Using time-series intervention analysis to understand U.S. Medicaid expenditures on antidepressant agents

Article Outline

• Abstract
• Introduction
• Methods
  • Data description
  • Data analytic procedures
  • Time-series interventions
• Results
  • Zoloft®
  • Prozac®
  • Wellbutrin®
  • Paxil®
  • Effexor®
  • Amitriptyline
  • Aggregate antidepressant expenditure time series
  • Model performance
• Discussion
• Limitations and future research
• Conclusions
• Acknowledgments
• Appendix. 
  • Overview to autoregressive integrated moving average model identification and estimation
  • General autoregressive integrated moving average model formulation
  • General autoregressive integrated moving average model formulation, including interventions
  • Description of the Koyck sequential method
  • Measurement of model performance
• References
• Copyright

Abstract 

Background

Medicaid programs' spending on antidepressants increased from $159 million in 1991 to $2 billion in 2005. The National Institute for Health Care Management attributed this expenditure growth to increases in drug utilization, entry of newer higher-priced antidepressants, and greater prescription drug insurance coverage. Rising enrollment in Medicaid has also contributed to this expenditure growth.

Objectives

This research examines the impact of specific events, including branded-drug and generic entry, a black box warning, direct-to-consumer advertising (DTCA), and new indication approval, on Medicaid spending on antidepressants.

Methods

Using quarterly expenditure data for 1991-2005 from the national Medicaid pharmacy claims database maintained by the Centers for Medicare and Medicaid Services, a time-series autoregressive integrated moving average (ARIMA) intervention analysis was performed on 6 specific antidepressant drugs and on overall antidepressant spending. Twenty-nine potentially relevant interventions and their dates of occurrence were identified from the literature. Each was tested for an impact on the time series. Forecasts from the models were compared with a holdout sample of actual expenditure data.

Results

Interventions with significant impacts on Medicaid expenditures included the patent expiration of Prozac^® (P<0.01) and the entry of generic paroxetine producers (P=0.04), which reduced expenditures on Prozac^® and Paxil^®, respectively, and the 1997 increase in DTCA (P=0.05), which increased spending on Wellbutrin^®. Except for Paxil^®, the ARIMA models had low prediction errors.

Conclusions

Generic entry at the aggregate level did not lead to a reduction in overall expenditures (P>0.05), implying that the expanding market for antidepressants overwhelmed the effect of generic competition.

Keywords: Time-series intervention analysis, Medicaid expenditures, Antidepressant drugs, Forecasting, Generic entry, Direct-to-consumer advertising

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Introduction 

Antidepressant drugs were the most prescribed medications in the United States throughout the 1990s,¹, ² and depression is among the most widespread mental health disorders, affecting an approximate 8-10% of the U.S. population.³ A total of $9.6 billion was spent on antidepressants in the United States in 2008, approximately 3.3% of total U.S. prescription sales.⁴ The prevalence and severity of depression is even higher in the Medicaid population.⁵ According to a review of the 2003 data from the National Comorbidity Survey and the National Household Survey on Drug Abuse, mental and substance abuse disorders are almost twice as common in Medicaid populations as in privately insured populations, and estimates of depression prevalence of Medicaid enrollees range from 18% to 20%.³ These findings are consistent with the fact that the Medicaid population is more exposed to several influential risk factors, such as poverty, unemployment, psychosocial stress factors, and chronic physical illnesses.⁶, ⁷ U.S. Medicaid programs' spending on antidepressants increased from $159 million in 1991 to $2.26 billion in 2003.⁸ In 2005, Medicaid's spending had dropped back to $2 billion, which represented about 5% of its total pharmaceutical budget.⁹ The 1158% increase in spending from 1991 through 2005 far outpaced the 46% increase in the consumer price index over the same time period.¹⁰

Antidepressants can be grouped into 3 classes: selective serotonin reuptake inhibitors (SSRIs); tricyclic antidepressants (TCAs); and other antidepressants, a category that includes monoamine oxidase inhibitors, heterocyclic agents, and several other antidepressants. Table 1 provides a complete list of antidepressants with brand name, generic name, and branded drug approval date. The TCAs, the first-generation antidepressants, are all now produced by generic manufacturers. SSRIs represent substantial progress in the treatment of depression, relative to TCAs, in terms of tolerability, dosing, and safety.¹¹, ¹² The other antidepressant class is comprised of older drugs approved in the 1960s along with some of the most recent antidepressant drugs, such as Cymbalta^®, which was approved by the Food and Drug Administration (FDA) in 2004.

Table 1. Antidepressant drugs approved in the United States

aSource: Food and Drug Administration: http://www.accessdata.fda.gov/scripts/cder/drugsatfda/.

