Adherence to long-term prophylactic treatment: microeconomic analysis of patients behavior and the impact of financial incentives

Transcription

1 Mann et al. Health Eonomis Review (219) 9:5 RESEARCH Adherene to long-term prophylati treatment: miroeonomi analysis of patients behavior and the impat of finanial inentives Klaus Mann 1*, Mihael Möker 2 and Joahim Grosser 2 Open Aess Abstrat The effetiveness of medial therapies depends ruially on patients adherene. To gain deeper insight into the behavioral mehanisms underlying adherene, we present a miroeonomi model of the deision-making proess of an individual who is initially in an asymptomati linial state and to whom a prophylati therapy is offered with the aim of preventing damage to health in the future. The fous of modeling is the optimization of an intertemporal utility funtion, where time-inonsistent preferenes are inorporated by a quasi-hyperboli disount funtion. The preditions of the model onur with experiene in linial pratie. Moreover, the introdution of time-inonsisteny reveals a self-ontrol problem of the individuals where resolutions made before may be given up at a later time. A more pronouned present bias leads to a derease in adherene and, onsequently, the gain in soietal welfare resulting from the prophylati therapy delines. Developing effetive strategies to improve adherene is a major hallenge in health are. As an example, the impat of finanial inentives offered to the patients on adherene and welfare are investigated on the basis of the model. The results are onsistent with empirial findings. The approah presented ontributes to a better understanding of the omplex interation of the relevant determinants for adherene, partiularly regarding the individuals self-ontrol problem. Keywords: Prophylati treatment, Adherene, Time-inonsistent preferenes, Self-ontrol, Finanial inentives Introdution The effetiveness of medial therapies depends ruially on the patient s adherene, i.e. the extent to whih the patient follows the reommendations of a health are provider, suh as taking mediation, following a diet or exeuting lifestyle hanges. In this regard, many studies have dislosed onsiderable defiienies in linial pratie assoiated with negative onsequenes for the patients. This partiularly holds for the long-term treatment of hroni diseases, with an average estimated adherene rate of 5% [1 4]. Moreover, poor adherene has a onsiderable eonomi impat with inreased health are osts for the soiety [5]. Although many different interventions have been desribed to improve * Correspondene: klaus.mann@unimedizin-mainz.de 1 Department of Psyhiatry and Psyhotherapy, University Medial Center Mainz, D Mainz, Germany Full list of author information is available at the end of the artile adherene for hroni health onditions, these approahes are usually omplex and have not proven to be very effetive [6 9]. Beause adherene has turned out to be a omplex behavior in the ontext of multiple influening fators, a profound understanding of this phenomenon is an indispensable requirement for the development of more effetive interventions. Adherene an be taken as a deision proess regarding the demand for health are goods and, thus, in priniple, an be analyzed by applying methods from miroeonomis. This approah might yield deeper insight into the behavioral mehanisms underlying adherene [1 17]. In this paper, we present a model of the deision-making proess of an individual who is initially in an asymptomati stage of disease and to whom a therapy is offered with the aim of preventing damage to health in the future. On the one hand, this inludes very prevalent The Author(s). 219 Open Aess This artile is distributed under the terms of the Creative Commons Attribution 4. International Liense ( whih permits unrestrited use, distribution, and reprodution in any medium, provided you give appropriate redit to the original author(s) and the soure, provide a link to the Creative Commons liense, and indiate if hanges were made.

