• • • Game theory is 'the study of of conflict and cooperation between intelligent rational decision-makers'. Game theory is mainly used in,, and, as well as, and. Originally, it addressed, in which one person's gains result in losses for the other participants.

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Today, game theory applies to a wide range of behavioral relations, and is now an for the science of logical decision making in humans, animals, and computers. Modern game theory began with the idea regarding the existence of mixed-strategy equilibria in two-person and its proof. Von Neumann's original proof used the on continuous mappings into compact, which became a standard method in game theory and. His paper was followed by the 1944 book, co-written with, which considered of several players. The second edition of this book provided an axiomatic theory of expected utility, which allowed mathematical statisticians and economists to treat decision-making under uncertainty. This theory was developed extensively in the 1950s by many scholars.

Game theory was later explicitly applied to biology in the 1970s, although similar developments go back at least as far as the 1930s. Game theory has been widely recognized as an important tool in many fields. With the going to game theorist in 2014, eleven game-theorists have now won the economics Nobel Prize. Was awarded the for his application of game theory to biology.

Main articles: and A game is cooperative if the players are able to form binding commitments externally enforced (e.g. A game is non-cooperative if players cannot form alliances or if all agreements need to be (e.g. Cooperative games are often analysed through the framework of cooperative game theory, which focuses on predicting which coalitions will form, the joint actions that groups take and the resulting collective payoffs.

It is opposed to the traditional non-cooperative game theory which focuses on predicting individual players' actions and payoffs and analyzing. Cooperative game theory provides a high-level approach as it only describes the structure, strategies and payoffs of coalitions, whereas non-cooperative game theory also looks at how bargaining procedures will affect the distribution of payoffs within each coalition. As non-cooperative game theory is more general, cooperative games can be analyzed through the approach of non-cooperative game theory (the converse does not hold) provided that sufficient assumptions are made to encompass all the possible strategies available to players due to the possibility of external enforcement of cooperation. While it would thus be optimal to have all games expressed under a non-cooperative framework, in many instances insufficient information is available to accurately model the formal procedures available to the players during the strategic bargaining process, or the resulting model would be of too high complexity to offer a practical tool in the real world. In such cases, cooperative game theory provides a simplified approach that allows to analyze the game at large without having to make any assumption about bargaining powers. Symmetric / Asymmetric [ ] E F E 1, 2 0, 0 F 0, 0 1, 2 An asymmetric game. Main article: A symmetric game is a game where the payoffs for playing a particular strategy depend only on the other strategies employed, not on who is playing them.

If the identities of the players can be changed without changing the payoff to the strategies, then a game is symmetric. Many of the commonly studied 2×2 games are symmetric. The standard representations of, the, and the are all symmetric games. Some [ ] scholars would consider certain asymmetric games as examples of these games as well.

However, the most common payoffs for each of these games are symmetric. Most commonly studied asymmetric games are games where there are not identical strategy sets for both players. For instance, the and similarly the have different strategies for each player.

It is possible, however, for a game to have identical strategies for both players, yet be asymmetric. For example, the game pictured to the right is asymmetric despite having identical strategy sets for both players. Zero-sum / Non-zero-sum [ ] A B A –1, 1 3, –3 B 0, 0 –2, 2 A zero-sum game. Main article: Zero-sum games are a special case of constant-sum games, in which choices by players can neither increase nor decrease the available resources. In zero-sum games the total benefit to all players in the game, for every combination of strategies, always adds to zero (more informally, a player benefits only at the equal expense of others).

Exemplifies a zero-sum game (ignoring the possibility of the house's cut), because one wins exactly the amount one's opponents lose. Other zero-sum games include and most classical board games including and. Many games studied by game theorists (including the famed ) are non-zero-sum games, because the has net results greater or less than zero. Informally, in non-zero-sum games, a gain by one player does not necessarily correspond with a loss by another. Constant-sum games correspond to activities like theft and gambling, but not to the fundamental economic situation in which there are potential.

It is possible to transform any game into a (possibly asymmetric) zero-sum game by adding a dummy player (often called 'the board') whose losses compensate the players' net winnings. Simultaneous / Sequential [ ]. Main articles: and are games where both players move simultaneously, or if they do not move simultaneously, the later players are unaware of the earlier players' actions (making them effectively simultaneous). (or dynamic games) are games where later players have some knowledge about earlier actions. This need not be about every action of earlier players; it might be very little knowledge.

For instance, a player may know that an earlier player did not perform one particular action, while he does not know which of the other available actions the first player actually performed. The difference between simultaneous and sequential games is captured in the different representations discussed above.

Often, is used to represent simultaneous games, while is used to represent sequential ones. The transformation of extensive to normal form is one way, meaning that multiple extensive form games correspond to the same normal form.

Consequently, notions of equilibrium for simultaneous games are insufficient for reasoning about sequential games; see. In short, the differences between sequential and simultaneous games are as follows: Sequential Simultaneous Normally denoted. A game of imperfect information (the dotted line represents ignorance on the part of player 2, formally called an ) An important subset of sequential games consists of games of.

A game is one of perfect information if all players know the moves previously made by all other players. Most games studied in game theory are imperfect-information games. [ ] Examples of perfect-information games include,,, and. Many card games are games of imperfect information, such as and. Perfect information is often confused with, which is a similar concept.

[ ] Complete information requires that every player know the strategies and payoffs available to the other players but not necessarily the actions taken. Games of incomplete information can be reduced, however, to games of imperfect information by introducing '. Combinatorial games [ ] Games in which the difficulty of finding an optimal strategy stems from the multiplicity of possible moves are called combinatorial games. Examples include chess and go. Games that involve may also have a strong combinatorial character, for instance.

