriptions.” Journal of General Internal Medicine 25(4):284-290.

8. Fischer, MA; Choudhry, NK; Brill, G; Avorn, J; Schneeweiss, S; Hutchins, D; Liberman, JN; Brennan, TA; Shrank, WH. 2010b. “The Tip of the Iceberg: Rates and Predictors of Medication Non-Adherence.” Brigham and Women’s Hospital-Harvard Medical School, working paper.

9. Osterberg, L; Blaschke, T. 2005. “Adherence to Medication.” New England Journal of Medicine 353(5):487-97.10. Gibson, TB; Mark, TL; Axelsen, K; Baser, O; Rublee, DA; McGuigan, KA. 2006. “Impact of Statin Copayments on

Adherence and Medical Care Utilization and Expenditures.” American Journal of Managed Care 12 Spec no.:SP11-9.

References

11. Gibson, TB; Song, X; Alemayehu, B; Wang, SS; Waddell, JL; Bouchard, JR; Forma, F. 2010. “Cost Sharing, Adherence, and Health Outcomes in Patients with Diabetes.” American Journal of Managed Care 16(8):589-600.

12. Rosenbaum, PR; Rubin, DB. 1983. “The Central Role of the Propensity Score in Observational Studies for Causal Effects.” Biometrika 70(1):41-55.

13. Shadish, WR; Cook, TD; Campbell, DT. 2002. Experimental and Quasi-Experimental Designs for Generalized Causal Inference. Boston, MA: Houghton Mifflin Company.

14. Angrist, JD; Pischke, JS. 2008. Mostly Harmless Econometrics: An Empiricist’s Companion. Princeton, NJ: Princeton University Press.

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16. Terza, JV; Basu, A; Rathouz, PJ. 2008. “Two-Stage Residual Inclusion Estimation: Addressing Endogeneity in Health Economic Modeling.” Journal of Health Economics 27(3):531-543.

17. Bound, J; Jaeger, DA; Baker, RA. 1995. "Problems with Instrumental Variables Estimation When the Correlation Between the Instruments and the Endogenous Explanatory Variables is Weak." Journal of the American Statistical Association 90(430):443-50.

18. French, MT; Popovici, I. In Press. “That Instrument is Lousy! In Search of Agreement When Using Instrumental Variables Estimation in Substance Use Research.” Health Economics.

19. McClellan, MB; McNeill, BJ; Newhouse, JP. 1994. “Does More Intensive Treatment of Acute Myocardial Infarction Reduce Mortality?” Journal of the American Medical Association 272:859-866.

20. Lindrooth, RC; Hoerger, TJ; Norton, EC. 2000. “Expectations Among the Elderly of Nursing Home Treatment.” Health Services Research 35(5 Part II):1181-1202.

21. Wooldridge, JM. 2001. Econometric Analysis of Cross Section and Panel Data. Boston, MA: MIT Press.