Journal of Clinical Epidemiology 66 (2013) S69eS83
What is the effect of area size when using local area practice style as an instrument? John M. Brooksa,*, Yuexin Tangb, Cole G. Chapmanb, Elizabeth A. Cookb, Elizabeth A. Chrischillesc a
University of Iowa, College of Pharmacy and College of Public Health, S-515 Pharmacy Bldg., 115 S. Grand Ave, Iowa City, IA 52242, USA b University of Iowa, College of Pharmacy, Iowa City, IA, USA c University of Iowa, College of Public Health, Iowa City, IA, USA Accepted 8 April 2013
Abstract Objectives: Discuss the tradeoffs inherent in choosing a local area size when using a measure of local area practice style as an instrument in instrumental variable estimation when assessing treatment effectiveness. Study Design: Assess the effectiveness of angiotensin converting-enzyme inhibitors and angiotensin receptor blockers on survival after acute myocardial infarction for Medicare beneficiaries using practice style instruments based on different-sized local areas around patients. We contrasted treatment effect estimates using different local area sizes in terms of the strength of the relationship between local area practice styles and individual patient treatment choices; and indirect assessments of the assumption violations. Results: Using smaller local areas to measure practice styles exploits more treatment variation and results in smaller standard errors. However, if treatment effects are heterogeneous, the use of smaller local areas may increase the risk that local practice style measures are dominated by differences in average treatment effectiveness across areas and bias results toward greater effectiveness. Conclusion: Local area practice style measures can be useful instruments in instrumental variable analysis, but the use of smaller local area sizes to generate greater treatment variation may result in treatment effect estimates that are biased toward higher effectiveness. Assessment of whether ecological bias can be mitigated by changing local area size requires the use of outside data sources. Ó 2013 Elsevier Inc. All rights reserved. Keywords: Instrumental variables; Local area practice styles; Angiotensin converting enzyme inhibitors and angiotensin receptor blockers; Acute myocardial infarction; Survival; Local average treatment effects
1. Introduction Instrumental variable (IV) estimators have been recognized as useful tools to assess the effectiveness of alternative treatments in health care using observational data [1,2]. The ‘‘instruments’’ required in IV studies must be measured factors that are strongly related to treatment choice but are unrelated to either study outcomes or other unmeasured factors related to study outcomes. Thus, instruments essentially provide an ex post randomization of treatment choice or exposure across patients [3e9]. IV methods yield estimates of the average treatment effect for the subset of patients whose treatment choices were mutable to changes in the instrument variable or ‘‘instrument’’ values [4,10e13]. IV estimates
Conflict of interest: The authors have no conflicts of interest related to the content of this article. * Corresponding author. Tel.: þ319-335-8763; fax: þ319-353-5646. E-mail address:
[email protected] (J.M. Brooks). 0895-4356/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.jclinepi.2013.04.008
have been labeled a local average treatment effect (LATE) and are thought to be most suitable to assess the effect of treatment rate changes in a population [7,8,10e14]. Many researchers have used local area practice style measures as instruments in IV analysis [15e28], which conjectures that patients residing in areas where physicians have stronger preferences for a particular treatment are more apt to receive that treatment and unmeasured confounding variables are unrelated to the differential patient access to physicians with distinct treatment preferences. Only two studies that used a local area practice style measure as instruments have reported whether their estimates were robust to adjustments in the size of the local area used to measure practice style [23,28], and there has been no discussion as to the potential effects of local area size on the properties of the resulting IV estimates. The size of the local area used to measure practice style may affect both the strength of the relationship between the instrument and treatment choice and whether the instrument is related
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What is new? Key findings The use of smaller local areas to measure practice styles as instruments exploits more treatment variation and results in smaller standard errors. However, if treatment effects are heterogeneous, the use of smaller local areas may increase the risk that local practice style measures are dominated by idiosyncratic differences in average treatment effectiveness across areas resulting in treatment effect estimates that are biased toward greater effectiveness. What this adds to what was known? Local area practice style measures can be useful instruments in instrumental variable analysis, but the use of smaller local area sizes to generate greater treatment variation may result in treatment effect estimates that are biased toward higher effectiveness. Assessment of whether ecological bias can be mitigated by changing local area size requires the use of outside data sources. What is the implication and what should change now? Researchers should be aware that if treatment effects are heterogeneous across patients, the use of small-sized local areas as the basis to measure local practice style as an instrument may result in treatment effect estimates that are biased in favor of treatment.
