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Original Article

Quantifying Delay in Access to New Medical Treatment

An Application of Risk Advancement Period Methodology

Krobot, Karl J.*; Miller, William C.*†; Kaufman, Jay S.*; Christensen, Dale B.; Preisser, John S.§; Ibrahim, Michel A.*

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doi: 10.1097/
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Sumatriptan was the first of a new class of drugs introduced in the 1990s that provided effective treatment for many migraine sufferers. In Germany, this drug was more accessible to patients with private health insurance, than to patients treated in the statutory health insurance system.1 The type of health insurance determined whether patients would participate in this innovation and, to a negligible extent, how intensively they would do so.2

Information to support decision-making processes in health care is typically presented to an especially broad group of recipients, including patients, physicians, health insurance funds, and healthcare policymakers. The format of such information is important.3,4 Apparently, multiple formats help avoid bias of human information processing4,5 and are preferred by healthcare decision-makers to demonstrate that decisions are made in the best interests of the individual or the country.4,6

One useful measure of risk communication is the risk advancement period.7 To obtain the risk advancement period, the relative risk is converted into an expression of how much earlier an event is estimated to occur if the patient is exposed to the risk factor in question. For example, a risk advancement period of 11 years can be used by a physician to explain to a 50-year-old smoker that he faces the same risk of suffering a heart attack as a 61-year-old nonsmoker.

In a first attempt to apply this measure to health services and health systems research, we set out to convey the provision of health care in the statutory and private health insurance systems in Germany. Specifically, we addressed the question of how long the typical patient with migraine in the statutory health insurance system lagged behind patients in the private system in their access to an effective new treatment of migraine headaches. We then discuss the general prospects and limitations of using risk advancement periods in healthcare epidemiology.



We used Germany's largest primary care database (MediPlus, IMS Health), which represents just under 1% of primary health care. The database is generally representative of primary care in Germany as judged by the geographic distribution, age, and sex of physicians, and the ratio of primary care internists and general practitioners. The diagnoses specified by the physicians are centrally coded by IMS HEALTH according to International Classification of Diseases, 10th Revision (ICD-10) criteria. Key data include demographic information on the practice-, physician-, and patient- and diagnosis-linked prescription data such as the drug and substance name, dosage form, package size, and strength of the prescription. All data collection processes are identical across insurance plans. Specialist treatment and self-treatment are not recorded in MediPlus.

Study Population

In Germany, sumatriptan was introduced for the treatment of migraine attacks with or without aura in early 1993. Data were available on an open cohort of 18- to 65-year-old migraine patients who were prescribed a product for migraine attack therapy as per ICD-10 G43 in the period from January 1, 1994, to November 30, 1994. Patients were able to enter and leave the cohort at any time. The patient age range was in keeping with sumatriptan's recommended use. The data had been selected primarily for another study question for which an 11-month time range was sufficient to sample patients reasonably representative of all migraine severities.

Exposure and Outcome

Migraine prescription visits were regarded as “exposed” if the patient had private health care insurance and “nonexposed” if the patient was covered under the statutory health insurance. Migraine prescription visits were characterized as resulting in a prescription for an oral or subcutaneous sumatriptan preparation or not.


Multiplicative risk (log-linear) models were used to estimate risk ratios of sumatriptan prescriptions by insurance status and period, ie, calendar time. In the models, the prescription visit was the unit of analysis and the panel practice was treated as a cluster. We used generalized estimating equations (GEE) with exchangeable correlation structure to account for the possibility of correlation of prescriptions within practices8; in other words, we used a common working correlation for pairs of prescriptions within a practice regardless of whether or not the pair corresponded to the same patient. We used the semi-robust Huber-White sandwich estimator of variance to give valid inference even if the assumed correlation structure was misspecified. The target of inference was the population-averaged effect.

The final model included health insurance, health insurance by linear patient age interaction, patient age, squared patient age, patient sex, physician age, physician sex, primary care specialist group (general practitioner or internist), community size (>100,000 inhabitants or less), and the period term.

The patients’ and physicians’ ages (on January 1, 1994) were centered at the mean of the cohorts and divided by 10 so as to express all ages in decades and regression coefficients in terms of change per decade of age. The period term (January 1–November 30, 1994) was linear on a multiplicative scale and modeled as a continuous variable divided by 365 so as to express regression coefficients in terms of change per year of calendar time. The period term thus took into account the effect of aging and era on the probability of receiving sumatriptan compared with standard nonserotoninergic migraine attack therapy. The higher probability of receiving sumatriptan in middle age, when migraine is clinically most severe, was modeled by a second-order term. Sample size did not allow separate analyses to be run for oral versus subcutaneous sumatriptan preparations.

Lag in Access to Health Benefits From Innovation

The major difference of the current approach to previous applications of the risk advancement period concept is that here the time variable considered in the denominator was calendar time rather than age.

