Conditional Probabilities of AIDS Disease Transitions Using Semi-Markov Models

Analyzing progression of diseases is vital to monitor patient's traversal over time through a disease. Clinical study settings present modeling challenges, as patients' disease trajectories are only partially observed, and patients' disease statuses are only assessed at clinic visit times. HIV disease is a continuum of progressive damage to the immune system from the time of infection to the manifestation of severe immunologic damage. We proposed a semi-Markov model and collected data at Yirgalem General Hospital. Our study found that for an HIV/AIDS patient the transition probability from a given state to the next worse state increases within the good states as time gets optimum and then decreases with increasing time during a follow up. In a specific state of the disease a patient will stay in that state with a non- zero probability in good states and a patient will transit to the next state either to the worst or to the good state with a non-zero probability. The probability of being in same state decreases over time. With the good or alive states, the probability of being in a better state is non-zero, but less than the probability of being in worst states. The survival probabilities are decreasing with increasing time. Therefore, we recommend that increased clinical care for patients on ART services should be strengthen and patients need to regularly check their CD4 T cell count in the appropriate day based on physician order to timely know and monitor their disease status to improve the survival probability and to reduce mortality.

Asociación del orden de parto y del componente racial con la prevalencia de mastitis clínica en un hato lechero especializado ubicado en el trópico alto de Colombia / Association of birth order and racial component with the prevalence of clinical mastitis in a specialized dairy herd located in the high tropics of Colombia / Associação da ordem de parto e do componente racial com a prevalência de mastite clínica em um rebanho leiteiro especializado situado no trópico alto da Colômbia

Resumen Introducción: conocer las variables asociadas a la prevalencia de mastitis clínica (PMC) ayuda a diseñar medidas de control más eficientes. Objetivos: cuantificar la PMC en un hato de especialización lechera, de acuerdo con la influencia del orden de parto (OP) y el efecto del componente racial (CR). Materiales y métodos: se realizó un estudio transversal, mediante el cual se calculó la PMC según el OP (1, 2, 3, 4, 5 y 6 o más), la probabilidad condicional (PC), la PMC para cada CR y la PMC según el OP para cada CR. Se realizó prueba de x2. Resultados: se observó una PMC global de 15 %. Se estableció una relación directamente proporcional entre el OP y la PMC. Las prevalencias calculadas fueron 9,9; 10,9; 12,2; 21,6; 21,7 y 21,4 %, para los OP 1, 2, 3, 4, 5 y 6 o más, respectivamente, con diferencias estadísticas significativas. La PC varió entre 9 % (1 y 2 OP) y 22,8 % (3 y 4 OP). Se observó una PMC de 16,7 % para la holstein (H), 8,9 % para el F1 de H por blanco orejinegro (BON) y de 9,4 % para la 3/4H x 1/4BON, sin diferencias significativas. No obstante, al comparar la H con los cruces por BON, sin importar el porcentaje del componente racial BON, se observaron diferencias estadísticas significativas. Conclusiones: la PMC incrementa con el aumento del OP; por tanto, los programas de vigilancia de la enfermedad deben intensificarse en vacas mayores. La raza BON aporta un factor de rusticidad a sus cruces que disminuye la PMC.

Abstract Introduction: The knowledge of the variables associated with the prevalence of clinical mastitis (PCM) can help to design more efficient control measures. Objectives: To quantify PCM in a specialized dairy herd, according to the influence ofbirth order (BO) and the effect of racial component (RC). Materials and methods: A transversal study was carried out to calculate PCM according to BO (1, 2, 3, 4, 5, and 6, or more), conditional probability (CP), PCM for each RC, and PCM according to BO for each RC. The x2 test was performed. Results: An overall PCM of 15% was observed. A directly proportional relationship was established between BO and PCM. The calculated prevalences were 9.9, 10.9, 12.2, 21.6, 21.7, and 21.4% for BO 1, 2, 3, 4, 5, and 6 or more, respectively, with significant statistical differences. CP varied between 9% (BO 1 and 2) and 22.8% (BO 3 and 4). A PCM of 16.7% was observed for Holstein (H) cows, 8.9% for Holstein F1 with Blanco Orejinegro cows (BON), and 9.4% for % H x V BON, with no significant differences. However, when comparing H with BON crosses, regardless of the percentage of the BON racial components, significant statistical differences were observed. Conclusions: PCM increases with increased BO; therefore, disease surveillance programs should be intensified in older cows. The BON breed contributes a rusticity factor to its crosses that decreases PCM.