to unmeasured confounding factors. One might expect that the larger the local area around a patient residence used to measure practice style the weaker the relationship will be between the instrument and the treatment choices for individual patients. Confounding emerges when local area practice style measures are correlated with differences in average unmeasured patient characteristics or ecological factors across areas that are related to patient outcomes. A priori relationships between local area size patient and ecological factors that may confound estimates do not generally exist. Ecological factors have been categorized as aggregate attributes (e.g., smoking rates, average health behaviors), contagion factors (e.g., flu prevalence), environmental factors (e.g., pollution, weather, sunlight hours); patterns of interaction among area individuals (e.g., social networks); and global factors (e.g., local regulations or market structures) [29]. One can envision that smaller local area sizes could introduce correlations between practice style and unmeasured neighborhood-level cultural and health behaviorerelated confounders. In contrast, use of larger local area sizes may introduce correlations with
regional unmeasured confounders related to regulatory structures, regional health care systems, and climate. In addition, if the relationships between individual treatment choice and local area practice style measures weaken as local area size increases, this increases the potential for unmeasured patient and ecological factors to confound the treatment effect estimates. However, the only possible approach to validate assumptions of no correlation between local area practice style measures and confounding factors for specific area sizes and is to obtain secondary data sources describing these factors and directly estimate the correlations by area size. If treatment effectiveness is heterogeneous across patients, another source of confounding related to local area size needs to be considered. ‘‘Essential heterogeneity’’ occurs when treatment effects are heterogeneous across patients and providers make treatment recommendations based on patient characteristics that are related to expected treatment effectiveness [19,21,30e32]. If the patient characteristics related to treatment effectiveness are unobserved by the researcher, we theorize that local area practice style measures will be positively correlated with average treatment effectiveness across areas causing LATE estimates to be biased toward positive treatment effectiveness. It will appear that higher treatment rates will yield better outcomes when in fact areas with higher treatment rates simply contained more patients apt to gain from treatment. However, as we discuss in Appendix A, as the number of patients used to define a local area increases, the favorable bias in LATE estimates from this effect will diminish. The objective of this study is to discuss the tradeoffs involved in choosing a local area size when using local area practice style as an instrument. We used IV methods to estimate the LATE of renineangiotensin system antagonists including angiotensin converting enzyme (ACE) inhibitors and angiotensin receptor blockers (ARBs) on 1-year patient survival among Medicare patients after acute myocardial infarction (AMI). ACE/ARB use post-AMI provides an interesting setting for this discussion because the benefits of ACE/ARBs are known to be heterogeneous across AMI patients with greater benefit for patients at higher risk of future cardiovascular events [33]. ACE/ARB survival benefit estimates from randomized controlled trials (RCTs) vary from 50 lives saved per 1,000 high-risk patients to 5 lives saved per 1,000 low-risk patients [34]. In addition, evidence shows substantial variation in ACE/ARB prescribing as only 50% of Medicare patients from two states received an ACE/ARB post-AMI in 2004 [35], and large geographic variation has been reported [36]. If providers believe ACE/ ARB benefits are heterogeneous across patients and ACE/ ARB treatments are sorted across AMI patients based on expected benefitsd‘‘essential heterogeneity’’ [19,37]dwe expect that local area ACE/ARB practice styles variation will reflect moderate-risk AMI patients whose ACE/ARB choices are more discretionary than either high- or lowrisk patients. As a result, IV estimates of LATE for ACE/
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ARB use on 1-year survival for post-AMI patients should fall between the RCT estimates described previously. In addition, all else equal, if essential heterogeneity is occurring we expect that LATE estimates will be biased high and that the bias will diminish as the size of the local area increases (see Appendix A). The consistency of our estimates is also conditional on the assumptions that local area ACE/ARB practice styles are unrelated to unmeasured average patient and ecological factors that affect cardiovascular patient outcomes, such as general provider access [38,39], characteristics of the health care delivery system [38,39], area socioeconomic status and homogeneity [38e44], pollution [45], social environment and support [39,46,47], and area health behaviors and disease prevention [47]. We used the driving area for clinical care (DACC) method to define local areas around Medicare AMI patient residence ZIP codes [23,25,28]. The DACC method enables researchers to create local area practice style measures for alternative size definitions based on threshold numbers of patients living within a specified driving time of each ZIP code. Defining local areas based on the number of patients instead of distances alone helps account for urban/rural differences in health care access as rural patients routinely drive greater distances for health care. Across local area size definitions, we contrasted ACE/ARB 1-year survival effectiveness estimates in terms of the strength of the relationship between local area practice styles and individual patient treatment choices as well as indirect assessments of the assumption of no correlation between local area practice style and unmeasured confounders.
2. Methods 2.1. Data and sample All Medicare claims files, enrollment information, and part D prescription drug events for patients hospitalized for their first AMI in 2008 who did not have AMI in 2006 and 2007 were obtained. We applied the Chronic Care Warehouse definition of AMI as an inpatient stay with an International Classification of Diseases, Ninth Revision code 410.xx (excluding 410.x2) in the first or second diagnosis position of the claim [48]. AMI stay admission and discharge dates were based on all Medicare institutional claims (acute, long-term care hospital, inpatient rehabilitation facility, critical-access hospital, and short-term nursing facility) with overlapping admission and discharge dates after an initial acute hospital admission with an AMI diagnosis. We restricted our sample to patients discharged alive; with continuous Medicare part A and B fee-for-service enrollment 12 months before their index AMI admission and 12 months after index discharge or until death; and with continuous part D enrollment 6 months before admission and 12 months after index discharge or until death. To ensure that all part D events were observable during a 30-day