This study focuses on 6 antidepressants: Prozac^®, Zoloft^®, Wellbutrin^®, Paxil^®, Effexor^®, and amitriptyline. Among all antidepressant drugs, the 5 branded drugs represented the largest expenditure market shares over the study time period, whereas expenditures for amitriptyline were greater than those for any other TCA. All 6 drugs have a long enough time series for the methodology used in this study to be successfully applied. Looking at Medicaid's total expenditure from the 1990s up to the mid-2000s, SSRIs represented the largest part of the spending (about 65%), with Prozac^®, Zoloft^®, and Paxil^® each having an annual expenditure of more than $100 million for several years in a row starting in the early 2000s.⁸ The second largest source of expenditure is for the class of other antidepressants (about 30%), among which 2 drugs account for most of the spending, with Effexor^® reaching $100 million and Wellbutrin^® more than $50 million during the time period of interest. TCAs account for a much smaller share of total expenditure (less than 5%) because of the combined effect of low utilization and availability of generic drugs. Among all TCAs, amitriptyline has much higher utilization figures than any other drug in this class, and represents about half of the total class expenditures.⁸

During the study period, there were substantial changes in the market for antidepressant drugs. First, new drug entry into the antidepressant drug class was substantial during the 1990s. Table 1 shows that 5 new SSRIS followed Prozac^® into the market during the study period. Several antidepressants in the other antidepressant class, including Effexor^®, Serzone^®, and Remeron^®, were introduced during the 1990s as well. With each entry, some downward pressure on Medicaid spending might be expected, in the form of lower prices and/or reduced utilization, on drugs already in the market.

Second, generic entry affected several of the antidepressants studied. The patent for Prozac^® expired in 2001. By 2003, most prescriptions for fluoxetine that were being reimbursed by Medicaid were for generic fluoxetine rather than Prozac^®. The average percentage of generic use in 2003, across all state Medicaid programs, was 92.1%.¹³ Wellbutrin^® and Paxil^® were protected by their patents during the study period. However, in the case of both these drugs, generic producers filed an application with the FDA seeking to enter the market with a generic version before expiration of the branded drug product's patents; that is, abbreviated new drug applications were submitted containing a paragraph IV certification.¹⁴ Indeed, there were a few generic producers of bupropion, beginning in the fourth quarter of 1999, and of paroxetine, beginning in the third quarter of 2003.¹³ Generic entry for all 3 drugs (fluoxetine, bupropion, and paroxetine) is expected to put downward pressure on Medicaid's spending on the branded medications (Prozac^®, Wellbutrin^®, and Paxil^®, respectively).

A third potential effect on Medicaid spending occurred at the end of the study period. Evidence emerged that antidepressants were associated with adolescent suicide, leading eventually to a black box warning for all drugs in this class. In March 2004, the FDA issued a statement that paroxetine (Paxil^®) should not be used in children or adolescents with major depressive disorders.¹⁵ There was also an FDA Public Health Advisory on March 22, 2004, concerning venlafaxine (Effexor^®) and sertraline (Zoloft^®), warning of increased risk of worsening depression or suicidal tendency in adults and children.¹⁵ Finally, there was the FDA requirement on October 15, 2004, that all manufacturers of all antidepressants include a black box warning on their antidepressant packages mentioning potential harmful side effects.¹⁵ These danger warnings are expected to reduce Medicaid spending.

Of course, not all changes in the market for antidepressants over the last 2 decades were expected to slow down the rise in expenditures. A significant change in the rules governing pharmaceutical marketing occurred in 1997, making it much easier to use direct-to-consumer advertising (DTCA). The FDA released in 1997 (and finalized in 1999) a guidance entitled “Consumer-Directed Broadcast Advertisements,” outlining an acceptable approach to fulfill the adequate provision requirement (giving information on side effects, contraindications, and effectiveness) from earlier legislation by referring to 4 sources from which consumers could obtain further information: their physician, a toll-free number, a print advertisement, and a Web site.¹⁶

In addition, advances in the understanding of the role of serotonin have led to the use of SSRIs in the treatment of other indications, such as alcoholism, anorexia nervosa, borderline personality disorder, bulimia nervosa, hot flashes, obsessive-compulsive disorder, panic disorder, posttraumatic-stress disorder, premature ejaculation, premenstrual syndrome, and social anxiety disorder.¹⁷, ¹⁸ Drugs in the other antidepressants class are used in the treatment of additional indications as well. In July 2000, Effexor^® was approved for the treatment of general anxiety disorder.¹⁵ Approvals for new indications are expected to increase the utilization of antidepressants and, hence, Medicaid spending on these medications. This research examines the impact of specific events, including branded-drug and generic entry, a black box warning, DTCA, and new indication approval on Medicaid spending on antidepressants.

