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Logo of nihpaAbout Author manuscriptsSubmit a manuscriptHHS Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
Arch Intern Med. Author manuscript; available in PMC 2013 December 30.
Published in final edited form as:
PMCID: PMC3875311


Matthew D. Solomon, M.D. Ph.D.,corresponding author1,2 Dana P. Goldman, Ph.D.,3 Geoffrey F. Joyce, Ph.D.,4 and José J. Escarce, M.D., Ph.D.5,6



Increased cost-sharing reduces utilization of prescription drugs, but there is little evidence about the exact mechanisms by which this reduction occurs or the factors associated with price-sensitivity.


We conducted a retrospective cohort study of 272,474 elderly individuals with employer-provided drug coverage from 1997 to 2002 from 59 different health plans. We assessed the relationship between prescription drug cost-sharing and the time until the initiation of drug therapy after a new diagnosis of hypertension, hypercholesterolemia, or diabetes.


For all study conditions, higher copayments were associated with delayed initiation of therapy. In survival models, doubling copayments resulted in large reductions in the predicted proportion of patients initiating pharmacotherapy at one and five years after diagnosis (55.0 vs 40.1% at 1 year and 81.7% vs 66.3% at 5 years, p<0.000 for hypertension; 40.2% vs 31.1% at 1 year and 64.3% vs 53.8% at 5 years, p<0.002 for hypercholesterolemia; 45.8% vs 40.0% at 1 year and 69.3% vs 62.9% at 5 years, p<0.041 for diabetes). However, patients’ rate of initiation and sensitivity to copayments strongly depended upon their prior experience with prescription drugs. Those with a history of prior drug use initiated earlier and were less price-sensitive. These results were robust to a wide range of sensitivity analyses.


High cost-sharing delays the initiation of drug therapy for patients newly diagnosed with chronic disease. This effect is greater among patients who lack experience with prescription drugs. Policy makers and physicians should consider the effects of benefits design on patient behavior in order to encourage the adoption of necessary care.


In the past decade, health plans have responded to rising prescription drug costs by implementing more restrictive insurance benefits, the hallmark of which has been increased cost-sharing (i.e., “copayments”), but has also included complex mechanisms such as sorting medications into “tiers” with varying copayments, mandatory generic substitution, and formularies.1 Several multi-year studies have demonstrated that these new arrangements reduce overall drug utilization and expenditures,24 and that the chronically ill are sensitive to out-of-pocket costs.5,6 However, detailed mechanisms by which these reductions occur have not been well investigated.

Medications are a crucial component of the therapeutic regimen for the chronically ill,7 and the interruption of drug therapy can have negative health consequences,8,9 particularly for the elderly, who have the highest rates of chronic disease and prescription drug use.1215 Studies measuring the effect of pharmacy benefits designs on drug treatment for the chronically ill are inconsistent,3,5,6,1621 but surveys of Medicare beneficiaries find cost to be the leading reason why patients don’t fill prescriptions, skip doses, or take smaller doses, followed by other causes, such as medication side-effects and beliefs about whether drugs improve health.22 Most empirical studies of cost-sharing have examined aggregate measures of utilization, such as total expenditures or days supplied, without explanations of how patients adjust their regimens. Although several studies suggest that sensitivity to cost-sharing depends upon a drug’s therapeutic class,5,21,23,24 and that increased cost-sharing may decrease “non-essential” drug use more than “essential” drug use,5,20,2529 few studies have dissected the multiple mechanisms by which patients reduce their utilization in the face of higher cost sharing.

To fill this gap, this study examines whether cost-sharing affects the initiation of drug treatment for patients newly diagnosed with chronic disease. A sophisticated understanding of the effects of drug benefits is crucial for policy-makers, who, rather than applying blunt tools to control utilization, need to target those most at risk for the potentially harmful effects of utilization reductions.



We linked enrollment files, pharmacy claims, medical claims, and the salient features of health plan benefits for retirees of 15 large employers from 1997 to 2002. Each employer offered one or more health plans to its elderly retirees for a total of 23 health plans covering 399,034 retirees. All but two employers that offered multiple health plans provided a single drug benefit to their retirees, such that retirees had no choice of drug benefits. The content of the claims files have been described elsewhere.3,5 The Appendix details the construction of our longitudinal datasets, which included complete utilization data for our subjects over full calendar years. These datasets included thirty-one plan-year combinations, and these plans covered 272,474 unique persons, which translated to 688,620 person-year observations.