There is no unified theory addressing combinatorial elements in games. There are, however, mathematical tools that can solve particular problems and answer general questions. Games of have been studied in, which has developed novel representations, e.g., as well as and (and ) proof methods to of certain types, including 'loopy' games that may result in infinitely long sequences of moves. These methods address games with higher combinatorial complexity than those usually considered in traditional (or 'economic') game theory. A typical game that has been solved this way is. A related field of study, drawing from, is, which is concerned with estimating the computational difficulty of finding optimal strategies.

Research in has addressed both perfect and imperfect information games that have very complex combinatorial structures (like chess, go, or backgammon) for which no provable optimal strategies have been found. The practical solutions involve computational heuristics, like or use of trained by, which make games more tractable in computing practice. Infinitely long games [ ].

Main article: Games, as studied by economists and real-world game players, are generally finished in finitely many moves. Pure mathematicians are not so constrained, and in particular study games that last for infinitely many moves, with the winner (or other payoff) not known until after all those moves are completed. The focus of attention is usually not so much on the best way to play such a game, but whether one player has a. (It can be proven, using the, that there are games – even with perfect information and where the only outcomes are 'win' or 'lose' – for which neither player has a winning strategy.) The existence of such strategies, for cleverly designed games, has important consequences in. Discrete and continuous games [ ] Much of game theory is concerned with finite, discrete games, that have a finite number of players, moves, events, outcomes, etc. Many concepts can be extended, however. Allow players to choose a strategy from a continuous strategy set.

For instance, is typically modeled with players' strategies being any non-negative quantities, including fractional quantities. Differential games [ ] such as the continuous are continuous games where the evolution of the players' state variables is governed. The problem of finding an optimal strategy in a differential game is closely related to the theory. In particular, there are two types of strategies: the open-loop strategies are found using the while the closed-loop strategies are found using method. A particular case of differential games are the games with a random. Seagate Hd Repair Tools. In such games, the terminal time is a random variable with a given function. Therefore, the players maximize the of the cost function.

It was shown that the modified optimization problem can be reformulated as a discounted differential game over an infinite time interval. Many-player and population games [ ] Games with an arbitrary, but finite, number of players are often called n-person games. Considers games involving a of decision makers, where the frequency with which a particular decision is made can change over time in response to the decisions made by all individuals in the population.

In biology, this is intended to model (biological), where genetically programmed organisms pass along some of their strategy programming to their offspring. In economics, the same theory is intended to capture population changes because people play the game many times within their lifetime, and consciously (and perhaps rationally) switch strategies.

Stochastic outcomes (and relation to other fields) [ ] Individual decision problems with stochastic outcomes are sometimes considered 'one-player games'. These situations are not considered game theoretical by some authors. [ ] They may be modeled using similar tools within the related disciplines of,, and areas of, particularly (with uncertainty) and. Although these fields may have different motivators, the mathematics involved are substantially the same, e.g.

[ ] Stochastic outcomes can also be modeled in terms of game theory by adding a randomly acting player who makes 'chance moves' ('). This player is not typically considered a third player in what is otherwise a two-player game, but merely serves to provide a roll of the dice where required by the game. For some problems, different approaches to modeling stochastic outcomes may lead to different solutions. For example, the difference in approach between MDPs and the is that the latter considers the worst-case over a set of adversarial moves, rather than reasoning in expectation about these moves given a fixed probability distribution.

The minimax approach may be advantageous where stochastic models of uncertainty are not available, but may also be overestimating extremely unlikely (but costly) events, dramatically swaying the strategy in such scenarios if it is assumed that an adversary can force such an event to happen. (See for more discussion on this kind of modeling issue, particularly as it relates to predicting and limiting losses in investment banking.) General models that include all elements of stochastic outcomes, adversaries, and partial or noisy observability (of moves by other players) have also been studied. The ' is considered to be partially observable (POSG), but few realistic problems are computationally feasible in POSG representation. Metagames [ ] These are games the play of which is the development of the rules for another game, the target or subject game.

Seek to maximize the utility value of the rule set developed. The theory of metagames is related to theory. The term is also used to refer to a practical approach developed by Nigel Howard. Whereby a situation is framed as a strategic game in which stakeholders try to realise their objectives by means of the options available to them.

Subsequent developments have led to the formulation of. Pooling games [ ] These are games prevailing over all forms of society. Pooling games are repeated plays with changing payoff table in general over an experienced path and their equilibrium strategies usually take a form of evolutionary social convention and economic convention. Pooling game theory emerges to formally recognize the interaction between optimal choice in one play and the emergence of forthcoming payoff table update path, identify the invariance existence and robustness, and predict variance over time. The theory is based upon topological transformation classification of payoff table update over time to predict variance and invariance, and is also within the jurisdiction of the computational law of reachable optimality for ordered system. Mean field game theory [ ] is the study of strategic decision making in very large populations of small interacting agents.

This class of problems was considered in the economics literature by and, in the engineering literature by and by mathematician and Jean-Michel Lasry. Representation of games [ ]. See also: The games studied in game theory are well-defined mathematical objects. To be fully defined, a game must specify the following elements: the, the information and actions available to each player at each decision point, and the for each outcome. (Eric Rasmusen refers to these four 'essential elements' by the acronym 'PAPI'.) A game theorist typically uses these elements, along with a of their choosing, to deduce a set of equilibrium for each player such that, when these strategies are employed, no player can profit by unilaterally deviating from their strategy. These equilibrium strategies determine an to the game—a stable state in which either one outcome occurs or a set of outcomes occur with known probability. Most cooperative games are presented in the characteristic function form, while the extensive and the normal forms are used to define noncooperative games.

Extensive form [ ]. An extensive form game The extensive form can be used to formalize games with a time sequencing of moves. Games here are played on (as pictured here). Here each (or node) represents a point of choice for a player.