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Methods 

Data description 

The Centers for Medicare and Medicaid Services (CMS) maintain a national Medicaid pharmacy claims database, which keeps track of the number of outpatient prescriptions and reimbursement amounts by national drug code (NDC) for all drugs reimbursed by state Medicaid programs, for 49 states (all except Arizona) and the District of Columbia. The first 5 digits of the NDC identify the manufacturer. Different states follow different reimbursement practices for ingredients and dispensing costs and may or may not require patient co-pays. A national summary, which comprises an aggregation of the state-level data, is also available and is used for this analysis. This data set is organized by year and provides quarterly data for every year starting in 1991.¹⁹ These national files are subject to occasional coding error, which was corrected if possible. The data are not corrected for federal or state manufacturer rebates and, hence, overestimate the actual amount spent by Medicaid for outpatient pharmaceuticals.⁹ From this data set, total reimbursement amounts for the 6 antidepressants under study were extracted. Although for Prozac^®, Zoloft^®, Wellbutrin^®, Paxil^®, and Effexor^®, data were collected only for the branded product (even after generic entry), all data were collected for amitriptyline; that is, reimbursements were added across all the producers of this TCA. Table 2 provides the Medicaid-spending data for the last 5 years of the study for each of the drugs. An aggregate expenditure time series for all antidepressants was created by summing across spending on all antidepressant drugs, including all those listed in Table 1, not just the 6 drugs studied individually. These aggregate spending data, for the last 5 years of the study, are provided in Table 2 as well.

Table 2. Medicaid reimbursements for antidepressants: 2001-2005

aData for the 1990s are available from the CMS Web site or from the authors on request.

bAll values are expressed in 1000s of current dollars.

cAggregate spending on all drugs (in 1000s of current dollars) listed in Table 1.

At the time the data collection was performed in spring 2005, the quarterly data on the CMS Web site were available from the first quarter of 1991 through the second quarter of 2004. The time-series intervention analysis was performed on these data. As the data for the following quarters became available, they were downloaded in the summer of 2007; data from the third quarter of 2004 to the fourth quarter of 2005 were retained as a holdout sample to compare the model forecasts with actual data to assess model performance.

Data analytic procedures 

The modeling approach is based on the autoregressive integrated moving average (ARIMA) model, developed by Box and Jenkins (1976) for univariate time series.²⁰ The idea behind their methodology is to find the best-possible weighted average for a single time series, with weights on past observations (autoregressive terms) and also on past error terms (moving average terms).

To understand the role, if any, of important events on Medicaid spending, various interventions were introduced into the time-series ARIMA model, following Pankratz (1991).²¹ Intervention models selected for the interventions described a little later were estimated; coefficients for the intervention parameters were tested for statistical significance. Significant interventions pertaining to a particular antidepressant were then combined into a single model that contained multiple interventions along with standard ARIMA parameters. Throughout the study, statistical significance required a P value less than or equal to 0.05.

The performance of the models was assessed by comparing the forecasted expenditures with a holdout sample of actual expenditure data for the forecasted quarters (from 2004 quarter 3 through 2005 quarter 4). The magnitude of error between the forecasted values and the actual values was measured using root mean squared error, mean absolute error, and mean absolute percentage error.

In an Appendix to this article, the steps involved in building and estimating an ARIMA model are described. Notation is presented for the basic ARIMA model without intervention. The notation is then augmented to include 1 or several interventions. A description of the sequential Koyck method, used to determine the specific type of intervention, is provided. Formulae for the model performance measures are also presented.

Time-series interventions 

From a study of the literature on antidepressant drugs, events that could affect Medicaid spending on each antidepressant studied were identified. The events fall into 5 categories. The first type of event is patent expiration. As the patent for a prescription drug expires, drug manufacturers can enter the market for this drug by producing a generic version of the drug, hence reducing the demand for the branded drug. The second type of event is the entry of a new branded drug. As new branded drugs become available in the market, one expects the demand curves for existing drugs to shift down and for Medicaid expenditure (price or utilization or both) to fall for existing drugs.²² The third type of event that could affect Medicaid's expenditure is FDA approval of an existing drug for a new indication. In this case, the new indication approval would broaden the population that could potentially benefit from the drug and increase the demand for that particular drug, which could translate into an increase in Medicaid's expenditure. Another event that occurred during the study period is the issuing of an FDA guidance on broadcast advertising in 1997, making it easier for drug companies to advertise on television. The last type of event is the identification of an adverse event that might result in an FDA warning. This type of event would put downward pressure on the demand for the corresponding drug, reduce the number of prescriptions written for the drug, and reduce Medicaid's expenditures. A total of 29 events are examined using intervention analysis. A list of the interventions is found in Table 3. The interventions modeled spanned the 5 types of interventions discussed in this section. Several potentially important events occurred too close to the end of the time period to be modeled effectively. They are examined further in the Discussion section. All statistical analyses were performed using the SAS/ETS software package for Windows (version 9.1; SAS Institute Inc., Cary, NC) and the ARIMA procedure.

