Methods for Equivalence and Noninferiority Testing

Classical hypothesis testing focuses on testing whether treatments have differential effects on outcome. However, sometimes clinicians may be more interested in determining whether treatments are equivalent or whether one has noninferior outcomes. We review the hypotheses for these noninferiority and equivalence research questions, consider power and sample size issues, and discuss how to perform such a test for both binary and survival outcomes. The methods are illustrated on 2 recent studies in hematopoietic cell transplantation.

Product placement in movies: a cross cultural study between Brazil and the USA

The broader objective of this study undertaking can briefly be articulated in particulate aims as follows: to measure the attitudes of consumers regarding the brand displayed by this strategy as well as to highlight recall, recognition and purchase intentions generated by product placement on consumers. In addition, check the differences and similarities between the behavior of Brazilian and American consumers caused by the influence of product placements. The study was undertaken targeting consumer audience in Brazil and the U.S. A rang3 modeling set ups were performed in order to realign study instruments and hypothesis towards the research objectives. This study gave focus on the following hypothesized models. H1: Consumers / Participants who viewed the brands / products in the movie have a higher brand / product recall compared to the consumers / participants who did not view the brands / products in the movie. H2: US Consumers / Participants are able to recognize and recall brands / products which appear in the background of the movie than Brazil. H3: Consumers / participants from USA are more accepting of product placements compared to their counterparts in Brazil. H4: There are discernible similarities in consumer / participant brand attitudes and purchase intentions in consumers / participants from USA and Brazil in spite of the fact that their country of origin is different. Cronbach’s Alpha Coefficient ensured the reliability of survey instruments. The study involved the use of the Structural Equation Modeling (SEM) for the hypothesis testing. This study used the Confirmatory Factor Analysis (CFA) to assess both the convergent and discriminant validities instead of using the Exploratory Factor Analysis (EFA) or the Principal Component Analysis (PCA). This reinforced for the use of the regression Chi Square and T statistical tests in further. Only hypothesis H3 was rejected, the rest were not. T test provided insight findings on specific subgroup significant differences. In the SEM testing, the error variance for product placement attitudes was negative for both the groups. On this The Heywood Case came in handy to fix negative values. The researcher used both quantitative and qualitative approach where closed ended questionnaires and interviews respectively were used to collect primary data. The results were additionally provided with tabulations. It can be concluded that, product placement varies markedly in the U.S. from Brazil based on the influence a range of factors provided in the study. However, there are elements of convergence probably driven by the convergence in technology. In order, product placement to become more competitive in the promotional marketing, there will be the need for researchers to extend focus from the traditional variables and add knowledge on the conventional marketplace factors that is the sell-ability of the product placement technologies and strategies.

Essays on Spatial Econometrics

Esta dissertação concentra-se nos processos estocásticos espaciais definidos em um reticulado, os chamados modelos do tipo Cliff & Ord. Minha contribuição nesta tese consiste em utilizar aproximações de Edgeworth e saddlepoint para investigar as propriedades em amostras finitas do teste para detectar a presença de dependência espacial em modelos SAR (autoregressivo espacial), e propor uma nova classe de modelos econométricos espaciais na qual os parâmetros que afetam a estrutura da média são distintos dos parâmetros presentes na estrutura da variância do processo. Isto permite uma interpretação mais clara dos parâmetros do modelo, além de generalizar uma proposta de taxonomia feita por Anselin (2003). Eu proponho um estimador para os parâmetros do modelo e derivo a distribuição assintótica do estimador. O modelo sugerido na dissertação fornece uma interpretação interessante ao modelo SARAR, bastante comum na literatura. A investigação das propriedades em amostras finitas dos testes expande com relação a literatura permitindo que a matriz de vizinhança do processo espacial seja uma função não-linear do parâmetro de dependência espacial. A utilização de aproximações ao invés de simulações (mais comum na literatura), permite uma maneira fácil de comparar as propriedades dos testes com diferentes matrizes de vizinhança e corrigir o tamanho ao comparar a potência dos testes. Eu obtenho teste invariante ótimo que é também localmente uniformemente mais potente (LUMPI). Construo o envelope de potência para o teste LUMPI e mostro que ele é virtualmente UMP, pois a potência do teste está muito próxima ao envelope (considerando as estruturas espaciais definidas na dissertação). Eu sugiro um procedimento prático para construir um teste que tem boa potência em uma gama de situações onde talvez o teste LUMPI não tenha boas propriedades. Eu concluo que a potência do teste aumenta com o tamanho da amostra e com o parâmetro de dependência espacial (o que está de acordo com a literatura). Entretanto, disputo a visão consensual que a potência do teste diminui a medida que a matriz de vizinhança fica mais densa. Isto reflete um erro de medida comum na literatura, pois a distância estatística entre a hipótese nula e a alternativa varia muito com a estrutura da matriz. Fazendo a correção, concluo que a potência do teste aumenta com a distância da alternativa à nula, como esperado.