Study Sample

We created algorithms to identify patients with newly diagnosed hypertension, hypercholesterolemia, and diabetes (HTN, CHOL, and DIAB) using ICD-9-CM diagnosis codes (see Appendix) that were designed to ensure “rule-out” diagnoses were excluded from the sample. We required patients to be observed for at least their first year in the data without any outpatient or inpatient physician visits with an ICD-9-CM code for the chronic disease (hereafter, “diagnosis”) and without filling any disease-specific medications. Subsequent to this “washout” period, we required them to have the diagnosis of interest recorded during a physician visit on at least two occasions, the first of which must have occurred prior to or the same day as their first disease-specific medication. The first diagnosis was the “index date” on which the patient was considered newly diagnosed with the condition. (See Appendix for details.) Studies that examine the validity of using claims data to identify patients with chronic disease find that various factors affect the sensitivity and specificity of different claims-based algorithms, 30,31 and suggest our algorithm would yield specificity levels of 0.85 to 0.90.

Disease-specific medications were identified by matching National Drug Codes between the Redbook Database and the pharmaceutical claims. Manual verifications and edits were completed by the authors with clinical experience (JE, MS). HTN medications included angiotensin receptor blockers, angiotensin converting enzyme inhibitors, beta blockers, calcium channel, blockers, thiazide diuretics, osmotic diuretics, potassium sparing diuretics, carbonic anhydrase inhibitors, alpha-1 inhibitors, alpha-2 agonists, and vasodilators. DIAB medications included insulins, sulfonylureas, metformin, thiazolidinediones, and alpha glucosidase blockers. CHOL medications included statins, bile acid sequestrants, nicotinic acid, and fibric acid derivatives.

Outcome variable

The primary outcome measure was the time until initiation of prescription drug therapy, defined as the number of days between a patient’s first diagnosis and first disease-specific prescription. Because patients were observed in the data from two to six years and may have been diagnosed at any time after their first year in the data, the outcome is right-censored. It was possible that patients who did not initiate drug therapy during the observation window may have begun therapy after we ceased to observe them.

Explanatory variables

The main explanatory variable in our analysis was an index that measured the generosity of a plan’s prescription drug benefits. To capture the complexities of modern prescription drug plans, which base price upon not only its tier but also where it is dispensed, we developed a single index that summarized the average annual out-of-pocket (OOP) expense that members of a standard sample would have paid for their prescription drugs had they faced the cost-sharing requirements of each plan. This out-of-pocket index (OOP index) is similar to what would be calculated for the medical consumer price index, but it is specific to each plan. Details on the creation of the OOP index have been described elsewhere5 and are included in the Appendix. The OOP index ranked plans by their cost-sharing structure in a manner consistent with their absolute and relative co-payment levels. We also calculated separate out-of-pocket indices for disease-specific medications to measure the out-of-pocket burden for specific drug classes, but these indices were highly correlated with the overall OOP index and yielded the same results.

Covariates in the models included indicators for age categories; an indicator for sex; median household income in the ZIP code of residence; a categorical variable for urban residence; indicators for the year of the index date to control for secular time trends; selected outpatient medical benefits to include an exogenous measure of outpatient medical utilization; and indicators for 15 comorbid conditions as health status controls, identified by ICD-9-CM codes from physician visits in the year prior to a patient’s index date. Finally, we included an indicator variable for any prescription medication use in the year prior to the index date and, in some models, the interaction of this indicator and the OOP index, to assess whether prior use of prescription drugs affected time until initiation of drug therapy and price responsiveness.

Statistical Analysis

Because the data were structured in a time-to-event framework, we employed survival analysis techniques. For unadjusted analyses, we used Kaplan-Meier methods and log rank tests to compare survival functions. For adjusted analyses, we estimated six multivariate Cox proportional hazards models. For each of the three study conditions, we estimated a main effects and interacted model. The main effects models included the variables described above and the interacted models included an additional variable that interacted the OOP index with the indicator for patients who had any drug use in the year prior to the index date. To make the results easier to understand, we used our multivariate models to predict the effect of doubling copayments on the time to initiation of therapy for each study condition. For the predictions, we chose an OOP index value near the 25th percentile for the plans in our sample (OOP index = 205), which corresponded to a 1-tier $5-$5-$5 / $10-$10-$10 retail / mail-order copayment plan, to ensure that doubling copayments would yield an OOP index value that was within sample (OOP index = 410). Finally, because survival models require t > 0, the outcome variable was transformed by adding one day to all values.