Table 3. Interventions tested in the current study

aThe new indication approvals are based on data from Clinical Pharmacology15

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Results 

Zoloft^® 

Following the methodology described earlier, the best-fitting ARIMA model is an autoregressive model with lag 1 and lag 3 on the first difference of the time series. None of the 3 tested interventions (the entry of Paxil^® in December 1992, the entry of Celexa^® in July 1998, or the posttraumatic-stress disorder indication approval for Zoloft^® in November 2001) has a statistically significant coefficient. Figure 1 shows the fitted model and the 95% prediction band around the estimates, along with the actual data. The equation for the best-fitting model is also given in Fig. 1.

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• Fig. 1 

  Predicted and actual Medicaid expenditures on Zoloft^®: 1991-2007.

Prozac^® 

For Prozac^®, the best-fitting model is a moving average model with lag 7 on the first difference of the time series plus a pulse-and-decay term for the single significant intervention—patent expiration in the third quarter of 2001. Its effect was negative and statistically significant (P<0.01). Figure 2 shows the actual data along with the estimates, model equation, forecasts, and prediction band. The model shows a $33.97 million drop in sales in the first quarter of patent expiration. In the next quarter (the fourth quarter of 2001), a $24.12 million drop is shown, whereas the first quarter of 2002 brings a $17.12 million drop. In this way, the effect of patent expiration dampens out over time. No statistically significant response was found for the entry of Zoloft^® in December 1991, the entry of Paxil^® in December 1992, or the entry of Celexa^® in July 1998. Moreover, there was no statistically significant effect of the FDA's approval of Prozac^® for bulimia nervosa in November 1996.

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• Fig. 2 

  Predicted and actual Medicaid expenditures on Prozac^®: 1991-2007.

Wellbutrin^® 

For Wellbutrin^®, the methodology suggested an autoregressive model with lag 2 and lag 3 on the first difference of the log-transformed series, with 1 significant (and positive) pulse-and-decay intervention associated with the rise in DTCA beginning in 1997 (P=0.05). The estimated model in Fig. 3 implies that the first quarter under the new advertising regime brought a 19% increase in Medicaid spending on Wellbutrin^® (approximately $1.2 million); the next quarter had a 15% increase; and so forth as the effect dampened over time. None of the other interventions, including the entry of Zoloft^®, Paxil^®, Effexor^®, or Celexa^®, or the launch of Wellbutrin XL^® in August 2003, tested for Wellbutrin^®, proved to have a statistically significant effect nor did the entry of generic bupropion producers in the third quarter of 1999 lead to a significant effect on the expenditure time series.

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• Fig. 3 

  Predicted and actual Medicaid expenditures on Wellbutrin^®: 1991-2007.

Paxil^® 

As for Prozac^®, the intervention methodology picks up the (negative) effect of generic entry on Medicaid expenditures on Paxil^® (P=0.04). The best-fitting model is one with an autoregressive lag 4 term and a moving average lag 3 term on the first difference of the time series, with a step-and-no-decay intervention. Figure 4 shows the actual time series, model equation, estimates, forecasts, and the 95% prediction band. In the first quarter of entry, and in each subsequent quarter, the model implies a $4.52 million drop in Medicaid spending relative to the previous quarter. Neither the entry of Effexor^® nor the entry of Celexa^® was shown to have a significant effect on the time series. The approval of Paxil^® for the treatment of seasonal affective disorder in May 1999 had no statistically significant effect either.

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• Fig. 4 

  Predicted and actual Medicaid expenditures on Paxil^®: 1991-2007.

Effexor^® 

The best model for Effexor^® is one with an autoregressive lag 1 term and a moving average lag 1 term on the first difference of the log-transformed series. Four interventions were considered in the case of this antidepressant: the entry of Serzone^® in December 1994, the entry of Remeron^® in June 1996, the entry of Celexa^® in July 1998, and the approval of Effexor^® for generalized anxiety disorder in July 2000. None of the 4 interventions tested had a statistically significant coefficient in the model. Figure 5 displays the results for this antidepressant.

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• Fig. 5 

  Predicted and actual Medicaid expenditures on Effexor^®: 1991-2007.

Amitriptyline 

For this generic TCA, the ARIMA methodology leads to a conclusion that the series is best described as a random walk on the first difference of the log-transformed series. The 2 interventions tested (the entry of Zoloft^® and the entry of Paxil^®) have nonsignificant effects. Figure 6 displays the results.