2 Mann et al. Health Eonomis Review (219) 9:5 Page 2 of 1 hroni pathologial onditions suh as hypertension, hyperlipidemia, and diabetes mellitus, whih may go unnotied for a long time, but may lead to serious health onsequenes if no antihypertensive or antidiabeti treatment is arried out in the long run. In addition, this also inludes numerous disorders, whih are haraterized by the absene of symptoms after a temporary episode of illness, but with a high risk of reurrene. Suh somati illnesses are for example the status post-stroke or post-myoardial infartion, whih need adequate prophylati treatment measures after remission to prevent the reourrene of ishemi events in the future. The majority of mental disorders also has a high propensity for relapses, e.g. depression and shizophrenia, and, therefore, need adequate maintenane therapy after remission to prevent future episodes of illness. The extent of the adherene problem and its onsequenes is illustrated in more detail by the example of hypertension. Although a number of effetive antihypertensive drugs are available, numerous studies have shown that a onsiderable proportion of patients do not take their mediation as presribed, whereby the reported adherene rates vary between studies due to differenes in the definition and measurement of adherene and the populations studied. Reent reviews and meta-analyses revealed that 45% [18] and 31% [19], respetively, of hypertensive patients were non-adherent to mediation. Another meta-analysis regarding drugs that prevent ardiovasular diseases inluding several antihypertensive drugs revealed a summary estimate for adherene of 5% in primary prevention and 66% in seondary prevention after a myoardial infartion [2]. There is a large data base demonstrating that lowering blood pressure leads to a redution of the risk for subsequent adverse outomes, for meta-analyses see [21 25]. Beside the negative onsequenes for the affeted persons, non-adherene also leads to signifiant eonomi burden for the health are system [26 28]. A model analysis on the basis of epidemiologial and eonomi data from five European ountries ould demonstrate that inreasing the adherene rate to antihypertensive mediation to 7% would lead to a signifiant redution of health are osts [29]. The ore element of the deision-making proess is the weighting of the various onsequenes of the pending therapy. The benefits of a prophylati treatment an only be expeted in the future, whereas the osts to be borne by the individual in terms of expenditures of time and money, undesired side effets and emotional distress our immediately. Against this bakground, the fous of modeling is the optimization of an intertemporal utility funtion, whih onsiders the individual s intertemporal preferenes and disounting of future onsequenes. While many patients initially onsent to the intended therapy, in the long run they often terminate the therapy early ontrary to the former agreement. Due to this disrepany between initial plans and later behavior, non-adherene proves itself as an expression of time-inonsistent behavior. Therefore, to inorporate this deviation from time-onsisteny, we modify the established disounted utility model traditionally applied for the analysis of intertemporal hoie in eonomis by replaing exponential disounting with a quasi-hyperboli disount funtion [3]. Apart from that, individuals are regarded as rationally behaving subjets who aim at maximizing their intertemporal utility using all available information. The remainder of the paper is strutured as follows. First, the individual s behavior is modeled. If time-inonsisteny is allowed in the form of a present bias, then non-adherene appears as an understandable phenomenon from the patient s viewpoint. Seond, the onsequenes of adherene on the individual and soietal welfare are analyzed. Third, to give an example of how worsening of adherene due to time-inonsisteny ould be ounterated by hanging the framework of health are delivery, the impat of finanial inentives offered to patients on adherene and individual and soietal welfare are investigated. Finally, we disuss the model against both linial and psyhologial bakgrounds, show the limitations and point out further extensions and appliations of the model. Modeling of individual behavior We set up a simple model based on three time periods where only two health states, healthy (h h )or sik (h s ), are onsidered (Fig. 1). The term healthy refers to a linial ondition that is asymptomati but that requires long-term therapy to prevent the ourrene of symptoms, i.e. transition to the sik state. At t =, the individual is in a healthy state (h h ) and enters into a treatment ontrat. In the following period t = 1, the individual is assumed to be still healthy (h h ), and he deides either to take the therapy as reommended (adherene) or to refuse it (non-adherene). The health state in period t = 2 depends on his behavior in the preeding period. If the individual had undergone the therapy, then the probability to stay further in a healthy state is p A, and the probability to fall ill is 1 p A. Otherwise, in the ase of non-adherene, the probability to remain healthy is redued to p NA < p A and the probability of illness 1 p NA is inreased. The deision outome in period t = 1 is partiularly determined by the osts to be borne by the individual due to treatment. We assume that treatment is free of harge so that in the ase of adherene only non-monetary osts our, whereas in the ase of non-adherene no osts arise (all monetary osts are borne by the soiety).