Given coefficient b1 for insurance status, coefficient b2 for period, and coefficient b3 for patient age Ai on January 1, 1994, the formula for the risk advancement period in the presence of an interaction between insurance status and patient age was7:

The asymptotic variance was:

Similar to the population preventive fraction, the population lag period was derived as the product of the risk advancement period and the prevalence of statutory health insurance patients in the entire target population. Sensitivity analyses included the number of defined daily sumatriptan doses prescribed when sumatriptan was given to patients in the 2 systems. The analyses were performed using Stata 7.0 (Stata Corp., College Station, TX).


We analyzed 22,618 prescriptions for the treatment of migraine that were issued to 8676 patients from 371 primary care practices on 20,785 days. Table 1 shows the most important characteristics differentiated according to insurance status. Overall, the 2 cohorts were very similar.

Characteristics of the Migraine Patient Cohort According to Type of Health Insurance

Table 2 shows the risk advancement period for the “risk” of receiving sumatriptan. For the patient age-mix of our sample, the regression coefficients for health insurance status and period were estimated as 0.7521 and 0.5407, with variance estimates of 0.0241 and 0.0150, respectively. The covariance between the 2 estimates was estimated as 0.0019. Application of the formula yielded a point estimate for the risk advancement period associated with private health insurance of 1.4 years with a 95% confidence interval (CI) of 0.6 to 2.2 years.

Lag of Access to Health Benefits From Oral and Subcutaneous Sumatriptan for the Treatment of Migraine in the Private versus Statutory Health Insurance Systems

The risk advancement period increased by 0.6 years for every 10 years of patient age, with a confidence interval of -0.1 to 1.3 years. Figure 1 illustrates this in detail. If the patient was older than 40 years, the data were consistent with the hypothesis that sumatriptan was received later in the statutory health insurance system than in the private insurance system. The typical 40-year-old patient with statutory health insurance waited exactly 1 year, and the typical 57-year-old patient exactly 2 years, according to the point estimates. Other than patient age, there were no statistically or clinically relevant interactions. Confounding by measured variables played a negligible role.

Lag (with 95% CI) in access to health benefits from oral and subcutaneous sumatriptan for the treatment of migraine by general practitioners for men and women in the statutory health insurance system according to age.

Most patients (94%) had statutory health insurance coverage. Accordingly, in the period under review, migraine treatment in primary care in Germany was delayed by 1.3 years in terms of access to sumatriptan. Sensitivity analyses revealed that when sumatriptan was given, it was prescribed in 1.1-fold quantities to private patients compared with patients with statutory health insurance as measured by the number of World Health Organization-defined sumatriptan daily doses. Thus, taking into account both the probability of receiving sumatriptan and the amount of sumatriptan prescribed, there was an estimated lag in patients with statutory health insurance of 1.6 years and 1.5 years for the nation as a whole. These estimates may be interpreted as the time the typical patient with migraine in the statutory health insurance system and in Germany, respectively, lagged behind in access to sumatriptan for relief of acute migraine headache (Table 3).

Lag in Access to Sumatriptan for the Treatment of Migraine in the German Statutory Health Insurance System and in the Country as a Whole


We used Brenner's risk advancement period method to assess access to sumatriptan, a drug innovation for migraine, among patients with statutory health insurance and those with private health insurance in Germany. This risk advancement period of 1.5 years is a calendar time difference. It implies that the typical patient with migraine headache in the statutory health insurance system lagged an estimated 1.5 years behind an otherwise identical patient in the private system in terms of having the same access to sumatriptan. Because we used a population-averaged model, our results reflect the characteristics of the 2 health systems rather than individual experiences. A random-effects approach addressing individual experiences would have been irrelevant in view of the fact that most patients are legally not entitled to switch insurance coverage.

The risk advancement period has been used primarily in etiologic cardiovascular epidemiology. For example, smoking, hypertension, and hyperlipidemia advance the clock for fatal and nonfatal myocardial infarctions by 7 to 12 years in middle-aged men.9–11 In healthcare epidemiology, defining risk advancement periods with respect to calendar time may also be useful. First, this method describes what the disparity in access to sumatriptan meant for a typical migraine patient in the statutory health insurance system: a “waiting time” of approximately 1.5 years, ie, an equivalent of approximately 50 lost healthy work and leisure hours, assuming 24 defined daily doses of sumatriptan per sumatriptan user-person-year2 and 1.5 productive hours gained per sumatriptan daily dose.12–14 Second, the population lag period makes it clear to what extent the primary care treatment of migraine in the whole country lagged behind; this was also on the order of 1.5 years. In addition, risk advancement periods can show that patients with statutory health insurance fall farther behind privately insured patients as a new drug asymptotically approaches its adoption limit in therapeutic practice. In other words, as long as a new therapy is still making its entrance into health care, access to its therapeutic benefits is merely delayed for those in the statutory health insurance system. After the new treatment has reached its steady-state, some in the statutory health insurance system will never have access to its benefits.

It may be tempting to avoid elaborate, individual-level analyses and to derive the denominator (period term) from aggregated drug statistics. This approach is invalid. First of all, the risk advancement period is based on probabilities, namely, how likely it was to receive sumatriptan as opposed to nontriptans for acute migraine care on a given day for a given patient consulting a given practice. With aggregate data, the magnitude, the functional form, and the variance of the denominator term would not be deducible. Moreover, ecologic fallacies may occur if a particular new intervention is used in parallel or sequentially for multiple indications and populations. In view of the properties of the risk advancement period concept, such approaches should be rejected from the outset.