Resumo Introdução: conhecer as variáveis associadas à prevalência de mastite clínica (PMC) ajuda a desenhar medidas de controle mais eficientes. Objetivos: quantificar a PMC em um rebanho de especialização leiteira, de acordo com a influência da ordem de parto (OP) e o efeito do componente racial (CR). Materiais e métodos: se realizou um estudo transversal, mediante o qual se calculou a PMC segundo o OP (1, 2, 3, 4, 5 e 6 ou mais), a probabilidade condicional (PC), a PMC para cada CR e a PMC segundo o OP para cada CR. Realizou-se exame de x2. Resultados: se observou uma PMC global de 15 %. Se estabeleceu uma relação diretamente proporcional entre o OP e a PMC. As prevalências calculadas foram 9,9; 10,9; 12,2; 21,6; 21,7 e 21,4 %, para os OP 1, 2, 3, 4, 5 e 6 ou mais respectivamente, com diferenças estatísticas significativas. A PC variou entre 9 % (1 e 2 OP) e 22,8 % (3 e 4 OP). Observou-se uma PMC de 16,7 % para a Holstein (H), 8,9 % para o F1 de H por branco orelhas negras (BON) e de 9,4 % para a 3/4H x 1/4BON, sem diferenças significativas. Não obstante, al comparar a H com os cruzamentos por BON, sem importar a porcentagem do componente racial BON, se observaram diferenças estatísticas significativas. Conclusões: a PMC incrementa com o aumento do OP; portanto, os programas de vigilância da doença devem intensificar-se em vacas mais velhas. A raça BON proporciona um fator de rusticidade aos seus cruzamentos que diminui a PMC.

An assessment of nurses' sufficient immunity when treating infectious patients using bumped-up binomial model.

Background: In times of an outbreak of a contagious deadly epidemic1-4 such as severe acute respiratory syndrome (SARS), the patients are quarantined and rushed to an emergency department of a hospital for treatment. Paradoxically, the nurses who treat them to become healthy get infected in spite of the nurses’ precautionary defensive alertness. This is so unfortunate because the nurses might not have been in close contact with the virus otherwise in their life. The nurses’ sufficient immunity level is a key factor to avert hospital site infection. Is it possible to quantify informatics about the nurses’ immunity from the virus? Methods: The above question is answered with a development of an appropriate new model and methodology. This new frequency trend is named Bumped-up Binomial Distribution (BBD). Several useful properties of the BBD are derived, applied, and explained using SARS data5 in the literature. Though SARS data are considered in the illustration, the contents of the article are versatile enough to analyze and interpret data from other contagious diseases. Results: With the help of BBD (3) and the Toronto data in Table 1, we have identified the informatics about the attending nurses’ sufficient immunity level. There were 32 nurses providing 16 patient care services. Though the nurses were precautionary to avoid infection, not all of them were immune to infection in those activities. Using the new methodology of this article, their sufficient immunity level is estimated to be only 0.25 in a scale of zero to one with a p-value of 0.001. It suggests that the nurses’ sufficient immunity level is statistically significant. The power of accepting the true alternative hypothesis of 0.50 immunity level, if it occurs, is calculated to be 0.948 in a scale of zero to one. It suggests that the methodology is powerful. Conclusions: The estimate of nurse’s sufficient immunity level is a helpful factor for the hospital administrators in the time of making work schedules and assignments of the nurses to highly contagious patients who come in to the emergency or regular wings of the hospital for treatment. When the approach and methodology of this article are applied, it would reduce if not a total elimination of the hospital site infections among the nurses and physicians.

Modelos bayesianos y funcionamientos inferenciales complejos / Bayes' models and complex inferential functioning / Modelos bayesianos e funcionamentos inferenciais complexos

Los procesos inferenciales de niños de cuatro años de edad son observados utilizando una tarea de coordinación de hasta cinco criterios de clasificación. Se encontraron tres tipos de razonamientos probabilísticos: adivinanza (37,8%), transicional (22,2%) resolutorio (40%). La búsqueda tipo adivinanza es el esbozo de una relación entre "búsqueda espacial" y reducción del espacio muestral sobre la base de las acciones concretas (intervenciones) aplicadas directamente a la tarea. La búsqueda tipo transicional es un laboratorio de experimentación que le permite al niño observar la relación entre las intervenciones y el resultado de dichas acciones donde se agencia una probabilidad condicional intra-variable. La búsqueda tipo resolutorio cristaliza una coordinación que implica operaciones clasificatorias con niveles sofisticados de abstracción porque se demanda la intersección de dos o más variables.

Inferential processes in four year old children are observed using a task that involves coordinating up to five classification criteria. Three types of probabilistic reasoning were found : riddle (37.8%), transitional (22.2%) and solving (40%). The riddle search type is the outline of a relationship between "space search" and sample space reduction based on individual concrete actions (interventions) applied directly to the task. The transitional search type is an experimental laboratory that allows the child to observe the relationship between interventions and the outcome of those actions where an intra-variable conditional probability is generated. The solving search type crystallizes a coordination that involves classification operations with sophisticated levels of abstraction since they demand the intersection of two or more variables.