3 Mann et al. Health Eonomis Review (219) 9:5 Page 3 of 1 Fig. 1 Model of a prophylati treatment. The model is based on three time periods t =, 1, 2 with health states h h, h s and onstant transition probabilities p A, p NA for adherene and non-adherene, respetively. Beause the medial onept of adherene implies aeptane of the treatment ontrat [1], the onsequenes of rejetion of the ontrat are not shown in detail. (Under the assumptions made, the path after rejetion is idential to the path after aeptane followed by non-adherene) The non-monetary osts, e.g. in the form of expenditures of time, undesired side-effets and emotional distress, show a large diversity in value among individuals. Aording to the approah taken by DellaVigna and Malmendier [31] who have analyzed the ontrat design of a profit-maximizing firm if onsumers have time-inonsistent preferenes, these osts are modeled as a random variable with distribution F() and density funtion f(), whereby the individual learns his ost type in period t = after having aepted the treatment ontrat. The instantaneous expeted utility u t experiened by the individual in periods t = 1, 2 results from the evaluation of the health state by the individual in the respetive periods: u 1 = u(h h ), u A 2 ¼ p A uðh hþþð1 p A Þ uðh s Þ for adherene and u NA 2 ¼ p NA uðh h Þþð1 p NA Þ uðh s Þ for non-adherene, respetively. The intertemporal utility at a given time is alulated as the sum of the disounted instantaneous utilities in sueeding periods. Various approahes have been developed for formal desription of intertemporal preferenes [3]. The traditional disounted utility model proposed by Samuelson [32] is haraterized by exponential disounting resulting in time-onsistent behavior, i.e. the deision outome does not depend on when the deision is made. However, empirial studies have revealed various deviations of real deision-making behavior from the preditions of this model. In partiular, in many ases, hyperboli disounting an be observed with dereasing disount rates over time [3, 33 36]. As a onsequene, regarding deisions to be made in the distant future, the individual behaves patiently pursuing his long-term goals, whereas when the time of making the deision is approahing, an inreasing onflit arises between the long-term plans and urrent temptations. The ause of this time-inonsisteny is a relatively high preferene for the present with a stronger weighting of immediately ourring onsequenes ompared with onsequenes in the distant future. Based on these fats, we inorporate time-inonsistent preferenes by a quasi-hyperboli disounting funtion. In addition to standard exponential disounting by a fator δ, the present period gets the weight 1 and all sueeding periods are weighted by the onstant fator < β 1. Aordingly, the intertemporal utility funtion at a given time t is U t ¼ u t þ β P T 1 k¼1 δk u tþk, where T periods are onsidered [3]. This approah goes bak to Phelps and Pollak [37] and has been benefiially applied to various fields of deision making haraterized by dynami inonsisteny [31, 38 41]. In the following, the deision-making proess in period t = 1 is analyzed from two different perspetives ( t = and t = 1). From the perspetive of period t =, when the individual has entered the treatment ontrat, the intertemporal utility U for adherene and non-adherene, respetively, is given by

4 Mann et al. Health Eonomis Review (219) 9:5 Page 4 of 1 U A ¼ βδ þ βδ u ð h hþ þ βδ 2 ½p A uh ð h Þþð1 p A Þ uðh s Þ ¼ βδ uðh h Þþβδ 2 ½p NA uh ð h Þþð1 p NA Þ uðh s Þ U NA The individual would deide at t = 1 in favor of adherene if the intertemporal utility in the ase of adherene turns out to be larger than or equal to the ase of non-adherene: U A UNA. Thus, the individual would like to be adherent at t =1if δ Δp Δu where the abbreviations Δu=u(h h ) u(h s )andδp = p A p NA are used. Regarding the whole population of all individuals who have entered into the treatment ontrat, the probability of adherene from the perspetive of t =is Z δ Δp Δu Fðδ Δp ΔuÞ ¼ fðþd Beside the distribution of osts, adherene depends on three parameters: adherene is higher with more effetive therapy (expressed by Δp), larger differene Δu between the evaluation of the healthy and sik states by the individual and less exponential disounting of future onsequenes. However, the individual s atual behavior in period t = 1 is determined by his evaluation of the onsequenes at this time. From the perspetive of period t = 1, when the individual deides whether he undergoes or delines the therapy, the intertemporal utility U 1 for adherene and non-adherene, respetively, is given by U A 1 ¼ þ uh ð h U NA Þþβδ ½p A uh ð h Þþð1 p A Þ uðh s 1 ¼ uh ð h Þþβδ ½p NA uh ð h Þþð1 p NA Þ uðh s Þ From this, as a riterion for adherene we have βδ Δp Δu and the probability of adherene is Z βδ Δp Δu Fðβδ Δp ΔuÞ ¼ fðþd For time-onsistent preferenes with β = 1, the deision outome in