Modeling and inference in functional data analysis
CD4+ T lymphocyte cell count serves as a surrogate marker of human immunodeficiency virus (HIV) disease progression as it indicates how healthy the immune system is. Since the first clinical discover of acquired immunodeficiency syndrome (AIDS) in 1981, it has been observed that a very small proportion of HIV-infected people can remain living asymptomatically while maintaining high CD4 counts for long periods, without any medical therapy. It is of pharmaceutical interest to identify these HIV nonprogressors and study how they naturally suppress HIV reproduction. The longitudinal CD4+ count data in this HIV study was measured at different unequally spaced visits for each HIV-infected volunteer. Functional data analysis was employed with extensive exploratory data analysis (EDA) including Spaghetti plot followed by a smoothing technique to extract the form of the underlying random function. The non-parametric repeated Hanning method was chosen to serve the latter purpose for its simplicity and flexibility. Linear regression was shown to be adequate of modeling CD4 counts over time. Finally, the inferential model, a prior-free, post-data probabilistic inference framework, was applied to identify HIV nonprogressors with posterior plausibility functions and compared to the classical Benjamini-Hochberg procedure for controlling false discovery rate (FDR) in simultaneous hypothesis testing problem using both the cd4 data and simulations.
Liu, Purdue University.
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