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MODELO ADITIVO DE AALEN: UNA APLICACIÓN A LOS DATOS DE SINUSITIS EN PACIENTES CON SIDA
AALEN ADDITIVE MODEL: A APPLICATION FOR DATA OF SINUSITE IN PATIENTS WITH AIDS
MODELO ADITIVO DE AALEN: UMA APLICAÇÃO PARA DADOS DE SINUSITE EM PACIENTES COM AIDS
Keywords:
covariables dependientes del tiempo, modelo de Aalen, riesgo aditivo (es)Time-dependent covariate, Aalen model, Additive risk (en)
covariáveis dependentes do tempo, modelo de Aalen, riscos aditivos (pt)
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2Departamento de Estatística-UFMG, Belo Horizonte, Brasil. Professor adjunto. E-mail: enricoc@est.ufmg.br
3Departamento de Estatística-UFPE, Recife, Brasil. Professora adjunta. E-mail: cristina@de.ufpe.br
Em estudos de sobrevivência, as vezes, o interesse não é apenas na distribuição do tempo de falha. É comum a comparação de tempos de sobrevivência de dois ou mais grupos bem como a verificação do efeito de covariáveis na resposta tanto em engenharia quanto, principalmente, em situações clínicas. A maneira mais eficiente de incorporar o efeito desses fatores no estudo é utilizar um modelo estatístico de regressão. Freqüentemente em estudos de sobrevivência o efeito das covariáveis de interesse pode variar ao longo do tempo de duração do estudo. Estas covariáveis são denominadas de dependentes do tempo e a inclusão delas na análise pode fornecer resultados mais precisos. Aalen propôs um modelo de risco aditivo que apresenta vantagens práticas quando as covariáveis são acompanhadas ao longo do tempo e os seus valores podem ser modificados durante o estudo. A principal vantagem desse modelo é que através de análise gráfica é possível verificar mudanças no tempo na influência de cada uma das covariáveis. Isto é, análises com este modelo fornecem informações detalhadas a respeito da influência temporal de cada covariável. Dessa forma o modelo aditivo de Aalen é apresentado neste trabalho com o objetivo de mostrar a sua importância na presença de covariáveis dependentes do tempo. Um banco de dados real envolvendo pacientes infectados pelo HIV e o tempo até o desenvolvimento de sinusite é utilizado para ilustrar o ajuste deste modelo.
Palavras chave: covariáveis dependentes do tempo, modelo de Aalen, riscos aditivos.
In survival analysis sometimes the interest is not just on the failure time distribution function. It is common treatment comparisons as well as studying the effect of covariates in the response. This fact happens in engineering and clinical studies. Covariates effects are usually incorporated in the analysis by using a regression model. Moreover, in some real situations, covariates may be monitored and measured along the follow-up period. These covariates are known as time-dependent covariates. Analysis that include these covariates can be more reliable. Aalen proposed an additive risk model that is very attractive. This model has showed some practical advantages especially when the covariates effects varies in time. The main advantage of this model it is that through graphical analysis it is possible to verify changes in the time in the influence of each one of the covariates. That is, analyses with this model supply information detailed regarding the secular influence of each covariate. This model is presented in this paper in terms of time-dependent covariates. A real data set related to HIV patients and time to develop sinusitis is used to illustrate the fit of the additive Aalen model.
Key words: Time-dependent covariate, Aalen model, Additive risk.
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