A SURVEY OF THE LIKELIHOOD APPROACH TO BIOEQUIVALENCE TRIALS

Bioequivalence trials are abbreviated clinical trials whereby a generic drug or new formulation is evaluated to determine if it is "equivalent" to a corresponding previously approved brand-name drug or formulation. In this manuscript, we survey the process of testing bioequivalence and advocate the likelihood paradigm for representing the resulting data as evidence. We emphasize the unique conflicts between hypothesis testing and confidence intervals in this area - which we believe are indicative of the existence of the systemic defects in the frequentist approach - that the likelihood paradigm avoids. We suggest the direct use of profile likelihoods for evaluating bioequivalence and examine the main properties of profile likelihoods and estimated likelihoods under simulation. This simulation study shows that profile likelihoods are a reasonable alternative to the (unknown) true likelihood for a range of parameters commensurate with bioequivalence research. Our study also shows that the standard methods in the current practice of bioequivalence trials offers only weak evidence from the evidential point of view.

Accurate and robust reconstruction of proximal femur from sparse intraoperative data and dense point distribution model for surgical navigation

Constructing a 3D surface model from sparse-point data is a nontrivial task. Here, we report an accurate and robust approach for reconstructing a surface model of the proximal femur from sparse-point data and a dense-point distribution model (DPDM). The problem is formulated as a three-stage optimal estimation process. The first stage, affine registration, is to iteratively estimate a scale and a rigid transformation between the mean surface model of the DPDM and the sparse input points. The estimation results of the first stage are used to establish point correspondences for the second stage, statistical instantiation, which stably instantiates a surface model from the DPDM using a statistical approach. This surface model is then fed to the third stage, kernel-based deformation, which further refines the surface model. Handling outliers is achieved by consistently employing the least trimmed squares (LTS) approach with a roughly estimated outlier rate in all three stages. If an optimal value of the outlier rate is preferred, we propose a hypothesis testing procedure to automatically estimate it. We present here our validations using four experiments, which include 1 leave-one-out experiment, 2 experiment on evaluating the present approach for handling pathology, 3 experiment on evaluating the present approach for handling outliers, and 4 experiment on reconstructing surface models of seven dry cadaver femurs using clinically relevant data without noise and with noise added. Our validation results demonstrate the robust performance of the present approach in handling outliers, pathology, and noise. An average 95-percentile error of 1.7-2.3 mm was found when the present approach was used to reconstruct surface models of the cadaver femurs from sparse-point data with noise added.

Datenanalyse. Das Null-Ritual und der Umgang mit Effekten in der Zeitschrift für Sportpsychologie