Applications of the risk advancement period must be carefully considered. Risk advancement periods in healthcare research are typically valid locally, ie, restricted to periods for which the “risk” of innovation over time (denominator) continually increases. New scientific findings, new treatment recommendations, health policy changes, or new drug entries can easily break this functional form. Further potential for error occurs if the position and nature of the healthcare hurdle is unknown. In our example, it was already known that the type of health insurance determined whether patients would participate in novel migraine treatment at all and, to a negligible extent, how intensively they would do so.2 Only in this way were we able to conclude that patients in the statutory health insurance system may have come into contact with sumatriptan 1.5 years later than patients with private health insurance. Otherwise, part of the lag period would have been taken up by the establishment of equitability of use among sumatriptan users. It would be even more fallacious to conclude that the situation would be remedied merely by introducing new treatments quickly. Although the “waiting time” for the individual would decrease, the number of “waiters” would increase accordingly. Thus, to ensure equitable health care for populations, the disparity by insurance type must be reduced.

In etiologic research, a major issue in the derivation of risk advancement periods concerns the validity of potential extrapolation beyond the range of values of the time variable. Similarly, in our study, there was some extrapolation beyond the timespan covered in the database; the time variable encompassed 11 months, whereas the estimates of the risk advancement period exceeded 1 year. However, this point may be less critical in healthcare research, because the focus is often placed on the question “what if the situation persists,” ie, on an assessment of the instantaneous situation.

We have discussed some general aspects and limitations of applying the risk advancement period concept to health services research, taking the German health system as a concrete example. Our conclusions cannot be generalized beyond the era of the second year of the statutory health insurance drug macrobudget and the introduction of sumatriptan. However, for this phase, our study permits the conclusion that the statutory health insurance system and the country as a whole lagged behind by approximately 1.5 years in terms of access to sumatriptan. We believe this approach can be a useful addition to the methods used in healthcare epidemiology.


1.Krobot KJ, Miller WC, Kaufman JS, et al. The disparity in access to new medication by type of health insurance: lessons from Germany. Med Care. In press.
2.Krobot KJ. Study II—characterization of the health-insurance-related hurdle to a pharmaceutical innovation in the second through the fourth year of the German Healthcare Structure Reform Act. In: Health Insurance-Related Access to Pharmaceutical Innovation in Germany. Methods and Applications [dissertation]. Chapel Hill, NC: University of North Carolina; 2001:84–109.
3.Edwards A, Elwyn G. How should effectiveness of risk communication to aid patients’ decisions be judged? A review of the literature. Med Decis Making. 1999;19:428–434.
4.Edwards A, Elwyn G, Covey J, et al R. Presenting risk information–a review of the effects of ’framing’ and other manipulations on patient outcomes. J Health Commun. 2001;6:61–82.
5.Klein WM. Objective standards are not enough: affective, self-evaluative, and behavioral responses to social comparison information. J Pers Soc Psychol. 1997;72:763–774.
6.Hux JE, Naylor CD. Communicating the benefits of chronic preventive therapy: does the format of efficacy data determine patients’ acceptance of treatment? Med Decis Making. 1995;15:152–157.
7.Brenner H, Gefeller O, Greenland S. Risk and rate advancement periods as measures of exposure impact on the occurrence of chronic diseases. Epidemiology. 1993;4:229–236.
8.Zeger SL, Liang KY, Albert PS. Models for longitudinal data: a generalized estimating equation approach. Biometrics. 1988;44:1049–1060.
9.Liese AD, Hense HW, Brenner H, et al. Assessing the impact of classical risk factors on myocardial infarction by rate advancement periods. Am J Epidemiol. 2000;152:884–888.
10.Keil U, Liese AD, Hense HW, et al. Classical risk factors and their impact on incident non-fatal and fatal myocardial infarction and all-cause mortality in southern Germany. Results from the MONICA Augsburg cohort study 1984–1992. Monitoring Trends and Determinants in Cardiovascular Diseases. Eur Heart J. 1998;19:1197–1207.
11.Ford ES, DeStefano F. Risk factors for mortality from all causes and from coronary heart disease among persons with diabetes. Findings from the National Health and Nutrition Examination Survey I Epidemiologic Follow-up Study. Am J Epidemiol. 1991;133:1220–1230.
12.Gross MLP, Dowson AJ, Deavy L, et al. Impact of oral sumatriptan 50 mg on work productivity and quality of life in migraineurs. British Journal of Medical Economics. 1996;10:231–246.
13.Cortelli P, Dahlof C, Bouchard J, et al. A multinational investigation of the impact of subcutaneous sumatriptan. III: Workplace productivity and non-workplace activity. Pharmacoeconomics. 1997;11(suppl 1):35–42.
14.Mushet GR, Miller D, Clements B, et al. Impact of sumatriptan on workplace productivity, nonwork activities, and health-related quality of life among hospital employees with migraine. Headache. 1996;36:137–143.
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