period t = 1 is idential to that in the preeding period t =, i.e. the individual keeps to his earlier resolve. In ontrast, in the ase of time-inonsistent preferenes with β < 1, the probability of adherent behavior in period t = 1 has dereased ompared with the evaluation in period t =. Under the assumption that F() is a stritly positive monotoni funtion, we have F(βδ Δp Δu)<F(δ Δp Δu). This is an expression for a self-ontrol problem of the individual. Due to hanged preferenes, the plan that had originally Þ been onsidered to be optimal for future behavior is no longer optimal from the perspetive of the later deision point of time. That is why the resolution made in the period before is given up at a later time. The less β is, the more the atual behavior deviates from the desirable in the long-term optimal behavior, i.e. the more severe is the self-ontrol problem of the individual. Welfare analysis To assess the impat of adherene on the soiety, we define the joint welfare funtion W = W I + W S, where W I is the welfare of a representative individual from the affeted population and W S is the monetary welfare omponent of the soiety resulting from treatment osts. Eah summand of the welfare funtion is defined as the expeted net utility from the perspetive of period t =1, i.e. the benefit after aepting the treatment ontrat less the remaining benefit in the ase that the ontrat had been rejeted (in the ase of rejetion, the individual s benefit is U NA 1, see Fig. 1). The welfare of an individual is (with expetation operator E) W I ¼ Fðβδ Δp ΔuÞ E U A 1 UNA ¼ Fðβδ Δp Δu ¼ Z βδ Δp Δu Þ E A ½ þβδ Δp Δu 1 fðþd þ Fðβδ Δp ΔuÞ βδ Δp Δu where the expeted osts in the ase of adherene, E A [], are alulated in the interval [, βδ Δp Δu], yielding E A ½ ¼1=Fðβδ Δp ΔuÞ R βδ Δp Δu fðþd. Thefirsttermintheequationaboveisnegativeand represents the osts to be borne by the individual. The seond positive term onstitutes the individual s benefitfromthetherapytobeexpetedinthefuture. For further statements, the distribution of must be speified. Supposing a uniform distribution of osts in the interval [, max ] with f()=1/ max and F()=/ max, the individual s welfare an be written as W I ¼ 1 þ max Z min ð βδ Δp Δu;max Þ d min ð βδ Δp Δu; maxþ βδ Δp Δu max 8 >< ðβδ Δp ΔuÞ 2 when βδ Δp Δu < max ¼ 2 max >: max 2 þ βδ Δp Δu when βδ Δp Δu max Of partiular importane is the individual s self-ontrol, whih is represented by the parameter β in the model. For δ Δp Δu < max, i.e. adherene from the perspetive of period t = is not omplete in the

5 Mann et al. Health Eonomis Review (219) 9:5 Page 5 of 1 population, with falling β, the expeted gain in welfare shows a quadrati derease from a maximum of (δ Δp Δu) 2 /2 max for β = 1 to for β =. The smaller β is, the less is adherene and the more the welfare gain deviates from the optimum in the ase of full self-ontrol. The monetary welfare of the soiety is determined by the expenses due to the prophylati therapy in period t =1, C A and C NA in the ase of adherene and non-adherene, respetively, where C NA < C A is assumed, as well as by the follow-up osts C F inurred by individuals falling ill in period t = 2, ontaining both medial osts and indiret osts due to produtivity loss. Considering the soiety s osts in the ase of ontrat rejetion (1 p NA ) δ C F, the monetary soietal welfare is W S ¼ Fðβδ Δp ΔuÞ ½C A þ ð1 p A Þ δ C F ð1 Fðβδ Δp ΔuÞÞ ½C NA þ ð1 p NA Þ δ C F þð1 p NA Þ δ C F ¼ Fðβδ Δp ΔuÞ C A ð1 Fðβδ Δp ΔuÞÞ C NA þ Fðβδ Δp ΔuÞ Δp δ C F where the soiety s disounting fator is assumed to be the same as for the individual. The first two summands reflet the prophylati treatment osts for adherent and non-adherent individuals, respetively, in period t = 1, and the third term represents the savings on follow-up osts inurred by individuals not falling ill in period t = 2 due to prophylati treatment. There are opposite effets with respet to adherene. With falling β, the treatment osts in period t = 1 derease (assuming C A > C NA ), whereas the burden on soiety due to ases of illness in period t = 2 inreases. The net effet is determined by the relationship between the expenses in period t = 1 and the follow-up osts in period t = 2. Under the assumption that the follow-up osts in ases of illness in period t = 2 are high ompared with the treatment osts in period t =1, W S is positive beause ases of illness an be prevented by prophylati therapy and a derease of β leads to a deline of W S. This an be seen from the partial derivative W S / β = f(βδ Δp Δu) δ Δp Δu (C A C NA Δp δ C F ), whih is positive if the follow-up osts in period t = 2 are suffiiently high ompared to the treatment osts in period t = 1 and the density funtion f(βδ Δp Δu) isgreater than (referring to the above analysis, assuming a uniform distribution of osts, this is the ase if adherene is not omplete). Under the assumptions made, both the individual s welfare and monetary soietal welfare