Nonparametric inference and uniqueness for periodically observed progressive disease models

In many studies examining the progression of HIV and other chronic diseases, subjects are periodically monitored to assess their progression through disease states. This gives rise to a specific type of panel data which have been termed “chain-of-events data”; e.g. data that result from periodic observation of a progressive disease process whose states occur in a prescribed order and where state transitions are not observable. Using a discrete time semi-Markov model, we develop an algorithm for nonparametric estimation of the distribution functions of sojourn times in a J state progressive disease model. Issues of uniqueness for chain-of-events data are not well-understood. Thus, a main goal of this paper is to determine the uniqueness of the nonparametric estimators of the distribution functions of sojourn times within states. We develop sufficient conditions for uniqueness of the nonparametric maximum likelihood estimator, including situations where some but not all of its components are unique. We illustrate the methods with three examples.     

College as an Investment: The Role of Graduation Rates in Changing Occupational Inequality by Race, Ethnicity, and Gender

In this paper, we examine whether investments in higher education have contributed to changes in occupational inequality by focusing on the impact of college completion rates on movement into desirable occupations between 1983 and 2002. Since forces generating inequality vary by gender, race, and ethnicity, we examine trends for white, black, and Hispanic men and women in our study. Utilizing Ordinary Least Squares Regression on data from 20 Current Population Surveys, we find a modest decrease in both gender and racial inequality in access to desirable occupations and an increase in inequality between Hispanics and members of the other groups. College completion accounts for the progress made by white women and for the declines among Hispanic men. It does not explain changes for African Americans, either between men and women or when compared to whites.