Capabilities and Equality of Health I

The concept of capabilities, introduced originally by Sen with the aim to provide a better basis for the theory of inequality, has inspired many researchers but has not found any simple formal representation which might be instrumental in the construction of a comprehensive theory of equality. In the present paper, we present a formalization of the concept of capabilities based on Lancasterian characteristics, whereby a functioning of an individual is a method for transforming an initial position to a final outcome. In this context, we investigate whether preferences over capabilities as sets of functionings can be rationalized by maximization of a suitable utility function over the set of functionings. Such a rationalization turns out to be possible only in cases which must be considered exceptional and which do not allow for interesting applications of the capability approach to questions of health or equality. The conclusion which can be obtained from the predominantly negative results is that a formal description of capabilities much involve ideas which go beyond the simple representation as a family of choice sets.capabilities; characteristics; equality of health

Capabilities and Equality of Health II: Capabilities as Options

The concept of capabilities, introduced originally by Sen, has inspired many researchers but has not found any simple formal representation which might be instrumental in the construction of a comprehensive theory of equality. In a previous paper (Keiding, 2005), we investigated whether preferences over capabilities as sets of functionings can be rationalized by maximization of a suitable utility function over the set of functionings. Such a rationalization turned out to be possible only in cases which must be considered exceptional and which do not allowfor interesting applications of the capability approach to questions of health or equality. In the present paper we extend the notion of rationalizing orderings of capabilities to a dynamical context, in the sense that the utility function is not yet revealed to the individual at the time when the capabilities are ordered. It turns out that orderings which are in accordance with such probabilistic utility assignments can be characterized by a smaller set of the axioms previously considered.Capabilities; characteristics; equality of health

On the Foundation of Guidelines for Health Economic Evaluation

In recent years, there has been increased interest in setting up guidelines for carrying out cost-effectiveness analysis of medical interventions, and some such guidelines have indeed been established. In the paper, we present a model of information retrievement and use in which we can study the role of guidelines. The main result, which is a version of the well-known theorem of Blackwell (1948), shows that in cases where there are sufficiently many decisions to be made on the basis of the information obtained, there can be no objective ranking of methods, except the trivial one stating that more information is better than less. The consequence is that guidelines, and the very detailed version known as the reference case approach, may have administrative advantages but can be harmful when considered as an aid towards better decisions.cost-effectiveness; guidelines; Blackwell’s theorem

Standardization and Control for Confounding in Observational Studies: A Historical Perspective

Control for confounders in observational studies was generally handled through stratification and standardization until the 1960s. Standardization typically reweights the stratum-specific rates so that exposure categories become comparable. With the development first of loglinear models, soon also of nonlinear regression techniques (logistic regression, failure time regression) that the emerging computers could handle, regression modelling became the preferred approach, just as was already the case with multiple regression analysis for continuous outcomes. Since the mid 1990s it has become increasingly obvious that weighting methods are still often useful, sometimes even necessary. On this background we aim at describing the emergence of the modelling approach and the refinement of the weighting approach for confounder control.Comment: Published in at http://dx.doi.org/10.1214/13-STS453 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Product-limit estimators of the gap time distribution of a renewal process under different sampling patterns

Nonparametric estimation of the gap time distribution in a simple renewal process may be considered a problem in survival analysis under particular sampling frames corresponding to how the renewal process is observed. This note describes several such situations where simple product limit estimators, though inefficient, may still be useful

Interaction sheaves on continuous domains

We introduce a description of the power structure which is inherent in a strategic game form using the concept of an interaction sheaf. The latter assigns to each open set of outcomes a set of interaction arrays, specifying the changes that coalitions can make if outcome belongs to this open set. The interaction sheaf generalizes the notion of effectivity functions which has been widely used in implementation theory, taking into consideration that changes in outcome may be sustained not only by single coalitions but possibly by several coalitions, depending on the underlying strategy choices. Also, it allows us to consider game forms with not necessarily finite sets of outcomes, generalizing the results on solvability of game forms obtained in the finite case in Abdou and Keiding (2003).Nash equilibrium; strong equilibrium; solvability; effectivity; acyclicity

Biological and sociological interpretations of age-adjustment in studies of higher order birth rates

Several studies of the effect of education on second or third birth rates (e.g. Hoem et al. (2001)) have used the concept of relative age at previous birth (B.Hoem (1996)). B.Hoem's idea was to focus on the social meaning of age at previous birth. We broaden the discussion by considering other interpretations of the explanatory power of the age at previous birth, particularly via known trends in biological fecundity. A mathematical analysis of the approach reveals side effects that have not been taken sufficiently into account. Our recommendation is not to use the relative age approach without supplementing it with the more traditional approach which includes the actual age at previous birth.education, fertility, higher order birth rates, relative age

Graphical Models for Inference Under Outcome-Dependent Sampling

We consider situations where data have been collected such that the sampling depends on the outcome of interest and possibly further covariates, as for instance in case-control studies. Graphical models represent assumptions about the conditional independencies among the variables. By including a node for the sampling indicator, assumptions about sampling processes can be made explicit. We demonstrate how to read off such graphs whether consistent estimation of the association between exposure and outcome is possible. Moreover, we give sufficient graphical conditions for testing and estimating the causal effect of exposure on outcome. The practical use is illustrated with a number of examples.Comment: Published in at http://dx.doi.org/10.1214/10-STS340 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

On the Continuity of Representations of Effectivity Functions.

An effectivity function assigns to each coalition of individuals in a society a family of subsets of alternatives such that the coalition can force the outcome of society’s choice to be a member of each of the subsets separately. A representation of an effectivity function is a game form with the same power structure as that speci?ed by the effectivity function. In the present paper we investigate the continuity properties of the outcome functions of such representation. It is shown that while it is not in general possible to find continuous representations, there are important subfamilies of effectivity functions for which continuous representations exist. Moreover, it is found that in the study of continuous representations one may practically restrict attention to effectivity functions on the Cantor set. Here it is found that general effectivity functions have representations with lower or upper semicontinuous outcome function.

Regulated Competition under Increasing Returns to Scale

This paper proposes a mechanism for the regulation of firms in the context of asymmetric information with the aim to induce firms to report its private information truthfully and to save information rents. Baron and Myerson (1982) have considered this problem and derived an optimal policy for regulating a monopolist with unknown costs. They show that it was possible to create a regulatory mechanism that induced the firm to report its private information truthfully. To secure this, a part of the mechanism is to pay the firm a subsidy. This article presents a regulatory mechanism which explores competition in the context of an industry characterized by increasing returns to scale. In contrast to the model in this article, the Baron and Myerson model doesn’t consider increasing returns to scale. In equilibrium each firm chooses to report truthfully without receiving any subsidy. However, the use of competition gives rise to an efficiency lost.