Descriptive Results

Table 1 describes the characteristics of our three study samples, which included 7879, 6450 and 4486 patients with newly diagnosed HTN, CHOL, and DIAB, respectively. Little overlap existed between the three samples; together, the analyses included 15,613 unique patients (=6657 + 5277 + 3679). Within each sample, however, the study conditions were the most frequent comorbid conditions in each others’ sample, among preexisting conditions that contributed additional cardiovascular risk. Osteoarthritis and gastric acid disorder were the most frequent preexisting comorbid conditions not contributing additional cardiovascular risk. The mean length of the observation window after diagnosis was 877 days for HTN (S.D. 540 days), 930 days for CHOL (S.D. 544 days), and 799 days for DIAB (S.D. 533 days). Age was similar across samples; for all conditions, nearly half of patients were between the ages of 65 and 74 (46.3% for HTN, 54.1% for CHOL, 47.5% for DIAB). The samples included more females than males; as age increased, the proportion of men decreased. Most patients used at least 1 other medication in the year prior to the index date (73.9% for HTN, 89.6% for CHOL, 87.1% for DIAB).

Table 1
Characteristics of Persons with Newly Diagnosed Chronic Disease, 1997–2002

Overall, the mean OOP index value at the plan level was 305 (S.D. 118) with an interquartile range of 220 to 370. Three-tier plans were the most prevalent in the sample and included the largest share of each sample’s patients (Table 2). In addition, three-tier plans were, on average, the most generous plans, as measured by the OOP index. This was due to two factors. First, three-tier plans had lower copayments for generic drugs (vs. 1- and 2-tier plans) and preferred brand drugs (vs. 2-tier plans) at retail pharmacies, and lower copayments at mail-order pharmacies across all tiers (vs. 1- and 2-tier plans). Second, mail-order copayments were higher in 1- and 2-tier plans versus 3-tier plans. The 5 coinsurance plans were the least generous plans, and had flat coinsurance rates of 25% (N=2), or 2-tier rates of 20%−45% (N=1) or 35%−60% (N=2).

Table 2
Mean Prescription Drug Benefits by Type of Rx Plan*

Table 3 lists examples of pharmacy benefits and OOP index values for plans in the lower, median, and upper percentiles of the OOP index our sample. Several formulations of plans, including 1-tier, 2-tier and 3-tier plans, yielded OOP index values near those used for our predictions (OOP index=205 and 410). As noted, the OOP index depended upon the magnitude of both retail pharmacy and mail-order cost-sharing arrangements.

Table 3
Mapping the Out-of-Pocket Index and Pharmacy Benefits Design

Figure 1 displays the Kaplan-Meier survival estimates for the number of days until a patient’s first prescription for their newly diagnosed HTN, CHOL, or DIAB. The figure separates survival functions for patients in plans above and below the median OOP index value. For all conditions, the rate of initiation was high in the first several months after diagnosis; subsequently, the rate of initiation slowed. Log-rank tests showed that, for each condition, survival functions for patients in high- and low-OOP index groups were significantly different (p<0.000 HTN, p<0.000 CHOL, p<0.036 DIAB). Thus, in the unadjusted data, higher cost-sharing was associated with delayed initiation of drug therapy. At five years after diagnosis, the percentage of patients remaining untreated with medications in our sample was 21.4% [19.8%−23.1%] for HTN, 36.0% [34.3%−37.8%] for CHOL, and 32.5% [30.1%–34.9%] for DIAB.

Figure 1
Unadjusted Kaplan-Meier Estimates of Time Until First Medication for Patients with Newly Diagnosed Chronic Disease, Above and Below Median Copay Levels 1997–2002*

Multivariate Results

(Note: Figure 1.5 presents the regression results from our six models for reviewers – not to be included in final proofs). After adjusting for covariates, doubling copayments resulted in large, statistically significant differences in predicted time until initiation for all study conditions (Figure 2). The predicted percentage of newly diagnosed patients initiating pharmacotherapy at one and five years after diagnosis was largest for patients with newly diagnosed HTN or CHOL (55.0 vs 40.1% at one year and 81.7% vs 66.3% at five years, p<0.000 for HTN; 40.2% vs 31.1% at one year and 64.3% vs 53.8% at five years, p<0.002 for CHOL; 45.8% vs 40.0% at one year and 69.3% vs 62.9% at five years, p<0.041 for DIAB). The difference in the median number of days until pharmacotherapy that resulted from doubling copayments was substantial for all study conditions (242 vs 774 days for HTN; 766 vs 1382 days for CHOL; 527 vs 813 days for DIAB).