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• Fig. 6 

  Predicted and actual Medicaid expenditures on amitriptyline: 1991-2007.

Aggregate antidepressant expenditure time series 

For this time series, additional quarters from the holdout sample were included to allow testing for the effect of the black box-warning intervention. The best candidate model is an autoregressive model with lag 3 on the first difference of the time series. Four interventions were investigated in the case of the aggregate time series. Although the generic-entry events (those for Prozac^® and Paxil^®) have nonsignificant effects in explaining overall antidepressant expenditures, the increase in DTCA and the black box warning, both have statistically significant impacts on expenditures—a positive (P=0.03) and negative (P=0.01) effect, respectively. Both interventions are pulses with decay. Figure 7 displays the results. The estimated model implies that the new advertising regime led to an $18.12 million increase in Medicaid spending in the third quarter of 1997; a $17.21 million increase in the fourth quarter; a $16.35 million increase in the first quarter of 1998; and so forth. By the third quarter of 2004, the effect of the advertising change had essentially dampened out. In that quarter, however, the black box warning brought a $35.16 million drop in Medicaid spending, followed by an interesting oscillation pattern in subsequent quarters. A $21.10 million rise in spending is shown for the fourth quarter of 2004; a fall of $12.66 million is implied for the first quarter of 2005; a rise of $7.59 million for the second quarter of 2005; and so forth.

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• Fig. 7 

  Predicted and actual Medicaid expenditures on antidepressants: 1991-2009.

Model performance 

For 5 of the drugs, the actual reimbursements during the holdout period fell within the forecast confidence bands. For Paxil^®, however, this was not the case. Values for the 3 measures of forecast error, as shown in Table 4, are consistent with what the confidence bands show. For 5 of the medications, there is no indication that the forecasts are unreasonable. The errors for Paxil^® are quite large, however, indicating that even the best model for Paxil^® did not predict the actual 2005 Medicaid reimbursements very well.

Table 4. Performance of the forecasting models

aFormulae are given in the Appendix. For each of the measures, a smaller value indicates better model performance. However, there is no absolute standard to which these values can be compared nor can the values be compared straightforwardly across different time series.

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Discussion 

Although Medicaid spending on antidepressants has risen exponentially over time, and reasonable explanations have been given in the literature for this phenomenal rise, it is not clear why the forces of competition seem to play virtually no role in even creating a dent in the upward climb. To delve into this issue, individual-drug time series were examined using state-of-the-art time-series intervention analysis to determine the effects of increased competition on Medicaid expenditure trends.

It is interesting that the best-fitting models for the antidepressants studied differ so much from each other. It is not the case that spending trends can be captured by the same ARIMA structure. The implication is that aggregation is risky. Each drug follows its own spending pattern. On the other hand, it seems as though each pattern can be captured by some ARIMA structure. Out of all the interventions tested on individual antidepressant time series, only 3 had statistically significant effects. Two of these interventions are generic entries for Prozac^® and Paxil^®, and these 2 interventions have a downward impact on Medicaid's expenditure on those 2 drugs. This finding corroborates the fact that generic drugs are usually less expensive than branded drugs.²³ Moreover, as more and more generic manufacturers enter the market, after patent expiration, generic drug prices continue to fall.²⁴ Although both patent expirations have a downward effect on Medicaid's expenditure, the nature of these 2 interventions is distinct, thus, influencing the time series differently. In the case of Prozac^®, there is a pulse with decay. The patent expiration has a temporary effect on the series. The decay means that the event has an effect for several periods and decreases in strength as time elapses. One explanation for this result is that after several time periods, the patent expiration does not have an effect anymore, because the generic version has been in the market for a long enough time that its presence does not affect the expenditure on Prozac^® per se. In the case of Paxil^®, generic entry seems to have a permanent effect as the best-fitting model has a step with no decay. The absence of decay indicates a permanent intervention that takes its full effect at the time of the event. The reason for this finding could be that generic entry of paroxetine occurs relatively close to the end of the time period under study. If entry had occurred earlier or if the time series had been modeled over a later time period, a pulse with decay might have been found. It is interesting to note that the third case of generic entry tested, the one corresponding to Wellbutrin^®, does not turn out to have a significant effect. Owing partly to the introduction of Wellbutrin XL^®, patients were slow to switch to generic bupropion. In fact, there were so few bupropion manufacturers supplying to Medicaid even at the end of the study period that the price of the generic drug remained relatively high.¹³

