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The misclassification simulation extrapolation (MC-SIMEX) method proposed by Küchenho et al. is a general method of handling categorical data with measurement error. It consists of two steps, the simulation and extrapolation steps. In the simulation step, it simulates observations with varying degrees of measurement error. Then parameter estimators for varying degrees of measurement error are obtained based on these observations. In the extrapolation step, it uses a parametric extrapolation function to obtain the parameter estimators for data with no measurement error. However, as shown in many studies, the parameter estimators are still biased as a result of the parametric extrapolation function used in the MC-SIMEX method. Therefore, we propose a nonparametric MC-SIMEX method in which we use a nonparametric extrapolation function. It uses the fractional polynomial method with cross-validation to choose the appropriate fractional polynomial terms. An example is provided based on data from the National Health and Nutrition Examination Survey.

Survival analysis is the study of time to event outcomes. Accelerated Failure Time models (AFT) serve as a useful tool in survival analysis to study the time of occurrence of an event and its relation to the covariates of interest. The accuracy of estimation of parameters in a model depends upon the correct measurement of covariates. Considering that perfect measurement of covariates is highly unlikely, it is imperative that the performance of the existing bias-correction methods be analyzed in AFT models. However, certain areas of bias-correction in AFT models still remain unexplored. One of these unexplored areas, is a situation where the survival times follow a log-logistic distribution. In this dissertation, we evaluate the performance of the Misclassification simulation extrapolation (MC-SIMEX) procedure, a well-known procedure for bias-correction due to misclassification, in AFT models where the survival times follow a standard log-logistic distribution. In addition, a modified version of the MC-SIMEX procedure is also proposed, that provides an advantage in situations where the sensitivity and specificity of classification are unknown. Lastly, the performance of the original MC-SIMEX procedure in lung cancer data provided by the North Central Cancer Treatment Group (NCCTG), is also evaluated.