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postindex treatment observation period, we further excluded patients who used hospice or skilled nursing care; were readmitted to inpatient care; or died within the 30day postindex discharge. Finally, because driving times between ZIP codes may have inconsistent meaning for geographically noncontiguous areas, we restricted our sample to patients living in the continental United States at AMI admission. The final sample size was 68,236. 2.2. Measures Patients were designated as having been prescribed an ACE/ARB post-AMI if they filled a prescription for an ACE/ARB within 30 days post-AMI discharge (one if an ACE/ARB prescription was filled within 30 days postAMI discharge, zero otherwise) [49]. The study outcome was a binary variable equaling one if the patient survived for 1 year after AMI discharge, zero otherwise. Measured covariates included patient demographics; baseline medical conditions for both the year before the AMI admission and during the index AMI stay; medications used during the 180 days before the AMI admission; AMI diagnosis type on admission; procedures during the AMI stay; complications during the AMI stay; other medications filled immediately after discharge (statins, beta blockers); part D variables including premium levels and deductible phase at diagnosis; whether patients were Medicaid dual eligible in their AMI index month; and socioeconomic characteristics for the patient residence ZIP code (per capita income, poverty rate, education level, English-speaking percentage). Full definitions of these variables are included in Appendix B. We defined local area practice style as the average intent of physicians in an area to prescribe ACE/ARBs for patients on AMI discharge. Because measurement of treatment intent is less clear for patients already using ACE/ ARBs when admitted for an AMI, to measure intent we used the patients who did not have ACE/ARBs available at home on their index AMI admission date based on previous prescription dates and days supplied figures on part D claims (N 5 43,842). For these patients, we created a variable equaling one if the patients filled an ACE/ARB prescription within 1 day of their first prescription claim in the first 30 days post-AMI discharge, zero otherwise. With these patients and this treatment definition, we measured local area ACE/ARB practice style at the patient ZIP code level using the DACC method. This method creates ‘‘local areas’’ around each patient residence ZIP code by consecutively adding patients from the next closest ZIP codes based on driving times between ZIP codes until a threshold number of patients is reached. Distinct local area sizes were created by varying the threshold number of patients from 10 to 200 patients in increments of 10. For the patients associated by the DACC method with each ZIP code for an area size definition, we calculated ZIP codeespecific area treatment ratios (ATRs) as the ratio of the number of patients receiving ACE/ARBs after AMI over the sum of
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the probabilities of their receiving an ACE/ARB after AMI. ACE/ARB probabilities were predicted using a multivariate logistic model of ACE/ARB choice over the patients with no ACE/ARBs available at index using the measured covariates described previously as independent variables. Patients in our full sample (N 5 68,236) were then assigned local practice style ATR values for each of the 20 area size definitions based on their residence ZIP code. 2.3. Analytical approach We applied the linear two-stage least squares (2SLS) IV estimator that has been used in several previous IV studies [10,18,19,21,22,28]. Linear 2SLS yields consistent estimates that are robust to underlying error distributions unlike other estimators based on distributional assumptions that yield inconsistent estimates if the assumptions are wrong [50,51]. In the first stage of 2SLS, a linear probability model of ACE/ARB choice was estimated for the 68,236 patients in our sample. Independent variables in the first stage model were the measured covariates described previously and the local area ACE/ARB practice style instrument. The instrument was specified empirically using nine binary variables that placed each patient residence ZIP code ATR within deciles of the distribution of ATRs across patients. In the second stage of 2SLS, a linear probability model of 1-year survival was estimated. The second-stage model specified all the noninstrument covariates from the first-stage model as independent variables plus the predicted ACE/ARB choice probability from the first stage. Using this approach, the estimated parameter
associated with the predicted ACE/ARB choice probability in the second-stage model is the LATE. We repeated this 2SLS method using ACE/ARB ATR values across the 20 different local area sizes. For each local area size, we estimated (1) the strength of the relationship between the instrument and ACE/ARB treatment choice via the Chow [52] F-value that tests whether the local area practice style instrument describes a statistically significant portion of the variation in ACE/ARB choice; (2) the ACE/ARB 1-year survival LATE estimate with respective standard error; (3) the Hausman overidentification test statistic [53]; and (4) the correlation between ACE/ARB ATR and overall life expectancy for the county containing each patient ZIP code [54]. Statistics (3) and (4) provide indirect assessments of whether the instruments are related to unmeasured confounding variables. The Hausman overidentification statistic tests the null hypothesis that the direct exclusion of the instrument from the second-stage 1-year survival equation was appropriate. A high Hausman statistic rejects the null hypothesis, suggesting a relationship between the instrument and survival [53]. The correlation parameter between local area ACE/ARB practice style and local area life expectancy suggests whether ACE/ARB practice styles are related to unmeasured differences in baseline patient health at diagnosis.
3. Results Table 1 describes the local areas defined using the DACC method by the number of threshold patients used.
Table 1. Statistics describing ZIP codes within local areas around patient residence ZIP codes by the threshold number of patient defining a local area Driving time in minutes required to reach patient threshold number
Number of ZIP codes required to reach patient threshold number
Threshold number of patients in local area
Mean
Minimum
Maximum
Mean
Minimum
Maximum
10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200
26.5 34.2 39.9 44.5 48.5 52.1 55.4 58.5 61.3 64.2 67.0 69.6 72.1 74.5 76.7 78.9 81.2 83.3 85.4 87.5
0.0 0.0 0.0 4.5 4.9 4.9 5.3 5.3 6.4 6.4 6.5 7.1 7.1 7.8 7.8 8.1 8.9 8.9 9.5 9.9
384.6 384.6 384.6 384.6 384.6 384.6 384.6 384.6 423.1 423.1 423.1 423.1 423.1 423.1 423.1 423.1 433.7 433.7 510.4 510.4
12.1 22.6 33.0 43.4 53.5 63.7 73.8 83.7 93.7 103.7 113.8 123.8 133.7 143.6 153.2 162.8 172.4 182.0 191.7 201.2
1 1 1 2 2 2 3 4 5 5 5 6 7 7 7 8 9 9 9 9
234 262 274 288 303 321 341 353 369 377 417 427 443 453 467 475 495 506 520 532
J.M. Brooks et al. / Journal of Clinical Epidemiology 66 (2013) S69eS83
Fig. 1. First-stage F statistics for the effect of local area practice style on angiotensin converting enzyme/angiotensin receptor blocker use by local area size (10e200 patients).
For 10-person local areas, it took an average of 26.5 driving minutes from each ZIP code and 12.1 ZIP codes to find sufficient patients, whereas for the 200-person local areas it
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took an average of 87.5 driving minutes from each ZIP code and 201.2 ZIP codes to find sufficient patients. Fig. 1 shows the relationship between the first-stage model Chow F statistics assessing the strength of the local area practice style instrument and individual patient ACE/ARB choice by local area size. All F statistics show statistically significant relationships between local area ACE/ARB practice styles and ACE/ARB choice, but the values of the F statistics fell (from 232 to 28) as the local area size increases. Fig. 2A and B presents maps of the northeastern United States illustrating the dispersion of ATR values for 10-patient and 200-patient areas, respectively. These figures show substantial geographic variation in the ACE/ARB use regardless of the local area size, but more practice style variation is revealed using the 10-patient sized local areas. Table 2 contrasts ACE/ARB treatment rates, unadjusted outcome rates, and selected measured covariate averages between patients grouped by ACE/ARB treatment choice, and the 1st and 10th deciles of the ACE/ARB ATR for 10-, 100-, and 200-patient defined local areas. We also report CochraneArmitage trend tests for each measured characteristic across the ATR deciles groups for each local area
Fig. 2. (A) Northeast US ACE/ARB area treatment ratios (ATRs) based on local areas defined using 10 patients around five-digit ZIP codes. (B) Northeast US ACE/ARB ATRs based on local areas defined using 200 patients around five-digit ZIP codes. ACE, angiotensin converting enzyme; ARB, angiotensin receptor blocker.
