Contributions to Modeling and Analysis of Method Comparison Data

Method comparison studies compare a new method of measuring a continuous variable with an established method that serves as a reference. Both methods have the same unit of measurement and none of them is considered error free. The major goals in these studies are to quantify the degree of similarity and agreement between the two methods. The motivation behind the comparison is that if two methods agree well, the cheaper, simpler, or the less invasive among them can be preferred or both can be used interchangeably. Such studies are common in biomedical sciences with medical devices, assays, measurement protocols, or clinical observers serving as methods. The most popular design for conducting these studies is the paired measurements design, which leads to one measurement by each method on every subject. These paired measurements method comparison data are often analyzed by modeling them using the classical measurement error model or a special case of it, a mixedeffects model. Motivated by real applications, this dissertation makes two contributions toward modeling and analysis of these data. First, we develop a segmented measurement error model assuming equal error variances. This model extends the classical measurement error model to allow a piecewise linear relationship between the measurements. The changepoint at which the transition takes place is treated as an unknown parameter in the model. We provide an expectation conditional maximization (ECM) algorithm to fit the model and propose segmented-specific evaluation of similarity and agreement using appropriate extensions of the existing measures. Bootstrapping and largesample theory of maximum likelihood estimators are used to perform the relevant inferences. We are also able to obtain an explicit expression for the Hessian matrix that is needed for this purpose. The proposed methodology is evaluated by simulation and is illustrated by analyzing a dataset containing measurements of digoxin concentration. This work is also generalized to allow unequal error variances in the segmented model. Second, we develop a Bayesian approach that uses informative priors for error variances within a mixed-effect model framework. This approach allows taking advantage of information about error variances that may be available from previous studies, potentially leading to their improved estimation. Half-normal and hierarchical half-normal distributions are used as prior distributions for error variances and data from previous studies are used to estimate the hyperparameters of these distributions. We discuss strategies for posterior simulation to estimate the model parameters and their functions. The proposed methodology is compared with its likelihood-based counterpart in a simulation study. It is illustrated by analyzing a dataset containing oxygen saturation measurements.