Ziel dieses Beitrages ist die Analyse der Anwendung empirischer Tests in der deutschsprachigen Sportpsychologie. Die Ergebnisse vergleichbarer Analysen, bspw. in der Psychologie, zeigen, dass zwischen Anforderungen aus Testkonzepten und empirischer Realität Unterschiede existieren, die bislang für die Sportpsychologie nicht beschrieben und bewertet worden sind. Die Jahrgänge 1994–2007 der Zeitschrift für Sportpsychologie (früher psychologie und sport) wurden danach untersucht, ob Forschungsfragen formuliert, welche Stichprobenart gewählt, welches Testkonzept verwendet, welches Signifikanzniveau benutzt und ob statistische Probleme diskutiert wurden. 83 Artikel wurden von zwei unabhängigen Bewertern nach diesen Aspekten kategorisiert. Als Ergebnis ist festzuhalten, dass in der sportpsychologischen Forschung überwiegend eine Mischung aus Fishers Signifikanztesten sowie Neyman-Pearsons-Hypothesentesten zur Anwendung kommt,das sogenannte „Hybrid-Modell” oder „Null-Ritual”. Die Beschreibung der Teststärke ist kaum zu beobachten. Eine zeitliche Analyse der Beiträge zeigt, dass vor allem die Benutzung von Effektgrößen in den letzten Jahren zugenommen hat. Abschließend werden Ansätze zur Verbesserung und der Vereinheitlichung der Anwendung empirischer Tests vorgeschlagen und diskutiert.

Impacto del entorno institucional en la financiación público-privada de infraestructuras de transporte

Actualmente el sector privado posee un papel relevante en la provisión y gestión de infraestructuras de transporte en los países de ingreso medio‐bajo, principalmente a través de los proyectos de participación público‐privada (PPPs). Muchos países han impulsado este tipo de proyectos con el fin de hacer frente a la gran demanda de infraestructuras de transporte existente, debido a la escasez de recursos públicos y a la falta de eficiencia en la provisión de los servicios públicos. Como resultado, las PPPs han experimentado un crecimiento importante en las últimas dos décadas a nivel mundial. A pesar de esta tendencia creciente, muchos países no han sido capaces de atraer la participación del sector privado para la provisión de sus infraestructuras o no han logrado el nivel de participación privada que habrían requerido para alcanzar sus objetivos. Según numerosos autores, el desarrollo y el éxito de los proyectos PPP de infraestructuras de transporte de cualquier país está condicionado por una diversidad de factores, siendo uno de ellos la calidad de su entorno institucional. La presente tesis tiene como objetivo principal analizar la influencia del entorno institucional en el volumen de inversión en proyectos de participación público‐privada de infraestructuras de transporte en los países de ingreso medio‐bajo. Para acometer dicho objetivo se ha realizado un análisis empírico de 81 países distribuidos en seis regiones del mundo, durante el periodo 1996‐2013. En el análisis se han desarrollado dos modelos empíricos aplicando principalmente dos metodologías: el contraste de hipótesis y los modelos de datos de panel Tobit. El desarrollo de estos modelos ha permitido analizar de una forma exhaustiva el tema de estudio. Los resultados obtenidos aportan evidencia de que la calidad del entorno institucional posee una influencia significativa en el volumen de inversión en los proyectos PPP de transporte. En general, en esta tesis se muestran evidencias empíricas de que el sector privado ha tendido a invertir en mayor medida en países con entornos institucionales fuertes, es decir, en aquellos países en los que ha existido un mayor nivel de Estado de derecho, estabilidad política y regulatoria, efectividad del gobierno, así como un mayor control de la corrupción. Además, aquellos países donde se ha registrado una mejora en el nivel de su calidad institucional también han experimentado un incremento en el volumen de inversión en PPP de transporte. The private sector has an important role in the provision and management of transport infrastructure in countries of medium‐low income, primarily through projects of public‐private partnerships (PPPs). Many countries have developed PPP projects to meet the high demand of transport infrastructure, due to the scarcity of public resources and the lack of efficiency in the provision of public services. As a result, PPPs have experienced a significant growth, worldwide, in the past two decades. Despite this growing trend, many countries have not been able to attract private sector participation in the provision of infrastructure or have not accomplished the level of private participation that would have required to achieve its objectives. According to various authors, the development of PPP projects for transport infrastructure is determined by a number of factors, one of them being the quality of the institutional environment. The main objective of this dissertation is to analyze the influence of the institutional environment on the volume of investment, in projects of public‐private partnerships for transport infrastructure in countries of medium‐low income. In order to meet this objective, we conducted an empirical analysis of 81 countries, in six regions of the world, during the period of 1996‐2013. The analysis used two empirical models, implementing different methodologies and various statistical techniques: hypothesis testing, and Tobit model using panel data. The development of these models allowed to carry out a more comprehensive analysis. The results show that the quality of the institutional environment has a significant influence on the volume of investment in PPP projects of transport. Overall, this dissertation shows that the private sector tends to invest more in countries with stronger institutional environments, i.e. countries where there has been a higher level of Rule of Law, political and regulatory stability, and an effective control of corruption. In addition, those that have improved the level of institutional quality have also experienced an increase in the volume of investment in PPP of transport.

