On the inference of partially correlated data with applications to public health issues

Correlated or matched data is frequently collected under many study designs in applied sciences such as the social, behavioral, economic, biological, medical, epidemiologic, health, public health, and drug developmental sciences in order to have a more efficient design and to control for potential confounding factors in the study. Challenges with respect to availability and cost commonly occur with matching observational or experimental study subjects. Researchers frequently encounter situations where the observed sample consists of a combination of correlated and uncorrelated data due to missing responses. Ignoring cases with missing responses, when analyzing the data, will introduce bias in the inference and reduce the power of the testing procedure. As such, the importance in developing new statistical inference methods to treat partially correlated data and new approaches to model partially correlated data has grown over the past few decades. These methods attempt to account for the special nature of partially correlated data. In this chapter, we provide several methods to compare two Gaussian distributed means in the two sample location problem under the assumption of partially dependent observations. For categorical data, tests of homogeneity for partially matched-pair data are investigated. Different methods of combining tests of homogeneity based on Pearson chi-square test and McNemar chi-squared test are investigated. Also, we will introduce several nonparametric testing procedures which combine all cases in the study.