The player is specified by a number listed by the vertex. The lines out of the vertex represent a possible action for that player.

The payoffs are specified at the bottom of the tree. The extensive form can be viewed as a multi-player generalization of a. To solve any extensive form game, must be used. It involves working backwards up the game tree to determine what a rational player would do at the last vertex of the tree, what the player with the previous move would do given that the player with the last move is rational, and so on until the first vertex of the tree is reached. The game pictured consists of two players. The way this particular game is structured (i.e., with sequential decision making and perfect information), Player 1 'moves' first by choosing either F or U (Fair or Unfair). Next in the sequence, Player 2, who has now seen Player 1 's move, chooses to play either A or R.

Once Player 2 has made his/ her choice, the game is considered finished and each player gets their respective payoff. Suppose that Player 1 chooses U and then Player 2 chooses A: Player 1 then gets a payoff of 'eight' (which in real-world terms can be interpreted in many ways, the simplest of which is in terms of money but could mean things such as eight days of vacation or eight countries conquered or even eight more opportunities to play the same game against other players) and Player 2 gets a payoff of 'two'. The extensive form can also capture simultaneous-move games and games with imperfect information. To represent it, either a dotted line connects different vertices to represent them as being part of the same information set (i.e. The players do not know at which point they are), or a closed line is drawn around them.

(See example in the.) Normal form [ ] Player 2 chooses Left Player 2 chooses Right Player 1 chooses Up 4, 3 –1, –1 Player 1 chooses Down 0, 0 3, 4 Normal form or payoff matrix of a 2-player, 2-strategy game. Main article: The normal (or strategic form) game is usually represented by a which shows the players, strategies, and payoffs (see the example to the right). More generally it can be represented by any function that associates a payoff for each player with every possible combination of actions.

In the accompanying example there are two players; one chooses the row and the other chooses the column. Each player has two strategies, which are specified by the number of rows and the number of columns. The payoffs are provided in the interior. The first number is the payoff received by the row player (Player 1 in our example); the second is the payoff for the column player (Player 2 in our example). Suppose that Player 1 plays Up and that Player 2 plays Left.

Then Player 1 gets a payoff of 4, and Player 2 gets 3. When a game is presented in normal form, it is presumed that each player acts simultaneously or, at least, without knowing the actions of the other. If players have some information about the choices of other players, the game is usually presented in extensive form. Every extensive-form game has an equivalent normal-form game, however the transformation to normal form may result in an exponential blowup in the size of the representation, making it computationally impractical. Characteristic function form [ ]. A four-stage The primary use of game theory is to describe and how human populations behave. Some [ ] scholars believe that by finding the equilibria of games they can predict how actual human populations will behave when confronted with situations analogous to the game being studied.

This particular view of game theory has been criticized. It is argued that the assumptions made by game theorists are often violated when applied to real world situations. Game theorists usually assume players act rationally, but in practice, human behavior often deviates from this model. Game theorists respond by comparing their assumptions to those used in. Thus while their assumptions do not always hold, they can treat game theory as a reasonable scientific akin to the models used. However, empirical work has shown that in some classic games, such as the, game, and the, people regularly do not play Nash equilibria. There is an ongoing debate regarding the importance of these experiments and whether the analysis of the experiments fully captures all aspects of the relevant situation.

Some game theorists, following the work of and, have turned to in order to resolve these issues. These models presume either no rationality or on the part of players. Despite the name, evolutionary game theory does not necessarily presume in the biological sense.

Evolutionary game theory includes both biological as well as cultural evolution and also models of individual learning (for example, dynamics). Prescriptive or normative analysis [ ] Cooperate Defect Cooperate -1, -1 -10, 0 Defect 0, -10 -5, -5 The Some scholars, like, [ ] see game theory not as a predictive tool for the behavior of human beings, but as a suggestion for how people ought to behave.

Since a strategy, corresponding to a of a game constitutes one's to the actions of the other players – provided they are in (the same) Nash equilibrium – playing a strategy that is part of a Nash equilibrium seems appropriate. This normative use of game theory has also come under criticism. Economics and business [ ] Game theory is a major method used in and business for competing behaviors of interacting. Applications include a wide array of economic phenomena and approaches, such as,, pricing,,,, formation,,,, and; and across such broad areas as,,,, and. This research usually focuses on particular sets of strategies known as. A common assumption is that players act rationally.

In non-cooperative games, the most famous of these is the. A set of strategies is a Nash equilibrium if each represents a best response to the other strategies. If all the players are playing the strategies in a Nash equilibrium, they have no unilateral incentive to deviate, since their strategy is the best they can do given what others are doing. The payoffs of the game are generally taken to represent the of individual players. A prototypical paper on game theory in economics begins by presenting a game that is an abstraction of a particular economic situation. One or more solution concepts are chosen, and the author demonstrates which strategy sets in the presented game are equilibria of the appropriate type. Naturally one might wonder to what use this information should be put.

Economists and business professors suggest two primary uses (noted above): descriptive and. Political science [ ] The application of game theory to is focused in the overlapping areas of,,,,, and. In each of these areas, researchers have developed game-theoretic models in which the players are often voters, states, special interest groups, and politicians. Early examples of game theory applied to political science are provided.

In his book, he applies the to the political process. In the Downsian model, political candidates commit to ideologies on a one-dimensional policy space. Downs first shows how the political candidates will converge to the ideology preferred by the median voter if voters are fully informed, but then argues that voters choose to remain rationally ignorant which allows for candidate divergence. Game Theory was applied in 1962 to the during the presidency of John F. It has also been proposed that game theory explains the stability of any form of political government.