Descripción de parámetros glóticos basados en el modelado de los pliegues vocales para la detección de patología de la voz

Las patologías de la voz se han transformado en los últimos tiempos en una problemática social con cierto calado. La contaminación de las ciudades, hábitos como el de fumar, el uso de aparatos de aire acondicionado, etcétera, contribuyen a ello. Esto alcanza más relevancia en profesionales que utilizan su voz de manera frecuente, como, por ejemplo, locutores, cantantes, profesores o teleoperadores. Por todo ello resultan de especial interés las técnicas de ayuda al diagnóstico que son capaces de extraer conclusiones clínicas a partir de una muestra de la voz grabada con un micrófono, frente a otras invasivas que implican la exploración utilizando laringoscopios, fibroscopios o videoendoscopios, técnicas en cualquier caso mucho más molestas para los pacientes al exigir la introducción parcial del instrumental citado por la garganta, en actuaciones consideradas de tipo quirúrgico. Dentro de aquellas técnicas se ha avanzado mucho en un período de tiempo relativamente corto. En lo que se refiere al diagnóstico de patologías, hemos pasado en los últimos quince años de trabajar principalmente con parámetros extraídos de la señal de voz –tanto en el dominio del tiempo como en el de la frecuencia– y con escalas elaboradas con valoraciones subjetivas realizadas por expertos a hacerlo también con parámetros procedentes de estimaciones de la fuente glótica. La importancia de utilizar la fuente glótica reside, a grandes rasgos, en que se trata de una señal vinculada directamente al estado de la estructura laríngea del locutor y también en que está generalmente menos influida por el tracto vocal que la señal de voz. Es conocido que el tracto vocal guarda más relación con el mensaje hablado, y su presencia dificulta el proceso de detección de patología vocal. Estas estimaciones de la fuente glótica han sido obtenidas a través de técnicas de filtrado inverso desarrolladas por nuestro grupo de investigación. Hemos conseguido, además, profundizar en la naturaleza de la señal glótica: somos capaces de descomponerla y relacionarla con parámetros biomecánicos de los propios pliegues vocales, obteniendo estimaciones de elementos como la masa, la pérdida de energía o la elasticidad del cuerpo y de la cubierta del pliegue, entre otros. De las componentes de la fuente glótica surgen también los denominados parámetros biométricos, relacionados con la forma de la señal, que constituyen por sí mismos una firma biométrica del individuo. También trabajaremos con parámetros temporales, relacionados con las diferentes etapas que se observan dentro de la señal glótica durante un ciclo de fonación. Por último, consideraremos parámetros clásicos de perturbación y energía de la señal. En definitiva, contamos ahora con una considerable cantidad de parámetros glóticos que conforman una base estadística multidimensional, destinada a ser capaz de discriminar personas con voces patológicas o disfónicas de aquellas que no presentan patología en la voz o con voces sanas o normofónicas. Esta tesis doctoral se ocupa de varias cuestiones: en primer lugar, es necesario analizar cuidadosamente estos nuevos parámetros, por lo que ofreceremos una completa descripción estadística de los mismos. También estudiaremos cuestiones como la distribución de los parámetros atendiendo a criterios como el de normalidad estadística de los mismos, ocupándonos especialmente de la diferencia entre las distribuciones que presentan sujetos sanos y sujetos con patología vocal. Para todo ello emplearemos diferentes técnicas estadísticas: generación de elementos y diagramas descriptivos, pruebas de normalidad y diversos contrastes de hipótesis, tanto paramétricos como no paramétricos, que considerarán la diferencia entre los grupos de personas sanas y los grupos de personas con alguna patología relacionada con la voz. Además, nos interesa encontrar relaciones estadísticas entre los parámetros, de cara a eliminar posibles redundancias presentes en el modelo, a reducir la dimensionalidad del problema y a establecer un criterio de importancia relativa en los parámetros en cuanto a su capacidad discriminante para el criterio patológico/sano. Para ello se aplicarán técnicas estadísticas como la Correlación Lineal Bivariada y el Análisis Factorial basado en Componentes Principales. Por último, utilizaremos la conocida técnica de clasificación Análisis Discriminante, aplicada a diferentes combinaciones de parámetros y de factores, para determinar cuáles de ellas son las que ofrecen tasas de acierto más prometedoras. Para llevar a cabo la experimentación se ha utilizado una base de datos equilibrada y robusta formada por doscientos sujetos, cien de ellos pertenecientes al género femenino y los restantes cien al género masculino, con una proporción también equilibrada entre los sujetos que presentan patología vocal y aquellos que no la presentan. Una de las aplicaciones informáticas diseñada para llevar a cabo la recogida de muestras también es presentada en esta tesis. Los distintos estudios estadísticos realizados nos permitirán identificar aquellos parámetros que tienen una mayor contribución a la hora de detectar la presencia de patología vocal. Alguno de los estudios, además, nos permitirá presentar una ordenación de los parámetros en base a su importancia para realizar la detección. Por otra parte, también concluiremos que en ocasiones es conveniente realizar una reducción de la dimensionalidad de los parámetros para mejorar las tasas de detección. Por fin, las propias tasas de detección constituyen quizá la conclusión más importante del trabajo. Todos los análisis presentes en el trabajo serán realizados para cada uno de los dos géneros, de acuerdo con diversos estudios previos que demuestran que los géneros masculino y femenino deben