Interval estimation of excess risk related effective doses in tobit models

INTERVAL ESTIMATION OF EXCESS RISK RELATED EFFECTIVE DOSES IN TOBIT MODELS by Jia Wang ADVISOR: Professor Nan Lin December 2009 Saint Louis, Missouri In this thesis we consider interval estimation of excess risk related effective dose (ERED) in dose-response studies using tobit model. Let P (x) be the probability of response at dose level x. Considering the background probability P (0), excess risk at dose level x > 0 is P (x) − P (0). Then ERED100p is the dose level at which p = P (x)−P (0) 1−P (0) . When P (0) = 0, ERED is same as the regular ED. Tobit regression model is used when the outcome variable in a dose-response study is left censored and continuous. We first describe the maximum likelihood estimation of EREDs in tobit model, and then we propose five interval estimation methods of EREDs, including the delta method, the Fieller method, the likelihood ratio method, the non-parametric bootstrap method and the parametric bootstrap method. For both non-parametric and parametric bootstrap methods, we consider three different ways to construct the confidence interval, including the percentile method, biascorrected model and bias-corrected accelerated method. Simulation studies show that when the normal assumption of the tobit model is met, i.e. the latent response is normally distributed, we recommend the delta method for ERED50 and the likelihood ratio method and the parametric bootstrap percentile method for ERED05. When the error distribution is non-normal but symmetric, we recommend the parametric bootstrap percentile method and the nonparametric bootstrap percentile method. When the error distribution is non-normal but asymmetric, we recommend the Fieller method, the likelihood ratio method and the parametric bootstrap bias-corrected method. When the error distribution is normal, the three nonparametric bootstrap methods are not recommended. When the error distribution is non-normal but symmetric, the parametric bootstrap bias-corrected method and the parametric bootstrap bias-corrected accelerated method are not recommended. When the error distribution is non-normal but asymmetric, the parametric bootstrap percentile method and the parametric bootstrap bias-corrected accelerated method are not recommended.