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Table 2. Acute myocardial infarction patient characteristics by ACE/ARB choice and local area practice styles defined using different area sizes (10, 100, 200) Local area practice style area size ACE/ARB in 30 d Selected measured covariates Number of patients
No 33,757
Yes
10-Person local areas
100-Person local areas
P-value (c ) 1st decile 10th decile
Trend test
6,824
P-value
2
34,479
6,824
a
1st decile 10th decile 6,825
6,825
Trend test
200-Person local areas a
P-value
1st decile 10th decile 6,821
6,821
Trend testa P-value
Column % 0 81.7
100 87.6
!0.0001* !0.0001*
35.0 82.8
64.0 84.7
!0.0001* 0.0054*
42.8 83.3
57.1 84.6
!0.0001* 0.5427
44.2 83.8
56.3 84.3
!0.0001* 0.4997
35.6 39.5 24.9
41.6 39 19.4
!0.0001* 0.2176 !0.0001*
36.9 39.9 23.2
38.5 39.4 22.1
0.0482* 0.0507 0.9851
36.8 40.6 22.5
40.1 37.3 22.6
!0.0001* !0.0001* 0.5585
36.4 40.5 23.1
38.8 38.4 22.8
0.0038* !0.0001* 0.2538
84.5 7.5 8.0 71.2 48.3
82.5 8.0 9.6 68.7 50.8
!0.0001* 0.0296* !0.0001* !0.0001* !0.0001*
84.8 7.6 7.6 70.2 49.4
82.6 9.4 8.0 70.3 48.2
0.0163* 0.2996 0.0299* 0.7837 0.1770
86.2 7.6 6.2 70.6 49.1
81.8 10.1 8.1 71.4 49.7
!0.0001* !0.0001* !0.0001* !0.0001* !0.0001*
87.9 6.9 5.2 69.2 52.1
79.8 11.1 9.1 70.2 48.0
!0.0001* !0.0001* !0.0001* !0.0001* 0.0012*
31.2 22.5 15.2 11.1 19.9 4.9 78.7 24.1
35.7 24.6 14.0 10.2 15.5 8.2 72.8 17.4
!0.0001* !0.0001* !0.0001* !0.0001* !0.0001* !0.0001* !0.0001* !0.0001*
31.7 23.3 16.2 11.1 17.8 5.8 77.3 21.6
32.8 23.1 14.8 10.7 18.6 6.5 77.4 21.4
0.1944 0.5597 0.0640 0.8890 0.5147 0.4406 0.3574 0.1961
31.7 23.3 15.0 11.1 18.8 5.9 77.8 21.5
32.8 23.4 13.7 11.4 18.6 6.5 76.7 21.5
0.5323 0.5941 0.2998 0.4147 0.2869 0.3104 0.4354 0.4023
32.7 23.9 14.8 10.9 17.6 5.7 77.6 20.6
33.0 23.2 14.8 11.0 17.9 6.6 75.9 21.2
0.7787 0.7940 0.5170 0.1480 0.9459 0.4593 0.2170 0.9066
34.8 50.0 28.2
25.3 62.8 43.1
!0.0001* !0.0001* !0.0001*
31.9 55.4 34.8
30.3 55.9 36.6
0.0252* 0.7898 0.0201*
30.9 54.8 34.7
30.9 55.2 38.4
0.3121 0.3402 0.0005*
30.6 56.2 35.2
30.7 55.7 37.1
0.7472 0.5336 0.0165*
Abbreviations: ACE/ARB, angiotensin converting enzyme/angiotensin receptor blocker; AMI, angiotensin receptor blocker; NSTEMI, non-ST elevation myocardial infarction. * P ! .05. a CochraneArmitage test of trend in characteristic value across patients grouped into deciles based on local area ACE/ARB practice style measure. For example, the P-value metro tests whether a linear trend in metro residence exists across the ACE/ARB practice styleebased patient groups. b Percent of patients with an ACE/ARB prescription in 30 days after AMI discharge. c Lived in a metropolitan area according to ruraleurban continuum codes developed by the United States Department of Agriculture Economic Research Service (http://www.ers.usda.gov/ topics/rural-economy-population/rural-classifications.aspx). Twenty patients had unknown metro size. d Mean per capita income in ZIP code below ZIP code mean. e Please refer [59]. f International Classification of Diseases, Ninth Revision (ICD-9) 410.0; 410.1. g ICD-9 410.7. h Patient had either angioedema (995.1); hyperkalemia (276.7); acute renal failure/acute tubular necrosis (584.xx); acute glomerulonephritis (580.xx); or chronic kidney disease (016.00, 016.01, 016.02, 016.03, 016.04, 016.05, 016.06, 095.4, 189.0, 189.9, 223.0, 236.91, 250.40, 250.41, 250.42, 250.43, 271.4, 274.1, 283.11, 403.01, 403.11, 403.91, 404.02, 404.03, 404.12, 404.13, 404.92, 404.93, 440.1, 442.1, 572.4, 582.xx, 583.xx, 585.xx, 586.xx, 588.xx, 591, 753.12, 753.13, 753.14, 753.15, 753.16, 753.17, 753.19, 753.20, 753.21, 753.22, 753.23, 753.29, 794.4).
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ACE/ARB Rx%b 1-yr survival % Age 66e75 76e85 85þ Race White Black Other Metroc Low per capita incomed Charlson Scoreedpreindex 0 1 2 3 4þ Anterior wall AMIf NSTEMIg ACE/ARB side effect conditiondpreindexh ACE/ARB side effect conditiondindexh Cardiac catheterization index ACE use in 180 d preindex
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size [55,56]. Of the patients in our sample, 50.5% received an ACE/ARB prescription in the 30 days after AMI discharge. Patients who received an ACE/ARB tended to be younger; had fewer comorbidities before AMI admission; had high-risk AMIs; were more likely to have had a cardiac catheterization during their AMI admission; were less likely to have conditions related to ACE/ARB side effects either before or during admission; and were more likely to have used an ACE/ARB before their index AMI. Grouping patients by the ACE/ARB ZIP code ATRs revealed substantial ACE/ARB treatment variation across local areas, but the extent of variation falls with the local area size. For example, ACE/ARB treatment rates varied from 35.0% to 64.0% moving from the 1st to 10th decile with the 10-patient local area size but varied only from 44.2% to 56.3% using the 200-patient local area size. Compared with grouping patients by ACE/ARB treatment, grouping patients by ZIP code ATRs increased the balance in all measured confounders except patient race. Fig. 3 presents the Hausman overidentification statistics for the IV model estimated for each local area size. The Hausman test statistic ranged from 0.47 to 2.21, and all were statistically insignificant except those estimated using the 60- and 100-person sized local areas. The Hausman test statistic appears to trend downward as local area size increases. Fig. 4 presents estimated correlations between local area ACE/ARB practice style measures and local area overall life expectancy across local area sizes. A small positive correlation between ACE/ARB practice style and local area life expectancy is observed that trends higher as local area size increases. Fig. 5 plots the LATE estimates and respective standard errors by local area size. Estimates of LATE ranged from 0.003 to 0.041 (i.e., 41 additional patients per 1,000 treated survive for 1 year after AMI). Only the IV estimate produced with the 10-person local area (0.041 or 41 patients per additional 1,000 treated survive 1 year) is statistically different from zero. IV estimates trend downward
Fig. 3. Overidentification F statistics by local area size (10e200 patients).