Another intervention with a significant impact on Wellbutrin^® expenditures is the jump in DTCA, as it became easier for pharmaceutical companies in 1997 following an FDA guidance on broadcast advertising. The intervention in this case is a pulse with decay. Broadcast advertising of Wellbutrin^® proved to be particularly successful; Glaxo's “no sexual side effects” slogan was undoubtedly well received by patients suffering from depression. In an article in Advertising Age, dated October 25, 1999, David Goetzl wrote, “In a nod to how much Prozac and Viagra have moved the marketing dialogue, Glaxo Wellcome today launches an ad campaign that links two once-taboo subjects: depression and sex.”²⁵ GlaxoSmithKline spent $108.1 million on Wellbutrin^® advertising in 2005, earning Wellbutrin^® rank 170 on Advertising Age's list of the top 200 megabrands.²⁶

None of the 5 FDA approvals for the use of antidepressants for additional indications besides depression turn out to be significant events. It is possible that the FDA approvals concern relatively few patients and, thus, generate only marginal increases in expenditure. Another explanation is that the off-label use of antidepressant drugs is so common that the actual approvals are little more than formalities.²⁷ It is also worth noting that none of the new branded drug entries constituted an intervention with an effect that was statistically significant. Competition from other branded manufacturers has had no effect on any of the expenditure series. Entry of new drugs seems to be expanding the market for antidepressants; if there is switching of patients between antidepressants, this movement is eclipsed by the overall market expansion. This result is consistent with those from a number of earlier descriptive studies using the Medicaid data.⁸, ²⁸, ²⁹, ³⁰, ³¹

For the aggregate antidepressant expenditure time series, the effects of generic entry for both Prozac^® and Paxil^® are nonsignificant. This is noteworthy, because these 2 events do have significant effects on individual drug spending. Even when the competitive effect of generic manufacturers brings down spending on individual antidepressants, the effect is not picked up in the expenditure series for the entire antidepressant class. Again, the expanding market for antidepressants overwhelms the effect of competition.

On the other hand, the effect of relaxed broadcast advertising is significant for the aggregate time series—as it was for Wellbutrin^®. Furthermore, the nature of the intervention is similar, a pulse with decay, and the estimated intervention coefficients indicate that the decay has a long-lasting effect. The significance of this intervention at the aggregate level needs some interpretation. It could either be the case that the increase in expenditure for Wellbutrin^® was so large that it was also reflected in the aggregate expenditure series, or it could be the case that the DTCA, which was made easier in 1997, spurred an increase in advertising for other individual antidepressants, thus causing an increase in Medicaid's expenditure. Prior research into the effects of DTCA on antidepressant spending indicates that, after a period of high class-level spending, there is an increase in the number of people diagnosed with depression who initiate medication therapy.³² Yet, it seems as though the choice of specific antidepressant is influenced much more by physician detailing than consumer advertising.³³ This research illustrates both the role of the physician as decision maker regarding specific medication and the pharmaceutical companies' abilities to expand the antidepressant market overall.

The black box warning is significant at the aggregate level. The downward pressure on expenditure could have been expected and is confirmed by the study. According to a recent article in this journal, the black box warning was effective in reducing both the adult and pediatric usages of antidepressants, although the former was unintended.³⁴ Indeed, 1 study found that SSRI prescriptions for youths decreased by approximately 22% in the United States after the FDA warnings were issued. This decrease was accompanied by a 14% increase in youth suicide rates between 2003 and 2004, the largest year-to-year change in suicide rates in this population during the 2.5 decades of data collection.³⁵ The temporary nature of this intervention (pulse with decay) is also informative, as it suggests that, after some time, the effect of the black box warning was mitigated. The difficulties in modeling the time series for Paxil^® and the significance of the black box warning at the aggregate level led to testing for the significance of this event on Paxil^®, as well, extending the drug's time series through 2005. Indeed, it turns out that this intervention is significant for Paxil^®. The black box warning was clearly responsible for the actual large drop in expenditures faced by Paxil^®, not captured earlier.

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Limitations and future research 

This research relies on claims data and, as such, is subject to the same limitations that characterize all such studies. In particular, these data do not indicate why (even if) antidepressants are being taken but only indicate that they are prescribed. Changes in spending cannot be decomposed into changes in the number of patients, the number of prescriptions filled per user, and changes in the composition of drugs used. Moreover, the time-series interventions unavoidably affected all spending on antidepressants; there was no comparison group of patients unaffected by the events, and hence, the changes in spending patterns cannot be definitively attributed to the interventions; it is possible that events correlated with the interventions were responsible for the observed changes in spending.

The data are for the U.S. Medicaid population only; hence, the results may not be applicable to other public and private insurance payers. Furthermore, only 1 therapeutic class of drugs and a single outcome (reimbursement for pharmaceuticals) have been studied. More could be learned by extending the analysis to other drug classes and to other outcomes, such as drug utilization.