Figure 2
Effect of Doubling Copayments on the Initiation of Drug Therapy for Patients with Newly Diagnosed Chronic Disease*
Table 1.5
Regression Results from Six Models of Time to Initiation of Drug Therapy*

Figure 3 demonstrates that the rate of initiation of drug therapy and the effect of doubling copayments depended upon a patient’s prior history of prescription drug use. Compared to patients with no drug use in the year prior to the index date, patients with any drug use in that period initiated pharmacotherapy earlier and were much less price-sensitive. For example, holding cost-sharing levels constant at the lower of our two predicted levels (OOP index = 205), the percent of patients initiating drug therapy by one year after diagnosis was much larger among patients with a history of prior drug use for all study conditions (60.7% vs. 40.3% for HTN, p< 0.000; 41.9% vs. 21.0% for CHOL, p< 0.000; 48.4% vs. 30.4% for DIAB, p< 0.000).

Figure 3
Effect of Doubling Copayments on the Initiation of Drug Therapy for Patients with Newly Diagnosed Chronic Disease With and Without Prior Drug Use*

Doubling copayments among patients with a history of prior drug use resulted in differences in the rate of initiation that were small in magnitude and statistically significant only for patients with newly diagnosed HTN or CHOL (60.7% vs. 54.4% at one year for HTN, p< 0.021; 42.0% vs. 36.3% at one year for CHOL, p< 0.027; 48.5% vs. 48.0% at one year for DIAB, p< 0.853). By contrast, among patients without a prior history of drug use, the effect of doubling copayments resulted in large, statistically significant differences in the survival function for all study conditions (40.3% vs. 16.6% at one year for HTN, p< 0.000; 21.1% vs. 9.5% at one year for CHOL, p< 0.002; 30.5% vs. 12.9% at one year for DIAB, p< 0.001).

Sensitivity Analyses

We conducted multiple sensitivity analyses to assess the robustness of our results. First, to ensure that “rule-out” diagnoses were not affecting our findings, we tested the model using restrictive inclusion criteria designed to produce samples with more homogenous and severe disease, including samples that required patients to have at least three outpatient physician visits for the disease condition after diagnosis, and requiring the 2nd and 3rd visits be at least 30 days apart. Second, we examined whether the type of drug used prior to initial diagnosis changed the observed effect of prior drug use and its interaction with cost-sharing. Specifically, we separated the effect of prior medications used to treat conditions that contributed additional cardiovascular risk (defined as drugs for HTN, CHOL, DIAB, CAD, CHF, and vascular disease) versus other medications. Third, we examined patients who used a small supply of medications in the prior year – as little as thirty days worth of medications – as well as patients who took only antibiotics in the prior year. Fourth, we estimated models that included controls for physician visits. Fifth, we examined alternative definitions for comorbid conditions. Finally, we excluded the oldest-old (age>80 yrs) and excluded plans requiring coinsurance, the least generous plans in our sample. None of these sensitivity analyses appreciably changed our findings.


Previous work has established that the chronically ill are sensitive to the cost of prescription drugs. Our study looked at one component of utilization: the initiation of drug therapy after diagnosis. We found that increased cost-sharing delays the initiation of medications to treat newly diagnosed chronic disease, suggesting that out-of-pocket costs may prevent patients from initiating medically necessary care.

In addition, we found that the initiation of drug therapy and sensitivity to prices depends on a patient's "experience" with prescription drug use. Relative to those without experience, patients with experience using prescription drugs were less price-sensitive and adopted therapy earlier, suggesting that patients differ in their willingness to initiate prescription drug therapy. In some patients, an initial resistance against treatment may be reduced once experience using prescription drugs is established. We found no threshold effect for the number of prior or concurrent medications at which the results of our models changed. Thus, our data suggest that out-of-pocket costs may prevent patients from initiating treatment – which could negatively impact health outcomes – but the magnitude of this effect strongly depends whether patients have experience used drugs in the past.

