Ambulance response time is a key measure used to assess EMS system performance. However, the speed with which ambulances respond to emergencies can be highly variable. In some cases, this is due to geography. In dense urban areas for example, the distances traveled are short, but traffic and other hindrances such as traffic calming measures and high rise elevators cause delays, while rural areas involve greater distances and longer travel times. There are two major components of response time: first, pre-travel delay to prepare for ambulance dispatch, and second the actual travel time to the callers location. Response time standards are often established in order to provide fast and reliable service to the most severely ill patients. Standards typically specify the percentage of time an emergency response team can get to a call within a certain time threshold. This is referred to as “coverage”. This thesis deals with the development of a new response time model that predicts not only the mean response time, but estimates its variability. The models are developed based on historical data provided by the Region of Waterloo EMS and will permit the Region to predict EMS coverage. By analyzing the historical data, we found that response times from EMS stations to geographical locations within the Region of Waterloo are characterized by lognormal distributions. For a particular station – location pair we can thus use this information to predict coverage if we are able to specify the parameters of the distribution. We do this by characterizing the travel time and pre-travel delay times separately, and then adding the two to estimate coverage. We will use a previously proposed model that estimates the mean travel time from a station to a demand point as a function of road types traversed. We also compare the results of this model with another well known model and show that the first model is suitable to apply to the Region of Waterloo. In order to estimate the standard deviation of the response time, we propose a simple but effective model that estimates the standard deviation as a function of mean response time.

Ambulance response time is a key measure used to assess EMS system performance. However, the speed with which ambulances respond to emergencies can be highly variable. In some cases, this is due to geography. In dense urban areas for example, the distances traveled are short, but traffic and other hindrances such as traffic calming measures and high rise elevators cause delays, while rural areas involve greater distances and longer travel times. There are two major components of response time: first, pre-travel delay to prepare for ambulance dispatch, and second the actual travel time to the callers location. Response time standards are often established in order to provide fast and reliable service to the most severely ill patients. Standards typically specify the percentage of time an emergency response team can get to a call within a certain time threshold. This is referred to as “coverage”. This thesis deals with the development of a new response time model that predicts not only the mean response time, but estimates its variability. The models are developed based on historical data provided by the Region of Waterloo EMS and will permit the Region to predict EMS coverage. By analyzing the historical data, we found that response times from EMS stations to geographical locations within the Region of Waterloo are characterized by lognormal distributions. For a particular station – location pair we can thus use this information to predict coverage if we are able to specify the parameters of the distribution. We do this by characterizing the travel time and pre-travel delay times separately, and then adding the two to estimate coverage. We will use a previously proposed model that estimates the mean travel time from a station to a demand point as a function of road types traversed. We also compare the results of this model with another well known model and show that the first model is suitable to apply to the Region of Waterloo. In order to estimate the standard deviation of the response time, we propose a simple but effective model that estimates the standard deviation as a function of mean response time.

Made available in DSpace on 2016-06-02T20:06:04Z (GMT). No. of bitstreams: 1 3437.pdf: 1348932 bytes, checksum: d4b8cd2d1775831eeea609373f32648d (MD5) Previous issue date: 2011-02-11 / Universidade Federal de Minas Gerais / Several authors have preferred to model survival data in the presence of covariates through the hazard function, a fact related to its interpretation. The hazard function describes as the instantaneous average of failure changes over time. In this context, one of the most used models is the Cox s model (1972), in which the basic supposition for its use is that the ratio of the failure rates, of any two individuals, are proportional. However, experiments show that there are survival data which can not be accommodated by the Cox s model. This fact has been determinant in the developing of several types of non-proporcional hazard models. Among them we mention the accelerated failure model (Prentice, 1978), the hybrid hazard model (Etezadi-Amoli and Ciampi, 1987) and the extended hybrid hazard models (Louzada-Neto, 1997 and 1999). Mackenzie (1996) proposed a parametric family of non-proportional hazard model called generalized time-dependent logistic model - GTDL. This model is based on the generalization of the standard logistic function for the time-dependent form and is motivated in part by considering the timeeffect in its setting and, in part by the need to consider parametric structure. The frailty model (Vaupel et al., 1979, Tomazella, 2003, Tomazella et al., 2004) is characterized by the use of a random effect, ie, an unobservable random variable, which represents information that or could not or were not collected, such as, environmental and genetics factors, or yet information that, for some reason, were not considered in the planning. The frailty variable is introduced in the modeling of the hazard function, with the objective of control the unobservable heterogeneity of the units under study, including the dependence of the units that share the same hazard factors. In this work we considered an extension of the GTDL model using the frailty model as an alternative to model data which does not have a proportional hazard structure. From a classical perspective, we did a simulation study and an application with real data. We also used a Bayesian approach to a real data set. / Vários autores têm preferido modelar dados de sobrevivência na presença de covariáveis por meio da função de risco, fato este relacionado à sua interpretação. A função de risco descreve como a taxa instantânea de falha se modifica com o passar do tempo. Neste contexto, um dos modelos mais utilizados é o modelo de Cox (1972) sendo que a suposição básica para o seu uso é que a razão das taxas de falhas, de dois quaisquer indivíduos, sejam proporcionais. Contudo, experiências mostram que existem dados de sobrevivência que não podem ser acomodados pelo modelos de Cox. Este fato tem sido determinante no desenvolvimento de vários tipos de modelos de risco não proporcional. Entre eles podemos citar o modelo de falha acelerado (Prentice, 1978), o modelo de risco híbrido (Etezadi-Amoli e Ciampi, 1987) e os modelos de risco híbrido estendido (Louzada- Neto, 1997 e 1999). Mackenzie (1996) propôs uma nova família paramétrica de modelo de risco não proporcional intitulado modelo de risco logístico generalizado dependente do tempo (Generalized time-dependent logistic model-GTDL). Este modelo é baseado na generalização da função logística padrão para a forma dependente do tempo e é motivado em parte por considerar o efeito do tempo em seu ajuste e, em parte pela necessidade de considerar estrutura paramétrica. O modelo de fragilidade (Vaupel et al., 1979, Tomazella, 2003, Tomazella et al., 2004) é caracterizado pela utilização de um efeito aleatório, ou seja, de uma variável aleatória não observável, que representa as informações que não podem ou não foram observadas, como por exemplo, fatores ambientais e genéticos, ou ainda informações que, por algum motivo, não foram consideradas no planejamento. A variável de fragilidade é introduzida na modelagem da função de risco, com o objetivo de controlar a heterogeneidade não observável das unidades em estudo, inclusive a dependência das unidades que compartilham os mesmos fatores de risco. Neste trabalho consideramos uma extensão do modelo GTDL utilizando o modelo de fragilidade como uma alternativa para ii modelar dados que não tem uma estrutura de risco proporcional. Sob uma perspectiva Clássica, fizemos um estudo de simulação e uma aplicação com dados reais. Também utilizamos a abordagem Bayesiana para um conjunto de dados reais.