Although time-series intervention analysis is appropriate for the objectives pursued in this study, it is worth noting that ARIMA modeling is also used specifically for forecasting future values of a time series. If forecasting were the primary objective, however, there are other types of approaches that might reduce forecast error relative to the approach taken here. For example, dynamic Bayesian models allow model parameters to adapt to changing circumstances over time; they do not remain constant as they do in ARIMA models and are updated following sequential use of Bayes' theorem. Although Pole et al (1994) suggest a simplifying methodology for implementing the Bayesian method, it is still quite labor intensive.³⁶

After 2005, the antidepressant drug market has continued to be dynamic, suggesting caution with respect to the predictions past the end of the study period. For example, the implementation of Medicare Part D in 2006 shifted some of the public spending on antidepressants from Medicaid to Medicare. Hence, it is expected that the Medicaid prescription-claims data would show a drop in spending as dual eligibles are switched to Medicare coverage.

The purpose of this study was not to decompose the rise in Medicaid expenditures into the rise in utilization and the rise in price per prescription. However, the national Medicaid prescription-claims data do support such research, and the results of 1 such study have already been published in this journal.⁸ The total number of prescriptions for antidepressants rose dramatically from 1991 to 1995. There was a shift in prescribing to the SSRIs and other antidepressants and away from the TCAs during this time period, although TCAs (all produced by generic manufacturers) still accounted for more than 10% of the prescriptions in 2005. Because drugs in the former 2 categories were significantly more expensive than the TCAs, this shift clearly contributed to the rise in Medicaid expenditures on antidepressants. Although payment per prescription did not seem to be nearly as important in explaining the rise in expenditures, some of the individual drugs did increase in price over time.⁸

Especially at the end of the study period, state Medicaid programs have been responding to rising pharmaceutical expenditures through a variety of cost-containment strategies. Some states have adopted prior authorization programs for more expensive drugs. Others have preferred drug lists or formularies. Almost all either encourage or require generic drugs if available, although minimal co-pays do not discourage branded-drug use. Some states have physician education programs. Furthermore, the federal government has mandated that states conduct drug utilization reviews, and requires rebates from pharmaceutical manufacturers.²⁴ The policies have been implemented at different times in different states, making it hard to identify a specific intervention date for a time-series analysis. Nevertheless, these policies may serve to reduce Medicaid spending in the future.

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Conclusions 

In this present study, the time-series analysis showed that events with significant impacts on Medicaid expenditures included the patent expiration of Prozac^® (P<0.01) and the entry of generic paroxetine producers (P=0.04), which reduced expenditures on Prozac^® and Paxil^®, respectively, and the 1997 increase in DTCA (P=0.05), which increased spending on Wellbutrin^®.

In this article, a univariate time-series analysis of Medicaid's expenditure on 6 particular antidepressant drugs and on total Medicaid antidepressant spending was undertaken. Time-series methodology was used to identify and select ARIMA models for each drug individually, and time-series intervention analysis was used to test for the impact, or lack thereof, of outside events on the expenditure time series. The final ARIMA models, along with the significant interventions, capture the behavior of the series well, according to comparisons with a holdout sample. Among the various outside events considered as interventions on the individual drugs, only 3 turned out to have significant effects. Generic entry was significant in 2 out of 3 cases, both with a downward effect, a pulse with decay in 1 case and a step with no decay in the other case. The only other type of event that had an impact on an individual time series was the increase in DTCA, with an upward effect. All other events, FDA approvals and new branded drug entry, did not have statistically significant effects. On the aggregate expenditure time series, generic entry of individual drugs did not have an impact, whereas relaxed DTCA regulations beginning in 1997 did have an upward effect. The black box warning had a significant downward effect on aggregate spending.

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Acknowledgments 

A previous version of this article was presented as a contributed poster at the 12th Annual Meeting of the International Society for Pharmacoeconomics and Outcomes Research, Arlington, VA, May 2007. The authors are very appreciative of the comments and suggestions of 3 anonymous referees. They caused the authors to focus carefully on the substantive contributions of the research rather than on the methodology itself. The authors would like to thank Merve Bayram for her help with the figures.

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Appendix. 

Overview to autoregressive integrated moving average model identification and estimation 

Before identification of the best-fitting model, the time series must be transformed, through first or second differencing or through a logarithmic transformation, if necessary, into one that is stationary, which means that the mean, the variance, and the autocorrelation function (ACF) of the process are constant through time. There are several ways to check for nonstationarity, including plotting the data to inspect visually for shifts in the series, observing a slow decay of the ACF, or performing the Dickey-Fuller test for stationarity.³⁷ Then, to identify the best-fitting autoregressive integrated moving average (ARIMA) model, the ACF and a partial autocorrelation function (PACF) for the stationary series are compared with the ACF and PACF of theoretical models. The extended sample ACF and minimum information criterion techniques are used to identify possible models to estimate.³⁷ Although these 2 techniques do not always return the same answer, they tend to agree fairly well.