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Fig. 4. Correlations of local area ACE/ARB area treatment ratio and local area overall life expectancy by local area size (10e200 patients).
moving from 10-person to 120-person local areas but trend upward for local areas defined using greater than 120 persons.
4. Discussion IV methods yield LATE estimates that are representative of the subset of patients whose treatment choices were responsive to the instrument specified in the analysis [13]. Methodologists have stressed that LATE estimates are best applied to policy questions that are closely aligned with the treatment variation generated by the instruments specified [57]. As such, our LATE estimates of ACE/ARBs on 1-year survival post-AMI using local area practice styles would be best used to address policy questions related to whether changes in existing ACE/ARB rates will affect patient survival. For example, what survival benefits will be gained by moving from a 50.5% ACE/ARB treatment rate to a 55% rate, or what benefits would be lost from reducing the ACE/ARB treatment rate to 45%? As has been argued,
Fig. 5. Instrumental variable parameter estimates and standard errors for the effect of angiotensin converting enzyme/angiotensin receptor blocker prescribing post AMI on 1-year survival and standard error by local area size (10e200 patients).
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estimates of LATE may be more appropriate for answering these questions than estimates from RCTs [4,12,14,58]. We found that the ATR-based measures of local practice style describe a statistically significant portion of variation in ACE/ARB use across all local area sizes. All F statistics across local area sizes were greater than 10, which is considered the threshold of ‘‘weak instruments’’ in the IV literature [18]. However, as seen in Fig. 1, as the local area size expands, the strength of the relationship between local area practice style measures and individual patient ACE/ ARB choice diminishes. A direct effect of this reduction can be seen in the increase in the standard errors of the ACE/ARB treatment effect estimates in Fig. 5. If the treatment effect standard error found in the 10-patient local area was maintained across local area sizes, six of the 20 treatment effect estimates would have been statistically significantly different from zero at the 0.05 level. We discussed two main sources of bias for LATE estimates using ATR-based measures of local area practice styles in IV estimation. We theorized in Appendix A that using ATR-based instruments will yield estimates of LATE with a positive bias but that this bias will diminish as local area size increases. It is also possible that for certain local area sizes ATR-based measures could be correlated with either average patient characteristics or ecological factors that affect outcome directly. Previous studies have suggested several potential confounding factors, but there are no a priori relationships that would associate these factors with ATR-based measures of local practice styles by local area size. We suggest researchers should look for anomalies in LATE estimates across local area sizes and search for secondary sources of information to assess the validity of estimates. We provide an example of this by estimating correlations between local area ACE/ARB ATR values and local area overall life expectancies. In future, research medical charts from the index AMI could be abstracted for a sample of patients in the highest and lowest ACE/ ARB ATR areas for several local area sizes to assess whether average patient characteristics such as AMI severity varies with ATR values across local area sizes. With respect to the effect of ACE/ARBs on 1-year survival post-AMI across local area sizes (Fig. 5), we found that only the LATE estimate from the 10-person local area size was statistically different from zero and that LATE estimates trended downward as local area size increased from 10 to 120 patients. This trend is consistent with the theory we provide in Appendix A that ATR-based measures of local area practice style will lead to LATE estimates with positive bias but that this bias will diminish as local area size increases. However, this trend clearly does not extend to local area definitions greater than 120 patients as LATE estimates trended upward for local area sizes using from 120 to 200 patients. The U-shaped relationship between LATE estimates and local area size suggests that correlations between local area size and unmeasured confounders exist, but this U-shaped relationship alone is insufficient to
pinpoint which local area sizes have the most prominent confounding problem. It is possible that correlations between unmeasured confounding factors and the ATRbased instruments exist in the large-sized local areas that bias LATE treatment effect estimates in a positive manner. We did find small positive correlations between the ATR values and life expectancy that get stronger as local area size increases that support this notion. On the other hand, it is possible that correlations between unmeasured confounding factors and the ATR-based instruments exist in the small-sized local areas that bias treatment effects toward zero (independent of the positive bias associated with essential heterogeneity). The overidentification statistic estimates in Fig. 3 trend lower with increased local area size, which provides some weight to this idea, but secondary data sources are needed to further understand the source of LATE estimate variation across area sizes. Just more than 50% of the AMI patients in our sample filled an ACE/ARB prescription in the 30 days after discharge from their index AMI. If ACE/ARB prescribing is sorted across AMI patients based on expected benefits (essential heterogeneity) we expected that the treatment rate variation identified by local area practice style differences reflects treatment choices for patients whose expected treatment benefits from ACE/ARBs are less definitive. As a result, we expected our estimates of the LATE of ACE/ARBs on 1-year patient survival to be lower than the upper limit RCT estimates (50 lives saved per 1,000 high-risk patients). Our LATE estimates using various local area sizes are all less than this upper limit. Our LATE estimates are best used to assess whether higher rates of ACE/ARB prescribing post-AMI will increase survival rates. If the IV assumptions hold, our results do not provide clear evidence that higher treatment rates will increase survival rates. Although our local practice styleebased instrument described a substantial portion of treatment variation across local area sizes and, for the most part, treatment effect estimates were positive, large treatment effect standard errors preclude the rejection of the null hypothesis that no survival benefits are available from higher ACE/ARB prescribing rates. Our results suggest that providers may be correctly sorting ACE/ ARB treatments to AMI patients in practice and that increasing the ACE/ARB treatment rate beyond 50% may do little to improve survival rates. However, care should be taken not to generalize these results to all AMI patients especially those patients who receive ACE/ARBs in current practice.
