Experimental design on the simplex

Optimum experimental designs depend on the design criterion, the model andthe design region. The talk will consider the design of experiments for regressionmodels in which there is a single response with the explanatory variables lying ina simplex. One example is experiments on various compositions of glass such asthose considered by Martin, Bursnall, and Stillman (2001).Because of the highly symmetric nature of the simplex, the class of models thatare of interest, typically Scheff´e polynomials (Scheff´e 1958) are rather differentfrom those of standard regression analysis. The optimum designs are also ratherdifferent, inheriting a high degree of symmetry from the models.In the talk I will hope to discuss a variety of modes for such experiments. ThenI will discuss constrained mixture experiments, when not all the simplex is availablefor experimentation. Other important aspects include mixture experimentswith extra non-mixture factors and the blocking of mixture experiments.Much of the material is in Chapter 16 of Atkinson, Donev, and Tobias (2007).If time and my research allows, I would hope to finish with a few comments ondesign when the responses, rather than the explanatory variables, lie in a simplex.ReferencesAtkinson, A. C., A. N. Donev, and R. D. Tobias (2007). Optimum ExperimentalDesigns, with SAS. Oxford: Oxford University Press.Martin, R. J., M. C. Bursnall, and E. C. Stillman (2001). Further results onoptimal and efficient designs for constrained mixture experiments. In A. C.Atkinson, B. Bogacka, and A. Zhigljavsky (Eds.), Optimal Design 2000,pp. 225–239. Dordrecht: Kluwer.Scheff´e, H. (1958). Experiments with mixtures. Journal of the Royal StatisticalSociety, Ser. B 20, 344–360.1

Revenue management under general discrete choice model of consumer behavior

Customer choice behavior, such as 'buy-up' and 'buy-down', is an importantphe-nomenon in a wide range of industries. Yet there are few models ormethodologies available to exploit this phenomenon within yield managementsystems. We make some progress on filling this void. Specifically, wedevelop a model of yield management in which the buyers' behavior ismodeled explicitly using a multi-nomial logit model of demand. Thecontrol problem is to decide which subset of fare classes to offer ateach point in time. The set of open fare classes then affects the purchaseprobabilities for each class. We formulate a dynamic program todetermine the optimal control policy and show that it reduces to a dynamicnested allocation policy. Thus, the optimal choice-based policy caneasily be implemented in reservation systems that use nested allocationcontrols. We also develop an estimation procedure for our model based onthe expectation-maximization (EM) method that jointly estimates arrivalrates and choice model parameters when no-purchase outcomes areunobservable. Numerical results show that this combined optimization-estimation approach may significantly improve revenue performancerelative to traditional leg-based models that do not account for choicebehavior.

On the performance of small-area estimators: Fixed vs. random area parameters

Most methods for small-area estimation are based on composite estimators derived from design- or model-based methods. A composite estimator is a linear combination of a direct and an indirect estimator with weights that usually depend on unknown parameters which need to be estimated. Although model-based small-area estimators are usually based on random-effects models, the assumption of fixed effects is at face value more appropriate.Model-based estimators are justified by the assumption of random (interchangeable) area effects; in practice, however, areas are not interchangeable. In the present paper we empirically assess the quality of several small-area estimators in the setting in which the area effects are treated as fixed. We consider two settings: one that draws samples from a theoretical population, and another that draws samples from an empirical population of a labor force register maintained by the National Institute of Social Security (NISS) of Catalonia. We distinguish two types of composite estimators: a) those that use weights that involve area specific estimates of bias and variance; and, b) those that use weights that involve a common variance and a common squared bias estimate for all the areas. We assess their precision and discuss alternatives to optimizing composite estimation in applications.

Small-area estimation with spatial similarity

A class of composite estimators of small area quantities that exploit spatial (distancerelated)similarity is derived. It is based on a distribution-free model for the areas, but theestimators are aimed to have optimal design-based properties. Composition is applied alsoto estimate some of the global parameters on which the small area estimators depend.It is shown that the commonly adopted assumption of random effects is not necessaryfor exploiting the similarity of the districts (borrowing strength across the districts). Themethods are applied in the estimation of the mean household sizes and the proportions ofsingle-member households in the counties (comarcas) of Catalonia. The simplest version ofthe estimators is more efficient than the established alternatives, even though the extentof spatial similarity is quite modest.

Network-based scoring system for genome-scale metabolic reconstructions

Background: Network reconstructions at the cell level are a major development in Systems Biology. However, we are far from fully exploiting its potentialities. Often, the incremental complexity of the pursued systems overrides experimental capabilities, or increasingly sophisticated protocols are underutilized to merely refine confidence levels of already established interactions. For metabolic networks, the currently employed confidence scoring system rates reactions discretely according to nested categories of experimental evidence or model-based likelihood. Results: Here, we propose a complementary network-based scoring system that exploits the statistical regularities of a metabolic network as a bipartite graph. As an illustration, we apply it to the metabolism of Escherichia coli. The model is adjusted to the observations to derive connection probabilities between individual metabolite-reaction pairs and, after validation, to assess the reliability of each reaction in probabilistic terms. This network-based scoring system uncovers very specific reactions that could be functionally or evolutionary important, identifies prominent experimental targets, and enables further confirmation of modeling results. Conclusions: We foresee a wide range of potential applications at different sub-cellular or supra-cellular levels of biological interactions given the natural bipartivity of many biological networks.

