Nonparametric regression-based

In a study of a pharmacodynamic model of HIV viral load (HIV-1 RNA copies) over time with 31 cov-ariates, the three different methods identified three different sets of important covariates. The NL-based method produced a set of covariates with the smallest number, whereas the LRT produced the largest set of important covariates. They concluded that EBE-based methods are the most reliable for covariate selection. They also found that nonparametric regression methods were more likely to select fewer important covariates than parametric regression methods. The authors then used Monte Carlo simulation to examine the power and Type I error rate of the methods. 

Another nonparametric regression method is CART (classification and regression trees). The basic concepts were outlined in Discriminant Analysis Section about tree-based classification. We remember from that chapter that CART is a recursive binary partition method based on a simple model constant for each region. If the residual sums of squares of responses is minimized. 

Current methods for supervised pattern recognition are numerous. Typical linear methods are linear discriminant analysis (LDA) based on distance calculation, soft independent modeling of class analogy (SIMCA), which emphasizes similarities within a class, and PLS discriminant analysis (PLS-DA), which performs regression between spectra and class memberships. More advanced methods are based on nonlinear techniques, such as neural networks. Parametric versus nonparametric computations is a further distinction. In parametric techniques such as LDA, statistical parameters of normal sample distribution are used in the decision rules. Such restrictions do not influence nonparametric methods such as SIMCA, which perform more efficiently on NIR data collections. 

Nonparametric approaches have been developed mainly because of the lack of knowledge about the dose-response relationship at the beginning of the Phase 1 trial and because of the small sample size in these trials. Most of them use the up-and-down scheme. Several authors proposed a design based on the random walk rules (RWR) (14,15), which provides an accurate estimate of MTD as a quantile, or the use of isotonic regressions. 

To present nonhnear regression methods based on parametric and nonparametric models. 

---