tratarse de forma independiente debido a las diferencias orgánicas observadas entre ambos. Sin embargo, en lo referente a la detección de patología vocal contemplaremos también la posibilidad de trabajar con la base de datos unificada, comprobando que las tasas de acierto son también elevadas. Abstract Voice pathologies have become recently in a social problem that has reached a certain concern. Pollution in cities, smoking habits, air conditioning, etc. contributes to it. This problem is more relevant for professionals who use their voice frequently: speakers, singers, teachers, actors, telemarketers, etc. Therefore techniques that are capable of drawing conclusions from a sample of the recorded voice are of particular interest for the diagnosis as opposed to other invasive ones, involving exploration by laryngoscopes, fiber scopes or video endoscopes, which are techniques much less comfortable for patients. Voice quality analysis has come a long way in a relatively short period of time. In regard to the diagnosis of diseases, we have gone in the last fifteen years from working primarily with parameters extracted from the voice signal (both in time and frequency domains) and with scales drawn from subjective assessments by experts to produce more accurate evaluations with estimates derived from the glottal source. The importance of using the glottal source resides broadly in that this signal is linked to the state of the speaker's laryngeal structure. Unlike the voice signal (phonated speech) the glottal source, if conveniently reconstructed using adaptive lattices, may be less influenced by the vocal tract. As it is well known the vocal tract is related to the articulation of the spoken message and its influence complicates the process of voice pathology detection, unlike when using the reconstructed glottal source, where vocal tract influence has been almost completely removed. The estimates of the glottal source have been obtained through inverse filtering techniques developed by our research group. We have also deepened into the nature of the glottal signal, dissecting it and relating it to the biomechanical parameters of the vocal folds, obtaining several estimates of items such as mass, loss or elasticity of cover and body of the vocal fold, among others. From the components of the glottal source also arise the so-called biometric parameters, related to the shape of the signal, which are themselves a biometric signature of the individual. We will also work with temporal parameters related to the different stages that are observed in the glottal signal during a cycle of phonation. Finally, we will take into consideration classical perturbation and energy parameters. In short, we have now a considerable amount of glottal parameters in a multidimensional statistical basis, designed to be able to discriminate people with pathologic or dysphonic voices from those who do not show pathology. This thesis addresses several issues: first, a careful analysis of these new parameters is required, so we will offer a complete statistical description of them. We will also discuss issues such as distribution of the parameters, considering criteria such as their statistical normality. We will take special care in the analysis of the difference between distributions from healthy subjects and the distributions from pathological subjects. To reach these goals we will use different statistical techniques such as: generation of descriptive items and diagramas, tests for normality and hypothesis testing, both parametric and nonparametric. These latter techniques consider the difference between the groups of healthy subjects and groups of people with an illness related to voice. In addition, we are interested in finding statistical relationships between parameters. There are various reasons behind that: eliminate possible redundancies in the model, reduce the dimensionality of the problem and establish a criterion of relative importance in the parameters. The latter reason will be done in terms of discriminatory power for the criterion pathological/healthy. To this end, statistical techniques such as Bivariate Linear Correlation and Factor Analysis based on Principal Components will be applied. Finally, we will use the well-known technique of Discriminant Analysis classification applied to different combinations of parameters and factors to determine which of these combinations offers more promising success rates. To perform the experiments we have used a balanced and robust database, consisting of two hundred speakers, one hundred of them males and one hundred females. We have also used a well-balanced proportion where subjects with vocal pathology as well as subjects who don´t have a vocal pathology are equally represented. A computer application designed to carry out the collection of samples is also presented in this thesis. The different statistical analyses performed will allow us to determine which parameters contribute in a more decisive way in the detection of vocal pathology. Therefore, some of the analyses will even allow us to present a ranking of the parameters based on their importance for the detection of vocal pathology. On the other hand, we will also conclude that it is sometimes desirable to perform a dimensionality reduction in order to improve the detection rates. Finally, detection rates themselves are perhaps the most important conclusion of the work. All the analyses presented in this work have been performed for each of the two genders in agreement with previous studies showing that male and female genders should be treated independently, due to the observed functional differences between them. However, with regard to the detection of vocal pathology we will consider the possibility of working with the unified database, ensuring that the success rates obtained are also high.

