| This thesis concerns spline fitting and discrimination as they apply to a problem relating to diabetic nephropathy (DN) in Pima Indians. The population has not only a high incidence of diabetes at young ages but also proteinuria. Defining DN phenotype may depend on separating those whose proteinuria starts at lower levels (microalbuminurics, or micros) from those at higher levels (macroalbuminurics, or macros). The first, most difficult step in quantifying DN involves summarizing the decline in glomerular filtration rate (GFR) for all subjects. We have multiple replications on each date with measurements, and subjects were analyzed periodically over a number of years. We do the above with a longitudinal smoothing spline model, which incorporates both errors of measurement and coefficients in random coefficient models using B-splines. This produces satisfactory estimated GFR curves. The algorithm has an EM flavor, alternating between estimating the covariance structure and the spline coefficients. This has been facilitated by my development of a simulation model that replicates accurately the structure of the observed data and allows testing of various estimation techniques. We use permutation tests to test for a difference between micros after they become macros and subjects first seen as macros and conclude that they are different with p < 0.01. We also apply the method to related data without replicates by making two simplifying assumptions. |
