A nonparametric subject-specific population method for deconvolution .2. External validation

A lot of attention has been given in the past to deconvolution and in particular to its nonparametric variants. In a companion paper (1), we present a fully nonparametric deconvolution method in which subject specificity is explicitly taken into account. To do so we use so-called ''longitudinal splines.'' A longitudinal spline is a nonparametric function composed of a template spline, in common to all subjects, and of a distortion spline representing the difference of the subject's function from the template. In this paper, we concentrate on testing and documenting the performance of this nonparametric methodology in terms of the approximation of unknown functions. We simulated population data using parametric functions, and use longitudinal splines to recover the unknown functions. We consider different estimation methods including (1) parametric nonlinear mixed effect, (2) least squares, and (3) two stage. Methods 2-3 are more robust than Method 1, and obtain reliable estimates of the unknown functions. The lack of robustness of Method 1 appears to be due to the misspecifications of the distribution of the subject's parameters. Results also suggest that in a data-rich situation nonparametric nonlinear mixed-effect models should be preferred.