Comparing Predictive Values of Two diagnostic tests

Positive and negative predictive values are important measures of accuracy whenone compares the accuracy of diagnostic tests. When more than one diagnostic tests areavailable, one may has to choose one of the possible diagnostic tests due to cost, time, orethical reason. We consider a pair study design on cohort study where two diagnostic testsare measured on every patients. Our parameter of interest is the log odds of predictive values.In first chapter, we review current methods on comparing diagnostic tests when goldstandards are available on every individual. We propose our method by series of logisticregressions and derive estimator and test statistics based on likelihood method. However, itis often the case that gold standard is not observed on every patient because it may be invasive.If we only consider those who have observed gold standard, the estimator may not bebiased. In Chapter 2 and 3, we extend the cases when gold standard is missing. We assumethat missing gold standard is missing at random, which is to depend on observed data. InChapter 2, we use semiparametric theory to derive a class of regular and asymptoticallynormal of our parameter of interest. Out of the class, we derive an estimator which is themost effcient in the class in using the information from available auxiliary covariates whichmay be associated with the outcome of gold standard. We also use auxiliary covariates inmodeling the probability of observing gold standard. In Chapter 3, through M-estimator,we derive another consistent estimator through imputation method.