CAUSAL INFERENCE WITH A CONTINUOUS TREATMENT AND OUTCOME: ALTERNATIVE ESTIMATORS FOR PARAMETRIC DOSE-RESPONSE FUNCTIONS WITH APPLICATIONS.

Causal inference with a continuous treatment is a relatively under-explored problem. In this dissertation, we adopt the potential outcomes framework. Potential outcomes are responses that would be seen for a unit under all possible treatments. In an observational study where the treatment is continuous, the potential outcomes are an uncountably infinite set indexed by treatment dose. We parameterize this unobservable set as a linear combination of a finite number of basis functions whose coefficients vary across units. This leads to new techniques for estimating the population average dose-response function (ADRF). Some techniques require a model for the treatment assignment given covariates, some require a model for predicting the potential outcomes from covariates, and some require both. We develop these techniques using a framework of estimating functions, compare them to existing methods for continuous treatments, and simulate their performance in a population where the ADRF is linear and the models for the treatment and/or outcomes may be misspecified. We also extend the comparisons to a data set of lottery winners in Massachusetts. Next, we describe the methods and functions in the R package causaldrf using data from the National Medical Expenditure Survey (NMES) and Infant Health and Development Program (IHDP) as examples. Additionally, we analyze the National Growth and Health Study (NGHS) data set and deal with the issue of missing data. Lastly, we discuss future research goals and possible extensions.

Selected Violin Concertos: In Search of a Missing Link

My dissertation presented seven violin concertos in three recital programs. Three of these concertos are acknowledged masterpieces performed in established concert venues throughout the world. They are the concertos of Mozart, Beethoven and Tchaikovsky. The other four are less standard and are composed by Viotti, Kreutzer, Rode and Spohr. These less standard concertos were popular during their time yet they seem not to have stood the test of time. A curriculum devoted exclusively to the standard concertos creates problems for the young violinist. The Mozart violin concertos are often the first standard concertos that the young violin student encounters. They are considered to be the least technically demanding of the standard concertos. The next most advanced standard concertos that the student will usually encounter are Bruch’s G minor concerto, Wieniawski’s D minor concerto and Barber’s concerto. The trouble is that the work on Mozart concertos does not adequately prepare a student for the next most advanced standard concerto. There is a discontinuous leap in the progression of technical difficulty between the Mozart concertos and the next most advanced concertos. Likewise the standard concerto repertoire provides no smooth historical or stylistic progression between the Mozart concertos and the next most advanced concertos. If the young violinist is limited to the standard repertoire then she has no smooth progression either technical, historical or stylistic. I seek to demonstrate that, by adding concertos of Spohr, Viotti, Kreutzer, and Rode to the standard violin curriculum, one could remedy this problem. The first and third recitals were performed in the Gildenhorn Recital Hall and the second recital in the School of Music’s Smith Lecture Hall, both at the University of Maryland. All three recitals can be found in the Digital Repository at the University of Maryland (DRUM).