Monitoring mortality as an indicator of influenza in Catalonia, Spain.

This study aimed to investigate the behaviour of two indicators of influenza activity in the area of Barcelona and to evaluate the usefulness of modelling them to improve the detection of influenza epidemics. DESIGN: Descriptive time series study using the number of deaths due to all causes registered by funeral services and reported cases of influenza-like illness. The study concentrated on five influenza seasons, from week 45 of 1988 to week 44 of 1993. The weekly number of deaths and cases of influenza-like illness registered were processed using identification of a time series ARIMA model. SETTING: Six large towns in the Barcelona province which have more than 60,000 inhabitants and funeral services in all of them. MAIN RESULTS: For mortality, the proposed model was an autoregressive one of order 2 (ARIMA (2,0,0)) and for morbidity it was one of order 3 (ARIMA (3,0,0)). Finally, the two time series were analysed together to facilitate the detection of possible implications between them. The joint study of the two series shows that the mortality series can be modelled separately from the reported morbidity series, but the morbidity series is influenced as much by the number of previous cases of influenza reported as by the previous mortality registered. CONCLUSIONS: The model based on general mortality is useful for detecting epidemic activity of influenza. However, because there is not an absolute gold standard that allows definition of the beginning of the epidemic, the final decision of when it is considered an epidemic and control measures recommended should be taken after evaluating all the indicators included in the influenza surveillance programme.

FAM-MDR: a flexible family-based multifactor dimensionality reduction technique to detect epistasis using related individuals

We propose a novel multifactor dimensionality reduction method for epistasis detection in small or extended pedigrees, FAM-MDR. It combines features of the Genome-wide Rapid Association using Mixed Model And Regression approach (GRAMMAR) with Model-Based MDR (MB-MDR). We focus on continuous traits, although the method is general and can be used for outcomes of any type, including binary and censored traits. When comparing FAM-MDR with Pedigree-based Generalized MDR (PGMDR), which is a generalization of Multifactor Dimensionality Reduction (MDR) to continuous traits and related individuals, FAM-MDR was found to outperform PGMDR in terms of power, in most of the considered simulated scenarios. Additional simulations revealed that PGMDR does not appropriately deal with multiple testing and consequently gives rise to overly optimistic results. FAM-MDR adequately deals with multiple testing in epistasis screens and is in contrast rather conservative, by construction. Furthermore, simulations show that correcting for lower order (main) effects is of utmost importance when claiming epistasis. As Type 2 Diabetes Mellitus (T2DM) is a complex phenotype likely influenced by gene-gene interactions, we applied FAM-MDR to examine data on glucose area-under-the-curve (GAUC), an endophenotype of T2DM for which multiple independent genetic associations have been observed, in the Amish Family Diabetes Study (AFDS). This application reveals that FAM-MDR makes more efficient use of the available data than PGMDR and can deal with multi-generational pedigrees more easily. In conclusion, we have validated FAM-MDR and compared it to PGMDR, the current state-of-the-art MDR method for family data, using both simulations and a practical dataset. FAM-MDR is found to outperform PGMDR in that it handles the multiple testing issue more correctly, has increased power, and efficiently uses all available information.

Economic evaluation of the levonorgestrel-releasing intrauterine system for the treatment of dysfunctional uterine bleeding in Spain

To compare the cost and effectiveness of the levonorgestrel-releasing intrauterine system (LNG-IUS) versus combined oral contraception (COC) and progestogens (PROG) in first-line treatment of dysfunctional uterine bleeding (DUB) in Spain. STUDY DESIGN: A cost-effectiveness and cost-utility analysis of LNG-IUS, COC and PROG was carried out using a Markov model based on clinical data from the literature and expert opinion. The population studied were women with a previous diagnosis of idiopathic heavy menstrual bleeding. The analysis was performed from the National Health System perspective, discounting both costs and future effects at 3%. In addition, a sensitivity analysis (univariate and probabilistic) was conducted. RESULTS: The results show that the greater efficacy of LNG-IUS translates into a gain of 1.92 and 3.89 symptom-free months (SFM) after six months of treatment versus COC and PROG, respectively (which represents an increase of 33% and 60% of symptom-free time). Regarding costs, LNG-IUS produces savings of 174.2-309.95 and 230.54-577.61 versus COC and PROG, respectively, after 6 months-5 years. Apart from cost savings and gains in SFM, quality-adjusted life months (QALM) are also favourable to LNG-IUS in all scenarios, with a range of gains between 1 and 2 QALM compared to COC and PROG. CONCLUSIONS: The results indicate that first-line use of the LNG-IUS is the dominant therapeutic option (less costly and more effective) in comparison with first-line use of COC or PROG for the treatment of DUB in Spain. LNG-IUS as first line is also the option that provides greatest health-related quality of life to patients.

