APPLICATION OF SEMIPARAMETRIC METHODS FOR REGRESSION MODELS WITH MISSING COVARIATE INFORMATION

This dissertation addresses regression models with missing covariate data. These methods are shown to be significant to public health research since they enable researchers to use a wider spectrum of data. Unbiased estimating equations are the focus of this dissertation, predominantly semiparametric methods utilized to solve for regression parameters in the presence of missing covariate data. The first aim of this dissertation is to evaluate the properties of an efficient score, an inverse probability weighted estimating equation approach, for logistic regression in a two-phase design. Simulation studies showed that the efficient score is more efficient than two other pseudo-likelihood methods when the correlation between the missing covariate and its surrogate is high. The second aim of this dissertation is to develop a methodology for left truncated covariate data with a binary outcome. To address this problem, we proposed two methods, a likelihood-based approach and an estimating equation approach, to estimate the coefficients and their standard errors for a regression model with a left truncated covariate. The estimating equation technique is close to completion, and once solved should be the most efficient method. The likelihood-based method is compared to standard methods of filling in the truncated values with the lower threshold value or using only the nontruncated values. Simulation studies demonstrated that the likelihood-based method has the best variance correction and moderate bias correction. The application of this method is illustrated in a sepsis study conducted at the University of Pittsburgh.