are positive. However, the gain in welfare is restrited by individuals self-ontrol problem. The less β is, the less is the inrease of welfare aused by the hane of prophylati treatment. Against this bakground, the searh for measures to redue the self-ontrol problem and, thus, to improve adherene is not only worthwhile from the individuals viewpoint but also from the perspetive of soiety. Impat of finanial inentives on adherene and welfare Starting from the model presented above, we now assume that adherent patients are rewarded with a monetary bonus in the amount of b >. However, as the individual s behavior an be observed only to a limited extent, an improper laim for a bonus put in by non-adherent individuals has to be onsidered. If the probability that a bonus abuse will be deteted is p D and under the assumption that moral aspets are no objet, then the intertemporal utility funtions from the perspetive of periods t = and t = 1, respetively, eah for adherene and non-adherene, will take the form U A U NA ¼ βδ ð b Þþβδ u ð h hþ þ βδ 2 ½p A uh ð h Þþð1 p A Þ uðh s Þ ¼ βδ ð1 p D Þ b þ βδ uðh h Þ þ βδ 2 ½p NA uh ð h Þþð1 p NA Þ uðh s Þ U A 1 ¼ ð b U NA Þþuh ð hþþβδ ½p A uh ð h Þþð1 p A 1 ¼ ð1 p D Þ b þ uh ð h Þ þ βδ ½p NA uh ð h Þþð1 p NA Þ uðh s Þ Þ uðh s Aording to the former argument, the riteria for adherene from the perspetive of period t = and t =1, respetively, are δ Δp Δu þ p D b βδ Δp Δu þ p D b and the orresponding probabilities of adherene are Z δ Δp ΔuþpD b Fðδ Δp Δu þ p D bþ ¼ fðþd Z βδ Δp ΔuþpD b Fðβδ Δp Δu þ p D bþ ¼ fðþd Due to df/db = f(βδ Δp Δu + p D b) p D >, the prospet of a bonus leads to an inrease of adherene. The higher the amount of the bonus b and the higher the probability of detetion p D, the higher is the probability of adherent behavior. In the ase of omplete observability of the individuals behavior (p D = 1), the entire amount of the bonus omes to fruition, and adherene will be maximized. For p D =, the bonus will be equally distributed among all individuals, and adherene will remain unhanged. Instead of rewarding adherent behavior, non-adherene ould alternatively be santioned. This an be Þ

6 Mann et al. Health Eonomis Review (219) 9:5 Page 6 of 1 formalized analogously by additional osts in period t = 1 in the event of non-adherene. The result is idential with an inrease of adherene depending on the amount of santion and the probability that non-adherene will be deteted. For welfare analysis, it must be onsidered that if the treatment ontrat is rejeted, no bonus will be paid out, whereas non-adherent individuals will be in reeipt of the bonus at least partially, aompanied by an inrease of their utility in the amount of (1 p D ) b. After aepting the treatment ontrat, the welfare of an individual is W I ¼ Fðβδ Δp Δu þ p D b ¼ Fðβδ Δp Δu þ p D bþ E A þ ð1 p D Þ b ¼ Z βδ Δp ΔuþpD b fðþd Þ E U A 1 UNA 1 þ ð 1 pd Þ b ½ þβδ Δp Δu þ p D b þ Fðβδ Δp Δu þ p D bþ ðβδ Δp Δu þ p D bþ þ ð1 p D Þ b Supposing a uniform distribution of osts in the interval [, max ], aording to the former alulation, the individual s welfare an be represented by W I ¼ >: 8 >< ðβδ Δp Δu þ p D bþ 2 þ ð1 p 2 D Þ b when βδ Δp Δu þ p D b < max max max 2 þ βδ Δp Δu þ b when βδ Δp Δu þ p D b max Finanial inentives lead to an inrease of the individual s welfare ( W I / b > ), resulting diretly from paying out of the bonus and indiretly from a heightened adherene. The monetary welfare of soiety omprises the treatment osts in period t = 1 and the follow-up osts inurred by individuals falling ill in period t = 2, aording to the previous modeling. In addition, soiety makes a payment in terms of the bonus. This is assoiated with further osts, whih inrease with a higher targeted probability of detetion p D. Under the assumption that these additional osts ome to a perentage λ of the bonus b, we have W S ¼ C NA Fðβδ Δp Δu þ p D b Þ ðc A C NA Δp δ C F Þ ½Fðβδ Δp Δu þ p D bþþð1 Fðβδ Δp Δu þ p D bþþ ð1 p D Þ ð1 þ λþ b Due to higher adherene, the bonus leads to an inrease of the net effet of treatment osts and follow-up osts. If the follow-up osts are suffiiently high, then this net effet is positive. However, due to paying out of the bonus and due to the additional osts involved, soiety s welfare diminishes. Total welfare W = W I + W S is given by W ¼ Z βδ Δp ΔuþpD b fðþd þ Fðβδ Δp Δu þ p D bþ βδ Δp Δu C NA Fðβδ Δp Δu þ p D bþ ðc A C NA Δp δ C F Þ ½Fðβδ Δp Δu þ p D bþþð1 Fðβδ Δp Δu þ p D bþþ ð1 p D Þ λb The bonus paid to the individuals is a redistribution on a sale of F(βδ Δp Δu + p D b) b +(1 F(βδ Δp Δu + p D b)) (1 p D ) b within the system, whih does not affet total welfare. However, all other omponents hange beause the probability of adherene inreases and additional osts arise due to paying out the bonus. Supposing a uniform distribution of osts in the interval [, max ] and restriting to the ondition that adherene is not omplete from the perspetive of