Os processos inferenciais de crianças de quatro anos são observadas através de uma tarefa de coordenação de até cinco critérios de classificação. Encontramos três tipos de raciocínio probabilístico: adivinhança (37,8%), de transição (22,2%), resolutório (40%). A pesquisa tipo adivinhança é o esboço de uma relação entre "pesquisa espacial" e redução do espaço da amostra com base em ações concretas (operações) aplicadas diretamente para a tarefa. A pesquisa do tipo de transição é um laboratório de experimentação que permite a criança observar a relação entre as intervenções e os resultados destas ações, onde se agencia uma probabilidade condicional intravariável. O tipo de pesquisa resolutório cristaliza uma coordenação que envolve operações classificatórias com níveis de abstração sofisticados, já que se exige a interseção de duas ou mais variáveis.

El debate acerca del efecto facilitador en problemas de probabilidad condicional: ¿ Un caso de experimentación crucial ? / The debate around the facilitation effect on conditional probability problems: Is this a case of crucial experimentation?

Se ha mostrado en la literatura de Psicología Cognitiva que las personas generalmente tienen dificultades para resolver problemas de probabilidad condicional. Sin embargo, también se ha mostrado que, bajo ciertas condiciones, las respuestas mejoran de manera significativa. Desde mitad de la década de 1990 hubo un gran debate acerca de cómo dar cuenta de dicho efecto facilitador. Se han propuesto dos hipótesis rivales, la hipótesis de frecuencias naturales que dice que el efecto facilitador se debe a presentar la información de manera frecuentista, y la hipótesis de conjuntos anidados que dice que dicho efecto se debe a la clarificación de las relaciones de conjunto del problema. En este artículo intentaremos clarificar el debate y analizar la evidencia empírica relevante. La pregunta a responder es la siguiente: ¿Se ha producido alguna experimentación crucial en favor de alguna de las dos hipótesis? Nuestra respuesta será negativa, aunque reconociendo que la hipótesis de conjuntos anidados parece hasta ahora, mejor respaldada que su rival.

In the early '70s, Tversky and Kahneman founded a research program in Cognitive Psychology called Heuristics and Biases. This program found extensive evidence that shows that people tend to commit reasoning errors when making judgments under uncertainty. A particular case is that people tend to fail when reasoning about conditional probability problems, that is, problems that ask for the probability of some event given the fact that another event has occurred (e.g. the probability of raining given that it is cloudy). But in the mid '90s, Gigerenzer and other evolutionary psychologists came along and gave an important turn to the state of the art. They showed that if the conditional probability problems used in the literature are framed in a different way, people's performance greatly improves. More specifically, if the problems present the information under a specific format called natural frequency format, around 50% of participants get the correct answer. Since the mid ´90s researchers engage in an important debate on how to account for such a facilitation effect. There are two main proposals, one by the Evolutionary Psychology Program and the other by Heuristic and Biases Program. The natural frequency hypothesis supported by the Evolutionary Program basically says that the natural frequency format is the responsible factor for the improvement in people's performance. The Heuristic and Biases Program, in turn, has proposed the nested-set hypothesis to explain the facilitation effect. The basic idea is that natural frequency versions tend to make transparent the relevant subset relations of the problem. When people see clearly the set relations involved in this kind of problems (the argument goes) they tend to use correctly base rates and thus, their performance improves. They point out that, according to this view, the success of the frequency effect does not have to do with natural frequency formats per se. They predict that any format whatsoever that make the relevant set relations clear will show the same effect. The key question is, then, as follows. Is this a case of crucial experimentation in favor of one of our rival hypotheses? In other words, is there an experiment or a series of experiments such that our rival hypotheses predict opposite results, so that we can claim one of them as victorious over the other? The empirical evidence on the matter is mixed. Some studies seem to support the natural frequency hypothesis while others seem to support the nested-set hypothesis. We will then try to clarify this debate by focusing on the diverse strategies and techniques used in the literature to settle the dispute. We will argue that the right strategy to discriminate between both hypotheses is to use genuine probability problems with a clarified set structure and see whether these conditions elicit or not a performance comparable to the natural frequency effect. Within this general strategy, we review the literature and found that there are three techniques, namely, the improved wording technique, the natural chance technique and the graphical representation technique that seem to provoke a performance as good as the one elicited by natural formats, giving, thus, a stronger support for the nested set hypothesis. However, a careful analysis shows that neither the improved wording technique nor the chance technique has provided both consistent and clear results in favor of the nested-set hypothesis. As for the graphical representation technique, the evidence still seems very slim. The improvement in performance was shown in two studies that worked with only one problem each. Furthermore, neither of these problems seems completely adequate. Thus, we do not think the last word about the matter has been said and more empirical work is needed to settle the issue.