Survival analysis involves data on the time to the failure of a particular event. Standard statistical methods are inappropriate when analyzing this data because it is often asymmetrical and censored. Several different distributions are commonly used when dealing with survival data, such as the exponential or Weibull. The exponential distribution is unrealistic when dealing with lifetimes of individuals. The Weibull distribution is more appropriate because it has two parameters. Survival data can be modelled using factorial designs with a Weibull distribution. The estimation of the parameters &thetas; and κ must be considered when modeling our data. These estimates can be found using R. The issue when modeling our data with the Weibull distribution is that researchers often assume that κ is constant. This may not be a valid assumption and may lead to unreliable results. This study explores what happens when the researcher assumes a model with a constant κ when κ is nonconstant. We simulated data using a survival regression with a Weibull distribution and estimated power in order to look at the robustness of our model, taking into consideration the effect of both sample size and censoring. A survival regression model using the Weibull distribution is fairly robust when sample sizes and parameters are large regardless of whether the data are censored. When sample sizes are small, it is important to check for the assumption of nonconstant ? and take steps to adjust the statistical models to ensure valid results.
|Advisor:||Rigdon, Steven E.|
|Commitee:||Chew, Song, Neath, Andrew|
|School:||Southern Illinois University at Edwardsville|
|Department:||Mathematics and Statistics|
|School Location:||United States -- Illinois|
|Source:||MAI 54/05M(E), Masters Abstracts International|
|Keywords:||Power, Shape parameter, Survival analysis, Weibull distribution|
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