Uso da distribuição Weibull Inversa na análise de sobrevivência - Barroso, Rodrigo Fernando Murça (Universidade Federal de São Carlos, 2024)
Survival analysis is widely used in fields such as medicine, engineering, and social sciences to model and predict the time until the occurrence of events of interest. Although the Weibull distribution is commonly applied, its limitations in scenarios with a high probability of early failures and extreme events motivate the search for alternatives. This study investigates the Inverse Weibull (WI) distribution, describing its structural properties, including hazard, survival, and quantile functions. For uncensored data, inference techniques based on the maximum likelihood method are developed to estimate the parameters and the median time in the WI model. Additionally, hypothesis tests for the parameters of the WI model are applied and compared in terms of Type I error and power. The WI model is then extended to regression for censored data, with point and asymptotic inference methods applied to the parameters and median time in proportional hazards, proportional odds, and accelerated failure time models. This study expands the applications of the WI distribution in survival analysis and provides methodological foundations for its implementation in practical contexts, as all the proposed models were evaluated through simulation studies and applied to real datasets.
Use of Inverse Weibull distribution in survival analysis
Keywords: Análise de sobrevivência; Distribuição Weibull Inversa; Máxima verossimilhança; Tempo mediano; Testes de hipóteses; Riscos proporcionais; Chances proporcionais; Tempo de falha acelerada; CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA::ANALISE DE DADOS; CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA::FUNDAMENTOS DA ESTATISTICA; CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA::INFERENCIA NAO-PARAMETRICA; CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA::INFERENCIA PARAMETRICA; CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA::REGRESSAO E CORRELACAO