period t = in the population (βδ Δp Δu + p D b < max ), as well as under the simplifying assumption of omplete observability of the individuals behavior (p D = 1), it follows W ¼ 1 ½ðβδ Δp ΔuÞ 2 2 βδ Δp Δu ðc A C NA Δp δ C F Þ 2 max 2 ðc A C NA Δp δ C F þ βδ Δp Δu λþ b ð1 þ 2 λþ b 2 C NA Assuming that the follow-up osts C F are high ompared with the prophylati treatment osts, and provided that the additional osts aused by managing the bonus payment are not too high (λ <(δ Δp C F (C A C NA ))/(βδ Δp Δu)), total welfare inreases due to the bonus, aording to a onave paraboli ourse. Then, the optimal amount of the bonus leading to maximum welfare results from the first-order ondition W/ b = : b ¼ δ Δp C F ðc A C NA Þ βδ Δp Δu λ 1 þ 2 λ In several health systems, patients have to make out-of-poket o-payments when they demand health are servies; thus, the bonus ould be realized in the form of a redution of this o-payment. By slight modifiation of the model presented above, the onsequenes of o-payment an be analyzed analogously. In addition to the osts, the o-payment has to be onsidered in period t = 1 for all adherent and partly also for non-adherent patients, whih is equivalent to a negative bonus. Implementation of o-payment leads to a derease of adherene and individual welfare. Regarding soietal welfare, the opposite effets beome obvious. The o-payment, less the ost of administration, benefits the soiety, whereas the gain in soietal welfare as a result from treatment is redued beause of the worse outome due to diminished adherene.

7 Mann et al. Health Eonomis Review (219) 9:5 Page 7 of 1 Disussion We have presented a miroeonomi model of the adherene behavior of an individual, who is in an asymptomati stage of disease and to whom a therapy is offered to prevent damage to health in the future. The model predits that adherene is higher when impairments due to the therapy are less, the treatment in respet of preventing illness in the future is more effetive and the resulting benefit when the individual remains healthy ompared to illness is greater. These results onur with experiene in linial pratie. Analyzing deision behavior from different temporal perspetives, the individual s self-ontrol problem ould be identified as a further deisive determinant of adherene, whih an partiularly serve as an explanation for early disontinuation of the therapy. The present bias, represented by the parameter β < 1, impliates time-inonsistent preferenes so that the atual deision omes into onflit with the plans made formerly. The smaller β is, the larger is the deviation of the atual behavior from the desired long-term optimal behavior, i.e. the more adherene is redued in the further ourse of treatment with regard to the original intent. Thus, this approah represents an extension of the appliation of hyperboli disounting to the formal desription of self-ontrol problems, as has already been done for other intertemporal deision-making situations, whih are initially assoiated with osts and only later promise a benefit [31, 38 41]. Aordingly, other intertemporal hoies an also been desribed, where an immediate benefit is to be expeted and osts only our after a delay. A typial example from mediine is addition. Based on empirial findings, both the sustained onsumption of a substane despite the assoiated future negative onsequenes and the loss of ontrol in the form of a relapse despite a previously formulated abstinene goal an be adequately desribed formally by a hyperboli disount funtion [42]. Moreover, further studies, reviewed in [43], have shown inreased disount rates in addits ompared to healthy ontrols and a orrelation between the strength of disounting and the severity of addition. Carrillo [44] has used a quasi-hyperboli disount funtion for a theoretial analysis of the deision-making in addition: while moderate onsumption has proven to be the best long-term strategy, exessive onsumption ours in the future when there is a strong propensity to onsume. Moreover, he ould demonstrate that, if the optimal onsumption behavior is not realizable due to a lak of ommitment about future behavior, abstinene is the seond best strategy offering protetion against exessive onsumption, provided that disounting is suffiiently strong. It should be mentioned here that hyperboli disount funtions provide a formal desription of time-inonsistent behavior in intertemporal hoies, whih does not raise the laim to explain the real underlying psyhologial mehanisms. Rather, on the psyhologial level, non-adherene appears as a omplex phenomenon, probably resulting as a joint produt of multiple distint mehanisms. Beside the onept of time disounting, transient viseral influenes as well as personality traits, suh as impulsivity or restritions to exerise self-ontrol, may be relevant psyhologial fators, e.g., whereby the extent of their ontribution varies depending on the individual and the ontext of