Collaborative explicit plasticity framework: a conceptual scheme for the generation of plastic and group-aware user interfaces

The advent of new advances in mobile computing has changed the manner we do our daily work, even enabling us to perform collaborative activities. However, current groupware approaches do not offer an integrating and efficient solution that jointly tackles the flexibility and heterogeneity inherent to mobility as well as the awareness aspects intrinsic to collaborative environments. Issues related to the diversity of contexts of use are collected under the term plasticity. A great amount of tools have emerged offering a solution to some of these issues, although always focused on individual scenarios. We are working on reusing and specializing some already existing plasticity tools to the groupware design. The aim is to offer the benefits from plasticity and awareness jointly, trying to reach a real collaboration and a deeper understanding of multi-environment groupware scenarios. In particular, this paper presents a conceptual framework aimed at being a reference for the generation of plastic User Interfaces for collaborative environments in a systematic and comprehensive way. Starting from a previous conceptual framework for individual environments, inspired on the model-based approach, we introduce specific components and considerations related to groupware.

Economic evaluation of the levonorgestrel-releasing intrauterine system for the treatment of dysfunctional uterine bleeding in Spain

To compare the cost and effectiveness of the levonorgestrel-releasing intrauterine system (LNG-IUS) versus combined oral contraception (COC) and progestogens (PROG) in first-line treatment of dysfunctional uterine bleeding (DUB) in Spain. STUDY DESIGN: A cost-effectiveness and cost-utility analysis of LNG-IUS, COC and PROG was carried out using a Markov model based on clinical data from the literature and expert opinion. The population studied were women with a previous diagnosis of idiopathic heavy menstrual bleeding. The analysis was performed from the National Health System perspective, discounting both costs and future effects at 3%. In addition, a sensitivity analysis (univariate and probabilistic) was conducted. RESULTS: The results show that the greater efficacy of LNG-IUS translates into a gain of 1.92 and 3.89 symptom-free months (SFM) after six months of treatment versus COC and PROG, respectively (which represents an increase of 33% and 60% of symptom-free time). Regarding costs, LNG-IUS produces savings of 174.2-309.95 and 230.54-577.61 versus COC and PROG, respectively, after 6 months-5 years. Apart from cost savings and gains in SFM, quality-adjusted life months (QALM) are also favourable to LNG-IUS in all scenarios, with a range of gains between 1 and 2 QALM compared to COC and PROG. CONCLUSIONS: The results indicate that first-line use of the LNG-IUS is the dominant therapeutic option (less costly and more effective) in comparison with first-line use of COC or PROG for the treatment of DUB in Spain. LNG-IUS as first line is also the option that provides greatest health-related quality of life to patients.

A microquasar model applied to unidentified gamma-ray sources

Among unidentified gamma-ray sources in the galactic plane, there are some that present significant variability and have been proposed to be high-mass microquasars. To deepen the study of the possible association between variable low galactic latitude gamma-ray sources and microquasars, we have applied a leptonic jet model based on the microquasar scenario that reproduces the gamma-ray spectrum of three unidentified gamma-ray sources, 3EG J1735-1500, 3EG J1828+0142 and GRO J1411-64, and is consistent with the observational constraints at lower energies. We conclude that if these sources were generated by microquasars, the particle acceleration processes could not be as efficient as in other objects of this type that present harder gamma-ray spectra. Moreover, the dominant mechanism of high-energy emission should be synchrotron self-Compton (SSC) scattering, and the radio jets may only be observed at low frequencies. For each particular case, further predictions of jet physical conditions and variability generation mechanisms have been made in the context of the model. Although there might be other candidates able to explain the emission coming from these sources, microquasars cannot be excluded as counterparts. Observations performed by the next generation of gamma-ray instruments, like GLAST, are required to test the proposed model.

Comparison of a deterministic and a data driven model to describe MBR fouling

Membrane bioreactors (MBRs) are a combination of activated sludge bioreactors and membrane filtration, enabling high quality effluent with a small footprint. However, they can be beset by fouling, which causes an increase in transmembrane pressure (TMP). Modelling and simulation of changes in TMP could be useful to describe fouling through the identification of the most relevant operating conditions. Using experimental data from a MBR pilot plant operated for 462days, two different models were developed: a deterministic model using activated sludge model n°2d (ASM2d) for the biological component and a resistance in-series model for the filtration component as well as a data-driven model based on multivariable regressions. Once validated, these models were used to describe membrane fouling (as changes in TMP over time) under different operating conditions. The deterministic model performed better at higher temperatures (>20°C), constant operating conditions (DO set-point, membrane air-flow, pH and ORP), and high mixed liquor suspended solids (>6.9gL-1) and flux changes. At low pH (<7) or periods with higher pH changes, the data-driven model was more accurate. Changes in the DO set-point of the aerobic reactor that affected the TMP were also better described by the data-driven model. By combining the use of both models, a better description of fouling can be achieved under different operating conditions