Appendix A To assess the properties of our local area practice style measures with regard to local area size, we derive a model of local practice style model based on geographic variation in provider treatment effectiveness beliefs. Similar results can be found using other local area factors as the source
J.M. Brooks et al. / Journal of Clinical Epidemiology 66 (2013) S69eS83
of practice style differences such as variation in the value of treatment outcomes across areas [31]. Let expected patient outcome be described by the following model: Yi 5 b0 þ ½ðb10 þ b1S Si Þ$PN $TiN þ b2 Xi þ b2 EN þ qiN ;
A1
where Yi is the outcome for patient ‘‘i.’’ N designates the size of the geographic area around patient ‘‘i’’ as defined by the shortest driving distance required to locate the N nearest patients with the same clinical condition. TiN is the treatment choice for patient ‘‘i’’ living in the N-sized area. ½ðb10 þ b1S Si Þ$PN represents the range of treatment effectiveness beliefs across patients with characteristics Si living in the N-sized area. Under this specification, treatment effectiveness is heterogeneous across patients based on Si. If Si is characterized in a manner so that higher values of Si increase treatment effectiveness b1S will be positive. PN represents average provider treatment effectiveness beliefs in N-sized area. The larger PN the more effective the providers in the area believe treatment is across the range of Si. EN is the ecological factor in the N-sized area that affect patient outcomes. Xi represents the measured characteristics for patient ‘‘i’’ that affect the outcome directly, whereas qiN represents the accumulated unmeasured characteristics of patient ‘‘i’’ living in the N-sized area that affect outcome. Furthermore, describe treatment choice for patient ‘‘i’’ living in the N-sized area as: TiN 5 a0 þ a1 Xi þ a2 Si þ a3 PN þ mi
A2
where TiN, Xi, PN, and Si are defined as aforementioned. Under essential heterogeneity, Si is specified in (A2) because providers are assumed to (1) assess Si for each patient; (2) have knowledge of the effect of Si on treatment effectiveness; and (3) recommend treatment choice based on the value of Si for each patient. Higher Si values increase treatment effectiveness so a2 in (A2) will be positive. If PN is measured so that larger PN represents stronger treatment effectiveness beliefs, a3 will also be positive. Xi has no direct relationship with treatment effectiveness in (A1) so the theoretical justification for specifying Xi in the treatment choice equation is unclear. However, we include Xi in (A2) to remain consistent with general convention. mi equals the accumulated unmeasured characteristics for patient ‘‘i’’ that affect treatment choice but do not affect outcome.
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If was able to be measured directly, PN could serve as a valid instrument under the following conditions (1) a3s 0; (2) Corr(PN, EN) 5 0; (3) Corr(PN, Si) 5 0; and (4) Corr(PN, qiN) 5 0. Under these conditions, IV estimation will yield a consistent estimate of the LATE of Ti on Yi b1PN , that is specific to the distribution of Si values for the subset of patient whose treatment choices were affected by PN. b1PN will likely represent patients with moderate Si values as patients with very high Si values will likely receive treatment regardless of PN and patients with very low Si values will likely not receive treatment regardless of PN. In this article, we measure PN using ATRs for the local area around each patient residence ZIP code of size N. TiN, Yi, and Xi are observed by the researcher. We assume Si is not correlated with the underlying PN and is distributed evenly across patients with a mean of mS and variance s2S . However, our ATR approach to measure local treatment preferences for areas of size N solves to the following: . PN T N a þa X þa S þP þm i i51 1 N 2 N N . 5 0 ATRN 5 P N b b þ a X a 0 1 Tbi N i51
A3 where Tbi equals the predicted probability of treatment for patient ‘‘i’’ conditional on Xi alone. SN equals the mean of Si in the local area of size N. Local areas, out of chance, with a larger SN will have more patients apt to gain from treatment and more patients choosing treatment conditional on Xi. As a result, our ATRN measure will vary with both PN and SN . Therefore, when ATRN is used as an instrument replacing PN in the empirical model of (A2) in the first stage of 2SLS, we expect that the ATRN value associated with each local area will be positively correlated with the unmeasured Si values for the patients within each local area. This positive correlation will result in an IV estimate of b1PN that is biased high relative to the true LATE for the subset of patients whose treatment choices were affected SN is distributed with mean mS and variby PN. However, . ance s2S N. Therefore, as N increases, the variance in SN across local areas will diminish and a larger portion of the treatment variation described by ATRN will be generated from variation in PN, and, all else equal, the positive bias associated with estimates of b1PN will diminish.