Our survival estimates were consistent with epidemiological studies from NHANES and other sources that estimate the proportion of patients who are aware they have a medical condition but remain untreated.3254 In our study, the proportion of newly diagnosed patients who had not initiated anti-hypertensive, anti-cholesterol, or anti-diabetes drug therapy by five years was 21.4%, 36.0%, and 32.5%, respectively. Consistent with our data, a variety of studies indicate that the proportion of patients aware of their hypertension but without drug treatment ranges from 8% – 68%.3239,53 In the Framingham Heart Study, 68.3% of patients with newly diagnosed hypertension had not initiated antihypertensive therapy by four years, including 53.9% of those with Stage II hypertension at baseline,53 and recent estimates range from 8% in a VA population34 to 38–55% in a community population.35

Untreated hypercholesterolemia among those aware of their condition is a well documented and chronic problem. Our estimate of the proportion diagnosed but untreated by five years is at the lower end of most population-based estimates, which range from 25% to 66%.32,36,41,42,46,51

Among diagnosed diabetics, estimates of the proportion without drug treatment range from 8% to 47%.45,50,56 Recent analyses of NHANES yield estimates ranging from 19%–28.6%,32,36,4749 and even 23.2% of diabetics who survived a myocardial infraction or stroke, a group likely to be hyper-vigilant about controlling cardiovascular risk factors, did not use antidiabetic medications.47 Although our estimate of the proportion of new diabetics who remained untreated after five years was slightly higher than NHANES estimates, NHANES subjects carried their diagnosis for two to three times longer than our five-year follow up period,32,57 and the proportion of untreated diabetics increases with age.45,55

There are several limitations to our study. First, our sample may not be generalizable to a younger population. However, Medicare Part D has increased the proportion of elderly retirees who have prescription drug insurance, and CMS has control over the basics of benefits design. Thus, our results may be particularly relevant for federal policy-makers setting standards for Medicare Part D insurance packages. Second, we could not completely control for selection of drug benefits. However, in all but two employers in the sample, employees had no choice of drug benefits, minimizing the possibility that employees selected plans suited to their anticipated needs, and patients in these two employers accounted for less than 2.5% of the sample. Excluding these patients did not change our results. Third, despite controls for comorbidities, disease severity may differ between patients with and without prior drug experience. Although administrative data do contain detailed clinical information contained in medical charts, our sensitivity analyses examining inclusion criteria designed to produce samples with more homogenous and severe disease did not change our findings. One initial treatment option for patients newly diagnosed with less severe disease is to initiate non-pharmaceutical therapy, such as diet modification and exercise. However, there was no a priori reason that disease severity was correlated with benefits generosity, since almost no patients in our study had a choice of drug benefits plans. Further, analysis of the NHANES has shown that patients diagnosed with hypertension without pharmacologic treatment have, for example, disease severe enough to warrant treatment (SBP>140).52

Despite these limitations, our results suggest a novel distinction between groups of patients, some of whom are price-sensitive to prescription drugs and others who are not. Although the majority of patients in our sample did have experience using prescription drugs, the large impact of cost-sharing on those without experience make this population a prime target for interventions to encourage appropriate treatment of chronic disease, particularly diseases that contribute to cardiovascular risk, such as those included in our study. Future research should explore the mechanisms underlying our results, such as the factors that may influence the effect of cost-sharing within specific patient populations, and should examine the health outcomes of varying times to initiation of drug therapy for chronic disease.

Our findings have implications for policy makers designing insurance benefits and for physicians treating patients with chronic disease. First, these results raise concerns about high cost-sharing levels for elderly, insured patients without experience using prescription drugs. Based on our findings, high cost-sharing levels could be a barrier to treatment for this population, and possibly result in poor health outcomes. Physicians should also heed these findings when treating patients with a new diagnosis of hypertension, hypercholesterolemia, or diabetes; those who do have experience with pharmacologic therapy may be much less likely to initiate prescribed treatments and may be very sensitive to cost-sharing levels.