Taking the simplest case of a monarchy, for example, the king, being only one person, does not and cannot maintain his authority by personally exercising physical control over all or even any significant number of his subjects. Sovereign control is instead explained by the recognition by each citizen that all other citizens expect each other to view the king (or other established government) as the person whose orders will be followed. Coordinating communication among citizens to replace the sovereign is effectively barred, since conspiracy to replace the sovereign is generally punishable as a crime. Thus, in a process that can be modeled by variants of the, during periods of stability no citizen will find it rational to move to replace the sovereign, even if all the citizens know they would be better off if they were all to act collectively. A game-theoretic explanation for is that public and open debate in democracies send clear and reliable information regarding their intentions to other states. In contrast, it is difficult to know the intentions of nondemocratic leaders, what effect concessions will have, and if promises will be kept. Thus there will be mistrust and unwillingness to make concessions if at least one of the parties in a dispute is a non-democracy.

On the other hand, game theory predicts that two countries may still go to war even if their leaders are cognizant of the costs of fighting. War may result from asymmetric information; two countries may have incentives to mis-represent the amount of military resources they have on hand, rendering them unable to settle disputes agreeably without resorting to fighting. Moreover, war may arise because of commitment problems: if two countries wish to settle a dispute via peaceful means, but each wishes to go back on the terms of that settlement, they may have no choice but to resort to warfare. Finally, war may result from issue indivisibilities.

Game theory could also help predict a nation's responses when there is a new rule or law to be applied to that nation. One example would be Peter John Wood's (2013) research when he looked into what nations could do to help reduce climate change. Wood thought this could be accomplished by making treaties with other nations to reduce green house gas emissions. However, he concluded that this idea could not work because it would create a to the nations. Biology [ ] Hawk Dove Hawk 20, 20 80, 40 Dove 40, 80 60, 60 The game. Main article: Unlike those in economics, the payoffs for games in are often interpreted as corresponding to.

In addition, the focus has been less on that correspond to a notion of rationality and more on ones that would be maintained by forces. The best known equilibrium in biology is known as the (ESS), first introduced in (). Although its initial motivation did not involve any of the mental requirements of the, every ESS is a Nash equilibrium.

In biology, game theory has been used as a model to understand many different phenomena. It was first used to explain the evolution (and stability) of the approximate 1:1. () suggested that the 1:1 sex ratios are a result of evolutionary forces acting on individuals who could be seen as trying to maximize their number of grandchildren. Additionally, biologists have used and the ESS to explain the emergence of. The analysis of and has provided insight into the evolution of communication among animals. For example, the of many species, in which a large number of prey animals attack a larger predator, seems to be an example of spontaneous emergent organization.

Ants have also been shown to exhibit feed-forward behavior akin to fashion (see 's ). Biologists have used the to analyze fighting behavior and territoriality. According to Maynard Smith, in the preface to Evolution and the Theory of Games, 'paradoxically, it has turned out that game theory is more readily applied to biology than to the field of economic behaviour for which it was originally designed'. Evolutionary game theory has been used to explain many seemingly incongruous phenomena in nature. One such phenomenon is known as. This is a situation in which an organism appears to act in a way that benefits other organisms and is detrimental to itself. This is distinct from traditional notions of altruism because such actions are not conscious, but appear to be evolutionary adaptations to increase overall fitness.

Examples can be found in species ranging from vampire bats that regurgitate blood they have obtained from a night's hunting and give it to group members who have failed to feed, to worker bees that care for the queen bee for their entire lives and never mate, to that warn group members of a predator's approach, even when it endangers that individual's chance of survival. All of these actions increase the overall fitness of a group, but occur at a cost to the individual. Evolutionary game theory explains this altruism with the idea of. Altruists discriminate between the individuals they help and favor relatives. Explains the evolutionary rationale behind this selection with the equation c.

Adobe Flash Player is required to view this feature. If you are using an operating system that does not support Flash, we are working to bring you alternative formats. Original Article Treatment of HCV with ABT-450/r–Ombitasvir and Dasabuvir with Ribavirin Jordan J. Feld, M.D., M.P.H., Kris V. Kowdley, M.D., Eoin Coakley, M.D., Samuel Sigal, M.D., David R. Nelson, M.D., Darrell Crawford, M.D., Ola Weiland, M.D., Humberto Aguilar, M.D., Junyuan Xiong, M.S., Tami Pilot-Matias, Ph.D., Barbara DaSilva-Tillmann, M.D., Lois Larsen, Ph.D., Thomas Podsadecki, M.D., and Barry Bernstein, M.D.

N Engl J Med 2014; 370:1594-1603 DOI: 10.1056/NEJMoa1315722. Methods In this multicenter, randomized, double-blind, placebo-controlled trial, we assigned previously untreated patients with HCV genotype 1 infection, in a 3:1 ratio, to an active regimen consisting of a single-tablet coformulation of ABT-450/r–ombitasvir (at a once-daily dose of 150 mg of ABT-450, 100 mg of ritonavir, and 25 mg of ombitasvir), and dasabuvir (250 mg twice daily) with ribavirin (in doses determined according to body weight) (group A) or matching placebos (group B). The patients received the study treatment during a 12-week double-blind period. The primary end point was sustained virologic response at 12 weeks after the end of treatment. The primary analysis compared the response rate in group A with the response rate (78%) in a historical control group of previously untreated patients without cirrhosis who received telaprevir with peginterferon and ribavirin. Adverse events occurring during the double-blind period were compared between group A and group B.

Results A total of 631 patients received at least one dose of the study drugs. The rate of sustained virologic response in group A was 96.2% (95% confidence interval, 94.5 to 97.9), which was superior to the historical control rate.

