Comparing Predictive Values of Two diagnostic tests

Abstract

Positive and negative predictive values are important measures of accuracy when one compares the accuracy of diagnostic tests. When more than one diagnostic tests are available, one may has to choose one of the possible diagnostic tests due to cost, time, or ethical reason. We consider a pair study design on cohort study where two diagnostic tests are 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 gold standards are available on every individual. We propose our method by series of logistic regressions and derive estimator and test statistics based on likelihood method. However, it is 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 be biased. In Chapter 2 and 3, we extend the cases when gold standard is missing. We assume that missing gold standard is missing at random, which is to depend on observed data. In Chapter 2, we use semiparametric theory to derive a class of regular and asymptotically normal of our parameter of interest. Out of the class, we derive an estimator which is the most effcient in the class in using the information from available auxiliary covariates which may be associated with the outcome of gold standard. We also use auxiliary covariates in modeling the probability of observing gold standard. In Chapter 3, through M-estimator, we derive another consistent estimator through imputation method.