The Assessment of Non-Linear Effects in Clinical Research

Abstract

Background: Novel models for the assessment of non-linear data are being developed for the benefit of making better predictions from the data. Objective: To review traditional and modern models. Results, and Conclusions: 1) Logit and probit transformations are often successfully used to mimic a linear model. Logistic regression, Cox regression, Poisson regression, and Markow modeling are examples of logit transformation; 2) Either the x- or y-axis or both of them can be logarithmically transformed. Also Box Cox transformation equations and ACE (alternating conditional expectations) or AVAS (additive and variance stabilization for regression) packages are simple empirical methods often successful for linearly remodeling of non-linear data; 3) Data that are sinusoidal, can, generally, be successfully modeled using polynomial regression or Fourier analysis; 4) For exponential patterns like plasma concentration time relationships exponential modeling with or without Laplace transformations is a possibility. Spline and Loess are computationally intensive modern methods, suitable for smoothing data patterns, if the data plot leaves you with no idea of the relationship between the y- and x-values. There are no statistical tests to assess the goodness of fit of these methods, but it is always better than that of traditional models.