Virologic failure during treatment and relapse after treatment occurred in 0.2% and 1.5%, respectively, of the patients in group A. The response rates in group A were 95.3% among patients with HCV genotype 1a infection and 98.0% among those with HCV genotype 1b infection. The rate of discontinuation due to adverse events was 0.6% in each study group. Nausea, pruritus, insomnia, diarrhea, and asthenia occurred in significantly more patients in group A than in group B (P. Figure 1 SAPPHIRE-I Study Design. During the 12-week double-blind period, patients received either ABT-450 with ritonavir (ABT-450/r)–ombitasvir and dasabuvir with ribavirin (group A) or matching placebos (group B).

Patients receiving placebo were treated with the active regimen for 12 weeks in an open-label fashion at the conclusion of the double-blind period. The dashed vertical line indicates the time point at which the primary analysis, which compared the rate of sustained virologic response at 12 weeks after the end of therapy in group A with the rate in a historical control group, was performed. The study is ongoing, and all patients who received the active regimen will be followed through post-treatment week 48. Figure 2 Rates of Sustained Virologic Response among All Patients and According to HCV Genotype in the Historical Control Group and in Group A.

To establish the noninferiority and superiority of ABT-450/r–ombitasvir and dasabuvir with ribavirin to the historical control (telaprevir and peginterferon–ribavirin) in all patients, the lower boundary of the 95% confidence interval for the rate of sustained virologic response at post-treatment week 12 among patients in group A (patients receiving ABT-450/r–ombitasvir and dasabuvir with ribavirin during the double-blind period) had to exceed 70% (for noninferiority) and 80% (for superiority). To establish the superiority of the active regimen to the historical control in HCV genotype 1a–infected patients and HCV genotype 1b–infected patients, the lower boundary of the 95% confidence interval for the rate of sustained virologic response at post-treatment week 12 among patients in these subgroups in group A had to exceed 75% and 84%, respectively. Dots indicate the point estimates in the control group. I bars indicate 95% confidence intervals. Numbers above the confidence intervals are the rates of sustained virologic response. Approximately 184 million people worldwide have chronic hepatitis C virus (HCV) infection, and more than 350,000 people die of HCV-related liver disease each year. Until recently, the standard of care for chronic HCV genotype 1 infection was a first-generation protease inhibitor, telaprevir or boceprevir, with peginterferon and ribavirin; this therapy resulted in rates of sustained virologic response of 67 to 75% among previously untreated patients.

The new standard of care is peginterferon and ribavirin combined with either the nucleotide nonstructural (NS) 5B polymerase inhibitor sofosbuvir or the protease inhibitor simeprevir. Peginterferon-based treatment is associated with clinically significant systemic events, including influenza-like symptoms and depression. Variables including patients' age, race, HCV genotype, IL28B genotype, HCV viral load at baseline, and degree of liver fibrosis have been shown to affect the response to peginterferon-based therapy and other therapies in development. ABT-450 is an HCV NS3/4A protease inhibitor with nanomolar potency in vitro. ABT-450 is administered with low-dose ritonavir, an inhibitor of the cytochrome P-450 enzyme CYP3A4. As a pharmacologic enhancer of ABT-450, ritonavir facilitates once-daily dosing, and administration of ABT-450 with ritonavir (ABT-450/r) results in higher drug exposures than administration of ABT-450 alone.

Ombitasvir (also known as ABT-267) is an HCV NS5A inhibitor with picomolar potency in vitro. Dasabuvir (also known as ABT-333) is a nonnucleoside NS5B polymerase inhibitor with nanomolar potency in vitro. In a phase 2b trial involving previously untreated patients with HCV genotype 1 infection, 96% of the patients who received ABT-450/r, ombitasvir, dasabuvir, and ribavirin for 12 weeks had a sustained virologic response at 24 weeks after the end of treatment, suggesting that a multitargeted approach may maximize the response rate, such that most patients would have a sustained virologic response without the development of drug resistance.

Here we report the results of the phase 3, international, multicenter, randomized, double-blind, placebo-controlled SAPPHIRE-I trial evaluating the safety and efficacy of 12 weeks of an all-oral regimen of ABT-450/r–ombitasvir and dasabuvir with ribavirin in previously untreated patients with HCV genotype 1 infection and no cirrhosis. Patients Patients were screened from November 2012 through May 2013 at 79 sites in North America, Europe, and Australia. Eligible patients were adults, 18 to 70 years of age, with chronic HCV genotype 1 infection, no cirrhosis, and a plasma HCV RNA level of more than 10,000 IU per milliliter, who had never received antiviral treatment for HCV infection. Patients were excluded if they had a positive test for hepatitis B surface antigen or anti–human immunodeficiency virus antibody during screening. Details of the eligibility criteria are provided in the, available with the full text of this article at NEJM.org. Study Design Patients were randomly assigned, in a 3:1 ratio, to active treatment (group A) or placebo (group B) ( Figure 1 SAPPHIRE-I Study Design. During the 12-week double-blind period, patients received either ABT-450 with ritonavir (ABT-450/r)–ombitasvir and dasabuvir with ribavirin (group A) or matching placebos (group B).

Patients receiving placebo were treated with the active regimen for 12 weeks in an open-label fashion at the conclusion of the double-blind period. The dashed vertical line indicates the time point at which the primary analysis, which compared the rate of sustained virologic response at 12 weeks after the end of therapy in group A with the rate in a historical control group, was performed. The study is ongoing, and all patients who received the active regimen will be followed through post-treatment week 48. Randomization was stratified according to HCV genotype (1a vs.

Non-1a) and IL28B genotype (CC vs. During the double-blind period, patients in group A received 12 weeks of treatment with oral coformulated ABT-450/r–ombitasvir (at a once-daily dose of 150 mg of ABT-450, 100 mg of ritonavir, and 25 mg of ombitasvir) and dasabuvir (at a dose of 250 mg twice daily) with ribavirin, administered twice daily in a dose that was determined according to body weight (1000 mg daily if the body weight was.

