Author ORCID Identifier


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Document Type


Degree Name

Doctor of Philosophy



First Advisor

Nitai D. Mukhopadhyay


Compositional data (CD) is mostly analyzed as relative data, using ratios of components, and log-ratio transformations to be able to use known multivariable statistical methods. Therefore, CD where some components equal zero represent a problem. Furthermore, when the data is measured longitudinally, observations are spatially related and appear to come from a mixture population, the analysis becomes highly complex. For this matter, a two-part model was proposed to deal with structural zeros in longitudinal CD using a mixed-effects model. Furthermore, the model has been extended to the case where the non-zero components of the vector might a two component mixture population. Maximum likelihood estimates for fixed effects and variance components are calculated by an approximate Fisher scoring procedure base on sixth-order Laplace approximation. The EM algorithm is used to estimate the probability of the mixture model.

The proposed model was used to analyze the radiation therapy effect on tissue change in one patient with non-small cell lung cancer (NSCLC). Five CT-scans were obtained during 24 months following RT. Instead of using voxel-level data, voxels were grouped into larger subvolumes called patches. Data in each patch can be represented by a vector in the form of CD with the proportions of tissue classified as dense, hazy, or normal. A statistical model of radiation-induced lung damage (RILD) over time for each patch as a function of time and dose was implemented. The predicted longitudinal compositions were classified to describe tissue change using cluster analysis. Finally, proposed method and cluster analysis were applied to two groups of patients with and without radiation pneumonitis (RP) to characterize tissue changes in RP.


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