In the estimation phase, the data are used to estimate the coefficients of the chosen model, which, in this case, may have at least 1 intervention parameter. In estimating the coefficients, the maximum likelihood method is used. Once the parameters are estimated, the validity of the estimated model is checked. To do so, a Chi-square test is performed on the aggregated residuals from the estimated model to verify that the residuals are random noise, which confirms that the estimated model indeed captures all the information the series could provide.³⁷ It is possible that more than 1 reasonable model will be identified. In this case, the Akaike Information Criterion and the Schwartz Bayesian Criterion are relied on to select the final model.³⁷

Interventions can be classified into 2 major types: pulse and step interventions.²¹, ³⁸ Pulse interventions refer to temporary effects and induce an effect on the time series for only a limited number of time periods, whereas step interventions lead to a permanent change in the time series under study.³⁹ Because, for this study, the form (step or pulse) of the intervention cannot be specified a priori, an empirical approach, which is referred to as the sequential Koyck method, is used to identify the intervention.²¹

General autoregressive integrated moving average model formulation 

The general ARIMA model is usually denoted as ARIMA(p,i,q), where p is the order of the autoregressive part (AR), q is the order of the moving average part (MA), and i, which stands for “integrated,” is the order of differencing applied to the series. In mathematical terms, the general ARIMA models can be expressed as follows (SAS online documentation):

withwhere

t is the time index

i is the order of the differencing

Y_t is the series of interest (the response series)

μ is the mean term

N_t is the disturbance series: a random error that is modeled using the ARIMA framework

B is the back shift operator (B×Y_t=Y_t−1)

φ(B) is the autoregressive operator and can be written as a polynomial in the back shift operator:

θ(B) is the moving average operator and can be written as a polynomial in the back shift operator:

a_t is random noise or white noise (zero-mean and constant-variance disturbance)

General autoregressive integrated moving average model formulation, including interventions 

Within the ARIMA framework, an intervention is modeled using an additional term, expressed as X_t. This term is a binary, nonstochastic variable, and in the case of a pulse intervention, it takes the value of 1 only for the time period when the intervention occurs. In the case of a step intervention, it takes a value of 1 starting in the time period when the intervention occurs as well as in all time periods thereafter. The nature of the coefficients modifying the intervention term affects the shape of the intervention modeled and the duration of the effect (single-period vs multi-period). With a single intervention term, the general ARIMA model (Equation 1) becomes

where

is a polynomial in the back shift operator:

is a polynomial in the back shift operator:

A model with multiple interventions can be built by simply adding the interventions specified individually.³⁶ This model can be expressed as

where is the jth intervention.

Description of the Koyck sequential method 

The sequential method is described in Pankratz (1991).²¹ The analysis starts by trying to fit a Koyck model for a pulse intervention. The transfer function for the Koyck model is of the form

where X_t is a pulse function. This model has only 2 parameters and is more specific than the general model mentioned in Equation 3, but the sequential method is an effective way to capture most types of interventions, because this model can represent most of the shapes a series could take as a result of an intervention. Once an attempt is made to fit this model, there are 3 possible outcomes:

(1)The coefficient estimate is not significant , and the conclusion is that the intervention is a pulse with no decay;

(2)The coefficient estimate is significant with , and the conclusion is that the intervention is a pulse with decay; or

(3)The coefficient estimate is significant with , and the conclusion is that the intervention is a step rather than a pulse.

In this third case, a Koyck model for a step intervention is fitted, which is of the same form as in the case of a pulse, except that X_t is now a step function. A conclusion on the nature of the intervention is based on 1 of the 3 following possible outcomes:

The earlier discussion considers the possible scenarios based on the significance and value of the estimate. It assumes that the intervention exists and that the coefficient estimate is significant. In this study, it is the significance of the coefficient estimate that is used to determine whether the intervention is significant. If the coefficient estimate is nonsignificant, then the conclusion is that the intervention has no significant effect. In other words, the hypothesis that the event has no impact on the times series cannot be rejected. On the contrary, if the coefficient estimate is significant, then the conclusion is that the intervention has a significant effect and that the event indeed had an impact on the time series. In this case, intervention analysis is pursued further according to the sequential method described earlier.

Measurement of model performance 

The root mean squared error (RMSE) is obtained by taking the square root of the average across all observations of the squared difference between the forecasted value and the observed value . That is,

where is the actual value at time t, is the forecasted value at time t, and n is the number of observations for which a forecast is computed.

The mean absolute error (MAE) is obtained by taking the average across all observations of the absolute value of the difference between the forecasted value and the observed value. In other words,

Finally, the mean absolute percentage error (MAPE) takes the original values of the series into account by dividing the absolute value of the difference by the observed value. Hence,

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