Study Oversight All the patients provided written informed consent. The study was conducted in accordance with the International Conference on Harmonisation guidelines, applicable regulations, and the principles of the Declaration of Helsinki.

The study protocol was approved by the independent ethics committee or institutional review board at each study site. The study was designed jointly by the study investigators and the sponsor (AbbVie).

The investigators gathered the data, and the sponsor conducted the data analyses. All the authors had full access to the data and signed confidentiality agreements with the sponsor regarding the data. The first draft of the manuscript was written by a medical writer who is an employee of the sponsor, with input from all the authors. All the authors reviewed and provided feedback on all subsequent versions of the manuscript and made the decision to submit the manuscript for publication. All the authors vouch for the completeness and accuracy of the data and analyses presented and affirm that the study was conducted and reported with fidelity to the (available at NEJM.org). Fp200a Sensor Driver Win7.

Safety Assessments Adverse events were assessed at each study visit. The investigator at each site classified events as mild, moderate, or severe. Data on all adverse events were collected from the start of study-drug administration until 30 days after receipt of the last dose. Data on serious adverse events were collected throughout the entire study period. Here we report data on adverse events and serious adverse events occurring during the double-blind period and the 30-day period after the last dose of active study drugs was administered. Clinical laboratory testing was performed at visits during the double-blind treatment period and at weeks 4 and 48 after the end of the treatment period. Efficacy End Points The primary efficacy end point was sustained virologic response (HCV RNA level.

Statistical Analysis Analyses were performed in the modified intention-to-treat population, which included all the patients who underwent randomization and received at least one dose of the study drug during the double-blind period. The primary efficacy analyses assessed noninferiority and superiority with respect to the rate of sustained virologic response at post-treatment week 12 associated with the active regimen (ABT-450/r–ombitasvir and dasabuvir with ribavirin) by comparing it with a calculated historical control rate of 78% (95% confidence interval [CI], 75 to 80). This control rate was based on response rates among previously untreated patients without cirrhosis who received telaprevir and peginterferon–ribavirin. To establish that the rate of sustained virologic response at post-treatment week 12 associated with the active regimen was noninferior to the historical control rate, the lower boundary of the 95% confidence interval for the rate of sustained virologic response at post-treatment week 12 in group A had to exceed the upper boundary of the 95% confidence interval for the control rate minus 10.5 percentage points (70%).

To establish that the rate of sustained virologic response at post-treatment week 12 associated with the active regimen was superior to the historical control rate, the lower boundary of the 95% confidence interval for the rate in group A had to exceed the upper boundary of the confidence interval for the historical rate (80%). The two-sided 95% confidence intervals were calculated with the use of the normal approximation to the binomial distribution. We calculated that a sample of 600 patients (450 patients in group A) would provide the study with more than 90% power to show noninferiority and superiority of the active regimen, assuming a rate of sustained virologic response at post-treatment week 12 of 92%. Secondary analyses assessed whether the rates of sustained virologic response at post-treatment week 12 in HCV genotype 1a–infected and HCV genotype 1b–infected subgroups of group A were superior to calculated rates for these subgroups in the historical control group (72% [95% CI, 68 to 75] in patients with HCV genotype 1a infection and 80% [95% CI, 75 to 84] in those with HCV genotype 1b infection).

If the lower boundary of the 95% confidence interval for the rate of sustained virologic response at post-treatment week 12 exceeded 75% among patients with HCV genotype 1a infection or 84% among those with HCV genotype 1b infection, the rate with the active regimen was considered to be superior to the historical control rate in that subgroup. Details of the noninferiority and superiority analyses and sample-size determination are provided in the. A fixed-sequence testing procedure was used to maintain the type I error rate at a level of 0.05 as the primary and secondary efficacy end points were analyzed in a specific order (see the ).

SAS software, version 9.3, for the UNIX operating system (SAS Institute) was used for all analyses. All statistical tests and 95% confidence intervals were two-sided, with a significance level of 0.05. Differences in baseline characteristics between the treatment groups were evaluated with the use of the chi-square test for categorical data and one-way analysis of variance for continuous data.

Comparisons of rates of normalization of the alanine aminotransferase level, adverse events, and laboratory abnormalities were performed with the use of Fisher's exact test. The relationship between prespecified baseline characteristics (e.g., fibrosis score) and the rate of sustained virologic response at post-treatment week 12 was analyzed by means of stepwise logistic regression to determine independent predictors of sustained virologic response at post-treatment week 12. The fibrosis score (on a scale from F0, indicating no fibrosis, to F4, indicating cirrhosis) was determined by means of liver biopsy (Metavir, Batts–Ludwig, Knodell, International Association for the Study of the Liver, Scheuer, Laennec, or Ishak scoring system), FibroTest, or FibroScan (Echosens). Additional details of the stepwise logistic-regression analysis and fibrosis scoring are provided in Table S2 in the.

Efficacy By week 4 of the double-blind treatment period, the HCV RNA level was below 25 IU per milliliter in 99.4% of the patients who were receiving the active regimen (461 of the 464 patients in group A with data available) (Fig. In the modified intention-to-treat analysis, the rate of sustained virologic response at post-treatment week 12 was 96.2% (95% CI, 94.5 to 97.9) in group A (455 of 473 patients) ( Figure 2 Rates of Sustained Virologic Response among All Patients and According to HCV Genotype in the Historical Control Group and in Group A. To establish the noninferiority and superiority of ABT-450/r–ombitasvir and dasabuvir with ribavirin to the historical control (telaprevir and peginterferon–ribavirin) in all patients, the lower boundary of the 95% confidence interval for the rate of sustained virologic response at post-treatment week 12 among patients in group A (patients receiving ABT-450/r–ombitasvir and dasabuvir with ribavirin during the double-blind period) had to exceed 70% (for noninferiority) and 80% (for superiority). To establish the superiority of the active regimen to the historical control in HCV genotype 1a–infected patients and HCV genotype 1b–infected patients, the lower boundary of the 95% confidence interval for the rate of sustained virologic response at post-treatment week 12 among patients in these subgroups in group A had to exceed 75% and 84%, respectively.