Inferring identify from DNA profile evidence.

The controversy over the interpretation of DNA profile evidence in forensic identification can be attributed in part to confusion over the mode(s) of statistical inference appropriate to this setting. Although there has been substantial discussion in the literature of, for example, the role of population genetics issues, few authors have made explicit the inferential framework which underpins their arguments. This lack of clarity has led both to unnecessary debates over ill-posed or inappropriate questions and to the neglect of some issues which can have important consequences. We argue that the mode of statistical inference which seems to underlie the arguments of some authors, based on a hypothesis testing framework, is not appropriate for forensic identification. We propose instead a logically coherent framework in which, for example, the roles both of the population genetics issues and of the nonscientific evidence in a case are incorporated. Our analysis highlights several widely held misconceptions in the DNA profiling debate. For example, the profile frequency is not directly relevant to forensic inference. Further, very small match probabilities may in some settings be consistent with acquittal. Although DNA evidence is typically very strong, our analysis of the coherent approach highlights situations which can arise in practice where alternative methods for assessing DNA evidence may be misleading.

Sobre a evasão estudantil na Escola Politécnica da Universidade de São Paulo: identificação e possíveis causas.

A evasão estudantil afeta as universidades, privadas e públicas, no Brasil, trazendo-lhes prejuízos financeiros proporcionais à incidência, respectivamente, de 12% e de 26% no âmbito nacional e de 23% na Universidade de São Paulo (USP), razão pela qual se deve compreender as variáveis que governam o comportamento. Neste contexto, a pesquisa apresenta os prejuízos causados pela evasão e a importância de pesquisá-la na Escola Politécnica da USP (EPUSP): seção 1, desenvolve revisão bibliográfica sobre as causas da evasão (seção 2) e propõe métodos para obter as taxas de evasão a partir dos bancos de dados do Governo Federal e da USP (seção 3). Os resultados estão na seção 4. Para inferir sobre as causas da evasão na EPUSP, analisaram-se bancos de dados que, descritos e tratados na seção 5.1, contêm informações (P. Ex.: tipo de ingresso e egresso, tempo de permanência e histórico escolar) de 16.664 alunos ingressantes entre 1.970 e 2.000, bem como se propuseram modelos estatísticos e se detalharam os conceitos dos testes de hipóteses 2 e t-student (seção 5.2) utilizados na pesquisa. As estatísticas descritivas mostram que a EPUSP sofre 15% de evasão (com maior incidência no 2º ano: 24,65%), que os evadidos permanecem matriculados por 3,8 anos, que a probabilidade de evadir cresce após 6º ano e que as álgebras e os cálculos são disciplinas reprovadoras no 1º ano (seção 5.3). As estatísticas inferenciais demonstraram relação entre a evasão - modo de ingresso na EPUSP e evasão - reprovação nas disciplinas do 1º ano da EPUSP, resultados que, combinados com as estatísticas descritivas, permitiram apontar o déficit vocacional, a falta de persistência, a falta de ambientação à EPUSP e as deficiências na formação predecessora como variáveis responsáveis pela evasão (seção 5.4).