deision-making. However, based on empirial data, time disounting has proved to be an important ontributing fator in various fields of intertemporal hoie [34, 43, 45 52]. An important approah to explain time-inonsistent preferenes on the psyhologial level is provided by the dual proess theories, whih make a onnetion to erebral funtions. Aording to Broas and Carillo [53], intertemporal deision proesses result from a omplex interation of an impulsive system, whih is responsible for the judgement of information with regard of immediate onsequenes, and a refletive system, whih makes judgements from a longer-term perspetive. These systems are based on different mehanisms of information proessing [54, 55]; meanwhile, there are also empirial findings onneting these psyhologial theories to neurobiologial proesses in the brain [56 61]. Against the bakground of these psyhologial aspets, hyperboli disounting represents a rather simple model, partiularly in the form of a quasi-hyperboli disount funtion, whih is often used due to its easier analytial tratability. In the literature, several extensions of the hyperboli disount model have been reported by adding additional arguments to the instantaneous utility funtion. Regarding additive behavior, e.g. the onept of habit formation has been proposed, where the utility from urrent onsumption is affeted by the extent of past onsumption [3]. Another interesting approah has been proposed by Loewenstein [3, 62, 63], whih inorporates utility from antiipation. This model assumes that instantaneous utility is determined not only by urrent onsumption, but also depends on antiipating future onsumption. This might be a relevant aspet also in the ontext of treatment adherene due to a greater onsideration of the benefits of prevention. Finally, multiple-self models are also to be mentioned whih view intertemporal hoies as the outome of a onflit between myopi selves and more farsighted ones, who alternatively take ontrol of behavior [3]. Emanating from the model, several strategies an be derived to promote adherene, partiularly to restrit the detrimental onsequenes of the self-ontrol problem, both on the patient-level and the health are system level. Regarding the physiian-patient relationship,

8 Mann et al. Health Eonomis Review (219) 9:5 Page 8 of 1 optimization of the therapy in the ase of insuffiient effetiveness or relevant side effets is of partiular signifiane. Beause adherene is determined by the patient s subjetive pereption of the treatment effets, information delivered by the providers plays a deisive role in terms of both the ontent and mode of transmission. In this ontext, the model shows also the area of onflit that the physiian is exposed to when informing the patient in linial routine. On the one hand, the physiian is obliged to inform the patient about all relevant side effets and risks; on the other hand, omprehensive information about these unfavorable aspets may release fears and, thereby, redue adherene. There is also the ompliating fat that some patients wish to abstain from additional information in order to not jeopardize their adherene. Suh behaviors, whih at first glane appear unreasonable, an turn out to be effetive oping strategies from the patient s view. Here, interesting extensions of the model may present themselves for a better understanding of those phenomena [64, 65]. Another approah to improve adherene is to raise the patient s awareness of his self-ontrol problem. A sophistiated individual an try to bind his atual behavior to his earlier intentions by using ommitment strategies to better ahieve his optimal goals for the long term. Starting from a paper by Strotz [66], in the previous deades, researhers have pointed to the importane of suh ommitment strategies [38, 67, 68]. Regarding this aspet, the model may also serve as a starting point to analyze the onditions under whih an individual will be prepared to make a ommitment onerning treatment that will restrit his freedom of ation in the future. In addition to measures on the individual level, interventions on the health are system level may also ontribute to improve adherene. As an example, we have analyzed the onsequenes of monetary inentives for adherent behavior. Adherene and individual welfare grow with the size of the reward, whih onurs with empirial findings [69 72]. Regarding the impat on soiety, opposite effets our: soietal welfare dereases due to the osts of the preventive measures, whereas the lower inidene of illness resulting in lower osts in the future leads to a gain in welfare. The higher the osts arising from the ourrene of symptomati illness in the future and the more effetive the prophylati therapy, the larger is the rise in soietal welfare. The appropriate amount of the bonus an be determined by maximizing the joint welfare of the individual and the soiety. However, the prevention of improper use of the bonus requires