Dots indicate the point estimates in the control group. I bars indicate 95% confidence intervals. Numbers above the confidence intervals are the rates of sustained virologic response. This rate was noninferior and superior to the historical control rate with telaprevir plus peginterferon–ribavirin. The rate of sustained virologic response at post-treatment week 12 was 95.3% (95% CI, 93.0 to 97.6) among patients with HCV genotype 1a infection (307 of 322 patients) and 98.0% (95% CI, 95.8 to 100) among those with HCV genotype 1b infection (148 of 151). These rates were superior to the historical control rates in the respective subgroups ( ). Figure 3 Rates of Sustained Virologic Response at Post-Treatment Week 12 in Group A, According to Subgroup and Baseline Variables.

The position of the circle indicates the rate of sustained virologic response at post-treatment week 12; the bars are 95% confidence intervals. The dotted vertical line indicates the overall rate of sustained virologic response at post-treatment week 12 in group A. Race and ethnic group were self-reported.

The body-mass index is the weight in kilograms divided by the square of the height in meters. The fibrosis score ranges from F0 (no fibrosis) to F4 (cirrhosis). No patient had a fibrosis score of F4. The 31 patients with a reduction in the ribavirin dose included 26 who had the dose modified owing to adverse events and 5 who had the dose modified for other reasons (e.g., weight change).

The rates in additional patient subgroups are provided in Table S3 in the. Shows the rates of sustained virologic response at post-treatment week 12 in additional patient subgroups. The rates were similarly high in all subgroups, including those defined by IL28B genotype (96.5% with CC and 96.0% with non-CC), race (96.4% among black patients and 96.2% among nonblack patients), fibrosis score at baseline (97.0% with a score of F0 or F1, 94.3% with a score of F2, and 92.5% with a score of F3), and baseline HCV RNA level (98.1% with a level. Virologic Failure during Treatment and Relapse Among the 473 patients in group A, 1 patient (0.2%) had virologic failure during the double-blind treatment period.

In this HCV genotype 1a–infected patient who had adhered to the treatment regimen, the HCV RNA level became quantifiable at treatment week 12. A total of 7 of 463 patients (1.5%) had a relapse by post-treatment week 12, of whom 5 had a relapse at or before the visit at post-treatment week 4. Each of the eight patients who had virologic failure during treatment or relapse had at least one amino acid variant that was known to confer resistance to one of the three direct-acting antiviral agents included in the regimen. The most frequently detected variants in the seven patients with HCV genotype 1a infection at the time of virologic failure during treatment or relapse were D168V (in six patients) in the protein NS3, M28T (in two) and Q30R (in three) in the protein NS5A, and S556G (in three) in the protein NS5B.

The single patient with HCV genotype 1b infection who had relapse had variants Y56H and D168V in the protein NS3, L31M and Y93H in the protein NS5A, and S556G in the protein NS5B at the time of relapse. Safety During the double-blind period, 87.5% of the patients who were receiving the active regimen (group A), as compared with 73.4% of those receiving placebo (group B), had an adverse event (P0.05 for both comparisons). Among adverse events that occurred in more than 10% of patients in either group, five occurred in significantly more patients in group A than in group B: nausea (23.7% vs. 13.3%), pruritus (16.9% vs. 3.8%), insomnia (14.0% vs.

7.6%), diarrhea (13.7% vs. 7.0%), and asthenia (12.1% vs. Discussion This large, international, phase 3 trial showed the efficacy of an interferon-free, all-oral antiviral therapy for previously untreated patients with HCV genotype 1 infection and no cirrhosis. In the modified intention-to-treat analysis, the rate of sustained virologic response at post-treatment week 12 among patients who received 12 weeks of ABT-450/r–ombitasvir and dasabuvir with ribavirin was 96.2%, a rate that was noninferior and superior to the historical control rate with telaprevir and peginterferon–ribavirin. This multitargeted regimen resulted in a low rate of virologic failure (virologic failure occurred during treatment in 0.2% of the patients, and relapse after the end of treatment in 1.5%), which limited the number of patients in whom drug resistance developed. The rate of sustained virologic response at post-treatment week 12 observed in our study compares favorably with the rates of 67 to 89% reported in phase 3 trials involving previously untreated patients with HCV genotype 1 infection who received peginterferon and ribavirin with a direct-acting antiviral agent, such as telaprevir, boceprevir, simeprevir, or sofosbuvir.

Findings from small, phase 2 studies suggest that peginterferon-free regimens of direct-acting antiviral agents with or without ribavirin may be associated with high rates of sustained virologic response at post-treatment week 12. The rate observed here is consistent with results of a phase 2b trial in which treatment for 12 weeks with ABT-450/r, ombitasvir, dasabuvir, and ribavirin was associated with a sustained virologic response at post-treatment week 24 in 96% of previously untreated patients with HCV genotype 1 infection.

The efficacy of different treatment regimens with antiviral agents may vary according to HCV genotype (1a or 1b). In this trial, the rates of sustained virologic response at post-treatment week 12 were similar among patients with HCV genotype 1a infection and those with HCV genotype 1b infection (95.3% and 98.0%, respectively). Previous reports have indicated reduced response rates with peginterferon-containing therapies among patients with certain characteristics, including IL28B non-CC genotype, black race, and high viral load. In this trial, the rates were high across these subgroups. The double-blind, placebo-controlled study design allowed the comparison of adverse events between patients receiving the active regimen and those receiving placebo.