Application of mixture models to detect differentially expressed genes

An important and common problem in microarray experiments is the detection of genes that are differentially expressed in a given number of classes. As this problem concerns the selection of significant genes from a large pool of candidate genes, it needs to be carried out within the framework of multiple hypothesis testing. In this paper, we focus on the use of mixture models to handle the multiplicity issue. With this approach, a measure of the local FDR (false discovery rate) is provided for each gene. An attractive feature of the mixture model approach is that it provides a framework for the estimation of the prior probability that a gene is not differentially expressed, and this probability can subsequently be used in forming a decision rule. The rule can also be formed to take the false negative rate into account. We apply this approach to a well-known publicly available data set on breast cancer, and discuss our findings with reference to other approaches.

Using mixture models to detect differentially expressed genes

An important and common problem in microarray experiments is the detection of genes that are differentially expressed in a given number of classes. As this problem concerns the selection of significant genes from a large pool of candidate genes, it needs to be carried out within the framework of multiple hypothesis testing. In this paper, we focus on the use of mixture models to handle the multiplicity issue. With this approach, a measure of the local false discovery rate is provided for each gene, and it can be implemented so that the implied global false discovery rate is bounded as with the Benjamini-Hochberg methodology based on tail areas. The latter procedure is too conservative, unless it is modified according to the prior probability that a gene is not differentially expressed. An attractive feature of the mixture model approach is that it provides a framework for the estimation of this probability and its subsequent use in forming a decision rule. The rule can also be formed to take the false negative rate into account.

Mixture models for detecting differentially expressed genes in microarrays

An important and common problem in microarray experiments is the detection of genes that are differentially expressed in a given number of classes. As this problem concerns the selection of significant genes from a large pool of candidate genes, it needs to be carried out within the framework of multiple hypothesis testing. In this paper, we focus on the use of mixture models to handle the multiplicity issue. With this approach, a measure of the local FDR (false discovery rate) is provided for each gene. An attractive feature of the mixture model approach is that it provides a framework for the estimation of the prior probability that a gene is not differentially expressed, and this probability can subsequently be used in forming a decision rule. The rule can also be formed to take the false negative rate into account. We apply this approach to a well-known publicly available data set on breast cancer, and discuss our findings with reference to other approaches.

Model evaluation and case series data

We discuss aggregation of data from neuropsychological patients and the process of evaluating models using data from a series of patients. We argue that aggregation can be misleading but not aggregating can also result in information loss. The basis for combining data needs to be theoretically defined, and the particular method of aggregation depends on the theoretical question and characteristics of the data. We present examples, often drawn from our own research, to illustrate these points. We also argue that statistical models and formal methods of model selection are a useful way to test theoretical accounts using data from several patients in multiple-case studies or case series. Statistical models can often measure fit in a way that explicitly captures what a theory allows; the parameter values that result from model fitting often measure theoretically important dimensions and can lead to more constrained theories or new predictions; and model selection allows the strength of evidence for models to be quantified without forcing this into the artificial binary choice that characterizes hypothesis testing methods. Methods that aggregate and then formally model patient data, however, are not automatically preferred to other methods. Which method is preferred depends on the question to be addressed, characteristics of the data, and practical issues like availability of suitable patients, but case series, multiple-case studies, single-case studies, statistical models, and process models should be complementary methods when guided by theory development.