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Appendix B. Variable Patient demographics Age
Definition/source Categories were 66e70, 71e75, 76e80, 81e85, more than 85
Gender
Categories were M, F
Race
Categories were unknown, white, black, other, Asian, Hispanic, Native American
Metro/nonmetro geographic location
Used ruraleurban continuum codes 1e9 developed by the USDA ERS: summarized to metro (1e3) and nonmetro (4e9) areas
Beneficiary summary files (2007e8) Beneficiary summary files (2007e8) Beneficiary summary files (2007e8) Beneficiary summary files (2007e8)
Part A (inpatient) Part A (inpatient), part B (outpatient, carrier)
Values 1 if in age category, 0 otherwise 1 if male, 0 female 1 if in race category, 0 otherwise 1 if in location category, 0 otherwise
1 if code occurs, 0 otherwise X
Part A/B Part A (inpatient), part B (outpatient, carrier)
X X
Part A (inpatient), part B (outpatient, carrier) Part A/B Part A (inpatient, SNF, HHA), part B (outpatient, carrier)
X
Part A (inpatient, SNF, HHA), part B (outpatient, carrier), Part D
X
X X
J.M. Brooks et al. / Journal of Clinical Epidemiology 66 (2013) S69eS83
Baseline medical history/comorbidities Time period Two sets of variables measured: (1) up to 365 days before admission and (2) during admission AMI At least one inpatient claim with DX codes 410.01, 410.11, 410.21, 410.31, 410.41, 410.51, 410.61, 410.71, 410.81, 410.91 (only first or second DX on the claim) [63] Stroke At least one inpatient claim or two HOP or carrier claims with DX codes 430, 431, 434.00, 434.01, 434.10, 434.11, 434.90, 434.91, 435.0, 435.1, 435.3, 435.8, 435.9, 436, 997.02 (any DX on the claim); if any of the qualifying claims have 800 DX code 804.9, 850 DX code 854.1 in any DX position or DX V57xx as the principal DX code, then exclude [63], exclude 435.X per Ref. [74] TIA ICD-9 codes 435.x in hospitalization or emergency encounter data [74] Heart failure DX 398.91, 402.01, 402.11, 402.91, 404.01, 404.11, 404.91, 404.03, 404.13, 404.93, 428.0, 428.1, 428.20, 428.21, 428.22, 428.23, 428.30, 428.31, 428.32, 428.33, 428.40, 428.41, 428.42, 428.43, 428.9 (any DX on the claim); at least one inpatient, HOP or carrier claim with DX codes [63] AF DX 427.31 (only first or second DX on the claim); at least one inpatient claim or two HOP or carrier claims with DX code [63] PVD DX 443.9, 441.x, 785.4, V43.4; Proc 38.48 [59] CKD DX 016.00, 016.01, 016.02, 016.03, 016.04, 016.05, 016.06, 095.4, 189.0, 189.9, 223.0, 236.91, 249.40, 249.41, 250.40, 250.41, 250.42, 250.43, 271.4, 274.10, 283.11, 403.01, 403.11, 403.91, 404.02, 404.03, 404.12, 404.13, 404.92, 404.93, 440.1, 442.1, 572.4, 580.0, 580.4, 580.81, 580.89, 580.9, 581.0, 581.1, 581.2, 581.3, 581.81, 581.89, 581.9, 582.0, 582.1, 582.2, 582.4, 582.81, 582.89, 582.9, 583.0, 583.1, 583.2, 583.4, 583.6, 583.7, 583.81, 583.89, 583.9, 584.5, 584.6, 584.7, 584.8, 584.9, 585, 585.1, 585.2, 585.3, 585.4, 585.5, 585.6, 585.9, 586, 587, 588.0, 588.1, 588.81, 588.89, 588.9, 591, 753.12, 753.13, 753.14, 753.15, 753.16, 753.17, 753.19, 753.20, 753.21, 753.22, 753.23, 753.29, 794.4 (any DX on the claim); at least one inpatient, SNF, or HHA claim or two HOP or carrier claims with DX codes [63] DX 249.00, 249.01, 249.10, 249.11, 249.20, 249.21, 249.30, 249.31, 249.40, 249.41, 249.50, Diabetes 249.51, 249.60, 249.61, 249.70, 249.71, 249.80, 249.81, 249.90, 249.91, 250.00, 250.01, 250.02, 250.03, 250.10, 250.11, 250.12, 250.13, 250.20, 250.21, 250.22, 250.23, 250.30, 250.31, 250.32, 250.33, 250.40, 250.41, 250.42, 250.43, 250.50, 250.51, 250.52, 250.53, 250.60, 250.61, 250.62, 250.63, 250.70, 250.71, 250.72, 250.73, 250.80, 250.81, 250.82, 250.83, 250.90, 250.91, 250.92, 250.93, 357.2, 362.01, 362.02, 366.41 (any DX on the claim); at least one inpatient, SNF, or HHA claim or two HOP or carrier claims with DX codes [63] AND add a dummy for insulin use from pharmacy claims
Source of data
Hypertension (complicated) Hypertension (uncomplicated) Hyperlipidemia COPD
CABG Stent
Part A/B
X
DX 401.1, 401.9 [65]
Part A/B
X
DX 272.xx or a pharmacy claim for a lipid-lowering medication [72] DX 491.0, 491.1, 491.20, 491.21, 491.22, 491.8, 491.9, 492.0, 492.8, 494.0, 494.1, 496 (any DX on the claim) [63] DX 140.xe172.x, 174.xe195.8, 200.xe208.x [59] DX 196.xe199.x [65] DX 493.0, 493.1, 493.9 [61] DX 410.00, 410.02, 410.10, 410.12, 410.20, 410.22, 410.30, 410.32, 410.40, 410.42, 410.50, 410.52, 410.60, 410.62, 410.70, 410.72, 410.80, 410.82, 410.90, 410.92, 411.0, 411.1, 411.81, 411.89, 412, 413.0, 413.1, 413.9, 414.00, 414.01, 414.02, 414.03, 414.04, 414.05, 414.06, 414.07, 414.10, 414.11, 414.12, 414.19, 414.2, 414.3, 414.8, 414.9 Proc 00.66, 36.01, 36.02, 36.03, 36.04, 36.05, 36.06, 36.07, 36.09, 36.10, 36.11, 36.12, 36.13, 36.14, 36.15, 36.16, 36.17, 36.19, 36.2, 36.31, 36.32 HCPCS 33510, 33511, 33512, 33513, 33514, 33516, 33517, 33518, 33519, 33521, 33522, 33523, 33533, 33534, 33535, 33536, 33542, 33545, 33548, 92975, 92977, 92980, 92982, 92995, 33140, 33141 (any DX, PROC, or HCPCS on the claim); at least one inpatient, SNF, HHA, HOP, or carrier claim with DX, procedure, or HCPC codes [63] ICD-9 procedure codes 36.0e36.39 [67] or CPT 33510e33536 [71] Stent alone CPT codes 92,980e92,981 [71]; ICD-9-CM procedure code 36.06, drug-eluting stent (ICD-9-CM procedure code 36.07), or both [73] Angioplasty only: ICD-9 procedure codes 36.01, 36.02, 36.05, 36.06 [67] [59]
Part A/B/D Part A/B
X X
Part A/B Part A/B Part A/B Part A (inpatient, SNF, HHA), part B (outpatient, carrier)
X X X X
Part A/B Part A/B
X X
Part A/B Part A/B
X 0e19 points possible
Part D
1 if prescription filled during time period, 0 otherwise X X X X X X