Fatigue and headache were the most common adverse events, but their frequency did not differ significantly between the study groups. The most common adverse events that occurred significantly more frequently among patients receiving the active regimen were nausea, pruritus, insomnia, diarrhea, and asthenia. The rate of discontinuation due to adverse events was 0.6% in each study group. The rate of serious adverse events was low, with such events occurring in 2.1% of the patients who received the active regimen (10 patients). The adverse-event profile for the active regimen compares favorably with that for a protease inhibitor plus peginterferon–ribavirin.

Rates of 9 to 12% for serious adverse events and rates of 10 to 16% for discontinuation due to adverse events have been reported among previously untreated patients receiving telaprevir or boceprevir with peginterferon–ribavirin. Clinically significant anemia leading to erythropoietin use, reduction of the ribavirin dose, and occasionally blood transfusions have also been reported.

In our study, among patients receiving the active regimen during the double-blind period, reductions in the hemoglobin level of grade 1 were common (in 47.5% of patients), hemoglobin reductions of grade 2 were uncommon (in 5.8%), and there were no hemoglobin reductions of grade 3 or 4. Modifications of the ribavirin dose due to adverse events were relatively uncommon (in 26 patients [5.5%]), and no patient discontinued the study drug owing to anemia. An elevated total bilirubin level was the most frequent laboratory abnormality of grade 3 or 4. The elevations were typically transient and were infrequently associated with jaundice. The elevations in the bilirubin level involved predominantly indirect bilirubin and were consistent with the known inhibitory effect of ABT-450 on the bilirubin transporters OATP1B1 and OATP1B3 and the known role of ribavirin in hemolysis. We excluded from our trial patients with cirrhosis and patients who were using medications contraindicated with ritonavir and ribavirin.

Although this study did not include patients who had received prior treatment, Zeuzem et al. Now report in the Journal that a study evaluating the same active regimen in patients who had received prior treatment with peginterferon–ribavirin has shown high rates of sustained virologic response at post-treatment week 12. In conclusion, a multitargeted approach combining the direct-acting antiviral agents ABT-450/r–ombitasvir and dasabuvir with ribavirin was associated with a high rate of sustained virologic response at post-treatment week 12, with a low rate of treatment discontinuation, among previously untreated patients with HCV genotype 1 infection and no cirrhosis. Supported by AbbVie. Feld reports receiving consulting fees from Boehringer Ingelheim, Gilead Sciences, Vertex Pharmaceuticals, Achillion Pharmaceuticals, Bristol-Myers Squibb, Idenix Pharmaceuticals, Janssen Pharmaceuticals, and Merck; and grant support from Roche, Boehringer Ingelheim, Gilead Sciences, Santaris Pharma, and Vertex Pharmaceuticals. Kowdley reports receiving fees for serving on advisory boards from Boehringer Ingelheim, Gilead Sciences, Ikaria Pharmaceuticals, Janssen Pharmaceuticals, Merck, Vertex Pharmaceuticals, Trio Health, Pharmasset, and Tekmira Pharmaceuticals; consulting fees from Novartis; and grant support from Beckman Coulter, Bristol-Myers Squibb, Intercept Pharmaceuticals, Mochida Pharmaceutical, Conatus Pharmaceuticals, Genentech, GlaxoSmithKline, Boehringer Ingelheim, Gilead Sciences, Ikaria Pharmaceuticals, Janssen Pharmaceuticals, Merck, Vertex Pharmaceuticals, and Pharmasset.

Pilot-Matias, Dr. DaSilva-Tillmann, Dr. Podsadecki, and Dr. Bernstein report being employees of and holding stock or stock options in AbbVie.

Sigal reports receiving fees for serving on an advisory board and lecture fees from Gilead Sciences; consulting fees from Otsuka Pharmaceutical and GlaxoSmithKline; and grant support from Gilead Sciences, Boehringer Ingelheim, Otsuka Pharmaceutical, Salix Pharmaceuticals, GlaxoSmithKline, Ikaria Pharmaceuticals, Hyperion Therapeutics, and Vertex Pharmaceuticals. Nelson reports receiving grant support from AbbVie, Boehringer Ingelheim, Bristol-Myers Squibb, Genentech, Gilead Sciences, Idenix Pharmaceuticals, Kadmon Pharmaceuticals, Merck, and Vertex Pharmaceuticals; and participating in continuing medical education activities with Clinical Care Options, Projects in Knowledge, and Practice Point Communications. Crawford reports receiving fees for serving on an advisory board from Bristol-Myers Squibb, Janssen Pharmaceuticals, and Gilead Sciences. Weiland reports receiving fees for serving on an advisory board and lecture fees from Gilead Sciences, Bristol-Myers Squibb, Medivir, Johnson & Johnson, and Merck. Aguilar reports receiving lecture fees from Santaris Pharma and Ironwood Pharmaceuticals. No other potential conflict of interest relevant to this article was reported. Provided by the authors are available with the full text of this article at NEJM.org.

This article was published on April 11, 2014, at NEJM.org. We thank the trial participants and coordinators who made this study possible; Sara Siggelkow, Tiffany Larson, Rajeev Menon, Amit Khatri, Prajakta Badri, Sandrine Schermack, Evelyn Lim, Helene Marie-Claude Bergeron, Hsiao-Ming Sharon Sun, Christine Collins, Rakesh Tripathi, Preethi Krishnan, Michelle Irvin, Jill Beyer, Thomas Reisch, and Gretja Schnell for contributions to the study; and Christine Ratajczak (AbbVie) for providing medical-writing services for an earlier draft of the manuscript.