More broadly, these results add to the growing chorus that our reliance on blunt instruments to influence prescription drug utilization, such as formularies and tiered copayments, which are primarily used to manage cost, need to be updated by more sophisticated tools that take into account therapeutic need as well as patients' complex response to insurance benefits.58,59 For example, recent evidence indicates that among people who have initiated medications for chronic disease, patients are less likely to adhere to their regimen if they begin with high copayments when compared to patients that begin with lower copayments that gradually increase.60 This suggests that new users are likely to be more price sensitive than continuing users, and is congruent with our finding that patients with prescription drug experience are less price-sensitive. Lessons such as these need to be incorporated into benefits design to ensure that patients who require medical therapy are not discouraged from initiating treatment.


This research was supported by the Agency for Healthcare Research and Quality (R03 HS013869-01) with additional funding from the California HealthCare Foundation. Data were provided by Ingenix, Inc. Dr. Goldman reports honoraria and consulting income from Amgen, Genentech, and UnitedHealth


RAND is solely responsible for the manuscript's content. Neither the Agency for Healthcare Research and Quality, nor California HealthCare Foundation, had any authority over the design and conduct of the study; the collection, analysis, preparation, and interpretation of the data; and preparation of the manuscript.

Appendix 1: ICD-9-CM Codes Used to Identify Chronic Conditions

Essential hypertension401
Hypercholesterolemia272.0, 272.1, 272.2, 272.4
Diabetes250, excluding [250.1, 250.x1, 250.x3]
Congestive heart failure428
Vascular disease440, 443
Coronary artery disease410, 412, 413
Gastric acid disorder530.1, 530.2, 530.81, 534, 535.5, 535.6,
Mental health disorders293, 294, 295, 296.2, 300.0, 311
Thyroid disorder240, 241, 242, 243, 244, 245, 246
Asthma/COPD491, 492, 493
Allergic Rhinitis477
Inflammatory bowel disease555, 556, 564.1
Chronic sinusitis473
Ulcer531, 532, 533

Appendix 2: Algorithm for Study Sample Eligibility

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Appendix 4: Calculation of Out-of-Pocket Index to Measure Plan Generosity

To capture plan generosity with a single variable, we developed an index that simulated the average annual out-of-pocket expenses that members of a standard sample would have paid had they faced the cost-sharing requirements and restrictions of each plan. To create the standard sample, one hundred people from each plan-year were randomly sampled and their drug claims pooled, creating a “market basket” of drugs. Each drug claim in the market basket was standardized into 30-day supply equivalents. Thus, a 90-day mail-order claim was converted to three 30-day claims. A plan’s average out-of-pocket cost for a 30-day supply of each drug was calculated and assigned to each corresponding 30-day drug claim in the market basket. Total costs were calculated for each individual (person-year), and the average total cost across individuals computed as the plan’s OOP index value.

Formally, if we define D as the universe of drug claims in the market basket, let d be a specific 30-day equivalent drug claim in the market basket, let p be a plan in a given year, let N be the number of persons in the standard sample, and let copaydp denote the average out-of-pocket payment for drug d in plan-year p, the value of the OOP index for each plan-year can be written as:

OOP Indexp=dDcopaydpN

Appendix 5: Additional information on eligibility criteria

We established several rules for including plans and beneficiaries in the study. Plans whose average pharmaceutical and medical utilization were significantly lower than the entire sample’s plan-level averages were excluded to ensure that we had complete utilization data for our subjects. We also excluded plans with enrollment of less than 1,000 members, to ensure ample variation in individual characteristics within plans. We examined only primary beneficiaries, and excluded dependents, to maximize the likelihood that our plans would be the main source of prescription drug insurance coverage for the study population. To ensure that a patient’s course of drug therapy could be followed longitudinally, only plans with at least two consecutive years of data were considered, and only patients who were enrolled continuously in each year were eligible.


Dr. Solomon had full access to all of the data in the study and takes responsibility for the integrity of the data and the accuracy of the data analysis.

Study concept and design: Solomon, Goldman, Joyce, Escarce

Acquisition of data: Solomon, Goldman, Joyce

Analysis and interpretation of data: Solomon, Goldman, Joyce, Escarce

Drafting of the manuscript: Solomon

Critical revision of the manuscript for important intellectual content: Solomon, Goldman, Joyce, Escarce

Statistical expertise: Solomon, Goldman, Joyce, Escarce

Obtained funding: Solomon, Goldman, Escarce

Administrative, technical, or material support: Solomon, Goldman, Joyce, Escarce

Supervision: Solomon, Goldman, Joyce, Escarce


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57. Author’s own estimates
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