PCI Charlson Comorbidity Index Baseline and postdischarge medications Time period 180 days before index admission date Drug classes All drug classes identified by linking part D claims to Multum Lexicon Plus data set (Copyright 2012 Lexi-Comp, Inc. and/or Cenner Multum, Inc.) Nitrates
Clopidogrel ACE inhibitors ARBs Beta blockers Lipid-lowering agents Calcium channel blockers Warfarin Diuretics (loop diuretics, thiazide diuretics, potassium-sparing diuretics),
X X X X X X
Part Part Part Part Part Part
D D D D D D
X X
Part D Part D
J.M. Brooks et al. / Journal of Clinical Epidemiology 66 (2013) S69eS83
Cancer (general) Metastatic cancer Asthma Non-AMI ischemic heart disease (AMI codes removed)
DX 402.10, 402.90, 404.10, 404.90, 405.1, 405.9 [65]
X X
(Continued ) S79
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Appendix B. Continued Variable
Subendocardial infarction (NSTEMI) Stroke
Any others? Complications during admission Cardiac arrest Ventricular arrhythmia Heart failure
Values
X
Part D
X
X
Part D
X
X
Part D
X
DX 410.0; 410.1 [66]
Part A/B
DX 410.7x [66]
Part A/B
1 if code occurs, 0 otherwise X
At least one inpatient claim or two HOP or carrier claims with DX codes 430, 431, 434.00, 434.01, 434.10, 434.11, 434.90, 434.91, 435.0, 435.1, 435.3, 435.8, 435.9, 436, 997.02 (any DX on the claim); if any of the qualifying claims have 800 DX code 804.9, 850 DX code 854.1 in any DX position OR DX V57xx as the principal DX code, then exclude [63]dexclude TIA codes below if separating Other AMI locations DX 410.5e410.6, 410.8e410.9 [66]
Part A/B
X
Part A/B
X
427.5 [60]
Part A/B
DX 427.1, 427.4, 427.41, 427.42 [70] DX 398.91, 402.01, 402.11, 402.91, 404.01, 404.11, 404.91, 404.03, 404.13, 404.93, 428.0, 428.1, 428.20, 428.21, 428.22, 428.23, 428.30, 428.31, 428.32, 428.33, 428.40, 428.41, 428.42, 428.43, 428.9 (any DX on the claim); at least one inpatient, HOP, or carrier claim with DX codes [63] DX 785.51 [60] DX458.x [79] or DX 458.0 [80] and DX 458.9, 785.5x, and 998.0 [78] Acute renal failure/acute tubular necrosis (DX 584.xx) or acute glomerulonephritis (DX 580.xx) [64,68] DX 995.91 [74] Secondary DX 481e483 [77]
Part A/B Part A (inpatient), part B (outpatient, carrier)
1 if code occurs, 0 otherwise X X
Cardiogenic shock Hypotension Renal failure Sepsis Pneumonia Procedures during hospitalization CABG ICD-9 procedure codes 36.0e36.39 [67] and CPT 33510e33536 [71] Stent
Source of data
ICD-9-CM procedure code 36.06), drug-eluting stent (ICD-9-CM procedure code 36.07) [73]
Part Part Part Part Part
A/B A/B A/B A/B A/B
Part A/B Part A/B
X X X X X 1 if code occurs, 0 otherwise X
J.M. Brooks et al. / Journal of Clinical Epidemiology 66 (2013) S69eS83
Other antihypertensives Fenofibrates and other lipid-lowering agents Antidiabetics alphaglucosidase, amylin analogues, biguanides, dipeptidyl peptidase-4 inhibitors, glucagonlike peptide 1 receptor agonists, insulin, meglitinides, sulfonylureas, thiazolidinediones, others (epalrestat, exenatide, glybuzole) Diagnosis on admission Anterior wall AMI
Definition/source
PCI Stress test Cardiac catheterization Echocardiography
Part A/B Part A/B
X X
Part A/B Part A (inpatient), part B (outpatient) Part A/B Part A/B
X X
Quartiles for beneficiary responsibility amount, total cost, and plan premium. Deductible phase separated into one of four categories: pre_ICL_phase, ICL_phase, catastrophic_phase, and unknown_phase
Part A/B/D
1 if in each category, 0 otherwise
All variables created as 1/0 based on whether the patient lived in a ZIP code area that was in the upper or lower 50th percentile for each value
2000 US Census
1 if above median, 0 otherwise
X X
Abbreviations: M, male; F, female; USDA, United States Department of Agriculture; ERS, Economic Research Service; AMI, acute myocardial infarction; DX, diagnosis; PROC, procedure; HOP, hospital outpatient; TIA, transient ischemic attack; ICD-9, International Classification of Diseases, Ninth Revision; AF, atrial fibrillation; PVD, peripheral vascular disease; CKD, chronic kidney disease; SNF, skilled nursing facility; HHA, Home Health Agency; COPD, chronic obstructive pulmonary disease; HCPCS, Healthcare Common Procedure Coding System; CABG, coronary artery bypass graft; CPT, Current Procedural Terminology; ICD-9-CM, International Classification of Diseases, Ninth Revision, Clinical Modification; PCI, percutaneous coronary intervention; ACE, angiotensin converting enzyme; ARBs, angiotensin receptor blocker; NSTEMI, non-ST elevation myocardial infarction; VAD, ventricular assist device; OOP, out of pocket.
J.M. Brooks et al. / Journal of Clinical Epidemiology 66 (2013) S69eS83
VAD Pacemaker implantation Insurance variables Entered coverage gap (Y/N) or number of months in coverage gap, patient OOP cost, *percent of drug class covered on plan’s formulary, *patient OOP cost of alternatives *Only available if CMS allows release of formulary finder file for the Part D data Socioeconomic status variables Percent below poverty, high school graduation rate, per capita income, percent English speaking
Angioplasty only: ICD-9 procedure codes 36.01, 36.02, 36.05, 36.06 [67] DX 89.4x, CPT 93015 or CPT codes 93,015e93,018, 93,350, 78,460e78,465, 78,472e78,483, 78,494, 78,496, 78,491e78,492 (includes nuclear imaging) [71] CPT codes 93,508, 93,510e93,529, 93,539e93,540, 93,543, 93,545e93,552 [71] On inpatient claim, ICD-9 procedure code 88.72; on outpatient claim, CPT 93307, 93320, 93325, 93308 [75] CPT 36533 and 36,489 [76] or ICD-9 procedure codes 37.62, 37.65, and 37.66 [69] ICD-9 procedure codes 37.80e37.89 [62]
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