an effetive monitoring system. Examples suessfully applied in pratie are therapeuti drug monitoring with regularly taking of blood samples to measure the onentration of mediation, the implementation of outpatient drug servies with daily short-term visits at home to administer mediation, and the intramusular administration of depot-antipsyhotis in shizophreni patients. Similar to a bonus system, the effets of patients o-payments for health are utilization an be analyzed. Higher ost sharing is assoiated with a lower likelihood of adherene, whih is also onsistent with empirial studies [73 75]. Several limitations have to be onsidered. The presented model is essentially based on the fundamental assumptions of neolassial theory that supposes individuals at rationally to maximize their intertemporal benefit. As the only deviation from traditional theory, time-inonsistent preferenes have been introdued. However, Simon [76] had already indiated the restritions of human ognitive apabilities and limited information. In the following deades, behavioral eonomis researh ould identify numerous further deision anomalies leading to deviations from traditional theory. Thus, for example, the presentation of the prospet of an inentive may have different effets depending on how the ontext is designed [77 79]. Besides the fat that intuitive ognitive mehanisms and heuristis are also important omponents of deision proesses [8, 81], emotional aspets in the ontext of deision making have gained partiular attention [82 85]. Aording to the risk-as-feeling model developed by Loewenstein et al. [86], emotions play a deisive role by both influening ognitive judgement proesses and direting the individual s behavior. It beomes inreasingly aepted now that deision outomes result from a synergisti interation of various ognitive and emotional proesses. Partiularly in the ontext of medial deisions, the relevane of these aspets is obvious. Regarding adherene, onfidene and empathy in the relationship between patient and physiian, and the support provided by the soial environment play an important role. In many ases, ognitive restritions also affet medial deision making, partiularly in older people or in patients suffering from mental disorders. These influening fators must be taken into aount both in individual deision-making situations and, in partiular, in poliy reommendations with regard to the enhanement of adherene. Conlusions The preditions of the model are onsistent with linial experiene and empirial findings, pointing out that the model inludes the relevant determinants for adherene and reflets their omplex interation. Thus, modeling an ontribute to a better understanding of this phenomenon. This holds partiularly for the self-ontrol problem with a derease of adherene in the ourse of treatment, whih beomes omprehensible as a onsequene of time-inonsistent preferenes of otherwise

9 Mann et al. Health Eonomis Review (219) 9:5 Page 9 of 1 rationally behaving individuals. These insights on the part of health are providers may ontribute to a better understanding of patients superfiially irrational and non-ompliant behavior. Regarding measures to improve adherene, modeling allows to assess the onsequenes of intended interventions in a theoreti way in the run-up to empirial studies or to a broad implementation in linial routine. However, with regard to poliy reommendations for linial pratie, one must be aware of the omplexity of the phenomenon of adherene with several influening fators whih are not overed by the neolassial framework underlying the model. Finally, the approah presented may serve as a starting point for extensions, inluding expliit modeling of the ognitive and emotional aspets of deision making. Abbreviations h h and h s : Health states healthy and sik.; A: Adherene; E: Expetation operator; NA: Non-adherene Aknowledgements Not appliable. Funding No funding was provided. Availability of data and materials Not appliable. Authors ontributions All authors ontributed to the oneption of the work. KM developed the theoretial formalism and wrote the manusript. All authors read the manusript ritially and approved the manusript for submission. Competing interests The authors delare that they have no ompeting interests. Publisher s Note Springer Nature remains neutral with regard to jurisditional laims in published maps and institutional affiliations. Author details 1 Department of Psyhiatry and Psyhotherapy, University Medial Center Mainz, D Mainz, Germany. 2 Chair of Eonomi Poliy, University of Hagen, D-5884 Hagen, Germany. Reeived: 7 August 218 Aepted: 31 January 219 Referenes 1. World Health Organization (WHO). Adherene to long-term therapies: evidene for ation adherene_report/en/. Aessed 15 May Osterberg L, Blashke T. Adherene to mediation. N Engl J Med. 25;353: Brown MT, Bussell JK. Mediation adherene: WHO ares? 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